Rough-walled fractures, forming proppant-packed assemblies, processes of forming, and uses thereof

Abstract

Aspects of the present disclosure generally relate to rough-walled fractures, processes for forming rough-walled fractures, and uses of rough-walled fractures. Aspects of the present disclosure also generally relate to proppant-packed assemblies, processes for forming proppant-packed assemblies, and uses of the proppant-packed assemblies. In an aspect, a process for forming a misaligned rough-walled fracture is provided. The process includes applying a compressive load on a geomaterial to fracture the geomaterial into two geomaterial segments; misaligning the two geomaterial segments; and coring around the two misaligned geomaterial segments to form a misaligned rough-walled fracture.

Description

Title: Rough-Walled Fractures, Forming Proppant-Packed Assemblies, Processes of Forming, and Uses ThereofFIELD

[0001] Aspects of the present disclosure generally relate to rough-walled fractures, processes for forming rough-walled fractures, and uses of rough-walled fractures. Aspects of the present disclosure also generally relate to proppant-packed assemblies, processes for forming proppant-packed assemblies, and uses of the proppant-packed assemblies.DESCRIPTION OF RELATED ART

[0002] Fractured subsurface systems provide much of the energy supply and fluid storage capacity for the world. There has been increasing demand for enhanced efficiencies in developments of fractured subsurface engineering technologies in energy, water, and environment sectors. The growth of such developments is linked to the level of understanding of and control over flow and transport through void and mineral- / proppant-filled fractures. One area that can substantially benefit these developments for both hydrocarbon recovery and clean energy applications is hydraulic fracturing (fracking) of unconventional reservoirs.

[0003] Relative permeability is often used to describe multi-phase flow in porous media at the macro scale. Such flow functions are input to commercial reservoir simulation platforms that are utilized to predict the reservoir and well production performance at the field scale. Despite the importance of void and proppant-packed hydraulic fractures in delivering reservoir fluids to the wellbore and injected fluids into reservoir, their relative permeability functions have not been adequately explored. Moreover, conventional relative permeability models such as the Corey model lack accurate physical foundations, are based mainly on experimental data of unfractured systems, and consider the fractures either as high permeability porous media (e.g., Corey model), or as small pipes, while another branch of theoretical models such as the X-curves neglects the phase interference. Furthermore, the limited reported data is often obtained from synthetic or artificial fractures or plain rock blocks that do not adequately represent the subsurface fractures, their wall roughness, and aperture topologies under stress. In addition, studies aimed at characterizing the relative permeability in propped fractures have been limited to gravity drainage through glass beads and cylindrical sandpacks. However, these studies do not accurately depict the flow processesencountered in void and propped fractures. Also, no experimental studies have been dedicated to systematically understand and characterize two and three-phase relative permeability functions in void and filled fractures under representative conditions.

[0004] Conventional investigations consider fractures as conductive mediums with varying aperture geometries and asperities, but mostly assume their flow and entrapment behavior to be analogous to non-fractured porous media. There is also a scarcity in systematically measured steady- state two-phase and three-phase relative permeability data in rough-walled fractures under different flow conditions and saturation histories. This has resulted in a lack of representative data / models / correlations that accurately describes macro- scale and micro- scale transport behavior of fractures under realistic conditions encountered in the subsurface. Overall, conventional laboratory- sc ale investigations on fractures do not mimic real- world conditions.

[0005] For laboratory investigations to better mimic real- world conditions observed in a field, e.g., those conditions observed in the subsurface, there is a need for roughwalled fractures, proppant-packed assemblies, and core samples that are realistic. There is also a need for processes for forming rough-walled fractures and processes for forming proppant-packed assemblies.SUMMARY

[0006] Aspects of the present disclosure generally relate to rough-walled fractures, processes for forming rough-walled fractures, and uses of rough-walled fractures. Aspects of the present disclosure also generally relate to proppant-packed assemblies, processes for forming proppant-packed assemblies, and uses of the proppant-packed assemblies. Rough-walled fractures and proppant-packed assemblies of the present disclosure represent real-world (or actual) conditions observed at formations such as aquifers and reservoirs. Unlike conventional technologies, rough-walled fractures and proppant-packed assemblies described herein realistically mimic conditions present in the field, e.g., those conditions observed in the subsurface such as conditions at which oil and gas reservoirs and similar geosystems may exist. Rough-walled fractures and proppant-packed assemblies described herein may be utilized in a laboratory setting to investigate various characteristics of hydraulically fractured geomaterials such as fluid flow behavior, oil-water interactions, solid-fluid interactions, the dynamics and mechanisms of imbibition and waterflooding, and surfactant screening. Theinvestigations and results of such investigations provide insight into real-world (fieldscale) conditions. As described above, conventional technologies may not be representative of real- world conditions and applications. As a result, the understandings and results gathered by use of conventional technologies cannot be utilized / upscaled effectively in the field. In contrast, aspects described herein can enable significantly improved understandings applicable to the field, thereby enabling an improved transition from pore to field scale. Such improved understanding can enable, for example, improved hydraulic fracturing processes among other oil recovery processes.

[0007] In further contrast to conventional technologies, aspects of the present disclosure enable testing and investigating, at the macro- and micro-level, proppant placement and flow in a fractured core sample, flow and transport in proppant packs within fractures of a porous medium, among other phenomenon. Aspects described herein also describe new methods of preparing propped and unpropped fractures, and measuring steady- state relative permeabilities in such fractures. Aspects of the present disclosure enable better prediction of oil recovery performance from a formation, gas (e.g., CO2and hydrogen) storage capacity in a fractured subsurface, enhanced geothermal systems, among other applications.

[0008] In an aspect, a process for forming a misaligned rough-walled fracture is provided. The process includes applying a compressive load on a geomaterial to fracture the geomaterial into two geomaterial segments; misaligning the two geomaterial segments by about 0.1 mm to about 5 mm; and coring around the two misaligned geomaterial segments to form a misaligned rough-walled fracture.

[0009] In another aspect, a process for preparing a proppant-packed fracture assembly is provided. The process includes positioning a first segment of a fractured core sample in a mold such that a void space is formed between a top of the mold and a fractured surface of the first segment of the fractured core sample. The process further includes forming a proppant layer on the fractured surface of the first segment of the fractured core sample by depositing proppant on a surface of the first segment of the fractured core sample such that the void space is at least partially filled with the proppant. The process further includes depositing a binding agent on the proppant layer. The process further includes positioning a fractured surface of a second segment of the fractured core sample on top of the proppant layer to form the proppant-packed fracture assembly.

[0010] In another aspect, a method of reproducing (or simulating or mimicking) actual fracturing conditions in a laboratory is provided. The method includes injecting a first fluid comprising a first wetting fluid or a first non- wetting fluid into a core holder housing a sample comprising a misaligned rough-walled fractured porous medium and optionally a proppant. The method further includes alternating a drainage flow cycle and an imbibition flow cycle by an unsteady-state method or a steady-state method under a net confining pressure. The method further includes determining a characteristic of the sample before, during, or after one or both of the drainage flow cycle or the imbibition flow cycle, the characteristic comprising hydraulic conductivity, permeability reduction, fluid occupancy, fluid distribution, fluid saturation, proppant embedment, fracture deformation, relative permeability, end-point relative permeability, steady- state relative permeability, unsteady- state relative permeability, steady-state relative permeability curves, unsteady-state relative permeability curves, or combinations thereof.

[0011] In another aspect, a method for predicting hydrocarbon recovery performance from a formation, gas storage capacity of a formation, or combinations thereof is provided. The method includes performing a method of reproducing actual fracturing conditions in a laboratory described herein; performing operation(s) on a proppant-packed assembly described herein; performing operation(s) on a misaligned rough-walled fracture described herein; or combinations thereof.

[0012] In another aspect, a method for testing two-phase flow through a fractured subsurface geomaterial and an optional proppant is provided. The method includes performing a method of reproducing actual fracturing conditions in a laboratory described herein; performing operation(s) on a proppant-packed assembly described herein; performing operation(s) on a misaligned rough-walled fracture described herein; or combinations thereof.

[0013] In another aspect, a method for testing three-phase flow through a fractured subsurface geomaterial and an optional proppant is provided. The method includes performing a method of reproducing actual fracturing conditions in a laboratory described herein; performing operation(s) on a proppant-packed assembly described herein; performing operation(s) on a misaligned rough-walled fracture described herein; or combinations thereof.

[0014] In another aspect is provided a misaligned rough-walled fracture described herein.

[0015] In another aspect is provided a proppant-packed fracture assembly described herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0016] So that the manner in which the above recited features of the present disclosure may be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to aspects, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only exemplary aspects and are therefore not to be considered limiting of its scope, may admit to other equally effective aspects.

[0017] FIG. 1 is a fractured Eagle Ford shale sample. The rough-walled fracture is aligned to the center of the core and runs uniformly through the core length.

[0018] FIG. 2 is a schematic diagram of the two-phase core-flooding apparatus utilized in Example I.

[0019] FIG. 3 is a schematic diagram of the experimental procedure for the verification of the accuracy and reproducibility of saturation measurements.

[0020] FIG. 4 is a schematic diagram of the experimental procedure to investigate the effect of saturation history on two-phase relative permeability.

[0021] FIG. 5 is a schematic diagram of the experimental procedure to study the effect of total flow rate on two-phase relative permeability.

[0022] FIG. 6 shows non-limiting data for steady-state oil-brine relative permeabilities of primary drainage (PD) and primary waterflooding (WF) conducted on a rough-walled fracture (Fluids: Soltrol 170 and brine; Fracture permeability: 71.68 D).

[0023] FIGS. 7 A and 7B illustrate non-limiting results of two-phase dodecane- brine flow experiments conducted on a horizontally (H) and vertically (V) oriented fracture. FIG. 7A: steady-state relative permeabilities of primary drainage; and FIG. 7B initial brine saturation at the end of primary drainage.

[0024] FIGS. 8 A and 8B illustrate non-limiting results of two-phase dodecane- brine flow experiments conducted on a horizontally (H) and vertically (V) oriented fracture: FIG. 8A: steady-state relative permeabilities of primary waterflooding; and FIG. 8B residual oil saturation at the end of primary waterflooding.

[0025] FIG. 9 shows non-limiting data for steady-state oil-brine relative permeabilities in fractured Sample EF-2 during primary drainage (PD).

[0026] FIG. 10 shows non-limiting data for steady-state oil-brine relative permeabilities in fractured Sample EF-2 during primary waterflooding (WF).

[0027] FIG. 11 shows non-limiting data for steady-state oil-brine relative permeabilities in fractured Sample EF-2 during secondary drainage (SD).

[0028] FIG. 12 shows non-limiting data for the degree of phase interference through oil and brine relative permeabilities cross-plot. PD is the primary drainage, WF is the primary waterflooding, and SD is the secondary drainage compared to Corey (dashed curve) and X-curve (dotted curve) models.

[0029] FIG. 13 shows non-limiting data for primary drainage steady-state oil-brine relative permeability data (sample EF-2) under capillary-dominated regime compared with X-curve (dotted curves) and Corey (dashed curves) models.

[0030] FIGS. 14A-14E illustrate non-limiting results for the effect of saturation history on steady-state two-phase relative permeability (Sample EF-3) during five flow cycles. FIG. 14A: full cycle of primary drainage and waterflooding; FIG. 14B: secondary drainage and waterflooding 4 / 5 cycle; FIG. 14C: tertiary drainage and waterflooding 3 / 5 cycle: FIG. 14D: quaternary drainage and waterflooding 2 / 5 cycle; and FIG. 14E: quinary drainage and waterflooding 1 / 5 cycle.

[0031] FIG. 15 shows non-limiting results for steady-state oil-brine relative permeabilities measured in fractured Sample EF-2 during capillary-dominated primary drainage (solid symbols) and various waterflooding tests conducted at 0.5 mL / min (hollow symbols), 1.0 mL / min (half solid symbols), and 2.0 mL / min (crossed hollow symbols) total flow rates.

[0032] FIG. 16 shows non-limiting data for variations of the residual oil saturation (Sor) with changes in the initial oil saturation (Soi) during waterflooding at flow rates of 0.5, 1.0, and 2.0 mL / min.

[0033] FIG. 17A shows an example procedure of fracturing a block of rock matrix and coring along the length of the fracture to obtain rough- walled fractured samples.

[0034] FIG. 17B shows drawings of photographs of fractured outcrop Eagle Ford shale block showing the two halves separated (left panel) and the half-block after drilling cores (right panel).

[0035] FIG. 18 shows non-limiting data for the grain size distribution of example silica (solid) and example ceramic (dashed) proppants.

[0036] FIG. 19 shows drawings of micro computed tomography (micro-CT) images of fluid occupancy within the silica proppant pack: grayscale (left panel) and segmented (right panel). (Oil, brine, and proppant are shown with different hatching).

[0037] FIG. 20 shows non-limiting data for the distribution of in situ oil-brine contact angles (CAs) measured on the surface of silica and ceramic proppants for a set of 100 measurements at randomly-selected locations. The vertical dashed lines represent the average CAs: Silica = 44.84° and Ceramic = 61.96°.

[0038] FIGS. 21 A and 21B show non-limiting data for the volume- weighted pore size distribution (PSD, diameters) in 40 / 70 silica and ceramic proppants utilized in this study. FIG. 21A (PSDs for fired Berea and Fountainbleau sandstones (dashed or dotted) for reference, and Volume- weighted throat size (radius); and FIG. 21B: throat length distributions of proppants generated from micro-CT image analysis.

[0039] FIGS. 22A and 22B show drawings of a Delrin mold utilized for proppant pack preparation, 8” long, 1.5” wide, and track depth of 0.75”.

[0040] FIG. 22C shows a Delrin mold housing one half of the core sample with a 0.9 mm gap (or clearance) between the top of the half-core and the top of the mold.

[0041] FIG. 22D shows an assembled propped core sample (e.g., a proppant packed assembly) wrapped in Teflon tape and heat shrink tube, with 100 mesh screens on either end. The core was oriented horizontally during the assembly process.

[0042] FIG. 23 shows non-limiting data for differential pressure profile (in inches of water) at the beginning of primary drainage, showing the oil breakthrough time and attainment of steady state.

[0043] FIG. 24A shows non-limiting data for primary drainage and waterflooding processes for the silica proppant pack (Kabs = 50D).

[0044] FIG. 24B shows non-limiting data for secondary drainage and waterflooding processes for the silica proppant pack (Kabs = 50D).

[0045] FIG. 25A shows non-limiting data for primary drainage and waterflooding processes for the ceramic proppant pack (Kabs = 60D).

[0046] FIG. 25B shows non-limiting data for secondary drainage and waterflooding processes for the ceramic proppant pack (Kabs = 60D).

[0047] FIG. 26A shows drainage relative permeability data of silica proppant from an example of the present application plotted against a first comparative model (Romm, solid and dashed lines) of unpropped fracture.

[0048] FIG. 26B shows drainage relative permeability data of silica proppant from an example of the present application plotted against a second comparative model (solid and dashed lines) of unpropped fracture.

[0049] FIG. 26C shows drainage relative permeability data of silica proppant from an example of the present application plotted against a third comparative model (solid and dashed lines) of unpropped fracture.

[0050] FIG. 26D shows drainage relative permeability data of silica proppant from an example of the present application plotted against the Brooks-Corey model for sandpacks.

[0051] FIG. 27A-27D shows drawings of operations for preparing of a proppant- packed fracture assembly.

[0052] FIG. 28 shows a schematic of an example flow apparatus utilized for Example III.

[0053] FIG. 29 shows a schematic of an example experimental procedure utilized for Example III.

[0054] FIG. 30 shows drawings of three-dimensional (3D) images of the proppant- packed assembly and drawings of 3D images at locations A and B of the proppant- packed assembly.

[0055] FIG. 31 shows non-limiting data for pore-fluid occupancy at location B at the end of gas injection.

[0056] FIGS. 32A-32C shows non-limiting data for oil and gas flow paths at location B at the end of various flow processes. FIG. 32A: gas injection; FIG. 32B: oil and gas injection (1:10 ratio); FIG. 32C: oil and gas injection (1:1 ratio).

[0057] FIG. 33 shows non-limiting data for fracture aperture under increasing closure stress, 30 / 50 intermediate strength proppant (ISP) ceramic proppant.

[0058] FIG. 34 shows non-limiting data for effective oil and gas permeability reduction versus increasing net confining stress.

[0059] FIGS. 35 A and 35B show non-limiting data for gas globules trapped by imbibition of oil (and / or brine) under a higher closure stress. FIG. 35A: gas phase under 500 psi confining stress; FIG. 35B: gas phase under 2,500 psi confining stress.

[0060] To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements and features of one aspect may be beneficially incorporated in other aspects without further recitation.DETAILED DESCRIPTION

[0061] Aspects of the present disclosure generally relate to rough-walled fractures, processes for forming rough-walled fractures, and uses of rough-walled fractures. Aspects of the present disclosure also generally relate to proppant-packed assemblies, processes for forming proppant-packed assemblies, and uses of the proppant-packed assemblies.

[0062] Aspects described herein may be performed on any suitable geomaterial. Geomaterials may include a porous medium. Geomaterials may include consolidated and unconsolidated sand or soil, unconventional (tight) or conventional rocks of sandstone and carbonate types, as well as any other suitable materials from geological formations such as rock, shale, etc. The geomaterial may be from an unconventional formation or a conventional formation. The geomaterial may be porous. The geomaterial may be oil-containing porous media. The geomaterial may include geothermal rocks such as granite and / or mantle, among other geothermal rocks. The geomaterial, such as a rock matrix, may include quartz, calcite (CaCOa), feldspar, dolomite (MgCOa), silica, illite, apatite, muscovite, rutile, gypsum, anhydrite, chamosite, clinochlore, zircon, biotite, pyrite, expansible clays, kaolinite, mica minerals, trace minerals, organic matter, or any combination thereof. In some examples, the rock matrix includes tight porous media. The geomaterial may be characterized as being water-wet, strongly water-wet, weakly water-wet, mixed-wet, neutral wet, weakly oil- wet, strongly oil- wet, or oil- wet porous media. The geomaterial may be any suitable porous media encountered in the subsurface, conventional, unconventional, shale, tight sand, carbonates, etc.

[0063] When proppants are described herein, any suitable proppant may be utilized. For example, proppants may include silica, coated sand, ceramic, or combinations thereof, among others. When fluids are described herein, any suitable fluid may be utilized. For example, fluids may include brine, mineral oil, crude oil, hydrocarbon gas, nitrogen gas, carbon dioxide, or combinations thereof, among others. Multiphase flowtests described herein may be conducted under unsteady- state or steady-state injection modes.

[0064] Aspects of the present disclosure generally relate to processes for forming a rough-walled fracture. The rough-walled fracture may be a misaligned or shifted roughwalled fracture. Misaligned or shifted rough-walled fractures described herein mimic and / or simulate fractures observed in the field. Misaligned or shifted rough-walled fractures include two segments (e.g., halves) of a fracture, where the two segments are not placed in a straight line or have some asymmetry with respect to the relative positions (or initial relative positions) of the two segments. The rough-walled fracture may form at least a portion of a core sample that may be tested during laboratory investigations of hydraulically fractured geomaterials. To the inventors’ knowledge, laboratory-scale sized misaligned (or shifted) rough-walled fractures have not been made before.

[0065] A rough-walled fracture refers to a fracture characterized by a surface exhibiting pronounced irregularities and undulations. A smooth- walled fracture refers to a fracture with a surface that is largely devoid of undulations and exhibits negligible roughness.

[0066] Unlike conventional technologies for investigating hydraulically fractured geomaterials, misaligned (or shifted) rough- walled fractures described herein actually mimic and / or simulate real- world fractures observed in the field.

[0067] The process for forming a misaligned rough-walled fracture may include stress-fracturing a geomaterial into two geomaterial halves. Here, a compressive load is applied to the geomaterial to fracture the geomaterial into two or more geomaterial pieces, such as two geomaterial halves. The stress -fracturing results in formation of fractures in the geomaterial that occur due to exposure to elevated compressive stress concentrated along a limited contact zone. These fractures propagate along weaker sections of the geomaterial, extending from one extremity to the other. Any suitable geomaterial may be used such as those geomaterials described herein. The geomaterial may be any suitable size and shape. For example, the geomaterial may be a block or a cylinder. A length dimension of the geomaterial may be from about 5 inches (in) to about 30 in, such as from about 8 in to about 20 in, such as from about 10 in to about 15 in, such as about 12 in. In some examples, the geomaterial is a block having dimensions of about 12 in by 12 in.

[0068] The stress-fracturing of the geomaterial (exerting the compressive load) may be performed by any suitable technique. For example, stress-fracturing may be performed by positioning a geomaterial on a hydraulic compression apparatus such as a Brazilian Test Apparatus (e.g., Marshall 850 Test Press) or similar machines. The geomaterial may be situated on a robust base and secured between the jaws of the machine. To ensure accurate fracture direction, the machine jaws may be fitted with plates / rods that have a narrow contact area extending along the length of the geomaterial. The stress-fracturing begins with the gradual increase of compression stress until the geomaterial ultimately fractures. In some examples, the stress utilized to stress-fracture the geomaterial may be from about 3,000 to about 7,000 psi, such as from about 4,000 to about 6,000 psi. The stress-fracturing operation creates fractures that align with natural lamination of the rock, mirroring the process by which hydraulic fractures are generated in real-world applications, e.g., in the field.

[0069] The process for forming the misaligned rough-walled fracture may further include misaligning (or shifting) the two geomaterial segments. Here, the two geomaterial segments (e.g., geomaterial halves) are intentionally misaligned by any suitable amount, such as from about 0.1 mm to about 5 mm, such as from about 0.3 mm to about 2.5 mm, such as from about 0.5 mm to about 1.5 mm, such as from about 0.7 mm to about 1.3 mm, such as from about 0.9 mm to about 1.1 mm, or from about 0.5 to about 1 mm. This misalignment reflects the variations in fracture surfaces encountered in the field, which stem from the contrast in principal stresses. It also allows for the development of realistic stress-induced fractures featuring misaligned surfaces, producing flow results that are representative of the underlying subsurface processes. The shifting or misalignment prevents full fracture alignment and closure under high confining stress conditions during, e.g., subsequent laboratory- scale investigations. Optionally, the two segments of the geomaterial can be separated prior to the coring operation (described below) to create different gaps in the resulting cores, enabling the predesign of proppant packing layers.

[0070] The misalignment of the two geomaterial segments may be with respect to an edge of the two geomaterial segments. For example, the first geomaterial segment (e.g., first halve 101a in FIG. 1) may have a top edge (an end 115 of the geomaterial segment) that is positioned at a location that is from about 0.1 mm to about 5 mm from a top edge of the second geomaterial segment (second halve 101b). Additionally, oraltematively, the first and geomaterial segments may have top edges that match a substantially similar (or the same) location a top edge (an end of the geomaterial segment) while the center of a first segment is positioned at a location that is from about 0.1 mm to about 5 mm from the center of the second segment.

[0071] The process for forming the misaligned rough-walled fracture may further include coring or drilling around the two misaligned (or shifted) geomaterial segments to form the misaligned rough-walled fracture. Here, and following the misalignment, the two geomaterial segments may be affixed to a drilling apparatus fitted with coring drill bits. The coring drill bits enable the extraction of fractured cores of varying dimensions. Coring may be performed using any suitable apparatus such as a bench drill press such as those available from Dake Corp.

[0072] Following coring, the misaligned rough-walled fracture may be in the form of a core sample. The misaligned rough-walled fracture or core sample comprising the misaligned rough-walled fracture may be used for laboratory scale investigations that more accurately reflect real-world conditions. For example, laboratory investigations using misaligned rough-walled fractures described herein may be utilized for coreflooding experiments. Laboratory investigations using misaligned rough-walled fractures described herein may be utilized to gain a better understanding of various characteristics of hydraulically fractured geomaterials such as fluid flow behavior, oilwater interactions, solid-fluid interactions, the dynamics and mechanisms of imbibition and waterflooding, and surfactant screening. The investigations and results of such investigations provide significantly better insight into real-world (field-scale) conditions relative to conventional fractures utilized for laboratory experiments. The misaligned rough-walled fracture mimics conditions encountered in actual fractures observed on a field site.

[0073] Aspects of the present disclosure also generally relate to processes for preparing a proppant-packed assembly (e.g., a proppant-packed fractured assembly). Proppant-packed assemblies described herein may mimic and / or simulate fractures observed in the field. FIGS. 22A-22D show various operations of a process for preparing a proppant-packed fracture assembly according to at least one aspect of the present disclosure. As shown in FIG. 22D, the proppant-packed assembly includes a first segment 2202 (e.g., a first half) of a fractured core sample, a second segment 2204 (e.g., a second half) of the fractured core sample and a proppant layer 2206 positionedbetween the first segment of the fractured core sample and the second segment of the fractured core sample. The proppant layer may be one or more layers. For example, the proppants may be multi-layer, uniform monolayer, or have non-uniform monolayer packing, representing different areas within the hydraulic fractures. Fractured core samples used for the proppant-packed assembly may be any suitable geomaterial described herein. The fractured core sample may be a rough-walled fracture or a smooth-walled fracture.

[0074] The process may include forming a mold using any suitable polymer material. In some examples, the mold may be made from Delrin homopolymer (e.g., an acetal homopolymer), though other polymers are contemplated. As shown in FIGS. 22A and 22B, the mold has a length, width, and a depth to house a first segment of a fractured core sample. Additionally, or alternatively, a mold may be purchased. Typically, the fractured core sample has a cylindrical shape. The cylindrical core sample has a radius. The depth of the mold is larger than a radius of the cylindrical core sample.

[0075] The process may further include positioning the first segment of the fractured core sample in the mold as shown in FIG. 22C. The first segment of the fractured core sample is positioned in the mold such that a fractured surface of the first segment of the fractured core sample faces the opening of the mold and perpendicular to the depth of the mold. The first segment of the fractured core sample is positioned in the mold such that a void space (or clearance) is formed between the top of the mold and fractured surface of the first segment of the fractured core sample. The void space or clearance may have any suitable dimensions such as a depth that is from about 0.5 mm to about 1.5 mm, such as from about 0.7 mm to about 1.3 mm, such as from about 0.9 mm to about 1.1 mm.

[0076] The process may further include depositing proppant on the fractured surface of the first segment of the fractured core sample to form a proppant layer. For example, an amount of proppant may be deposited on the fractured surface of the first segment of the fractured core sample such that the void space or clearance is at least partially filled or filled with the proppant. Any suitable proppant may be utilized. Illustrative, but non-limiting, examples of proppants may include silica, ceramic, coated sand, or combinations thereof. The proppants may be water-wet, oil-wet, or combinations thereof. Oil-wet proppants may include proppants coated in ahydrophobic resin. The proppant layer formed may have any suitable thickness (measured as the distance between the top of the mold and the fractured surface of the first segment of the fractured core sample. The thickness may of the proppant layer may be from about 0.1 mm to about 2 mm, such as from about 0.2 mm to about 1.8 mm, such as from about 0.3 mm to about 1.6 mm, such as from about 0.5 mm to about 1.5 mm, such as from about 0.7 mm to about 1.3 mm, such as from about 0.9 mm to about 1.1 mm. One or more proppant layers may be formed.

[0077] The process may further include depositing a binding agent on the proppant layer. The binding agent serves to hold grains of the proppant together and in place on the surface of the first segment of the fractured core sample. The binding agent may include suitable material such as an aqueous fluid or a non-aqueous fluid. The choice of aqueous fluid versus non-aqueous fluid may depend of the proppant utilized. For example, when the proppant is silica, ceramic, coated sand, or combinations thereof, a binding agent comprising an aqueous fluid (such as water or distilled water) may be utilized. As another example, when the proppant comprises a resin-coated proppant, a non-aqueous fluid may be utilized. The binding agent may be deposited on the proppant layer by any suitable technique such as spraying the binding agent onto the proppant layer. The binding agent may be a temporary binding agent, whereby the binding agent may be removed prior to experiments.

[0078] The process may optionally include freezing the binding agent and proppant layer. For example, when an aqueous fluid is utilized as the binding agent, freezing of the aqueous fluid turns the proppant layer into a solid wafer. Freezing may be accomplished by exposing to liquid nitrogen for a suitable duration. The freezing operation may be performed when, for example, it is desired to transport the core assembly. In this example, the frozen water is utilized as a temporary binding agent such that experiments may be performed on the thawed proppant-packed assembly when the proppant-packed assembly is placed in a core holder.

[0079] The process may further include positioning a fractured surface of a second segment of the fractured core sample on top of the proppant layer to form the proppant- packed fracture assembly. The positioning the fractured surface of the second segment of the fractured core sample on the top of the proppant layer may be performed while the proppant layer is the solid wafer. As shown in FIG. 22D, the proppant-packed fractured assembly includes the first segment (e.g., first half) of a fractured core sample,the second segment (e.g., second half) of the fractured core sample and the proppant layer positioned between the first segment of the fractured core sample and the second segment of the fractured core sample.

[0080] The process may further include performing a post-treatment process on the proppant-packed fractured assembly. The post-treatment process may be performed to hold the assembly together and hinder movement of the first and second halves of the fractured core sample, mitigate proppant mobilization, or combinations thereof. The post-treatment process may include wrapping at least a portion of a circumference of the proppant-packed fracture assembly to hinder relative movement of the first segment and second segment of the fractured core sample. For example, at least a portion of the circumference may be wrapped in Teflon tape. Additionally, or alternatively, the posttreatment process may include positioning a mesh screen on each end of the proppant- packed fracture assembly, each end of the proppant-packed fracture assembly perpendicular to the circumference of the proppant-packed fracture assembly. The mesh screens may have any suitable mesh size and may be made of any suitable material, such as 100-mesh stainless steel screens. The mesh screens mitigate potential proppant mobilization. The mesh screens also mitigate flow line blockage when the proppant-packed fracture assembly is utilized in core-flooding experiments. Additionally, or alternatively, the post-treatment process may include wrapping the proppant-packed fracture assembly in a heat shrink tube.

[0081] The process for forming the proppant-packed fracture assembly is highly- reproducible and may be used to make single layer or multi-layer proppant packs. The proppant-packed fracture assembly, whether post- treated or not, may be used for performing, e.g., laboratory investigations such as core-flooding experiments among many other experiments. Laboratory investigations using the proppant-packed fracture assemblies described herein may be utilized to gain a better understanding of various characteristics of hydraulically fractured geomaterials such as fluid flow behavior, oilwater interactions, solid-fluid interactions, the dynamics and mechanisms of imbibition and waterflooding, and surfactant screening. The investigations and results of such investigations provide insight into real- world (field- scale) conditions.

[0082] Aspects described herein also generally relate to uses of misaligned roughwalled fractures of the present disclosure and to uses of proppant-packed assemblies of the present disclosure. Such uses may include, for example, reproducing actualfracturing conditions in a laboratory, such as core-flooding experiments among other uses.

[0083] A method of reproducing (or mimicking or simulating) actual fracturing conditions in a laboratory may include injecting a first fluid comprising a first wetting fluid or a first non-wetting fluid into a core holder housing a sample comprising a misaligned rough-walled fractured porous medium and optionally a proppant. Suitable misaligned rough-walled fractures that may be utilized are described herein. The geomaterial of the misaligned rough-walled fractures is a porous media. Suitable geomaterials are described herein. The sample that includes the misaligned roughwalled fractured porous medium comprises a geomaterial from a naturally fractured formation, a geomaterial from a hydraulically fractured formation, or combinations thereof.

[0084] When the sample includes a proppant, any suitable proppant-packed assembly described herein may be utilized as at least a portion of the sample. Illustrative, but non-limiting, examples of suitable proppants are described herein.

[0085] The method of reproducing actual fracturing conditions in the laboratory may further include alternating a drainage flow cycle and an imbibition flow cycle by an unsteady- state method or a steady-state method under a net confining pressure. Suitable implementations of drainage flow cycles and imbibition flow cycles are described in the examples though other suitable drainage and imbibition flow cycles are contemplated. Any suitable net confining pressure may be utilized. For example, the net confining pressure may be from about 200 psi to about 10,000 psi, such as from about 200 psi to about 7,000 psi.

[0086] The method of reproducing actual fracturing conditions in the laboratory may further include determining a characteristic of the sample before, during, or after one or both of the drainage flow cycle or the imbibition flow cycle. Illustrative, but non-limiting, examples of characteristics that may be determined may include hydraulic conductivity, permeability reduction, fluid occupancy, fluid distribution, fluid saturation, proppant embedment, fracture deformation, relative permeability, end-point relative permeability, steady- state relative permeability, unsteady- state relative permeability, steady-state relative permeability curves, unsteady-state relative permeability curves, or combinations thereof. The determining operation is further described in the Examples Section.

[0087] Wetting fluids may include aqueous fluids such as water and brine. Nonwetting fluids may include non-aqueous fluids such as a hydrocarbon, oil, or combinations thereof.

[0088] When the first fluid comprises the first wetting fluid, the drainage flow cycle may include injecting a non-wetting fluid or co-injecting a non-wetting fluid and a second wetting fluid at increasing fractional flow ratios into the sample to displace the first wetting fluid. When the first fluid comprises the first wetting fluid, the imbibition flow cycle may include injecting a third wetting fluid or co-injecting a third wetting fluid and a non-wetting fluid at increasing fractional flow ratios into the sample to displace the non-wetting fluid, the first, second, and third wetting fluids being the same or different. For example, when the first wetting fluid comprises a first brine fluid, the drainage flow cycle may include injecting a hydrocarbon (e.g., oil) or co-injecting a hydrocarbon (e.g., oil) and second brine fluid at increasing hydrocarbon / brine fractional flow ratios into the sample to displace the first brine fluid; and the imbibition flow cycle may include injecting a third brine fluid or co-injecting a third brine fluid and a hydrocarbon at increasing brine / hydrocarbon fractional flow ratios into the sample to displace the hydrocarbon, the first, second, and third brine fluids being the same or different.

[0089] Alternatively, when the first fluid comprises the first non-wetting fluid, the drainage flow cycle may include injecting a wetting fluid or co-injecting a wetting fluid and a second non-wetting fluid at increasing fractional flow ratios into the sample to displace the first non- wetting fluid; and the imbibition flow cycle may include injecting a third non- wetting fluid or co-injecting a third non-wetting fluid and a wetting fluid at increasing fractional flow ratios into the sample to displace the wetting fluid, the first, second, and third non-wetting fluids being the same or different. For example, when the first non-wetting fluid comprises a first hydrocarbon, the drainage flow cycle may include injecting brine or co-injecting brine and a second hydrocarbon at increasing brine / hydrocarbon fractional flow ratios into the sample to displace the first hydrocarbon; and the imbibition flow cycle may include injecting a third hydrocarbon or co-injecting a third hydrocarbon and brine at increasing hydrocarbon / brine fractional flow ratios into the sample to displace the brine, the first, second, and third hydrocarbon being the same or different.

[0090] The measuring and / or determining the characteristic may include imaging the sample with X-ray, such as X-ray computed tomography (X-ray CT). So that the sample may be imaged, at least a portion of the core holder may be made of an X-ray transparent material such as carbon fiber. To image or visualize the wetting fluid, at least one of the wetting fluids utilized for the method may include a contrasting agent such as an iodide salt. To image or visualize the non-wetting fluid, at least one of the non-wetting fluids utilized for the method may include a contrasting agent such as an iodinated hydrocarbon.

[0091] The method of reproducing actual fracturing conditions in the laboratory may further include injecting a first gas after the drainage flow cycle or after the imbibition flow cycle. Any suitable gas may be utilized such as CO2, methane, N2, or combinations thereof. The method may further include co-injecting hydrocarbon (e.g., oil) and a second gas after the injecting of the first gas, the first gas and second gas fluids being the same or different. When a gas is utilized, the gas may further include a contrasting agent. The contrasting agent of the gas serves to enable imaging of the gas injected.

[0092] Implementations of the method of reproducing actual fracturing conditions in the laboratory may be utilized in a method for predicting hydrocarbon recovery performance from a formation such as a naturally fractured formation or a hydraulically fractured formation. Hydrocarbon recovery performance may include oil recovery performance, natural gas recovery performance, or combinations thereof. Additionally, or alternatively, implementations of the method of reproducing actual fracturing conditions in the laboratory may be utilized in a method for predicting gas storage capacity of a formation such as a naturally fractured formation or a hydraulically fractured formation. Predicting hydrocarbon recovery performance and predicting gas storage capacity of a formation utilizing aspects described herein are described further in the Examples Section. Gas storage capacity of the formation may include a CO2storage capacity of the formation, a hydrogen storage capacity of the formation, or combinations thereof.

[0093] Implementations of aspects described herein may be utilized to test two- phase flow and / or three-phase flow through a fractured subsurface geomaterial and an optional proppant. Here, rough-walled fractures described herein may be utilized as the fractured subsurface geomaterial. When two-phase or three-phase flow through afractured subsurface geomaterial and a proppant, proppant-packed assemblies of the present disclosure may be utilized. By utilizing rough-walled fractures and / or proppant- packed assemblies of the present disclosure, a researcher obtains more accurate data than when utilizing conventional technologies for at least the reason that rough-walled fractures and / or proppant-packed assemblies actually mimic real- world conditions observed in a subsurface.

[0094] Aspects of the present disclosure may be further understood by the following non-limiting examples. The following non-limiting examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how to make and use aspects of the present disclosure, and are not intended to limit the scope of aspects of the present disclosure.Examples

[0095] The results presented in Examples I- III are a consequence of, at least, using rough-walled fractures described herein and / or proppant-packed assemblies described herein. Such rough-walled fractures and proppant-packed assemblies mimic or represent real-world conditions observed in the subsurface — e.g., conditions at which formations, oil and gas reservoirs, and geosystems may exist. The results presented in Examples I-III are significantly different — and significantly more accurate — than studies using conventional technologies because conventional technologies are not capable of mimicking real-world conditions and instead use non-representative conditions.Example I. Relative Permeability Hysteresis and Residual Trapping in Roughwalled Fractures: Investigating the Effects of Flow Rate and Saturation History Using the Steady-state Approach

[0096] In Example I, the inventors found that significant phase interference was observed for the oil-brine flow in rough-walled fractures. The inventors further found that Corey and X-curve correlations rendered inadequate to represent the fracture relative permeabilities measured using the steady-state technique. In addition, the inventors found that residual oil saturation and oil relative permeability decreased with the decline in the initial oil saturation. The inventors also found that the waterflooding residual oil trapped in rough-walled fractures decreased as the total flow rate increased.

[0097] Understanding multi-phase flow in a fractured subsurface is important for energy supply, fluid storage, and environmental engineering applications. Relativepermeability is used to characterize multi-phase fluid transport in permeable media. The relationship between relative permeability and fluid saturation is influenced by various factors including the flow rate and saturation history of the displacement process. In Example I, the steady-state measurement technique was utilized to characterize two-phase relative permeabilities and residual trapping in water-wet rough-walled fractures induced in Eagle Ford shale rock samples. The results demonstrated that conventional Corey and X-curve correlations significantly underestimate or significantly overestimate the fracture relative permeabilities measured using the steady-state technique as the conventional correlations fail to capture certain attributes of fracture flow behavior including the role and magnitude of phase interference under different conditions. The saturation history influenced both the relative permeabilities of the wetting (brine) and non-wetting (mineral oil) fluid phases and the residual saturations during waterflooding. Generally, the residual oil saturation and oil relative permeability decreased with the decline in the initial oil saturation. Furthermore, at similar brine saturations, the oil relative permeability during waterflooding improved as the total flow rate was increased. This increase was attributed to the high mobility of the connected oil phase within the fracture and the water-wet characteristics of the fracture walls. The brine relative permeability trend, however, followed that of its counterpart measured under the capillary-dominated regime and only exceeded that at very high brine saturations. Moreover, at higher flow rates, residual oil trapping was significantly reduced due to the higher efficiency of the viscous-dominated displacement process. The results suggest that a high total flow rate in water- wet fractures maintains a high non- wetting phase relative permeability over a wide range of water-cut values and reduces the residual non-wetting phase saturation in the fracture at the end of waterflooding.

[0098] Relative permeability is used to characterize / de scribe multi-phase fluid transport in subsurface permeable media. It is a macroscopic manifestation of porescale displacement processes occurring within a medium that incorporates characteristics of the porous medium / fluids / flow system including fluid-rock and fluidfluid interactions (e.g., wettability and interfacial tension), fluid properties (e.g., viscosity and density), flow conditions (e.g., flow rate), and void space attributes (e.g., pore / fracture geometry and connectivity). An accurate characterization of relative permeability may be useful in understanding, predicting, and / or enhancing subsurfaceengineering technologies in the energy, water, and environment sectors. The most reliable relative permeability data are obtained experimentally. However, it may be challenging, costly, and time-consuming to acquire representative steady-state relative permeability data, especially in heterogeneous and complex systems such as those involving fractures. Thus, conventional approaches rely on empirical correlations with little-or-no physical basis, such as those by Brooks-Corey and van Genuchten, to generate relative permeability functions that do not adequately represent multi-phase fluid transport in porous / fractured permeable media. Alternatively, history-matching of field production data is used to produce a non-unique relative permeability realization that offers weak agreement with laboratory measurements.

[0099] Conventional efforts have been directed toward understanding the relative permeability of intact (unfractured) porous rocks.

[0100] L1. Measurement Techniques. This section describes steady-state and unsteady- state techniques.

[0101] 1.1.1. Steady-State Technique. In a steady-state experiment, multiple fluid phases are simultaneously injected into a medium and the effective permeabilities of the phases are obtained at equilibrium conditions (e.g., constant saturation and pressure drop) for a defined flow rate. The inlet flow rate ratios are then changed, and the process is repeated until the relative permeability values for a range of fluid saturations are obtained. Because of equilibrium, the steady- state method is conventionally considered as the most consistent and accurate technique for obtaining relative permeability data. During the measurement, the fluid saturation is determined either by mass balance of the injected and produced fluids, or by imaging, spectroscopy, and visualization techniques. For tight rocks, the duration of steady-state tests is very long due to reaching equilibrium. However, the test duration is shorter for fractured rocks, as the steady state may be reached within hours rather than days or weeks. Consequently, efforts have been directed to characterize the steady- state two-phase relative permeability through fractured media. Conventional studies investigating two-phase relative permeability of various artificial fractures setups have concluded that the relative permeability curves were not a unique function of saturation but rather of the media, while capillary and gravity forces have significant effects on relative permeability and recovery. However, due to the lack of strong capillarity and the variations between these systems several conflicting observations have been reported. For example, it has been reported that flowin a glass setup is similar to that in pipes rather than that in porous media, that the relative permeability in narrow vertical fractures is a function of fluid saturation, and that, while relative permeability is not equal to saturation, the X-curve model may be used to describe their data. Other studies have used imaging and resistivity in situ measurement techniques to characterize two-phase relative permeability of actual fractured rocks. These latter studies found that the relative permeability of fractured rocks was not represented by the predictions of the Corey model and was lower than the X-curve fracture model.

[0102] 1.1.2. Unsteady -State Technique. The unsteady- state or transient measurement method involves injecting a single driving phase into the fracture at constant pressure or flow rate to displace the resident fluid(s). The flow rate, pressure drop response, and composition of the effluent are then used to calculate the relative permeability. The unsteady- state technique carries large uncertainties and approximations because relative permeability curves are not unique functions of saturation. Case-specific data generated from these measurements may not be reliable and does not guarantee repeatability. Furthermore, simplifying assumptions such as linear displacement, incompressibility, and reservoir homogeneity add to the uncertainty in the data interpretation. However, unsteady- state methods are frequently used because the measurements are simple and less time-consuming.

[0103] Investigations into unsteady- state relative permeability have been conducted using conventional techniques to understand two-phase flow through artificial fractures of rock blocks or parallel glass plates. It has been found that the fluid transported through fractures was in the form of a liquid film, and the liquidtransmissibility within the fracture was a function of the fracture aperture. Moreover, the reported relative permeability was not a linear function of saturation. Others have reported that relative permeability values of parallel glass and aluminum plates followed the Corey-type model, and due to the phase interference, the sum of the relative permeability of the phases was less than unity. Studies on actual fractures have also demonstrated that fractured core relative permeability profile has a curvature and cannot be considered a straight line as assumed in the conventional X-curve model.

[0104] 1.1.3. Stability of Flow through Fractures. Two-phase fluid flow through fractures is governed by the relative magnitude of capillary, viscous, and gravity forces. The imbalance between these forces is referred to as flow instability. The relationshipsbetween the forces are expressed using capillary number (viscous / capillary forces) and bond number (gravity / capillary forces). Tables 1-1 and 1-3 summarize conventionally- used expressions for capillary and bond numbers for flow through fractures. However, the equations of these two dimensionless numbers suffer from many deficiencies and fail to account for the fracture and fluid properties, such as wettability, permeability, and the orientation of the flow. This results in misrepresentations of the forces that govern flow through rough-walled fractures and prevent an accurate determination of displacement regimes. For example, some of these models neglect the effect of wettability or the inclination angle, or use an approximation for the fracture permeability.

[0105] 1.1.4. Effect of the Flow Rate on Relative Permeability. The effect of flow rate on two-phase relative permeability originates from the ratio between capillary and viscous forces. Several studies have investigated this effect, resulting in conflicting findings. Various studies found that oil-brine relative permeability curves in water-wet and mixed-wet sandstone cores are independent of flow rate. However, several studies reported the opposite, attributing the dependence of the relative permeability on the flow rate in a mixed-wet media to microscopic fluid distributions. This difference in interpretations leaves many questions unanswered about the exact role of the flow rate in two-phase relative permeability and residual phase trapping, especially in roughwalled fractures. A drawback of conventional studies in the fracture domain is the lack of consideration of capillary, gravity, and viscous forces effects on relative permeability and residual trapping. In particular, conventional studies attribute the microscopic fluids distribution to capillary forces and not the fluid injection rate.

[0106] 1.1.5. Residual Trapping. Residual trapping, or non- wetting phase trapping, in fractures describes a process that arises while recovering the non- wetting phase from the medium. Through this process, a portion of the non-wetting phase is hydraulically disconnected and trapped due to the action of capillary forces (capillary trapping) or bypassing when the wetting phase spontaneously imbibes (or is forcedly injected) into the porous media. A comprehensive understanding of the entrapment physics governing this process is useful for developing processes that ensure maximum recovery fromhydrocarbon geosystems or maximum trapping in the case of geological sequestration of CO2. The majority of experimental studies to date are directed to investigating this phenomenon in non-fractured porous media. Consequently, there is a scarcity of studies that analyze the physics of fluid transport and trapping through rough-walled fractures.

[0107] 1.1.6. Non-limiting Gaps in Conventional Studies. Recent investigations consider fractures as conductive mediums with varying aperture geometries and asperities, but mostly assume their flow and entrapment behavior to be analogous to non-fractured porous media. Even though recent in situ (pore- scale) studies improve the current understanding of flow in fractures at the micro scales, there remains a scarcity in systematically measured steady-state two-phase relative permeability data in rough-walled fractures under different flow conditions and saturation histories. This has resulted in a lack of representative data / models / correlations that accurately describe macro-scale transport behavior of fractures under realistic conditions encountered in subsurface. Conventional relative permeability models, which lack accurate physical foundations, are mainly based on the experimental data of unfractured systems and consider the fractures either as high permeability porous media (e.g., Corey model), or as small pipes, while another branch of theoretical models such as the X-curves neglects the phase interference. Furthermore, the limited reported data is often obtained from synthetic or artificial fractures or plain rock blocks that cannot adequately represent the subsurface fractures, their wall roughness, and aperture topologies under stress.1,2, Materials

[0108] 1.2.1. Fracture Preparation. Experiments were performed on three fractured Eagle Ford shale outcrop core samples (1.5 inches in diameter and 8 inches in length) from Texas, United States. Petrophysical properties and mineralogical characteristics of the specimens were characterized using plugs from the same shale block. Helium porosity and permeability values were obtained utilizing a Coretest™ AP-608 Automated Porosimeter-Permeameter. Helium was utilized to avoid inaccurate estimation of the properties due to gas adsorption. The shale rock samples were found to have 0.25% average porosity and 1.5 nano-D average gas-permeability based on measurements performed on five core plugs. Eagle Ford shale rock was selected for use in the flow experiments because of its ultra-low porosity and permeability, though other rock specimens may be utilized. It minimized the matrix-fracture fluid exchanges and allowed the flow to occur entirely inside the fracture. The isolation of the flow insidethe fracture was utilized for obtaining the relative permeability and saturation data of only the fracture without any contributions from the surrounding rock matrix. This is because the flow through the rock matrix and exchanges of fluid between the fracture and matrix may affect the saturation distribution and relative permeability values of the combined medium, and may limit the applications of measurements to specific rock types. Because the fluids flowed only through the fracture, the hydraulic diameter for non-circular channels utilizing the average fracture aperture was used in Darcy’s equation to calculate the absolute and relative permeabilities of the fractures.

[0109] 1.2, 1,1. Example preparation of rough-walled fractures. Fractured samples were prepared by initially stress-fracturing a shale block, then shifting the two halves by 0.5-1 mm to prevent full fracture alignment and closure under high confining stress conditions. These small shifts are representative of natural fractures in subsurface reservoirs because of the stress-induced displacement consequent to the variations between principal stresses acting on the fracture surfaces. The samples were subsequently obtained through coring around the two halves 101a, 101b of the block, creating a rough-walled fracture 100 as shown in FIG. 1 showing a side view (length 110) of the rough-walled fracture and the end 115. In contrast, conventional fracture preparation procedures introduce defects that may alter the mechanics of flow. For example, fracturing a pre-drilled core through the Brazilian-test method or any compression process usually results in substantial alterations on the sides of the fracture that in turn establishes high aperture flow channels leading to severe misrepresentation of the flow dynamics in the fracture. Similarly, the smooth walls in sawed samples depict a type of fracture that is unrepresentative of the natural counterparts in actual reservoirs.

[0110] As another example, a rock block / cylinder (e.g., 12 inches x 12 inches) was positioned on a hydraulic compression apparatus, similar to those employed in the Brazilian test. The rock block was situated on a robust base and secured between the jaws of the machine. To ensure accurate fracture direction, the machine jaws were fitted with plates / rods that have a narrow contact area extending along the length of the block. The procedure began with the gradual increase of compression stress until the rock ultimately fractures, at which point the stress used to break the rock block is recorded (typically 3000-7000 psi). Subsequently, the two segments of the fractured block are intentionally misaligned (e.g., by 0.5- 1.5 mm) and affixed to a drilling apparatus fittedwith coring drill bits, enabling the extraction of fractured cores of varying dimensions. The samples were subsequently obtained through coring around the two halves of the block, creating a rough-walled fracture.

[0111] 1.2.2. Fluid Properties. Filtered Soltrol 170 mineral oil and 1 wt% KC1 brine were utilized as the oil and water (non-wetting and wetting) phases, respectively. The KC1 brine was employed in the experiments mainly to inhibit the swelling of the clay minerals and to avoid changes in the mechanical properties of the shale matrix. Selected properties of the fluids used in the two-phase flow experiments — density and viscosities of the oil and brine phases and interfacial tension (IFT) between the two — were measured at ambient conditions (e.g., 20°C and 11.4 psi) and are summarized in Table 1-3. Dodecane was used in some preliminary tests during the design of the experimental procedure.Table 1-31.3. Experimental Methods

[0112] 1.3.1. Experimental Setup. Flow experiments were performed using two (2) identical two-phase core-flooding systems 200 as shown in FIG. 2 that were custom- designed for flow measurements in mediums with small pore volumes and high hydraulic conductivities (minimal pressure drops), such as fractures. The systems were equipped with Hastelloy core-holders 201 and tubing with pressure and temperature ratings of 10,000 psi and up to 150°C, respectively. The pressure drop across the fracture was recorded using two high-accuracy Rosemount™ smart pressure transducers 203a, 203b with resolution down to 0.0004 psi. The pressure transducers 203a, 203b were connected at both ends of the core holder 201 via lines L2 and L4. High-pressure dome back pressure regulators 205, coupled to core holder 201 via line L6, were employed to establish reliable boundary conditions at the outlet of the core holder 201. The sample (e.g., fracture) under investigation is placed in the core holder201. During core-flooding experiments, one high-precision, dual-cylinder, pulse-free Quizix™ 5000 pump 215 (with flow rate and pressure resolutions of 0.00001 cc / min and 0.1 psi, respectively) was utilized to control the back pressure and the confining pressure (overburden pressure) using mineral oil from bucket 225. The mineral was injected to the core holder 201 via line L5. Two high-precision, dual-cylinder, pulse- free Quizix™ 5000 pumps 211, 213 were dedicated to fluid injections. Dual-cylinder pumps 211 injected a hydrocarbon, e.g., oil, from bucket 221 into the core holder 201 via line LI. Dual-cylinder pumps 213 injected brine from bucket 223 into the core holder 201 via line L3. Rupture disks (RD) were placed on lines coupled to pumps 211, 213, and 215. Effluent fluids from the core holder 201 were collected using 50 mL burettes 209 with 0.1 mL resolution (enhanced to 0.01 mL resolution with a cathetometer) for saturation measurements using the material balance technique with the material balance 210 shown. Much of the hardware of the core-flooding system 200 was disposed within an oven 207 indicated by the dashed line.

[0113] 1.3.2. Experimental Procedure. The dry core sample halves (see EIG. 1) were first vacuum-saturated with 1 wt% KC1 brine for 2-3 days to avoid fluid exchange between the rock matrix and the fracture during the flow experiments. The two segments were then placed together, wrapped with Teflon, and loaded into the core holder to create a fractured core assembly. The assembly was vacuumed, flushed with gaseous CO2for 30 seconds, and vacuumed again to remove the bulk CO2from the fracture conduit. The latter step was continued for a limited amount of time to avoid over-drying of the fracture walls. The fracture was subsequently fully (100%) saturated with the brine and the experimental conditions were established. The pore volume of the fracture was measured using the volumetric material balance method. The absolute permeability of the fracture was determined by injecting brine at various flow rates, ranging from 0.1-2 mL / min, and recording the pressure drops across the fracture length. The above-mentioned steps established initial conditions in the fractured samples before the samples were subjected to various two-phase flow tests outlined below.

[0114] To reach the selected experimental design, several preliminary steady-state two-phase relative permeability experiments were conducted to investigate the effects of viscous, capillary, and gravity forces on flow stability in rough- walled fractures. Subsequently, four main groups of flow tests, referred to as Groups A-D hereafter in Example I, were performed on horizontally-placed fractured core samples underexperimental conditions. Table 1-4 provides a summary of these main flow experiments. The values of capillary and bond numbers were obtained experimentally from each test using equations described herein. In Table 1-4, EF is Eagle Ford fractured shale sample; CD is Capillary Dominated, RP is Relative Permeability; PD is Primary Drainage; PWF is Primary Waterflooding; SD is Secondary Drainage; SWF is Secondary Waterflooding; TD is Tertiary Drainage; TWF is Tertiary Waterflooding; QD is Quaternary Drainage; QWF is Quaternary Waterflooding; QnD is Quinary Drainage; QnWF is Quinary Waterflooding; 1st is first; 2nd is second; 3rd is third; Seq is sequence.Table 1-4

[0115] The first group (A) of experiments was designed to verify the accuracy of the fluid saturation measurements and reproducibility of the generated results. To this end, two independent techniques (e.g., volumetric and gravimetric methods) were utilized to measure the saturations during one full cycle (e.g., primary drainage and waterflooding) of steady- state, capillary-dominated relative permeability tests. To investigate the reproducibility of the measurements, the primary cycle was followed by two additional cycles (secondary and tertiary cycles) and the results were plotted against the first cycle. The second group (B) of experiments was designed to study the effect of saturation history on two-phase relative permeability under capillary- dominated flow regime. To this end, several steady-state waterflooding tests were performed at different initial water saturations established at the end of the preceding oil drainage. The third group (C) of experiments was designed to probe the effect of flow rate on two-phase relative permeabilities and the associated hysteresis byconducting several steady- state, waterflooding experiments at various total flow rates. Finally, in the fourth group (D) of experiments was designed to investigate the effect of flow rate on non- wetting phase residual trapping. The following subsections describe the experimental procedures utilized to: i) evaluate the stability of flow in fractures (e.g., preliminary tests), ii) validate the saturation measurement technique (e.g., Group A), and iii) conduct the target steady-state two-phase flow experiments (e.g., Groups B-D).

[0120] I.3.2.1, Evaluation of Flow Stability in Fractures. Preliminary two-phase relative permeability experiments on vertically-oriented fractures manifested in various flow instability problems. These problems were diagnosed systematically by investigating the balance between the forces governing the flow in the fracture such as capillary, viscous, and gravity forces. The balance between these forces may be expressed in terms of capillary and bond numbers as shown in Tables 1-1 and 1-2. Several sets of steady-state relative permeability experiments were performed to test the balance between these forces and identify a set of flow parameters and boundary conditions that lead to stable capillary-dominated flow regimes (e.g., Nca< 10-4and Bo< 0.2) under which reproducible relative permeability data may be generated for fracture systems of interest. The first set of experiments were designed to increase the contribution of capillary forces (minimizing viscous fingering) by changing the oil phase from Soltrol 170 to dodecane. Compared to Soltrol 170, dodecane has lower viscosity (relatively similar to the injected brine) and produces a higher interfacial tension with the aqueous phase. The second set of tests focused on reducing the effect of gravity by positioning the core-holder horizontally. In the third set, the capillarity of the fracture was controlled by varying the fracture aperture and confining stress. The fourth set was used to identify a balance between low enough total flow rates that would result in a capillary-dominated flow regime and high enough total flow rates that would generate accurately measurable pressure drops along the fracture. Finally, a sensitivity analysis was performed. The sensitivity analysis may incorporate all the test data to select suitable experimental conditions, fluids, flow rates, and fracture orientation that would ensure the stability of flow and reproducibility of the steady-state relative permeability data. Table 1-4 lists the final values of capillary and bond numbers associated with the main flow experiments.

[0121] I.3.2.2. Validation of Saturation Measurement Technique, This group of experiments (Group A) were performed to validate the accuracy and reproducibility of the fluid saturation measurements using the volumetric method. To this end, two independent methods (e.g., volumetric and gravimetric) were used independently in experiments A-l and A-2 to determine the saturations in sample EF-1 during one full cycle of steady- state relative permeability measurements conducted under capillary- dominated flow regime. For the volumetric method, the fluid saturations were calculated by comparing the volumes of brine injected into and produced from the sample. The fluid saturations obtained gravimetric ally were calculated using the change in the weight of the core holder housing the sample before and after each steady-state point and considering the fluids densities. Afterward, the flow experiments were continued with the secondary and tertiary drainage and waterflooding cycles (Experiments A- 3 to A-6) using the volumetric technique to determine saturations and thereby verify the reproducibility of the measurements. The flow tests in this group were conducted under identical flow conditions (e.g., total flow rate and fractional flow ratios) (see FIG. 3). FIG. 3 is a schematic diagram of the experimental procedure for the verification of the accuracy and reproducibility of saturation measurements: a) is the dry sample (which may have dimensions that are about 8 inches in length and 1.5 inches in diameter); bl) is applying net confining stress of 400 psi to the dry-shifted fracture sample; b2) is measuring the dry sample weight with the core holder; c) is vacuum saturation (Sw=l; 100% brine saturation) and measuring the wet sample weight; d) is the absolute permeability measurement; e) and f) show the first cycle which includes primary drainage with total flow rate Qtotal(oil + brine) of 0.5 mL / min and primary waterflooding with Qtotal= 0.5 mL / min, respectively (volumetric and gravimetric); g) and h) show the second cycle which includes secondary drainage with Qtotal= 0.5 mL / min and secondary waterflooding with Qtotal= 0.5 mL / min, respectively (volumetric); i) and j) show the third cycle which includes tertiary drainage with Qtotal= 0.5 mL / min and tertiary waterflooding with Qtotal= 0.5 mL / min, respectively (volumetric).

[0122] I.3.2.3. Steady-State Two-Phase Relative Permeability Experiments. All relative permeability experiments were implemented using the steady- state technique (co-injection of oil and brine). In steady-state experiments, the drainage process refers to decreasing water saturation by monotonically increasing oil / water fractional flowratio while the waterflooding / imbibition process signifies increasing water saturation by monotonically decreasing oil / water fractional flow ratio in steps. In each step, flow was continued until no changes in pressure drop and saturation could be observed, e.g., until steady- state equilibrium was established. During each steady- state point, the saturations of oil and brine phases in the fractures were measured by recording the volume of injected fluids, changes in volumes and weights of the fluids collected in the burettes at the outlet of the core sample, and applying a material balance technique. The effluent volume and weight readings were quantified using a stadiometer telescope with a precision up to 0.01 mL and a sensitive balance with 0.01 g accuracy, respectively. The relative permeability values were calculated using the recorded pressure drop in each step and applying Darcy’s equation for each fluid phase.

[0123] To investigate the dependency of steady-state oil-brine relative permeability curves on the saturation history, several cycles of steady-state capillary-dominated waterflooding tests were performed on sample EF-3, starting from different initial water saturations (Swi) established during the preceding steady-state drainage process. This was achieved by switching to waterflooding after halting the drainage process in 4 / 5, 3 / 5, 2 / 5, and 1 / 5 of its full cycle (see FIG. 4). FIG. 4 is a schematic diagram of the experimental procedure to investigate the effect of saturation history on two-phase relative permeability: a) is the dry sample (which may have dimensions that are about 8 inches in length and 1.5 inches in diameter); b) is applying a net confining stress to the dry-shifted fracture sample; c) is vacuum saturation (Sw=1; 100% brine saturation); d) is the absolute permeability measurement; e) and f) show the first cycle which includes primary drainage with total flow rate Qtotal(oil + brine) of 0.5 mL / min and primary waterflooding with Qtotal= 0.5 mL / min, respectively; g) and h) show the second cycle which includes secondary drainage 4 / 5 cycle with Qtotal= 0.5 mL / min and secondary waterflooding with Qtotal= 0.5 mL / min, respectively; i) and j) show the third- fifth cycle which includes the drainage while reducing no. cycles to (3 / 5), (2 / 5), and (1 / 5) (Qtotal= 0.5 mL / min) and the waterflooding to residual oil saturation (S,,r ) (Qtotal= 0.5 mL / min), respectively.

[0124] To probe the effect of total flow rate on oil-brine relative permeability curves, several steady-state waterflooding experiments were performed on sample EF- 2 with total flow rates of 0.5, 1.0, and 2.0 mL / min. Capillary-dominated drainage was used to establish a similar SWiin the fracture prior to each waterflooding. After eachcycle, the sample was removed, cleaned, and loaded back into the core holder to eliminate the effect of saturation history. The aforementioned procedure was then followed to reach a similar SWi, and the sample was subsequently subjected to steadystate waterflooding at a higher total flow rate as shown in FIG. 5. FIG. 5 is a schematic diagram of the experimental procedure to study the effect of total flow rate on two- phase relative permeability: a) is the dry sample (which may have dimensions that are about 8 inches in length and 1.5 inches in diameter); b) is applying net confining stress of 400 psi to the dry-shifted fracture sample; c) is vacuum saturation (Sw=l; 100% brine saturation) and measuring the wet sample weight; d) is the absolute permeability measurement; e) and f) show the first cycle which includes primary drainage with total flow rate Qtotal(oil + brine) of 0.5 mL / min and primary waterflooding with Qtotal= 0.5 mL / min, respectively; g) is removing and cleaning the fracture sample; h) and i) show the second cycle which includes drainage with Qtotal= 0.5 mL / min and waterflooding with Qtotal= 1.0 mL / min, respectively; j) is removing and cleaning the fracture sample; k) and 1) show the third cycle which includes drainage with Qtotal= 0.5 mL / min and waterflooding with Qtotal= 2.0 mL / min, respectively.

[0125] The effect of total flow rate on residual oil trapping through capillary- and viscous-dominated waterflooding experiments was also studied. Here, two steady-state waterflooding experiments were carried out at a total flow rate of 1.0 mL / min and 2.0 mL / min. The maximum rate (2.0 mL / min) was selected such that no significant effects of higher flow rate were observed. Three stages of flooding at each flow rate were performed (D-1 to D-12) starting from select levels of initial oil saturation (e.g., B-l to B-10).1.4, Non-limiting Results

[0126] 1.4.1. Sample Characterization. Mineralogy of selected Eagle Ford shale samples was characterized using x-ray diffraction (XRD) and quantitative evaluation of minerals by scanning electron microscope (QEMSCAN) techniques. The Eagle Ford shale was mainly composed of calcite (78.24%) and quartz (16.33%), with trace amounts of dolomites, clays, pyrite, feldspars, and gypsum. The wettability of Eagle Ford samples to KC1 brine and Soltrol 170 was quantified via sessile drop contact angle measurements on four slices from different cores. The results show that the samples were weakly water-wet with mineral oil-brine contact angles ranging from θ = 67-85° due to the heterogeneity of the shale surface. The average contact angle θ = 75° wasadopted for the calculation of the Bond and capillary numbers in Tables 1-1 and 1-2. Three fractured samples (EF-1 to EF-3) with comparable absolute permeabilities were selected for the flow experiments. Table 1-5 presents the pore volumes and absolute permeabilities of the fractures under experimental conditions, e.g., back pressure and confining pressure. The temperature was maintained at 20°C for the experiments. Sample EF-1 was selected for saturation measurement verification (Groups A tests) due to its higher fracture pore volume to facilitate a meaningful comparison between the volumetric and gravimetric methods. Samples EF-2 and EF-3 (samples with similar fracture pore volumes and absolute permeabilities) were used in the main relative permeability experiments (Groups B-D, see Table 1-4).Table 1-5

[0127] 1.4.2. Saturation Measurement Verification. An independent gravimetric saturation measurement was conducted as a reference to determine the reliability of the experimental saturation data quantified volumetrically. The saturation of each phase was obtained throughout a full cycle of drainage and waterflooding. Table 1-6 shows the variation of the brine saturation in the fracture during steady- state drainage and waterflooding relative permeability experiments. The brine saturation values shown in Table 1-6 were obtained volumetrically and gravimetrically during drainage and waterflooding in sample EF- 1. Pore-volume weight (PVW) refers to the total weight of fluids occupying the fracture void space. The results demonstrated that differences in the saturations measured using volumetric and gravimetric methods were negligible, confirming the high accuracy of the former. For example, for the injection cycles, the difference in the average brine saturation in the fracture was 0.3- 1.3%. Based on these results, the less time-consuming volumetric material balance method was adopted for the rest of the experiments.Table 1-6

[0128] 1.4.3. Stability of Flow through Fractures. To represent the balance between the viscous and capillary forces within a fracture more accurately, conventional capillary number equations presented in the literature were modified to incorporate the effects of wettability as well as the viscosities of the defending and the displacing fluids. To this end, the capillary number formula for two-phase flow in rough-walled fractures was used as the starting point:

[0129] Also considered were the viscosities of the defending and the displacing fluids as shown in the correlation:

[0130] The modified capillary number relationship is then given by Eq. 5:wherein: μdis the viscosity of the displacing fluid, μDis the viscosity of the displaced fluid, and krdis the relative permeability of the displacing fluid.

[0131] Several preliminary steady-state two-phase relative permeability tests were performed with different fluids (e.g., Soltrol 170, dodecane, and brine) over a range of experimental conditions (e.g., absolute permeability, confining stress, and flow rate) to evaluate the capillary number expressions presented in the literature. Conventional models do not include various forces influencing the displacement processes duringtwo-phase flow through rough- walled fractures. This leads to significant variations between the capillary numbers estimated by these models and reduces the confidence in determining the dominant displacement regime. For example, for an experiment conducted on a fracture with 71.68 D absolute brine permeability and 1.0 mm average aperture using Soltrol 170 and 1 wt% KC1 brine, the capillary number calculations based on three conventional models from the literature indicated that the displacement occurred under capillary-dominated regime. However, as presented in FIG. 6, the resulting relative permeability curves show significant hysteresis between the drainage and imbibition steps, and they were not reproducible when the tests were repeated under similar experimental conditions. This suggested that the flow process was not under capillary-dominated regime based on the invasion percolation model, in which under a capillary-dominated scheme the drainage process is controlled only by piston-like displacement that follows the path of least resistance. The uniqueness of this process allows for a confident repeatability to the drainage displacement when capillary forces are dominant under similar flow conditions. On the other hand, the modified relationship presented herein (Eq. 5) generated higher capillary number (see Table 1-7) signifying that the same process had not occurred under capillary-dominated flow regime. Table 1-7 shows capillary number values calculated using different correlations from the literature and the modified model presented in this work (Eq. 5). The rock, fluid, and flow properties utilized for calculating the capillary numbers in this table are found in the experimental section.Table 1-7

[0132] The effect of gravity on the flow behavior was investigated by changing the fracture orientation from vertical to horizontal. FIGS. 7A, 7B and FIGS. 8A, 8B show a comparison of the relative permeability trends obtained using a fracture in vertical and horizontal orientations during replicated drainage and waterflooding tests, respectively. The fracture had an absolute permeability and pore volume of 55.86 D and 3.53 mL, respectively. As shown in FIGS. 7A, 7B, at the beginning of the drainageprocess and at high water saturations, water relative permeability displayed an acute decrease in the vertical fracture compared to that in the horizontal counterpart. At the end of drainage, in the vertical fracture, the initial water saturation was 6% higher than that in the horizontal one. Also, the oil relative permeability in the vertical fracture tended to be greater for a given saturation compared to that in the horizontal medium during the entire drainage process. The data in FIGS. 8 A, 8B show that the waterflooding test in the vertical fracture led to a 5% lower residual oil saturation than that in the horizontal one. Similar relative permeability trends were observed for the waterflooding process. The significant variations in the final saturations and relative permeabilities between the vertical and horizontal fractures during drainage and waterflooding processes may be a factor when designing hydrocarbon recovery simulations. Caution may be practiced when selecting the orientation of the fractures and their associated flow properties for numerical modeling efforts. Based on these findings, in the four main groups of flow experiments performed in this study — Groups A, B, C, and D, — horizontally oriented fractures were utilized to minimize the effect of gravity on the flow process. Additionally, the Bond and the modified capillary numbers were calculated for the experiments to determine the net confining stress and the flow rates that maintain a capillary-dominated flow regime during the flow processes and thereby minimize the effect of gravity and viscous forces (e.g., Nca< 5xl0-5and Bo< 10’1). This was done to generate reproducible steady-state relative permeability curves under stable flow conditions in fractures, which are more relevant and applicable to the current science and engineering needs.

[0133] 1.4.4. Steady-State Oil-Brine Relative Permeability. The steady-state oilbrine relative permeabilities of the rough-walled fractures were measured by conducting two-phase flow experiments that included primary drainage, primary waterflooding, and secondary drainage processes. FIGS. 9-11 present the results generated using sample EF-2 under a capillary-dominated flow regime.

[0139] 1.4.4.1, Drainage. The primary drainage (PD) experiment was conducted at0.5 mL / min total flow rate under capillary-dominated flow regime with an oil / brine viscosity ratio of M=2.27 and a capillary number of Aca=3.46E-05. At the beginning of the displacement, oil and brine were co-injected into the fracture at flow rates of 0.1 and 0.4 mL / min, respectively (see FIG. 9). Initially, oil as the non- wetting phase only invaded the large aperture regions connected to the fracture inlet due to its low flowrate, thereby forming the first oil-filled patches that impeded the flow of brine and consequently increased the pressure drop of the fluids moving through the medium. As the flow process continued, oil pressure increased as the volume of oil accumulated, resulting in dislodging brine from low threshold capillary pressure zones (e.g., large aperture elements), while creating a connected path of least resistance to the fracture outlet. Following the breakthrough, the oil continued to displace brine from neighboring low capillary pressure regions, improving the oil relative permeability to kro= 0.055 and increasing phase interference, both of which caused significant decreases in the brine relative permeability krw = 0.112. When the steady-state condition was established, the oil and brine flowed in the pre-set paths with their saturations being at equilibrium with a remaining brine saturation of Sw= 0.672. Subsequently, the oil flow rate was gradually increased to 0.2 mL / min, 0.3 mL / min, 0.4 mL / min, and 0.5 mL / min while the brine flow rate was reduced accordingly to maintain a total flow rate of 0.5 mL / min. The higher oil flow rate during each step may facilitate the oil invasion into tighter fracture regions. After these segments, the remaining brine saturation was reduced to 0.519, 0.398, 0.285, and 0.138, respectively. At the end of the drainage process, where only oil was flowing, the entire injected volume moved through the pre- established paths of least resistance leading to a more uniform saturation distribution (e.g., no significant change in endpoint brine saturation after conducting a bump flow test with 1.0 mL / min and 2.0 mL / min flow rates) with a final oil relative permeability of kro= 0.194. The low oil relative permeability at the end of the steady-state drainage experiment may be caused by the high phase interference in the fracture.

[0140] I.4.4.2. Waterflooding. The brine phase completely covers the fracture surface in water-wet rough-walled fractures, with layers that remain connected during drainage. As a result, during waterflooding, brine may be transferred through these wetting layers as well as the fracture centers. Fracture layer flow occurs at low brine flow rates when the hydraulic conductivity of the layers is sufficient to transport the injected brine with minimum pressure drop. At higher brine flow rates, the wetting layers may swell to accommodate the additional supplied brine. However, there exists a threshold injection rate beyond which the fracture wetting layers are inadequate for directing the additional brine. As a result, brine pressure increases (oil-brine capillary pressure decreases) and exceeds the threshold entry pressure of narrow aperture regions, displacing oil from the center of the fracture from such areas (transition fromfracture layer to local bulk flow). The contribution of each mechanism was determined by the fracture aperture, fluid properties and brine flow rate. The dominance of each mechanism was regulated in order to achieve the lowest pressure drop to transport the supplied brine through the fracture.

[0141] The imbibition experiment was commenced by switching the drainage oil / brine flow ratios, lowering the oil flow rate to 0.4 mL / min, and increasing the brine flow rate to 0.1 mL / min (see FIG. 10). In the start of the displacement, brine as the wetting-phase was favored by the fracture surface. Thus, the injected brine volume was directed to swell the wetting layers covering the facture walls and the arc menisci (AMs), triggering capillary-driven processes such as snap-off events in narrow aperture regions and where fracture walls met, and forming new main terminal meniscus (MTM) interfaces in the fracture. During this time, brine started occupying more fracture volume, reducing the area open to the flow of oil phase and lowering oil relative permeability. Furthermore, brine could potentially trap portions of oil ganglia in large aperture areas surrounded by narrow apertures zones through snap-off. The disconnected oil globules, in turn, increased phase interference and decreased the oil relative permeability while limiting that of brine to low values as well. As the brine volume grew and developed a sufficient pressure, brine started to displace more oil from the narrow regions of the fracture. The resulting relative permeabilities of brine and oil were 0.014 and 0.128, respectively, with remaining oil saturation of Sor= 0.715.

[0142] To continue the waterflooding process, the brine flow rate was progressively raised to 0.2 mL / min, 0.3 mL / min, 0.4 mL / min, and 0.5 mL / min. The remaining oil saturations were 0.582, 0.446, 0.318, and 0.160, respectively. With increasing water flow rate, thicker wetting phase layers were favorably formed to conduct the additionally injected brine while snap-off events continued to create new MTM interfaces in the fracture, transitioning the water transport mechanism from fracture layer flow to local bulk flow. Higher brine flow rates were expected to reduce the oilbrine capillary pressure in the fracture and overcome the threshold capillary pressure used to displace oil from the center of the fracture, thereby enabling piston-like and pore-body filling mechanisms through MTMs. When the brine invaded the majority of the fracture center, it established a low-resistance flow path which suppressed any additional brine to oil-displacement, resulting in a water relative permeability of 0.176 and residual oil saturation of Sor= 0.160.

[0143] Following the waterflooding, a secondary drainage (SD) test was performed to examine whether the corresponding relative permeability behavior is impacted by post-waterflooding fluid configuration, compared to the primary drainage (PD) where the displacement was initiated at Sw= 1 (see FIG. 11). The fractional flow rates utilized in this experiment were identical to the ones in primary drainage. Initially, the injected oil volume mostly reconnected the separated oil channels rather than developing new flow paths. However, oil favored reconnecting the areas with minimum threshold capillary pressures, which led to the bypassing of some oil-filled spaces surrounded by brine. These separated oil zones posed additional phase interference as they obstructed both oil and brine mobilities, hence reducing their relative permeabilities to km= 0.042 and krw = 0.096, respectively at remaining brine saturation of Sw= 0.667, which are slightly lower than their counterparts measured during primary drainage. As oil fractional flow rate increased, more isolated spaces were reconnected to the bulk oil phase. At the end of secondary drainage, the oil relative permeability was km= 0.0.203 with a remaining water saturation of SWi= 0.145, which is similar to that of primary drainage. That is, even though the SD relative permeability curves were initially lower than their counterparts in PD, they produced the same trends at higher oil saturations and reached similar end-point values at the end of the drainage process.

[0144] Phase interference during the drainage and imbibition processes in the fracture could be realized by cross -plotting the oil and brine relative permeabilities as illustrated in FIG. 12. For comparison, the calculated trends for the X-curve and the Corey models are also shown. The results demonstrated that the primary and secondary drainage values were comparable and follow a similar trend because the drainage process is mainly dominated by piston-like displacement. Moreover, the degree of phase interference was observed to increase during the waterflooding experiment (FIG. 12). In addition, the trend obtained by the experiments differed significantly from those generated by the X-curve and the Corey models, with the sum of the measured oil and brine relative permeabilities being between 0.12-0.19, indicating substantial phase interference (e.g., krw+ kro« 1).

[0145] To further highlight these deviations, some of the data in FIG. 12 are replotted in FIG. 13, which compares the experimentally-measured steady-state oilbrine relative permeabilities of primary drainage with the values predicted by the X- curve and Corey models. The X-curve shows the largest deviation from theexperimental data due to the neglect of phase interference associated with the flow through fracture. In addition, the Corey model significantly overestimates the oil and brine relative permeabilities for a wide range of saturations. For example, brine relative permeability at brine saturation of 0.700 and the oil relative permeability at oil saturation of 0.820 are overestimated by 160% and 232%, respectively. Nevertheless, the Corey model provided a reasonable approximation of the brine relative permeability at low brine saturations (e.g., Sw< 0.5) because of the decrease in phase interference corresponding to the flow of brine on the fracture walls and in tight fracture regions at the end of the drainage displacement. However, a poor approximation for oil relative permeability at low oil saturations (e.g., So< 0.5) was observed. This is because oil as the non- wetting phase encountered more interference while establishing a path of least resistance through the large aperture regions of the fracture.

[0146] 1.4.5. Effect of Saturation History on Relative Permeability. To evaluate the dependency of the oil-brine relative permeability on saturation history, five cycles of steady- state drainage and imbibition experiments were performed on fractured Sample EF-3 under a capillary-dominated flow regime at 0.5 mL / min total flow rate (Experiments B-l to B-10). A different initial brine saturation was established at the end of the drainage in each cycle by halting the displacement process at 5 / 5, 4 / 5, 3 / 5, 2 / 5, and 1 / 5 successions. The cycles were then completed by performing waterflooding tests until the corresponding residual oil saturations were reached. FIGS. 14A-E shows the oil-brine relative permeabilities of the aforementioned five cycles (a)-(e), respectively. The primary drainage in cycle (a) began with oil and brine flow rates of 0.1 mL / min and 0.4 mL / min, respectively. As the displacement progressed, oil entered fracture sections with low entry pressures. As a result, the brine relative permeability declined to krw = 0.104 at a relatively high brine saturation of Sw= 0.70. The oil relative permeability at this point increased only to kro= 0.052. By the end of drainage, the oil relative permeability had increased to kro= 0.191 at a remaining brine saturation of Sw= 0.179. These values are similar to their counterparts measured on fractured Sample EF-2.

[0147] During the primary waterflooding, the initial displacement process was dominated by the flow of brine thorough the wetting layers on the fracture walls as well as snap-off events consequent to the swelling of these occupancy features. At this point, the flow paths available to brine were limited to narrow regions while the oil phase stilloccupied the larger connected areas within the fracture. Furthermore, at the beginning of the imbibition process, the increase in oil trapping and bypassing in the large aperture areas of the fracture surrounded by narrow openings hindered the flow of both fluids and limited their conductivities and, as a result, both relative permeabilities were reduced. As the brine saturation and flow rate increased in the fracture, more efficient displacement mechanisms such as piston-like events triggered by the MTMs became dominant, leading to more swept oil at the end of the process. Primary waterflooding resulted in brine relative permeability of krw = 0.135 at a residual oil saturation of Sor= 0.156, which corresponds to 19% of the initial oil saturation established at the end of the primary drainage. These values and the overall trend of waterflooding relative permeabilities were similar to their counterparts measured on fractured Sample EF-2. Such similarities may arise from the similar absolute permeabilities (see Table 1-5) and perhaps fracture wall roughness of Samples EF-2 and EF-3 despite potentially different aperture maps that they may possess. Similar behavior was observed in the subsequent flow cycles.

[0148] By the end of waterflooding in cycle (a), the residual oil volume was hydraulically disconnected in the facture. In the beginning of secondary drainage in cycle (b), the injected oil volume was mainly directed to re-establishing the detached flow paths rather than developing new transport channels. However, oil favorably reconnected the spaces that had the least amount of pressure to break through the fracture, resulting in bypassing of large oil-filled areas surrounded by brine-filled narrow regions that had higher capillary pressures to invade. These isolated oil zones provided no contribution to the mobility of oil, hence increased the phase interference and reduced the relative permeability for both oil and brine to km= 0.037 and km = 0.070, at remaining brine saturation of Sw= 0.562. Further increase in oil fractional flow rate was expected to re-connect additional isolated regions to the bulk oil phase but the recorded relative permeabilities of both phases remained lower than their counterparts in cycle (a) due to bypassing of some isolated oil blobs. By halting the drainage at 4 / 5 of its full cycle, a higher remaining water saturation of Sw= 0.236 was established (compared to Sw= 0.179 established in the first cycle). The oil and brine relative permeabilities evolved to km= 0.110 and km = 0.001 at this point. During the secondary waterflooding, oil and brine were mobile as the displacement from a higher initial water saturation was started. Moreover, brine had a higher fractional flow rate compared toprimary waterflooding. The progress of oil entrapment mechanism here is similar to primary waterflooding with brine restoring the previous trapping regions while also forming new confining sections because the fluid distribution is different from the one in primary waterflooding. The new trapping zones increased the phase interference, resulting in a relative permeability to oil of kro= 0.084 and to brine of krw = 0.026 at a remaining oil saturation of Sor= 0.639. Moreover, the residual oil saturation at the end of waterflooding in cycle (b) was Sor= 0.235 (e.g., 30.7% of the initial oil saturation) which is higher than that for the primary cycle Sor= 0.16. Furthermore, slightly higher initial brine saturation at the beginning of secondary waterflooding (5W= 0.236) may have provided a better brine connectivity at initial stages of the displacement, leading to higher areas of upswept oil and residual trapping due to early bypassing. At the same time, the initial brine saturation and the starting brine flow rate may have not been high enough to trigger more efficient brine-to-oil displacements through MTM interfaces.

[0149] During the drainage in the following cycles, both oil and brine relative permeabilities improved marginally compared to the previous cycle but remained lower than the values in cycle (a). By the end of these cycles, the remaining brine saturation was Sw= 0.414 for cycle (c), Sw= 0.590 for cycle (d), and Sw= 0.740 for cycle (e). The oil relative permeability at the end of drainage successions decreased as the remaining brine saturation increased while that of brine increased. As the initial brine saturation increased for the following successive waterflooding processes (cycles c, d, and e), brine retained ample flow areas across the medium, resulting in reduced entrapment and segmentation of the oil flowing through the fracture center. Consequently, the relative permeabilities of oil and brine remained similar to those observed during the drainage. Furthermore, the higher brine saturation in the fracture and starting brine flow rate at the beginning of waterflooding promoted more efficient pore- scale displacements through MTM interfaces, such as piston-like and pore-body filling, and reduced the frequency of oil segmentation and trapping by snap-off. This is evident by the lower residual oil saturation at the end of the waterflooding tests commenced at higher brine saturation (lower Soi), e.g., Sor= 0.16 at 3 / 5 cycle, 0.134 at 2 / 5 cycle, and 0.122 at 1 / 5 cycle. The endpoint brine relative permeability at Sor, however, remained relatively similar for the five cycles (km = 0.135, 0.13.3, 0.132, 0.127, and 0.125 in cycles (a), (b), (c), (d), and (e), respectively). That is, saturation history did notsignificantly affect the end-point brine relative permeability despite the variations it caused in the residual oil saturation.

[0150] Overall, and similar to conventional porous media, saturation history may considerably impact fracture relative permeability trends and waterflooding residual oil saturations. Therefore, caution may be practiced when simulating multi-phase in subsurface fractures that are subject to varying injection and production histories.

[0151] 1.4.6. Effect of Flow Rate on Relative Permeability. To investigate the effect of the total (oil + brine) flow rate on two-phase relative permeability in the fracture, multiple steady- state waterflooding tests at different total flow rates were conducted starting from relatively similar pre-established initial brine saturations (Sample EF-2, Experiments C-l to C-6). The tests were intended to mimic capillary- and viscous-dominated flow regimes encountered in fractures depending on their distances from production or injection wells. FIG. 15 illustrates the variation of oilbrine relative permeability values with flow rates under capillary-dominated (e.g., 0.5 mL / min) and non-capillary-dominated (e.g., 1.0 mL / min and 2.0 mL / min) regimes. Under capillary-dominated waterflooding, the oil and brine relative permeability values were lower than that of the primary drainage. This is due to the increase of phase interference during waterflooding caused by brine wetting-layer flow and snap-off in small fracture elements, leading to more oil trapping and limiting the oil flow through the larger fracture apertures. The trapped oil globules may not be further mobilized under capillary-dominated flow regime and hence the trapped oil globules may create considerable resistance to the brine flow at higher water / oil fractional flow ratios. Similar behavior was also observed in water- wet porous media.

[0152] With increasing the waterflooding total flow rate to 1.0 mL / min, both oil and brine fractional flow rates were doubled, yet the paths accessible to each phase at the beginning of the displacement remained similar to those of the capillary-dominated waterflooding. This was corroborated by reaching similar remaining brine saturations after each primary drainage as well as the high reproducibility of the drainage relative permeability curves. However, the higher flow rate allowed for displacement events to happen relatively quicker, the wetting-layers were thought to grow thicker to conduct the additional brine supplied at the fracture inlet, providing higher brine mobility while the brine pressure was not sufficient to invade the fracture center. Thereafter, with increasing water / oil fractional flow, the high pressure drop of the brine flow promptedthe piston-like and pore-body filling mechanisms to dominate the displacement in the center of the fracture and thereby decreased the frequency of snap-off trapping as well as the bypassing through selective capillary percolation (e.g., viscous stable displacement). Moreover, the higher oil flow rate provided enough pressure for the oil to maintain and expand its flow path through the larger aperture regions of the fracture. The competition between these two displacements resulted in both phases encountering less interference, resulting in higher brine and oil relative permeability values compared to the flow tests under capillary-dominated flow regime. The waterflooding relative permeability curves followed a path similar to that of primary drainage in this scenario. By the end of the displacement, the brine relative permeability increased to krw = 0.254 with a residual oil saturation of Sor= 0.194. Here, the endpoint water relative permeability was greater than that of oil at the end of primary drainage, which may be due to the higher brine flow rate providing sufficient pressure to efficiently displace oil from the fracture through forced imbibition. As a result, brine was able to utilize parts of the low resistance flow region that were previously inaccessible. Similar trends were also observed in conventional porous media.

[0153] After a third primary drainage, the total waterflooding flow rate was increased to 2.0 cc / min. Initially, brine wetting-layers were formed to conduct the additional volume of brine being injected into the fracture with minimal pressure drop. Further increasing the brine flow rates resulted in significant loss in the oil flow area as brine dominated the flow through the center of the fracture, causing the majority of the oil in the center of the fracture to be displaced. This, in turn, established a higher brine relative permeability of krw= 0.307 at a residual oil saturation of S,,r= 0.169 at the end of waterflooding. As shown in FIG. 15, the waterflooding oil and brine relative permeability values increased with the increase in the total flow rate and surpassed the primary drainage curves during the viscous-dominated flow. Overall, it may be concluded that a higher total flow rate during waterflooding reduces the phase interference in the fracture and results in higher oil relative permeabilities at any given saturations. Higher brine relative permeabilities, however, may be expected once brine dominates the flow through the center of the fracture at a later stage of waterflooding (e.g., Sw>0.5).

[0154] 1.4.7. Impact of Saturation History and Flow Rate on Residual Trapping.The impact of saturation history on residual trapping within the fracture was studied byperforming multiple waterflooding tests starting from different initial oil saturations. These saturations were established from preceding oil drainage processes (Experiments B-l to B-10). Furthermore, some of the above flow cycles were repeated at different total waterflooding flow rates (e.g., 0.5 mL / min, 1.0 mL / min, and 2.0 mL / min) to investigate the impact of flow dynamics on the residual trapping (Experiments D-l to D-12). FIG. 16 presents the variation of the residual oil saturation under the above- mentioned initial saturation and flow rate conditions. Under a capillary-dominated flow regime, a greater residual trapping was generally observed with the increase in the initial oil saturation established in the fracture prior to the waterflooding process. As a result, the flow is dominated by AM displacements (snap-off segmentation and trapping), especially in the small aperture regions of the fracture, which results in oil trapping in larger neighboring elements. The abnormal behavior observed at high initial oil saturations were attributed to a combination of pre-waterflooding fluid configuration and brine mobility at early stages of waterflooding, which are detailed in Example 1.4.5. As the flow rate increased, the amount of residual trapping decreased considerably while the above-mentioned general relationship between the initial and residual oil saturations remained valid. Moreover, the higher flow rate provided a higher brine pressure to displace the large oil-filled fracture elements that were not mobilized under the capillary-dominated flow regime. The difference in residual oil saturations corresponding to any given initial oil saturation, however, diminished with further increase in the flow rate (e.g., from mL / min 1.0 to 2.0 mL / min). That is, the impact of waterflooding total flow rate on residual trapping was more pronounced from 0.5 mL / min (capillary-dominated flow) to 1.0 mL / min (non-capillary flow) displacements compared to the counterparts from 1.0 to 2.0 mL / min. This behavior could be attributed to high hydraulic conductivity and weak capillary properties of rough-walled fractures compared to conventional porous media. These features along with the fluid transport mechanisms that are unique to fractures — such as wetting-layer flow on fracture walls promoting snap-off at low brine rates — amplify fracture response to slight deviation from capillary-dominated flow regime. Once the displacement regime is switched to non-capillary flow, an increase in brine flow rate may be expected to have less significant impact on the displacement and trapping patterns.

[0155] Overall, in Example I, the effects of flow rate and saturation history on oilbrine relative permeability hysteresis and residual oil trapping in water-wet rough-walled fractures were systematically investigated using the steady-state technique. Selected, non-limiting findings include the following:

[0156] (a) Due to their high hydraulic conductivity and relatively weak capillary properties compared to conventional porous media, two-phase flow and trapping through the rough-walled fractures showed strong dependency on the balance between forces governing the flow (e.g., capillary, viscous and gravitational forces) represented by capillary and bond numbers. Deviations from capillary-dominated regimes and stable flow conditions, even though common in various natural and engineered subsurface processes, may result in fracture relative permeability measurements that lack reproducibility and are highly case-dependent.

[0157] (b) A new expression for capillary number incorporating the known parameters governing two-phase displacements in rough-walled fractures was derived and tested to accurately categorize flow regimes in fractures.

[0158] (c) Significant phase interference was observed for the oil-brine flow in rough-walled fractures, which renders the commonly used X-curve model and Corey model inadequate to represent the steady-state oil-brine relative permeabilities measured in this study.

[0159] (d) Saturation history significantly affected the relative permeability trends and residual oil saturations in the fracture. This was due to the changes in fluid configuration and redistribution and the resulting phase interference. In general, as the initial oil saturation increased, so did the residual oil saturation. This behavior was attributed to the absence of MTMs at the beginning of waterflooding tests initiated at high oil saturations, and increased frequency of snap-off trapping events as a result. However, an opposite trend was observed for flow under capillary-dominated regime at very high initial oil saturation (e.g., SOi> 85%). This behavior may be attributed to a combination of pre-waterflooding fluid configuration in the fracture and the brine mobility at early stages of waterflooding.

[0160] (e) At the same water saturation, the oil relative permeability during waterflooding improved as the total flow rate and the deviation from the capillary- dominated regime increased. By contrast, the increase in the brine relative permeability at early stages of the waterflooding was insignificant and its trend followed the same path as that in the capillary-dominated test. However, relatively higher brine relativepermeabilities were observed as brine dominated the flow through the center of the fracture at late stage of the waterflooding test.

[0161] (f) Lower residual oil trapping was observed at higher total flow rates during the waterflooding process. This may be due to the higher pressure drop of the flow prompted the piston-like and pore-body filling mechanisms to dominate the displacement and thereby decreased the frequency of snap-off trapping as well as the bypassing through selective capillary percolation (e.g., viscous stable displacement). In addition, the higher flow rate provided a higher brine pressure to displace the large oil- filled fracture elements that were not mobilized under the capillary-dominated flow regime. The difference in residual oil saturations corresponding to any given initial oil saturation, however, diminished with further increase in the flow rate.

[0162] The results presented in Example I are significantly different — and significantly more accurate — than studies using conventional technologies because conventional technologies are not capable of mimicking real-world conditions and instead use non-representative conditions.Example II. Steady-state Two-phase Oil / Brine Relative Permeability Measurements in Proppant-packed Rough- walled Fractures

[0163] Examining multi-phase flow behavior in proppant- and mineral-filled fractures is used to maximize exploitation of fractured subsurface for hydrocarbon production, CO2sequestration, underground hydrogen storage, and geothermal energy applications. Experimental data and models in this area are scarce. Conventionally, researchers have relied on simple fracture models (e.g., X-curves) and relative permeability data generated for sandpacks and glass beads to predict multi-phase flow in void and filled fractures. However, such models and experimental data do not adequately represent the complex geometry, flow, and environment conditions of these subsurface conduits.

[0164] An objective of the study presented in Example II is to provide the very first representative steady- state two-phase oil / brine relative permeability curves in roughwalled fractures packed with water-wet 40 / 70 sand (silica) or surface-coated ceramic proppants. Steady- state drainage (nonwetting-phase displacing wetting-phase) and imbibition (wetting-phase displacing nonwetting-phase) tests were performed under a wide range of saturation histories (full cycle and scanning curves) to study relative permeability hysteresis of the mediums. Residual saturations and phase permeabilitieswere also compared to evaluate two-phase flow behavior in each proppant pack. Pore space topology and in situ wettability of the packs were characterized using high- resolution x-ray microtomography and used to explain the underlying pore-scale displacement mechanisms responsible for the measured relative permeability trends. The inventors observed that the commonly used X-curves model (Romm’s curves and their variations) significantly overestimated the brine and oil phase relative permeabilities (e.g., krwand kro) for fractures packed with silica and ceramic proppants. The krocurves during imbibition were measured to be higher than their counterparts during drainage in both proppants. A lower initial water saturation and a higher endpoint oil relative permeability was measured in the ceramic proppant at the end of the drainage process, and km in this proppant was much higher than that in the silica proppant irrespective of the flooding process. The improved insight and extensive relative permeability data generated under this study may be used to develop and validate next-generation physics-based models that may accurately predict multi-phase flow through filled fractures of interest and to inform Darcy-scale flow simulations of fractured subsurface.

[0165] II.1, Introduction. Recently, there has been increasing demand for enhanced efficiencies in developments of fractured subsurface engineering technologies in energy, water, and environment sectors. The growth of such developments is linked to the level of understanding of and control over flow and transport through void and mineral- / proppant- filled fractures. One area that may substantially benefit these developments for both hydrocarbon recovery and clean energy applications is fracking of unconventional reservoirs. As of 2019, shale reservoirs contributed 60% of U.S. oil production. However, oil recovery from unconventional reservoirs, e.g., shale plays, tight sands, etc., is typically less than 10%. Different enhanced oil recovery (EOR) techniques have been implemented to change the physical and chemical characteristics of such geosystems and enhance their production. Yet, many believe that it is more practical and economical to manipulate the mechanical and multi-phase flow properties of hydraulically-induced fractures to delay the intrinsic production loss faced by unconventional reservoirs after several months of flow back. Rationales behind this approach include the ultra-tight nature of rock matrix and presence of induced fracture networks that substantially reduce the chance of success in deploying conventional EOR schemes, the higher level of control over the hydraulic fracturing processcompared to other fluid injection-based techniques, the low cost of testing and screening of proppants, and the ability to analyze data that may be collected from every stage of each hydraulically fractured well. Furthermore, proppant-packed fractures are a primary production pathway in an unconventional reservoir. Therefore, the overall well performance throughout its lifespan highly depends on the conductivity and multiphase flow properties of these conduits. For at least the reasons mentioned above, understanding multi-phase flow behavior in proppant-packed fractures under varying flow and stress conditions is of increasing importance to maximizing hydrocarbon recovery from unconventional reservoirs.

[0166] Conventional proppant studies available in the literature have primarily focused on the effects of overburden stress on the hydraulic conductivity of propped fractures. Properties such as proppant packing (e.g., mono- and multi-layer distribution), the mechanical strength of the proppant grains and neighboring rock matrix, and proppant shape and size significantly affect the deformation behavior and absolute permeability of propped fractures under varying stresses. In addition, the proppant type (e.g., coated or uncoated, sand or ceramic), size (20 / 40, 30 / 50, 40 / 70, and 100 mesh), and surface wetting characteristics (water-wet, neutral-wet, or oil-wet) impact transport properties of proppant-packed fractures under multi-phase flow conditions. Changes in the flow regime (capillary- or viscous-dominated flow), production history, and solid surface wettability (due to, for instance, aging) are also known to impact fluids’ saturations and relative permeability functions within sandpacks, which are similar mediums to propped fractures.

[0167] Relative permeability function, which is the manifestation of the underlying pore-scale displacement events, is often used to describe multi-phase flow in porous media at the macro scale. Such flow functions are input to commercial reservoir simulation platforms that are utilized to predict the reservoir and well production performance at the field scale. Despite the significance of proppant-packed hydraulic fractures in delivering reservoir fluids to the wellbore and vice versa, their relative permeability functions have not been adequately explored. Multi-phase flow through fractures often comes with the crude assumption of a linear relationship between the relative permeability and fluid saturation. The closest studies aimed at characterizing the relative permeability in propped fractures are limited to gravity drainage through glass beads and cylindrical sandpacks. However, these studies fail to accurately depictthe flow processes encountered in propped fractures, where matrix-proppant-fluid interactions govern the preferential fluid transport pathways, residual trapping, and fluid mobility during production.

[0168] To the best the inventors’ knowledge, no experimental studies have been dedicated to systematically understand and characterize two and three-phase relative permeability functions in propped fractures under representative conditions. Example II aims to, for example, provide a unique set of representative steady-state two-phase oil / brine relative permeability curves for proppant-filled fractures. Herein is presented a new methodology to create highly-reproducible multi-layer proppant packs using two common water-wet proppants (silica and surface-coated ceramic).

[0169] Rough-walled fractured outcrop shale samples were utilized as the matrix to prepare the proppant-packed fractured assemblies. These assemblies were then subjected to a series of carefully-designed core-flooding experiments. The fluid saturations were determined using the material balance technique. Steady-state two- phase oil / brine relative permeability curves were obtained for both types of proppants over the entire saturation ranges of drainage and waterflooding tests. The experiments were performed at ambient temperature, with confining and pore pressures of 3,500 psig and 1,000 psig, respectively.

[0170] Results of this study presented in Example II may be utilized in, for example, the evaluation, characterization, and modeling applications of post-fracturing well production performance in unconventional reservoirs and for making informed decisions during the proppant selection process for hydraulic fracturing treatments, among other applications. Additionally, the improved insight and the extensive relative permeability data generated in this study has direct applications in the development of fractured (filled or void, induced or natural) and / or unconsolidated subsurface for underground hydrogen storage, carbon sequestration, and enhanced geothermal energy. IL2, Materials and Measurements

[0171] II.2.1. Rock samples. A process described to obtain macro- scale roughwalled fractured rock samples as described herein (See Example 1.2.1.1) was applied to an Eagle Ford shale outcrop rock and used as the rock matrix phase in this study.

[0172] II2.2. Proppants. Two types of proppants, e.g., silica and surface-coated ceramic, were selected to prop the fractured shale samples. FIG. 18 shows the grain sizedistribution of the proppants from sieve analysis (API STD19C:2018 Section 6, ref). Both proppants had over 90% of the grains in the 210 to 420 pm (40 / 70) mesh range.

[0173] II.2.3. Fluids. 1 wt% potassium chloride (KC1) solution and filtered Soltrol170 mineral oil were utilized as the wetting and non-wetting phases, respectively. KC1 minimizes swelling of the trace amount of clays present in the rock. The mineral oil was filtered by passing it through activated silica and alumina to remove moisture and polar components from the oil that could alter the wettability of the proppant or the rock. The density and viscosity of the brine and oil phases were measured to be 1.01 g / mL, 0.79 g / mL, 1.01 cP, and 2.52 cP, respectively, using an Anton Paar densitometer and viscometer at 1,000 psig and ambient temperature.

[0174] II2.4. Interfacial Tension (IFT) and Contact Angle (CA) Measurements.Brine-Oil IFT was measured at experimental conditions with the pendant drop method using a high pressure, high temperature (HPHT) IFT measurement apparatus. The IFT setup included an HPHT Hastelloy C-276 cell, a high -resolution camera, and a Quizix 5000 pump. A description of the IFT apparatus and measurement procedures may be found elsewhere. The tests were repeated three times, and the average IFT value was 29.027 mN / m at 1,000 psig and ambient temperature. The high-resolution camera from this setup was also utilized to measure the contact angle between the rock, oil, and brine at experimental conditions. The tests were repeated two times, and the average contact angle between the rock and the fluids was measured to be 79.7°. A HeliSCAN micro- CT scanner (FEI) was utilized to acquire pore-scale resolution images of the proppant packs saturated with the oil and brine at experimental conditions. These images were utilized to characterize the in situ wettability of the proppants. The 1 wt% KC1 working brine was doped with 5 wt% sodium iodide (Nal) solution to enhance the contrast between the brine and oil phases in the micro-CT images. FIG. 19 shows drawings of the raw (grayscale, left panel) and segmented (right panel) two-dimensional (2D) images of a region of interest (ROI), with different hatching depicting the brine, oil, and proppant, respectively. The image processing method used to measure the contact angles from the micro-CT images is provided elsewhere. FIG. 20 shows the distribution of in situ contact angles measured for each proppant type. The average oil-brine contact angles (indicated by the vertical dashed lines) were 44.84° and 61.96° for the silica and the ceramic proppants, respectively.

[0175] II.2.5. Preparation of Proppant Packed Fracture Assemblies. A process described to obtain macro- scale proppant packed rough- walled fractured rock samples was applied to an Eagle Ford shale outcrop rock sample fractured using aspects of processes for forming rough-walled fractures described herein (e.g., Example 1.2.1.1.).

[0176] Steps described in this sub-section were finalized after multiple tests under different conditions and fine-tuning of parameters to prepare reproducible proppant packs. A 38.1 mm (1.5”) wide, 203.2 mm (8”) long, and 19.05 mm (0.75”) deep track was machined in a flat slab of Delrin homopolymer 2200 (FIG. 22A and FIG. 22B) and used to hold one half of the fractured core sample. The depth of the track ensured that the half-core (e.g., first segment 2202) could have a specific clearance between 0.9 to 1.1 mm on top of the mold. This clearance was then filled in with proppant (see FIG. 22C). Once the proppant was filled in, a fine mist of distilled water was sprayed on the entire mold assembly to wet the proppant grains. The assembly was then frozen at - 32°C for 5 to 8 minutes. The frozen water acted as a temporary binding agent, turning the entire proppant pack into a single solid wafer. This optional step facilitated the sample assembly process. Afterward, the other half-core (e.g., second segment 2204) of the core was placed on top of the proppant pack (e.g., proppant layer 2206) and the entire assembly was taken out of the mold and wrapped with Teflon tape. 100-mesh stainless steel screens were placed at both ends of the assembly to mitigate potential proppant mobilization and flow line blockage during the core-flooding experiments. These steps were completed while the proppant wafer was still frozen.

[0177] Core diameters were measured before and after propping the core in three locations to obtain the average proppant-pack thickness. This average proppant-pack thickness along with the diameter of the core sample (1.5” or 38.1 mm) resulted in a rectangular cross-section for fluid flow. This rectangular cross-sectional area of the propped fracture was used to measure the absolute permeability of the proppant pack (FIG. 22D). The assembly was then wrapped in a heat shrink tube. Finally, the completed propped fractured core assembly was weighed and placed in a constant temperature oven for three days at 65 °C to dry the proppant grains. It is noted that the sample was held in a horizontal position during the entire process, minimizing gravity settling of proppant grains (FIG. 22D).

[0178] After the core sample was removed from the oven, weighed, and cooled down to room temperature, it was horizontally placed inside a Hassler- type core holderand subjected to 175 psig confining pressure to inhibit the movement of the proppant grains. Gaseous CO2was injected through the core at a low flow rate (0.2 mL / min to 0.5 mL / min) to dry any residual moisture out of the proppant pack.

[0179] The proppant pack thickness and the proppant concentration in the fractures were similar for the core samples prepared using the above procedure, minimizing potential variations in the hydraulic conductivities of different specimens that have been noted in previous studies to the extent reasonably possible.II.3. Experimental Setup and Procedure

[0180] II.3.1. Experimental Setup. Two (2) two-phase core-flooding systems capable of operating at 120°C and 10,000 psig were designed and manufactured inhouse for relative permeability experiments (FIG. 2). The wetted parts of the systems were made of a corrosion-resistant material (Hastelloy C-276). Brine and oil phases were delivered to the assembly at constant flow rates via dual-cylinder Quizix 5000 pumps. These pumps provide constant, pulse-free fluid delivery in paired modes with a 0.0003 mL / min to 15 mL / min flow rate range. The overburden pressure and the backpressure were sustained at 3,500 psig and 1,000 psig, respectively, using a Quizix 5000 pump. A Hassler-type core holder was utilized to house the core samples. Two Rosemount differential pressure transducers were connected in parallel to each system with ranges of 0-500 inch H2O (0-18.0365 psig) and 0-300 psig. Dome-loaded backpressure regulators (Core Laboratories) were utilized to receive the effluent at constant backpressure and discharge into burettes of 0.1 mL accuracy at ambient conditions for material balance calculations. The effluent volume measurement accuracy was enhanced to 0.001 mL by using an Eberbach digital cathetometer. The experiments were performed at ambient temperature. The total fluid flow rate (oil flow rate + brine flow rate) was set at 0.5 mL / min for the experiments. During the experiments, the core was maintained at an inclination of 1° from horizontal, e.g., practically horizontal. This slight inclination was chosen for bond number calculations.

[0181] H.3.2. Experimental Procedure. Relative permeability experiments were performed on two fractured assemblies, one packed with 40 / 70 sand and one packed with 40 / 70 ceramic proppant, at a fixed total flow rate (Qtotal) of 0.5 mL / min. Steadystate primary drainage was first performed from 100% brine saturation (SW= 1) by increasing the fractional flow of oil (fo= Qoii / Qtotal) from zero to one, followed by steady- state primary imbibition (waterflooding) by reducing fofrom one to zero.

[0182] II.3.2.1. Initial Conditions. The proppant pack was dry and under 175 psig of confining pressure after the core assembly process (Example II.2.5). The confining and pore pressures were ramped up to 3,500 psig and 1,000 psig, respectively, over a period of 1 h under constant brine injection and the pore volume of the proppant pack was measured. Brine was then injected at four different flow rates and the corresponding differential pressures (AP) were recorded to calculate the absolute permeability (Kohs') of the proppant pack using the Darcy equation. The widths (or apertures) of the propped fractured samples were measured prior to loading the sample in the core holder.

[0183] II.3.2.2. Main Experiments. The following procedure was followed to perform relative permeability tests:

[0184] (I) After establishing Sw= 1 and measuring Kabs, the steady-state primary drainage test commenced by co-injecting both the brine and the oil into the sample at a fixed total flow rate of 0.5 mL / min with increasing oil / water fractional flow rate fo(from zero to one) in steps. For every fractional flow rate, the measurement was considered complete when steady state was attained. Steady state was assumed to be achieved when:(a) The pressure drop across the sample was constant for an extended period of time (at least 30 min).(b) The volume of fluids injected equaled the volume of fluids produced (e.g., no change in saturation).

[0185] (II) Increase / o in increments of 20% while maintaining Qtotal= 0.5 mL / min.

[0186] (III) Initial water saturation (SWi) was established at the end primary drainage at / oof 1, e.g., there was no flow of brine and only oil was injected through the core.

[0187] (IV) Primary drainage test was followed by steady- state primary imbibition (waterflooding), where fodecreased from one to zero in steps, maintaining the same criteria for attaining steady state. Residual oil saturation (SOr) was attained at the end of primary waterflooding process, when fo= 0, e.g., the oil flow rate was set to zero.

[0188] The value of Qtotalwas finalized after testing multiple flow rates that would provide an acceptable balance between a low enough flow rate for a capillary- dominated flow regime (Capillary Number range of 10-5and 10-6) and a high enough pressure drop across the sample. Furthermore, the almost horizontal orientation of thecore resulted in negligible gravity effects (bond number ~10-6), indicating that the flow was dominated by capillary forces.II.4. Non-limiting Results

[0189] The non-limiting results presented in this section show an example of the significant differences in the relative permeability measurements arising from the use of representative aspects described herein — e.g., misaligned rough-walled fractures and proppant-packed assemblies — during this study.

[0190] With the commencement of Primary Drainage (PD), AP ramped up as oil started to invade the proppant pack. As shown in FIG. 23, at time t = IBT, oil breakthrough occurred after which the AP dropped until t = tss when the steady- state condition was established. As mentioned earlier, steady state was achieved once i) AP became stable and ii) there were no changes in the fluid saturations in the proppant pack. FIG. 24A and FIG. 25A show the steady-state oil-brine relative permeability curves during the primary drainage and primary waterflooding processes for the silica and ceramic proppant packs, respectively. Drainage process is driven by piston-like pore-scale displacement events which are governed by threshold capillary pressure of pore and throat elements. Throat radii are smaller than the pores they are connected to, and have a higher threshold capillary pressure. Hence, once a throat becomes invaded by the non-wetting phase (oil) through piston-like displacement, the connected pore would get invaded automatically.

[0191] The pore size distribution (PSD) and throat size distribution (TSD) of the proppant packs (see FIGS. 21A and 21B) showed a uniformity in the pore and throat sizes in both proppant packs compared to conventional sandstones. The uniformity indicated that there would exist a narrow range of threshold capillary pressures above which the invading phase (oil) may enter into a large number of pores and throats in these proppant packs. Hence, at the beginning of PD, when the local oil phase pressure reached the threshold capillary pressures of these pores and throats, they were displaced by oil through piston-like displacement. Because the proppant pack is water wet, oil preferably displaces brine from larger elements with considerable contribution to the proppant pack pore volume. In addition, the average coordination numbers of the proppant packs’ pore spaces are much higher than those in conventional sandstones (Table II-3), meaning one pore on average is connected to more nearby pores / throats in the proppant packs than in sandstones. This highlights that a larger portion of the totalpore volume of proppant packs were accessible to oil invasion relative to conventional sandstones. A combination of these factors explains the pronounced reduction in brine saturation at the early stages of primary drainage from Sw= 1-00 to Sw= 0.65 and 0.63 in the silica and ceramic proppants, respectively, as shown in FIGS. 24 and FIG. 25. Table 11-3 shows average coordination number, average equivalent throat radius, and average equivalent throat length for 0.5% of the largest pores by size compared against all pores and throats in the silica and ceramic proppant packs, from segmented micro- CT images (total of 8,431 pores and 33,961 throats).Table 11-3

[0192] The primary drainage process was continued with a step- wise increase in f0though the reduction in the brine saturation was not as pronounced as that observed at the beginning of drainage. This manifested in greater reduction in the consecutive Swvalues in the ceramic proppant compared to those of the silica proppant. Initial water saturation (Swi) values of 0.30 and 0.23 were established at the end of PD in the silica and ceramic proppants, respectively. The end-point oil relative permeability (kro) values at respective SWivalues were measured to be 0.23 and 0.42. The low end-point krovalues in fractures packed with both proppants could be attributed to the tendency of water as the wetting phase to occupy the pore-throat junctions and bridge between the water-wet proppant grains, which may substantially restrict the flow of oil, resulting in low krovalues. Narrower PSD and TSD of the silica proppant pack explains the higher SWiand lower kroat the end of primary drainage compared to those of the ceramic proppant pack. Such characteristics of the silica pack may not allow a substantial increase in oil pressure at higher fovalues; consequently oil-water capillary pressure for oil-to-brine displacements in smaller flow-constrictive elements may not be satisfied.

[0193] The trends observed in the present study are far from the straight-lines (Romm’s model and X-curves) conventionally used to describe the relative permeability function in fractures. FIGS. 26A-26C compare conventional unpropped fracture models against example drainage relative permeability curves measured for the silica proppant. In FIG. 26A, the dashed and solid lines refer to Romm’s model (a conventional model), while the designation “this study” refers to example results using aspects of the present disclosure. In FIG. 26B, the dashed and solid lines refer to another conventional model, while the designation “this study” refers to example results using aspects of the present disclosure. In FIG. 26C, the dashed and solid lines refer to another conventional model, while the designation “this study” refers to example results using aspects of the present disclosure. The conventional models grossly overestimated brine and oil relative permeabilities. End-point wetting-phase saturation is a prerequisite constraint in the Brooks-Corey model for sandpacks, which may be acquired from the experiments described herein. Applying the data from this study along with the best- fitted pore size distribution parameter (λ) of 3.7 into the Brooks-Corey model still overestimated krw and krovalues (FIG. 26D), but to a lesser extent than the unpropped fracture models. Using these conventional models is not recommended because of their potential to introduce considerable uncertainties when simulating the production performance of stimulated reservoir rock volumes containing propped fractures. In FIG. 26D, the dashed and solid lines refer to the Brooks-Corey model, while the designation “this study” refers to example results using aspects of the present disclosure.

[0194] After PD, the fovalues were varied in the reverse order (from 1 to 0) to perform steady-state primary waterflooding (PWF), as presented in FIG. 24A and FIG. 25A. As shown in these figures (especially in FIG. 24A, silica proppant pack), at the beginning of PWF and for a considerable range of saturation, the krovalues in both proppants were higher than their counterparts measured during PD. This trend was most likely caused by two pore-scale mechanisms. First, the oil flow pathways that were previously established during PD (mainly through the center of larger pores) continuedto be the dominant conduit for flow of oil across the proppant pack during the initial stages of PWF. Secondly, as PWF progressed, the brine phase transporting through smaller pores and wetting layers did not begin to invade larger oil-filled pores until later stages of waterflooding, despite step-wise reduction in fo. The overall effect of these two mechanisms was that the oil phase that occupied larger pores for much of the waterflooding process had less resistance to flow at a given saturation and for its respective focompared to its counterpart at the same saturation during PD.

[0195] The reduction in kroduring PWF in the ceramic proppant was faster than in the silica proppant because of the wider PSD and TSD of the ceramic proppant. A wider distribution of pore and throat sizes in the ceramic proppant would present more oil- filled pores for invasion by brine during PWF, resulting in a quicker reduction in kroand a corresponding increase in krw- At the end of PWF, residual oil saturations (Sor) of 0.17 and 0.25 were established in the silica and ceramic proppants, respectively. The end-point water relative permeability (krw) values at S,,r in the silica and ceramic proppant packs were measured to be 0.20 and 0.55, respectively.

[0196] Greater oil relative permeability (kro) during PWF compared to PD is unique to unconsolidated porous media, sandpacks, and glass sphere assemblies. This trend has been previously observed by others. Some have described these unique relative permeability trends observed in unconsolidated porous media at the pore scale by categorizing the non- wetting (oil) phase into isolated and dendritic fractions. The isolated fractions of oil are completely surrounded by brine and do not contribute to flow. The dendritic fraction may be considered as a branching of the main flowing oil phase that terminates into dead ends. During drainage, the dendritic fraction is connected to the main flowing fraction of oil but does not exhibit flow itself, thereby lowering the krovalues. On the other hand, during waterflooding, the “branches” of these dendritic fractions become disconnected because of the invasion by brine. This leaves only the main pathways of oil open to flow. In other words, during waterflooding, the oil phase flowing via well-established oil channels through the center of larger pores faces much less resistance compared to that during drainage, leading to higher krovalues as seen in this study over a considerable saturation range of the waterflooding.

[0197] Comparing the two-phase flow performance of the two proppants, kroand krwvalues in the ceramic proppant were higher than those in silica, irrespective of theflooding process. This indicated that the ceramic proppant pack may have a higher oil conductivity after well cleanup and / or in geosystems with similar watercuts, but may also experience faster and more effective cleanup after the well is placed back to production because of its higher krwvalues. Such behavior may be attributed to the higher effective permeabilities in the ceramic proppant because of a combined effects of larger average pore and throat sizes, a slightly lower aspect ratio, and weaker waterwet characteristics compared to the silica proppant (see Table II- 3 and FIG. 20).

[0198] Following the PD and PWF experiments, secondary drainage (SD) and secondary waterflooding (SWF) were performed. Note that the SD started at the Sorestablished at the end of the PWF. The experimental procedure described in Example II.3.2.2 was followed for SD and SWF, and the corresponding relative permeability curves are plotted in FIG. 24B and FIG. 25B. Although the overall trends of the SD and SWF curves in both proppants qualitatively followed those of the PD and PWF curves, there was a quantitative difference between the SD and SWF curves in the silica proppant; krovalues in secondary curves were higher than the primary curves while the krwcurves were lower. Furthermore, a higher SWiwis established at the end of SD compared to that of PD. To eliminate the possibility of the behavior observed in the inventors’ study being specific to the sample used, a different sample propped with the silica proppant was prepared, and the same set of experiments were repeated. A similar trend was observed on the second sample as well. The lower relative permeability values of the wetting phase in silica proppant during the secondary flooding compared to those in the primary flooding have been observed by other researchers in studies of gravity assisted brine-gas and oil-gas floods in sandpacks. In such studies, the researchers attributed this reduction to the lower wetting phase saturation at the beginning of SD.

[0199] In the inventors’ study presented herein, the SD and SWF curves in the ceramic proppant pack, on the other hand, almost retraced the primary ones, indicating a weaker dependence on the saturation history during full-cycle tests. Such dissimilarities in the silica and ceramic packs may be caused by the differences in their pore space features as well as fluid-proppant surface interactions.

[0200] To the inventors’ knowledge, aspects of the present disclosure provide the very first systematic steady-state oil / brine relative permeability curves in rough-walled proppant-packed fractured shale samples. Rough- walled fractures were packed withtwo different types of proppants, e.g., silica and surface-coated ceramic, widely used in hydraulic fracturing operations. Drainage and imbibition relative permeability curves were generated Pore space topology and in situ wettability of the proppant packs were characterized using high-resolution x-ray microtomography and used to explain the underlying pore-scale displacement mechanisms responsible for the observed relative permeability trends. Residual saturations and phase permeabilities were compared to evaluate the two-phase flow performance of each proppant pack.

[0201] Selected, non-limiting findings from Example II include the following: First, steady-state relative permeability curves measured as described herein deviated significantly from the predictions of the conventional models and correlations widely used for fractures, e.g., cross curves (X-curves). Both krw and krovalues were much lower than those assumed in these models. Second, during PD, a sharp initial reduction in the krwwas observed in both proppants. This may be attributed to the narrow PSD and TSD and relatively high coordination numbers of the proppant packs. Third, a pronounced hysteresis was observed in the silica proppant between primary and secondary drainage processes while the ceramic proppant showed only nominal hysteresis. Fourth, both km and krocurves were much higher in the ceramic proppant than silica proppant irrespective of fluid saturations and flow processes investigated, indicating higher mobility of both fluids in the ceramic proppant. Fifth, the relative permeability dissimilarities observed between the two proppant packs may be primarily attributed to the differences in their pore space geometrical features and wettability characteristics, which are dictated by the proppant shape, size, sphericity, roundness, surface properties, and mechanical strength under closure stress.

[0202] The results presented in Example II are significantly different — and significantly more accurate — than studies using conventional technologies because conventional technologies are not capable of mimicking real-world conditions and instead use non-representative conditions.Example III. In Situ Study of Three-Phase Flow through Proppant-Packed Fractures

[0203] Results of a micro-scale experimental investigation on three-phase oil / gas / brine flow through proppant-packed fractured shale samples under increasing net confining stress of up to 7000 psi are presented in Example III. A miniature coreflooding apparatus integrated with a high-resolution X-ray micro-CT scanner wasutilized to perform the flow experiments. Geomechanical deformation and its impact on displacement mechanisms governing fluid transport within the packed fractures were investigated at the pore scale under certain flow and stress conditions. These conditions were designed to, e.g., represent the fracking stage and reservoir depletion under increasing closure stress. Intermediate-strength 30 / 50 ceramic was utilized as proppant in the study as it showed higher tendency for maintaining the flow paths under high stress conditions by impeding geomechanical and multi-phase flow factors that lead to production loss. Such proppants break into two / three pieces under severe stress conditions which prohibits further bullet-like embedment and fracture closure by redistributing the stress among the broken pieces and / or other proppant grains. As a result, fracture aperture reduced by only 6.5% under 7000 psi closure stress. Effective oil and gas permeabilities however reduced two / three fold, which may be mainly due to multi-phase flow factors. Brine bridging between the grains and within the porethroat junctions could possibly restrict the flow of producing hydrocarbon within the hydraulic fractures. Snap-off of oil to gas was also observed within the proppant pack which caused significant trapping of large gas globules and effective oil / gas permeability reduction. Increasing the closure stress or / and increasing oil / gas production ratio could also contribute to a higher gas trapping and conductivity loss in gas-condensate shale reservoirs.III.1 , Introduction

[0204] Hydrocarbon exploitation from unconventional reservoirs has increased substantially over the last two decades. However, typically less than 10% of such reserves are recoverable with the current technological advances. Furthermore, the first- year declines of hydrocarbon recovery from unconventional reservoirs in the U.S. are in the 40% to 50% range. Developing a better understanding of production and decline mechanisms that are encountered in such resources are important. Given the complex and often ultra-tight nature of reservoir rock matrix, many believe that the ongoing research and development efforts to mitigate production decline from unconventional reservoirs may be channeled towards engineering the mechanical and multi-phase flow properties of hydraulically induced fractures.

[0205] During hydraulic fracturing treatment, a fracturing fluid — mostly water mixed with certain chemicals — is injected into the formation at pressures sufficiently high to break down the rock and induce fractures. Induced fractures enhance the well-formation surface area and facilitate transport of hydrocarbon from the reservoir rock matrix towards the wellbore. Various types of proppant grains are mixed with the fracturing fluid and placed within induced fractures preventing them from closure after the well is allowed to flow back. The choice of proppants, e.g., type, strength, specific gravity, size, shape, and surface wetting characteristics, as well as their proper placement within hydraulic fractures may be important as they provide the long-term conductivity of fracture conduits.

[0206] Several studies have investigated the geomechanical factors that are responsible for fracture closure and permeability reduction in different packing arrangements of proppants, e.g., multi-layer, uniform monolayer, and non-uniform monolayer packing, representing different areas within the hydraulic fractures. A recent in situ study reported that, when the mechanical strength of the proppants was much higher than the rock matrix, the proppants embedded into the fracture walls under high stress conditions. In contrast, when proppants had a lower mechanical strength compared to their neighboring rock, they crushed under stress resulting in fracture closure. Such geomechanical deformations and fracture closures are believed to occur more severely at locations where a lower concentration of proppant grains are placed, e.g., intermediate and far distances.

[0207] Hydrocarbon production from unconventional reservoirs is also affected by multi-phase transport properties of propped fractures, which are governed by, for example, saturation histories, phase trapping, and fluid-fluid displacement events that take place at the pore / micro scale. Multiple fluid phases, e.g., water, oil, and gas, are often produced through proppant-packed fractures during various stages of depletion depending on reservoir fluid type, e.g., volatile oil, gas-condensate, etc., and its PVT properties as well as reservoir pore and bottom-hole pressure conditions. In ultra-tight reservoirs, well bottom-hole pressure often falls below reservoir bubble point / dew point pressure shortly after the well is allowed to flow back. This in turn results in coexistence and flow of three fluid phases within hydraulic fractures as fracture pore pressure is closely linked to well bottom-hole pressure. Depending on the wettability of the proppant pack, spreading characteristics of fluids, and flow rate conditions, one or two of the three fluid phases may become trapped within the fracture, blocking the path of flow, and thereby reducing the relative permeability of the medium to other fluid(s). Therefore, understanding multi-phase flow behavior in proppant-packedfractures under flow and stress conditions relevant to reservoir depletion scenarios has direct implications in understanding the mechanisms that contribute to production decline in unconventional reservoirs. Furthermore, improved insight developed on such pore-scale mechanisms has applications in analyzing production data and reducing uncertainties when the hydrocarbon recovery from a stimulated reservoir rock volume is predicted using reservoir simulation tools. Managing the produced fracturing fluid and reservoir brine as well as transporting water and associated chemicals for a restimulation treatment are also examples of applications that may be important to groups working on different aspects of flow through porous media.

[0208] Due to the complex nature of three-phase flow phenomena, conventional studies in this area are limited to measuring hydraulic conductivity (single-phase permeability) of proppant packs under increasing closure stress. With respect to multiphase flow characterization, the effects of gravity, fracturing fluid IFT, and proppant grains wettability on recovery of fracturing fluid while being displaced by nitrogen have been investigated. In the investigations, the flow tests were performed through a plain experimental cell packed with proppant grains while fluids occupancies were mapped with a camera. However, no closure stress was applied during these experiments.

[0209] To date, however, there is a lack of fundamental research on pore-scale displacement mechanisms governing three-phase flow through hydraulic fractures. An aim of the study presented in Example III includes providing, to the best of the inventors’ knowledge, the first in situ investigation of three-phase oil / gas / brine flow through proppant-packed fractures under varying flow and stress conditions. These conditions are designed to, e.g., represent depletion of a typical shale volatile oil and / or gas-condensate reservoir through hydraulic fractures over their production lifetime span. Trapping of oil and gas at various stages of production are studied at the pore scale through imbibition of reservoir brine and oil into producing oil and gas phases, respectively.

[0210] During the main step of the experiments, oil and gas were continuously injected into the medium to represent natural depletion of above-mentioned reservoirs when the fracture pore pressure drops below the bubble point / dew point and the medium further undergoes a higher effective closure stress. Pore space deformation and phase trapping under increasing closure stress were captured and quantified at the pore scale using x-ray microtomography to explain the effective oil / gas permeabilityreduction mechanisms under three-phase flow conditions. In addition, by using 30 / 50 ceramic intermediate- strength proppant (ISP) in this study, findings regarding the type and strength of proppants for successful hydraulic fracturing treatments are supported. III.2. Experiments

[0211] Three-phase oil / gas / brine flow experiments through a fractured shale sample packed with 30 / 50 ceramic ISP were performed. Flow processes were designed to, e.g., represent the depletion of volatile-oil and gas-condensate shale reservoirs through hydraulic fractures at various stages of production. The flow tests were conducted by using a reservoir-condition three-phase miniature core-flooding system integrated with a high-resolution x-ray micro-CT scanner. The experiments were divided into three main groups. The first two groups were relevant to saturation histories that the above-mentioned reservoirs experience due to reservoir pressure drawdown, e.g., above and below bubble point and dew point curves. These experiments were performed under a constant effective stress of 500 psi. The third group of the tests was performed to represent the simultaneous production of oil and gas through hydraulic fractures (when fracture pore pressure drops into the two-phase PVT envelope) under increasing stress conditions, e.g., 500, 2500, and 5500 psi. The effective stress was ultimately increased to 7000 psi to investigate the geomechanical deformation of the ISP under very high stress conditions. The flow experiments were carried out at ambient temperature and 100 psi back pressure.

[0212] III2.1. Materials. The rock sample was obtained from a shale reservoir in the Middle East. Water-wet ceramic proppants were also collected from the hydraulic fracturing operations of the same shale reservoir. To prepare the proppant-packed fractured shale assembly, a miniature core sample (8 mm in diameter and 50 mm in length) was cut from a 38-mm-diameter shale core plug. Afterwards, a uniform stress was applied on the miniature sample using a modified Brazilian test to induce a roughwalled fracture that resulted in breaking the sample into two pieces along the length and parallel to the bedding. The sample was then packed with 2 to 3 layers of 30 / 50- mesh ceramic ISP and wrapped with heat shrink tube to hold the assembly firmly. Two 200-mesh (70 pm) screens were placed at the inlet and outlet faces of the sample to suppress migration of any proppant and / or shale fragments toward the core holder fittings and production lines. FIGS. 27A-27D present drawings of photographs collected during selected operations of the sample preparation steps. FIG. 27A showsthe two halves of the fracture, FIG. 27B shows proppant on a first half of the fracture, and FIG. 27C shows the two halves of the fracture positioned on either side of a proppant layer. FIG. 27D shows the proppant-packed assembly wrapped with a heat shrink tube 2703 around the perimeter of the proppant-packed assembly and mesh screens 2701 positioned on ends of the proppant-packed assembly. Brine, Soltrol 170, and nitrogen were utilized as the wetting, intermediate-wetting, and non-wetting phases, respectively. Other gases besides nitrogen may be utilized. Brine composition was identical to that of the fracturing fluid used in the field operations. 4.5 wt% sodium iodide (Nal) and 13 vol% iodooctane were respectively added to brine and Soltrol 170 as tagging agents to enhance the contrast between the three fluids in the X-ray micro- CT images. Table III- 1 lists the properties of the fluids utilized in Example III at the experimental conditions (25°C and 100 psig).Table III- 1

[0213] Based on the interfacial tension (IFT) values measured between the three pairs of fluids, the spreading coefficient (see Eq. III-l) was calculated to be positive meaning that Soltrol 170 spreads over brine in the presence of nitrogen resulting in a spreading fluid configuration in the porous medium.wherein: S is the spreading coefficient; and and are the interfacial tensionvalues between gas-water, water-oil, and gas-oil fluid pairs, respectively.

[0214] III2.2. Experimental Apparatus. A high pressure, high temperature three- phase miniature core-flooding apparatus integrated with a high-resolution X-ray micro- CT scanner was utilized to perform the experiments. FIG. 28 shows a schematicdiagram of the experimental setup of the core-flooding system 2800. The core-flooding system 2800 included five pulse-free programmable dual-cylinder Quizix™ pumps 2811, 2813, 2815, 2817, and 2819, a high pressure custom-built miniature core holder 2801 made of carbon fiber, and Rosemount™ differential pressure transducers array 2803. Dual-cylinder pump 2811 retracted brine from bucket 2821 and injected the brine into the core holder 2801 via line L2. Dual-cylinder pump 2813 retracted hydrocarbon (e.g., oil) from bucket 2823 and injected the hydrocarbon into the core holder 2801 via line L3. Dual-cylinder pump 2815 retracted gas (e.g., N2) from bucket gas cylinder 2825 and injected the gas into the core holder 2801 via line LI. A backpressure Quizix pump 2819 received the effluent from the outlet face of the core holder 2801 at a constant backpressure via L4 and discharged it into a container 2831. An overburden Quizix pump 2817 maintained the confining stress by applying a pre-determined pressure on a rubber sleeve housing the core assembly inside the core holder 2801 via line L5. Hastelloy tubing was utilized between the components of the core-flooding system outside the X-ray CT scanner 2833 while flexible PEEK tubing was connected to the core holder mounted inside the CT scanner to reduce the vibration and torque exerted on the holder while being scanned. The imaging system was a Versa XRM-510 manufactured by Zeiss with five different objectives (0.4X, 4X, 10X, 20X, and 40X). The X-ray source could reach a voltage of 30-160 kV and a power of 1-10 W. A resolution of 700 nm to 64 pm was attainable depending on the optical and geometrical magnifications utilized. An ANDOR™ camera with different camera binnings (e.g., 1, 2, 4, and 8) was utilized to obtain tomography projections at different angles.

[0215] III2.3. Experimental Procedure. The proppant pack assembly was placed in the core holder. An initial confining stress of 500 psi was applied. CO2was then injected to remove air from the proppant pack and connected lines. The core and connected tubing were then vacuumed for 24 h to remove CO2from the system. The entire proppant pack assembly was scanned at 7.5 μm resolution and the acquired images were further utilized to select two locations of interest to be scanned repeatedly during each flow and stress cycle (called locations A and B hereafter). The core was then fully (100%) saturated with brine by injecting several pore volumes of the fluid and subsequently increasing the pore pressure (to 800 psi) to dissolve any possibly trapped CO2. Absolute brine permeability of the medium was measured by recording pressure drop responses of various brine flow rates. Afterwards, the pressure of thesystem (pumps, lines, and the core holder) was reduced to 100 psi and the backpressure was maintained at this value for the rest of the experiments.

[0216] Three main groups of experiments were targeted in this study. Under the first group (Group 1 shown in FIG. 29), primary drainage (PD1) was commenced by injecting oil into the core with a flow rate of 0.01 cc / min. Steady state conditions were assured when the pressure drop across the sample stabilized and consecutive test scans confirmed no changes in the fluid occupancy. Main scans were then acquired to address the initial brine saturation, pore-fluid occupancy, and oil flow paths within the proppant pack. Afterwards, this process was followed by an imbibition flow test with a brine flow rate of 0.05 cc / min. Micro-CT images obtained at the end of the imbibition test were utilized to map trapped oil globules within the pore space. These steps, e.g., primary drainage with oil and imbibition with brine, represents early stages of production in oil reservoirs where the reservoir pressure is above the bubble point and both oil and brine are being produced during the flowback process. Once the pressure falls below the bubble point, gas comes out of solution and flows through the hydraulic fractures. This process was resembled in a laboratory- scale study by injecting gas into the proppant pack, which was at the residual oil saturation established through the preceding waterflooding.

[0217] The second group of experiments (Group 2 shown in FIG. 29) commenced with the previous gas injection process to resemble early stages of production from a gas-condensate reservoir where the pore pressure is above dew point. As the reservoir pressure reduces due to depletion, condensate is formed and subsequently flows through fractures along with gas. Therefore, oil and gas were co-injected into the sample at increasing oil / gas fractional flow rates and the proppant pack and its residing fluids were imaged at each step. Ultimately, only oil was injected into the sample (flow of gas was halted) to trap the gas. In situ fluid occupancy maps obtained at this stage were utilized to investigate the flow path of condensate within the proppant pack at initial water saturation (SWi) and residual gas saturation (Sgr).

[0218] In the third group of experiments (Group 3 shown in FIG. 29), oil and gas were injected into the medium at a constant ratio of 1:1 while the net confining stress was gradually increased from 500 to 2500 and 5500 psi. These steps represent production of both volatile-oil / gas-condensate reservoirs through hydraulic fractures during mid to late stages of production when the reservoir pressure continuously dropswithin the two-phase envelope. In the last step of the experiments, the net confining stress was increased to 7,000 psi to further investigate the geomechanical deformation of the proppant pack assembly under severe stress conditions.

[0219] FIG. 29 summarizes the example experimental procedure 2900 followed for Example III on the proppant-packed assembly for Groups 1, 2, and 3 described above: I) is applying net confining stress of 400 psi to the dry sample (which may have dimensions that are about 50 mm in length and 10 mm in diameter); II) is vacuum saturation (Sw=l; 100% brine saturation); III) is PD1 with the flow rate of oil (Qo) of 0.01 cc / min; IV) is the imbibition flow test with a brine flow rate of 0.05 cc / min; V) is the gas injection with a flow rate of gas (Qg) of 0.1 cc / min; VI) is the co-injection of oil and gas with a Qo of 0.01 cc / min and Qgof 0.1 cc / min; VII) is the co-injection at increasing oil / gas fractional flow rates (e.g., Qo of 0.05 cc / min and Qgof 0.05 cc / min); VIII) is the injection of oil at a Qo of 0.1 cc / min while the flow of gas was halted; IX) shows the oil and gas injected into the medium at a constant ratio of 1:1 (Qo of 0.05 cc / min and Qgof 0.05 cc / min) while the net confining stress increased from 500 psi to X) 2500 psi to XI) 5000 psi and XII) then to 7000 psi. X-ray CT scanning (shown by numeral 2901) may be performed during one or more operations shown in FIG. 29 using X-ray CT scanner 2833.III.3. Data Acquisition and Image Analysis

[0220] A voltage of 90kV, power of 8 W, and imaging exposure time of 2 seconds were utilized as acquisition parameters during the main scans. An ANDOR camera with an objective of 0.4X was utilized to acquire 4,000 projections while the core holder was rotating from -100 to +100 degrees. The projections were then reconstructed by considering a center shift adjustment for any out-of-enter movement while rotating. The above-mentioned parameters were chosen for the proppant-packed shale sample to increase the signal-to-noise ratio in the acquired images. Each reconstructed data set (raw data) was imported into Avizo 9.4 software for further analysis. Selected image processing steps were then performed as follows: first, the non-local means filter was applied on the images to reduce the salt and pepper noise and generate smoother data sets. Next, the target image sets that were collected under the same confining stress condition, were aligned with their corresponding reference image sets by manually moving them, pixel-by-pixel, in the X, Y, and Z directions until a suitable registration was achieved. After the data sets were registered, a volume edit module was applied toassign zero value for the exterior of scanned locations. Each data set was then segmented to brine, oil, and gas by applying a modified histogram thresholding method. Details of the image segmentation procedure may be found elsewhere. Segmented images were utilized to visualize the fluid occupancy and study pore-scale mechanisms governing transport at different saturation histories and stress conditions. Geomechanical deformation, e.g., proppant embedment / disintegration and fracture closure, was analyzed through filtered gray-scale images. FIG. 30 presents drawings of 3D images along the length of the entire proppant-packed assembly as well as 3D images that were collected at locations A and B of the proppant-packed assembly. Table III- 2 lists the dimensions, image resolution, and distances of locations A and B from the inlet.Table III-2III.4. Non-limiting Results

[0221] IH.4.1. Proppant Pack Properties. 30 / 50 ISP ceramic proppants showed superior sphericity (~0.9) and roundness (-0.8) compared to the other types of proppants that had been examined in previous studies, e.g., white sand and resin-coated sand. As a result, ISP tends to create a pore space with relatively larger throats (smaller pore-throat aspect ratios), which is an ideal medium for multiple fluid phases to flow through. The proppant pack had average porosities of 45 and 36% at locations A and B under an initial confining stress of 500 psi. The absolute permeability of the proppant pack to brine was measured to be 42 Darcy (D) under this stress condition.

[0222] IIL4.2. Primary Oil Drainage and Water Injection. In the first flow step,100% brine saturated medium was subjected to flow of oil (0.01 cc / min) reaching an initial brine saturation of 20%. The values reported hereafter in Example III are the average of values measured at locations A and B. Brine was then injected to trap 48% oil within the proppant pack. These steps are carried out to represent, for example, early stages of a flowback process during which oil first displaces the fracturing water fromthe proppant pack as well as later stages of production during which formation water or remaining frack water may be produced and trap the oil in the fractured medium.

[0223] After the fracture pore pressure drops below the bubble point (in an oil reservoir) due to reservoir depletion, gas starts to come out of the live oil and mobilizes in the hydraulic fractures. Gas saturation and flow rates further increase with the reservoir depletion. Thus, gas was injected to the medium at the end of preceding imbibition with increasing flow rates. An additional 20% trapped oil was ultimately recovered through the gas injection phase. Because brine, oil, and gas are the most wetting-, intermediate, and non- wetting phases, respectively, brine occupies the small pores and bridges between the grains and gas flows through big pores while being covered with a blanket of oil. Existence of the oil layers is due to the fact that oil / gas / brine IFT values cause the oil phase to spread. This is the case in majority of volatile oil and gas-condensate fluid systems. The blanket of oil around the connected gas phase reconnects the trapped oil globules and ultimately reduces the residual oil saturation in the medium. FIG. 31 depicts such occupancy within the proppant pack at the end of gas injection.

[0224] Oil was then injected to the medium along with gas while its flow rate increases (and gas flow rate decreases) to represent the production from a gas condensate reservoir that falls below dew point in which oil or condensate comes out of gas and flows through the hydraulic fractures. FIGS. 32A-32C show 3D maps of oil and gas flow paths during various stages of the above-mentioned flow processes. Oil was ultimately injected to the medium while gas flow was stopped reaching a very low residual gas saturation, e.g., 5%. In the last step of the experiments, the medium was drained with both oil and gas (ratio of 1:1 and with a flow rate of 0.05 cc / min for each) to represent the natural depletion of volatile oil or gas-condensate reservoirs during the majority of their production lifetime. The net confining stress was also increased by steps to 2500 and 5500 psi while maintaining the flow of oil and gas. Increasing the net confining stress to 2500 psi, did not have a significant effect on the medium. Under the conditions tested, no embedment or proppant breaking / crushing was observed at this stage.

[0225] The shale surface, however, experienced some spalling and deformation. By increasing the net confining stress to 5500, proppant grains experience slight embedment and some level of cliffing / breaking to two / three pieces. As a result, theproppant pack stays relatively open and productive unlike the shale samples packed with white sand and resin-coated sand which showed severe proppant crushing and embedment (and consequently fracture closure) under 5000 psi stress conditions, respectively. Intermediate strength of the ISP ceramic proppants has impeded these drawbacks by breaking and redistributing the exerted stress between the broken particles. Not all proppant grains experience breaking. The ones that do so may be the main ones that carry the maximum applied stress. When proppant grains break, the proppant grains may relocate / rearrange slightly and the exerted stress may be redistributed between the broken pieces and other proppant grains leading to a more uniform stress field. The observed behavior prevented the fracture from closure even under very severe stress conditions, e.g., 7000 psi.

[0226] FIG. 33 shows the fracture aperture reduction versus increasing confining stress. The fracture aperture reduces only 6.5% under 7000 psi closure stress. FIG. 34 depicts the effective oil and gas permeability reduction versus increasing net confining stress. Because the ISP ceramic proppants successfully maintained the hydraulic fractures, questions are raised regarding what multi-phase flow factors cause the reduction of effective oil and gas permeability (two to three times) despite the fact that fracture aperture has almost remained unchanged. By increasing the confining stress, pore-throat junctions experience the most reduction in size since they are formed by contact areas of proppant grains. Reduction in the throat causes the wetting phase, e.g., brine, to bridge and close the throats more efficiently restricting flow of oil and gas through the system. In addition, by reducing the pore-throat junctions under a higher closure stress, gas globules were more prone to be trapped by imbibition of oil through snap-off mechanism.

[0227] FIGS. 35 A and 35B show drawings of 3D images of the gas phase during continuous oil / gas injection under 500 and 2500 psi closure stress. Gas experiences more frequent trapping by oil or by oil and brine under a higher closure stress. Trapped gas globules may further block the path of the flow of continuous oil and gas phases contributing to a higher effective hydrocarbon permeability reduction. The “X” in FIG. 35B refers to oil-to-gas snap-off within pore-throats due to stress. So far, ISP ceramic proppants have shown high performance in maintaining the propped fractures open under severe stress conditions. In order to further eliminate multi-phase flow factors that are responsible for effective hydrocarbon permeability reduction, neutral-wetsurfaces or special types of coating may be considered to impede brine bridging or gas trapping within the hydraulic fractures. Moreover, adding surfactant to the fracturing fluid may also ease the displacement of brine by oil and gas from the proppant pack at the initial stage of the production.

[0228] No wettability alteration was observed within the proppant pack. Wettability alteration was previously observed in the sample packed with resin-coated sand that experienced significant embedment. Questions are raised here if the wettability alteration has a direct relationship with embedment. Wettability alteration, uniformly and non-uniformly, may not be desirable and may cause trapping of producing fluids within the medium and further reduce the effective hydrocarbon permeability. Improved insight could be further used to design more efficient proppants to maintain the hydraulic conductivity of the propped fractures for extended period of time. In this regard, strength and shape of the proppants may be the controlling parameters. Special types of coating could also be considered to prevent the surface of proppant grains from deposition of organic matter and subsequent wettability alterations.

[0229] Example III describes a micro- scale experimental investigation on three- phase gas / oil / brine flow through proppant-packed fractured shale samples under increasing closure stress of up to 7000 psi. Geomechanical deformation and subsequent multi-phase flow factors responsible for effective oil / gas permeability reduction were captured at the pore scale. Selected, non-limiting findings from Example III include the following:

[0230] Selected, non-limiting findings include the following. First, 30 / 50 ISP ceramic proppants were found to be much more successful than white sand and resin- coated sand in maintaining the hydraulic fractures conductivity. Second, bullet-like embedment under significant closure stress and proppant breaking / crushing under relatively low stress conditions are drawbacks of respectively modified resin-coated and basic white sand proppants used widely in hydraulic fracturing operations. Third, ISP ceramic proppants break into two / three pieces under severe stress conditions and prior to significant embedment. This geomechanical behavior in turn redistributes the exerted stress on the broken particles and / or other proppant grains preventing them from severe embedment and fracture closure. Fourth, shale mineralogy, e.g., clay and organic matter content, and mechanical properties may be considered in designing modified proppants in a manner that they resist low closure stress conditions but breakprior to significant embedment. Fifth, high sphericity and roundness of ISP ceramic proppants constructed a pore space with relatively lower pore-throat aspect ratios which in turn reduced the multi-phase restrictions for flow. Sixth, increasing the net confining stress impacted the pore-throat junctions the most causing more brine bridging between the proppant grains and in small throats. This could have contributed to effective oil / gas permeability reduction under a higher closure stress. Seventh, reducing pore-throat junction sizes under a higher closure stress also triggers oil-to-gas snap-off causing significant gas trapping within the proppant pack. The amount of gas trapping may further increase when the ratio of oil / gas production rate increases. This phenomenon further reduces effective oil / gas permeability through the hydraulic fractures contributing to production loss. Eighth, no wettability alteration was observed in this series of experiments which may be due to insignificant embedment.

[0231] The results presented in Example III are significantly different — and significantly more accurate — than studies using conventional technologies because conventional technologies are not capable of mimicking real-world conditions and instead use non-representative conditions.Aspects Listing

[0232] The present disclosure provides, among others, the following aspects, each of which may be considered as optionally including any alternate aspects:

[0233] Aspect 1. A process for forming a misaligned rough-walled fracture, comprising: applying a compressive load on a geomaterial to fracture the geomaterial into two geomaterial segments; misaligning the two geomaterial segments by about 0.1 mm to about 5 mm; and coring around the two misaligned geomaterial segments to form a misaligned rough-walled fracture.

[0234] Aspect 2. The process of aspect 1, wherein: the misaligned rough- walled fracture mimics and / or simulates fractures observed in the field; and / or the misaligned rough-walled fracture forms at least a portion of a core sample.

[0235] Aspect 3. The process according to any one of the preceding aspects, wherein the core sample is utilized for laboratory experiments.

[0236] Aspect 4. The process according to any one of the preceding aspects, wherein the geomaterial comprises carbonate, sandstone, unconventional shale, geothermal rock, or combinations thereof.

[0237] Aspect 5. The process according to any one of the preceding aspects, wherein the carbonate is tight carbonate, or wherein the sandstone is tight sandstone, or combinations thereof.

[0238] Aspect 6. The process according to any one of the preceding aspects, wherein the misaligned rough-walled fracture mimics conditions encountered in actual fractures observed on a field site.

[0239] Aspect 7. A process for preparing a proppant-packed fracture assembly, the process comprising: positioning a first segment of a fractured core sample in a mold such that a void space is formed between a top of the mold and a fractured surface of the first segment of the fractured core sample; forming a proppant layer on the fractured surface of the first segment of the fractured core sample by depositing proppant on a surface of the first segment of the fractured core sample such that the void space is at least partially filled with the proppant; depositing a binding agent on the proppant layer; and positioning a fractured surface of a second segment of the fractured core sample on top of the proppant layer to form the proppant-packed fracture assembly.

[0240] Aspect 8. The process of aspect 7, further comprising: performing a post-treatment process on the proppant-packed fracture assembly, the post-treatment process comprising: wrapping at least a portion of a circumference of the proppant- packed fracture assembly to hinder relative movement of the first segment and the second segment of the fractured core sample; positioning a mesh screen on each end of the proppant-packed fracture assembly, each end of the proppant-packed fracture assembly perpendicular to the circumference of the proppant-packed fracture assembly; or combinations thereof.

[0241] Aspect 9. The process according to any one of aspects 7 or 8, wherein: the binding agent comprises an aqueous fluid; andafter depositing the aqueous fluid on the proppant layer and before positioning the fractured surface of the second segment of the fractured core sample on top of the proppant layer, the process further comprises freezing the proppant layer into a solid wafer.

[0242] Aspect 10. The process according to aspect 9, wherein: the positioning the fractured surface of the second segment of the fractured core sample on the top of the proppant layer is performed while the proppant layer is the solid wafer.

[0243] Aspect 11. The process according to any one of aspects 7-10, wherein the first segment and the second segment of the fractured core sample are smooth-walled or rough- walled fractures.

[0244] Aspect 12. The process according to any one of aspects 7-11, wherein the fractured core sample comprises carbonate, sandstone, unconventional shale, geothermal rock, or combinations thereof.

[0245] Aspect 13. The process according to any one of aspects 7-12, wherein the proppant is silica, ceramic, coated sand, coated ceramic, or combinations thereof.

[0246] Aspect 14. The process according to any one of aspects 7-13, wherein the proppant is water-wet, oil-wet, or combinations thereof.

[0247] Aspect 15. A method of reproducing actual fracturing conditions in a laboratory, comprising: injecting a first fluid comprising a first wetting fluid or a first non-wetting fluid into a core holder housing a sample comprising a misaligned rough-walled fractured porous medium and optionally a proppant; alternating a drainage flow cycle and an imbibition flow cycle by an unsteady- state method or a steady-state method under a net confining pressure; and determining a characteristic of the sample before, during, and / or after one or both of the drainage flow cycle or the imbibition flow cycle, the characteristic optionally comprising hydraulic conductivity, permeability reduction, fluid occupancy, fluid distribution, fluid saturation, proppant embedment, fracture deformation, relative permeability, end-point relative permeability, steady- state relative permeability, unsteady- state relative permeability, steady-state relative permeability curves, unsteady- state relative permeability curves, or combinations thereof.

[0248] Aspect 16. The method according to aspect 15, wherein, when the first fluid comprises the first wetting fluid: the drainage flow cycle comprises injecting a non-wetting fluid or co-injecting a non-wetting fluid and a second wetting fluid at increasing fractional flow ratios into the sample to displace the first wetting fluid; and the imbibition flow cycle comprises injecting a third wetting fluid or co-injecting a third wetting fluid and a non- wetting fluid at increasing fractional flow ratios into the sample to displace the non-wetting fluid, the first, second, and third wetting fluids being the same or different.

[0249] Aspect 17. The method according to aspect 16, wherein, when the first wetting fluid comprises a first brine fluid: the drainage flow cycle comprises injecting a hydrocarbon or co-injecting a hydrocarbon and a second brine fluid at increasing hydrocarbon / brine fractional flow ratios into the sample to displace the first brine fluid; and the imbibition flow cycle comprises injecting a third brine fluid or co-injecting a third brine fluid and a hydrocarbon at increasing brine / hydrocarbon fractional flow ratios into the sample to displace the hydrocarbon, the first, second, and third brine fluids being the same or different.

[0250] Aspect 18. The method according to aspect 15, wherein, when the first fluid comprises the first non-wetting fluid: the drainage flow cycle comprises injecting a wetting fluid or co-injecting a wetting fluid and a second non- wetting fluid at increasing fractional flow ratios into the sample to displace the first non-wetting fluid; and the imbibition flow cycle comprises injecting a third non-wetting fluid or co-injecting a third non-wetting fluid and a wetting fluid at increasing fractional flow ratios into the sample to displace the wetting fluid, the first, second, and third non-wetting fluids being the same or different.

[0251] Aspect 19. The method according to aspect 18, wherein, when the first nonwetting fluid comprises a first hydrocarbon: the drainage flow cycle comprises injecting brine or co-injecting brine and a second hydrocarbon at increasing brine / hydrocarbon fractional flow ratios into the sample to displace the first hydrocarbon; and the imbibition flow cycle comprises injecting a third hydrocarbon or co-injecting a third hydrocarbon and brine at increasing hydrocarbon / brine fractional flow ratios into the sample to displace the brine, the first, second, and third hydrocarbon being the same or different.

[0252] Aspect 20. The method according to any one of aspects 15-19, wherein: the core holder is at least partially made of carbon fiber; and the method further comprises imaging the sample with x-ray computed tomography.

[0253] Aspect 21. The method according to any one of aspects 15-20, wherein: the sample is void of proppants; or the sample includes proppants, minerals, or combinations thereof.

[0254] Aspect 22. The method according to any one of aspects 15-21, wherein the net confining pressures is from about 200 psi to about 10,000 psi, such as from about 200 psi to about 7,000 psi.

[0255] Aspect 23. The method according to any one of aspects 15-22, further comprising: injecting a first gas after the drainage flow cycle or imbibition flow cycle.

[0256] Aspect 24. The method according to aspect 23, further comprising: coinjecting oil and a second gas after the injecting of the first gas, the first gas and second gas fluids being the same or different.

[0257] Aspect 25. The method according to any one of aspects 15-24, wherein the misaligned rough-walled fractured porous medium comprises a fractured geomaterial.

[0258] Aspect 26. The method according to aspect 25, wherein the fractured geomaterial comprises carbonate, sandstone, unconventional shale, geothermal rock, or combinations thereof, such as tight carbonate, tight sandstone, or combinations thereof.

[0259] Aspect 27. The method according to any one of aspects 15-26, wherein when the sample includes the proppant, the proppant is characterized by a proppant grain distribution comprising: a multi-layer proppant distribution mimicking fractures close to a well; a uniform mono-layer proppant distribution mimicking fractures at intermediate distances from a well; and / or a non-uniform mono-layer proppant distribution mimicking fractures far away from a well.

[0260] Aspect 28. The method according to any one of aspects 15-27, wherein the proppant comprises silica, ceramic, coated sand, or combinations thereof.

[0261] Aspect 29. The method according to any one of aspects 15-28, wherein: at least one wetting fluid comprises a first contrasting agent; at least one non- wetting fluid a second contrasting agent; a gas, when injected, comprises a third contrasting agent; or combinations thereof.

[0262] Aspect 30. The method according to aspect 29, wherein: the first contrasting agent comprises an iodide salt; the second contrasting agent comprises an iodinated hydrocarbon; or combinations thereof.

[0263] Aspect 31. The method according to any one of aspects 15-30, wherein the sample comprising the misaligned rough-walled fractured porous medium comprises asample from naturally fractured formation, a sample from a hydraulically fractured formation, or combinations thereof.

[0264] Aspect 32. A method for predicting hydrocarbon recovery performance from a formation, gas storage capacity of a formation, or combinations thereof, the method comprising: performing the method according to any one of aspects 15-31; performing operation(s) on a proppant-packed assembly described herein; performing operation(s) on a misaligned rough-walled fracture described herein; or combinations thereof.

[0265] Aspect 33. The method according to aspect 32, wherein hydrocarbon recovery performance comprises oil recovery performance, natural gas recovery performance, or combinations thereof.

[0266] Aspect 34. The method according to any one of aspects 32 or 33, wherein the formation is a naturally fractured formation or a hydraulically fractured formation.

[0267] Aspect 35. The method according to any one of aspects 32-34, wherein the gas storage capacity of the formation comprises a CO2storage capacity of the formation, a hydrogen storage capacity of the formation, or combinations thereof.

[0268] Aspect 36. A method for testing two-phase flow through a fractured subsurface geomaterial and an optional proppant, the method comprising: performing the method according to any one of aspects 15-35; performing operation(s) on a proppant-packed assembly described herein; performing operation(s) on a misaligned rough-walled fracture described herein; or combinations thereof.

[0269] Aspect 37. A method for testing three-phase flow through a fractured subsurface geomaterial and an optional proppant, the method comprising: performing the method according to any one of aspects 15-35; performing operation(s) on a proppant-packed assembly described herein; performing operation(s) on a misaligned rough-walled fracture described herein; or combinations thereof.

[0270] Aspect 38. A misaligned rough-walled fracture described herein.

[0271] Aspect 39. A proppant-packed fracture assembly described herein.

[0272] As is apparent from the foregoing general description and the specific aspects, while forms of the aspects have been illustrated and described, various modifications may be made without departing from the spirit and scope of the present disclosure. Accordingly, it is not intended that the present disclosure be limited thereby. Likewise, the term “comprising” is considered synonymous with the term “including.” Likewise whenever a formulation, a composition, an element or a group of elements is preceded with the transitional phrase “comprising,” it is understood that we also contemplate the same formulation, composition or group of elements with transitional phrases “consisting essentially of,” “consisting of,” “selected from the group of consisting of,” or “is” preceding the recitation of the formulation, composition, element, or elements and vice versa, e.g., the terms “comprising,” “consisting essentially of,” “consisting of’ also include the product of the combinations of elements listed after the term.

[0273] References cited herein are incorporated by reference herein in their entirety to indicate the state of the art as of their publication or filing date and it is intended that this information may be employed herein, if desired, to exclude specific aspects that are in the prior art.

[0274] For purposes of this present disclosure, and unless otherwise specified, all numerical values within the detailed description and the claims herein are modified by “about” or “approximately” the indicated value, and consider experimental error and variations that would be expected by a person having ordinary skill in the art. For the sake of brevity, only certain ranges are explicitly disclosed herein. However, ranges from any lower limit may be combined with any upper limit to recite a range not explicitly recited, as well as, ranges from any lower limit may be combined with any other lower limit to recite a range not explicitly recited, in the same way, ranges from any upper limit may be combined with any other upper limit to recite a range not explicitly recited. Additionally, within a range includes every point or individual value between its end points even though not explicitly recited. Thus, every point or individual value may serve as its own lower or upper limit combined with any other point or individual value or any other lower or upper limit, to recite a range not explicitly recited.

[0275] As used herein, the indefinite article “a” or “an” shall mean “at least one” unless specified to the contrary or the context clearly indicates otherwise. For example, aspects comprising “a fluid” include aspects comprising one, two, or more fluids, unless specified to the contrary or the context clearly indicates only one fluid is included.

[0276] While the foregoing is directed to aspects of the present disclosure, other and further aspects of the disclosure may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims

ClaimsWhat is claimed is:

1. A process for forming a misaligned rough-walled fracture, comprising: applying a compressive load on a geomaterial to fracture the geomaterial into two geomaterial segments; misaligning the two geomaterial segments by about 0.1 mm to about 5 mm; and coring around the two misaligned geomaterial segments to form a misaligned rough-walled fracture.

2. The process of claim 1, wherein the misaligned rough-walled fracture forms at least a portion of a core sample.

3. The process of claim 2, wherein the core sample is utilized for laboratory experiments.

4. The process of claim 1, wherein the geomaterial comprises carbonate, sandstone, unconventional shale, geothermal rock, or combinations thereof.

5. The process of claim 1, wherein the carbonate is tight carbonate, or wherein the sandstone is tight sandstone, or combinations thereof.

6. The process of claim 1, wherein the misaligned rough-walled fracture mimics conditions encountered in actual fractures observed on a field site.

7. A process for preparing a proppant-packed fracture assembly, the process comprising: positioning a first segment of a fractured core sample in a mold such that a void space is formed between a top of the mold and a fractured surface of the first segment of the fractured core sample; forming a proppant layer on the fractured surface of the first segment of the fractured core sample by depositing proppant on a surface of the first segment of the fractured core sample such that the void space is at least partially filled with theproppant; depositing a binding agent on the proppant layer; and positioning a fractured surface of a second segment of the fractured core sample on top of the proppant layer to form the proppant-packed fracture assembly.

8. The process of claim 7, further comprising: performing a post-treatment process on the proppant-packed fracture assembly, the post-treatment process comprising: wrapping at least a portion of a circumference of the proppant-packed fracture assembly to hinder relative movement of the first segment and the second segment of the fractured core sample; positioning a mesh screen on each end of the proppant-packed fracture assembly, each end of the proppant-packed fracture assembly perpendicular to the circumference of the proppant-packed fracture assembly; or combinations thereof.

9. The process of claim 7, wherein: the binding agent comprises an aqueous fluid; and after depositing the aqueous fluid on the proppant layer and before positioning the fractured surface of the second segment of the fractured core sample on top of the proppant layer, the process further comprises freezing the proppant layer into a solid wafer.

10. The process of claim 9, wherein: the positioning the fractured surface of the second segment of the fractured core sample on the top of the proppant layer is performed while the proppant layer is the solid wafer.

11. The process of claim 7, wherein the first segment and the second segment of the fractured core sample are smooth- walled or rough- walled fractures.

12. The process of claim 7, wherein the fractured core sample comprises carbonate, sandstone, unconventional shale, geothermal rock, or combinations thereof.

13. The process of claim 7, wherein the proppant is silica, ceramic, coated sand, coated ceramic, or combinations thereof.

14. The process of claim 7, wherein the proppant is water-wet, oil-wet, or combinations thereof.

15. A method of reproducing actual fracturing conditions in a laboratory, comprising: injecting a first fluid comprising a first wetting fluid or a first non-wetting fluid into a core holder housing a sample comprising a misaligned rough-walled fractured porous medium and optionally a proppant; alternating a drainage flow cycle and an imbibition flow cycle by an unsteadystate method or a steady- state method under a net confining pressure; and determining a characteristic of the sample before, during, or after one or both of the drainage flow cycle or the imbibition flow cycle, the characteristic comprising hydraulic conductivity, permeability reduction, fluid occupancy, fluid distribution, fluid saturation, proppant embedment, fracture deformation, relative permeability, endpoint relative permeability, steady-state relative permeability, unsteady-state relative permeability, steady-state relative permeability curves, unsteady-state relative permeability curves, or combinations thereof.

16. The method of claim 15, wherein, when the first fluid comprises the first wetting fluid: the drainage flow cycle comprises injecting a non-wetting fluid or co-injecting a non-wetting fluid and a second wetting fluid at increasing fractional flow ratios into the sample to displace the first wetting fluid; and the imbibition flow cycle comprises injecting a third wetting fluid or coinjecting a third wetting fluid and a non- wetting fluid at increasing fractional flow ratios into the sample to displace the non-wetting fluid, the first, second, and third wetting fluids being the same or different.

17. The method of claim 16, wherein, when the first wetting fluid comprises a firstbrine fluid: the drainage flow cycle comprises injecting a hydrocarbon or co-injecting a hydrocarbon and a second brine fluid at increasing hydrocarbon / brine fractional flow ratios into the sample to displace the first brine fluid; and the imbibition flow cycle comprises injecting a third brine fluid or co-injecting a third brine fluid and a hydrocarbon at increasing brine / hydrocarbon fractional flow ratios into the sample to displace the hydrocarbon, the first, second, and third brine fluids being the same or different.

18. The method of claim 15, wherein, when the first fluid comprises the first nonwetting fluid: the drainage flow cycle comprises injecting a wetting fluid or co-injecting a wetting fluid and a second non- wetting fluid at increasing fractional flow ratios into the sample to displace the first non- wetting fluid; and the imbibition flow cycle comprises injecting a third non-wetting fluid or co- injecting a third non-wetting fluid and a wetting fluid at increasing fractional flow ratios into the sample to displace the wetting fluid, the first, second, and third non-wetting fluids being the same or different.

19. The method of claim 18, wherein, when the first non- wetting fluid comprises a first hydrocarbon: the drainage flow cycle comprises injecting brine or co-injecting brine and a second hydrocarbon at increasing brine / hydrocarbon fractional flow ratios into the sample to displace the first hydrocarbon; and the imbibition flow cycle comprises injecting a third hydrocarbon or co- injecting a third hydrocarbon and brine at increasing hydrocarbon / brine fractional flow ratios into the sample to displace the brine, the first, second, and third hydrocarbon being the same or different.

20. The method of claim 15, wherein: the core holder is at least partially made of carbon fiber; and the method further comprises imaging the sample with x-ray computed tomography.

Images