Sytems and methods for saturation of rock samples and associated permeability measurements

Abstract

A system for saturating a core sample of rock includes a vessel with an inner surface defining a receptacle that receives and holds the core sample and a saturating fluid. The vessel defines an opening into the receptacle at a first end of the vessel. A piston is configured to fit within the opening and the receptacle and travels to seal the vessel. A pump directs hydraulic fluid to the piston, wherein the pump pushes the hydraulic fluid against the piston to maintain a saturation pressure within the receptacle to accommodate the saturating fluid filling pore throats within the core sample. The core sample may include bores that provide additional surface area subject to the saturation pressure. The system calculates a numeric permeability of the core sample and a measured permeability of the core sample while simultaneously saturating the core sample over a time period.

Description

SYTEMS AND METHODS FOR SATURATION OF ROCK SAMPLES AND ASSOCIATED PERMEABILITY MEASUREMENTSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and incorporates by reference United States Provisional Patent Application Serial No. 63 / 581,576 filed on September 19, 2023, entitled Systems and Methods for Saturation of Rock Samples.

[0002] This application further claims priority to and incorporates by reference United States Provisional Patent Application Serial No. 63 / 617,765 filed on January 4, 2024, entitled Systems and Methods for Saturation of Rock Samples and Associated Permeability Measurements.FIELD

[0003] This application relates to the field of fluid flow through pore throats of rock formations that may be sources of hydrocarbons for energy production.BACKGROUND

[0004] In most conventional reservoirs, volumetric fluid content is the main contributor to the evaluation of hydrocarbon and water production. For organic-rich mud rocks, however, assessment of hydrocarbon / water production can be affected by rock components, fluid mobility, and geochemistry. Fluid flow in the pore network depends on the preferential movement of different fluid phases. Understanding the fluid-flow characteristics of a rock bed is essential for the assessment of the primary recovery of hydrocarbons from reservoirs and enhancing the ability to exploit reserves successfully. In one non-limiting example, there are various mechanisms and factors at play in organic-rich mud rocks that impact the fluid-flow characteristics. At nano-scale-size pores such as those in the case of organic-rich mud rocks, the fluid flow becomes a transitional flow. There is adsorption on the surface of kerogen and clay minerals. The wettability of the pores also depends on whether they are organic pores or inorganic pores. To understand the preferential movement of different fluids in the reservoir, saturation-dependent relative permeability measurements, among other kinds of assessments, are important. Therefore, saturating the core samples form the basis for such experimental measurements.

[0005] Laboratory -based methods for saturating tight core samples take significant time which can make the process expensive and not feasible. The conventional experimental setups used in the field require high back pressure systems which mandates additional safety features to be built, adding to the complexity of the setup. Even with the safety features and the pressure system added in, the efficiency of the setup is not optimal can lead to multiple months for a single relative permeability measurement. This leads to unreasonably high prices for saturation-dependent core measurements in tight rocks.

[0006] Prior art techniques for core sample saturation led to lack of control on water saturation level, non-uniform distribution of water saturation along the length of the core, and long time duration to complete the saturation process. These drawbacks are particularly prevalent in certain set-ups, such as saturation with centrifugal forces. Centrifuges used in this art often required high speeds of up to 10,000 revolutions per minute in very expensive equipment that still required 4-5 days for a full saturation. With such high rotation speeds, experiments had to deal with high temperatures, additional sensors necessary to monitor the process, and there was always potential that the process would damage the core samples of rock.

[0007] Conventional saturation methods often exerted fluid pressure only on one surface or one side of a core sample. Saturation moves much faster with fluid pressure on as many surfaces as possible in a core sample.

[0008] Permeability Background

[0009] Successful utilization and development of organic -rich mudrock reservoirs require reliable estimation of fluid content and characterization of fluid flow in the porous media. Estimation of dynamic properties such as fluid flow is a step forward toward the evaluation of fluid production. Fluid flow in the pore network depends on the preferential movement of different fluid phases (wetting and non-wetting phases). Understanding the fluid- flow characteristics can enhance the prediction of the primary recovery of hydrocarbons from reservoirs as well as the ability to exploit reserves successfully. The fluid-flow characteristics in reservoirs with low permeability and complex pore structures are difficult to quantify but are extremely important for production from these reservoirs. The quantification of fluid flow is generally done through experimental techniques, which can be timeconsuming and unreliable in the case of organicrich mudrocks. Fluid- flow characterization requires an assessment of permeability and saturation dependent relative permeability.Saturating tight rock samples such as organic-rich mudrocks can be time consuming. It might also not be feasible to saturate the ultra-tight sample to desired saturation levels for reliable relative permeability assessment. All the aforementioned factors can lead to unreliable estimation and poor understanding of fluid flow in organic -rich mudrocks. The use of the steady- state technique commonly forms the basis of saturation-dependent relative permeability measurements. Numerous authors (Jones and Owens 1980; Chowdiah 1987; Firoozabadi and Aziz 1991) have documented the use of core flooding setup for saturating core samples with a particular fluid phase and for determining the relative permeability of low-permeability core samples. The high injection entry pressure required for the tight organic-rich mudrock samples hinders the saturation process with this setup and leads to an extensive time duration required to saturate the samples. The time-consuming nature of the experiment can make the measurements following the saturation process expensive and, in some cases, not feasible. The saturation profile can also be uneven along the axis of the core sample due to capillary-end effects (Heavy side et al. 1983) during core flooding. This uneven saturation profile can significantly affect saturation-dependent relative permeability measurements.

[0010] Previous publications have also extended the estimation of permeability using unsteady- state methods as well, where the differential pressure, fluid injection and outlet flow rates, and fluid saturation values are recorded while one fluid is injected in the core sample (Johnson et al. 1959; Jones and Roszelle 1978; Honarpour and Mahmood 1988; Toth et al. 2001). Wang et al. (2012) used the unsteady- state method along with JBN (Johnson-Bossier- Naumann) analysis method to determine gas permeability in tight samples with permeability values ranging from 0.5 to 40 pD. Using the abovementioned techniques for assessing permeability and saturation-dependent relative permeability in tight rock samples can lead to huge uncertainties in permeability estimates. Using steady-state techniques in tight rock samples would require low flow rates for gas and brine, which are difficult to measure and regulate accurately (Haskett et al. 1988) and require a long stabilization time. On the other hand, using unsteady- state methods is also challenging due to increased viscous and capillary-end effects in tighter rock samples.

[0011] Pulse-decay measurement is another widely employed option for measuring permeability in tight rock samples (Jones 1997; Feng et al. 2017; Bhandari et al. 2019; Zhang et al. 2020). Many authors documented the long time duration required for pressure decline tostop in the case of pulse decay measurements in tight rock samples, which makes these measurements time-consuming (Gan et al. 2018; Gonzalez et al. 2020).

[0012] There are also uncertainties with the timing of the pulse creation and incorporating that uncertainty into the numerical solution, which can affect the reliability of the permeability measurements. In the case of tight rock samples such as organic-rich mudrocks, the permeability estimation depends on the accuracy of the pressure data recorded using the pressure transducers. In the case of pulse-decay setup, the use of multiple pressure transducers can add to the possibility of leaks and uncertainty in data recording.

[0013] Performing relative permeability measurements using the steady- state method is challenging due to the possible capillary end effects and the long duration of attaining steady-state. Estimating gas relative permeability using the pressure-decay setup is possible but the time taken for saturating the tight samples to different saturation levels is long. Moreover, the maximum possible saturation attainable is low using conventional saturation methods such as vacuum saturation and spontaneous imbibition in the case of organic-rich mudrocks.

[0014] Saturation Background

[0015] Organic-rich mudrock reservoirs play a critical role in today’s race to meet energy demands. Understanding of these complex reservoirs is still in a very nascent stage. Assessment of fluid production from these tight reservoirs can be affected by rock components, fluid mobility, and geochemistry. The fluid-flow characteristics can be essential for the assessment of the primary recovery of hydrocarbons from these reservoirs and enhancing the ability to exploit reserves successfully. Characterization of fluid flow would require saturation-dependent measurements such as capillary pressure and relative permeability measurements. Therefore, the starting point would be saturating samples with different fluid phases at different saturation levels to perform the aforementioned measurements. However, saturation of organicrich mudrock samples has proven to be challenging mainly due to (a) the time taken to saturate these tight rock samples and (b) the lack of control over the saturation level during the saturation process. The use of specialized equipment such as a high-pressure core-flooding setup or ultra-high-speed centrifuge can be beneficial, but it becomes very expensive to perform such measurements.

[0016] In the case of conventional rock samples, saturating the core is done using core-flood setups where brine is injected into a core holder containing the core at highpressure under confining stress until we achieve a steady- state condition at the outlet (Jones and Owens 1980; Chowdiah 1987; Firoozabadi and Aziz 1991; Perrin et al. 2009; Chiao et al. 2017; Ren et al. 2018). Some researchers have experimented with specialized high-injection pressure (e.g., greater than 8000 psi) setups for saturating tight core samples (Jones and Owens 1980; Ramiro-Ramirez et al. 2021). The use of such specialized setups can be expensive and require additional safety protocols that can hinder the saturation process. Moreover, using a core-flooding setup where the saturating fluid is injected on one face of the core sample can lead to an uneven saturation profile (Heavyside et al. 1983), especially in the case of a tight organic-rich mudrock sample.

[0017] Some researchers have used alternative techniques for saturating core samples. These techniques include the evaporation process rather than saturating the samples (Thomas and Ward 1972; Sampath and Keighin 1981; Walls et al. 1982; Ward and Morrow 1987). However, this process cannot control the saturation level that needs to be achieved for saturation-dependent measurements. Moreover, the samples cannot be cleaned before starting the process. The centrifuge method is also a popular method for the saturation of core samples (Slobod et al. 1951; Hagoort 1980; Ward and Morrow 1987; Newsham et al. 2018). However, extremely high rotational speeds are needed to saturate tight samples, which requires specialized centrifuge equipment. The use of a centrifuge poses another disadvantage, leading to an uneven saturation profile, which can impact saturation-dependent petrophysical measurements such as relative permeability. The system can also heat up at high angular speeds that would be required for organic -rich mudrock samples.

[0018] Gonzalez et al. (2020) reported the use of 6000 rev / min to desaturate tight sandstone core samples with permeability in the range of 1-10 mD. This rotational speed is expected to be significantly higher for tight organic-rich mudrocks. The spontaneous imbibition process is also a popular technique for saturating core samples (Peng et al. 2019). However, the level of saturation that can be achieved would depend on the permeability and the pore-throat size of the sample.

[0019] The presence of natural fractures in organic-rich mudrocks has been well documented, which is another source of challenge for saturating these rocks. Ukar et al. (2020) documented the presence of natural fractures in the Vaca Muerta formation from outcrops and core samples. Abu-Mahfouz (2019) showcased the genesis of the natural fractures in the Belqa Group of Jordan. The stresses imposed on the natural fractures are amplified during the coring process and can lead to broken samples. Without a procedure formaking laboratory measurements on these imperfect samples, they can be wasted. Wastage also happens in the case of cuttings. Recently, researchers have started using cuttings for different analyses such as geochemical analyses, porosity estimation, and pore-size distribution (Chang et al. 2020; Dash et al. 2023; Xie and Reffell 2022). The use of cuttings for quantification of fluid-flow properties, such as saturation dependent relative permeability measurements, can be beneficial. However, as a first step, new methods are needed for fast saturation of irregular- shaped rock samples.SUMMARY

[0020] In a non-limiting embodiment, a computer implemented method of calculating saturation dependent permeability of a core sample having pores therein includes estimating pore volume of the core sample prior to saturation; estimating permeability of the core sample prior to saturation; saturating the core sample within a chamber of a sample cell; while saturating the core sample, iteratively measuring permeability of the core sample at selected times over a time interval; while saturating the core sample, iteratively measuring saturation levels of the core sample at the selected times; and saving, in computer memory, paired data comprising values for a permeability of the core sample and saturation level of the core sample at the selected times.

[0021] In another embodiment, estimating pore volume prior to saturation includes using computed tomography (CT) scans to estimate bulk volume of the core sample.

[0022] In another embodiment, estimating pore volume prior to saturation includes gravimetric measurements.

[0023] In another embodiment, estimating pore volume prior to saturation further includes nuclear magnetic resonance (NMR) measurements.

[0024] In another embodiment, estimating pore volume prior to saturation further includes calculating grain volumes of the core samples with a helium porosimeter.

[0025] In another embodiment, estimating pore volume prior to saturation includes selecting an estimated pore volume from gravimetric measurements of the core sample, NMR measurements of the core sample, grain volumes of the core samples, or an average of the gravimetric measurements of the core sample, NMR measurements of the core sample, and grain volumes of the core samples, or a statistically weighted combination of the gravimetricmeasurements of the core sample, NMR measurements of the core sample, and grain volumes of the core samples relative to a bulk volume of the core sample.

[0026] In another embodiment, saturating the core sample includes establishing saturation fluid pressure within a chamber that holds the core sample and a saturation fluid therein, wherein a saturation fluid pressure is exerted by the saturation fluid on surfaces within the core sample and on exterior surfaces of the core sample.

[0027] In another embodiment, the method further includes maintaining the saturation fluid pressure with a syringe pump moving a hydraulic fluid onto a piston sealing the chamber.

[0028] In another embodiment, saturating the core sample includes maintaining the saturation fluid pressure at 2500 psi.

[0029] In another embodiment, saturating the core sample includes maintaining the saturation fluid pressure at a value from 1500 psi to 2500 psi, inclusive.

[0030] In another embodiment, the saturation fluid includes a mixture comprising potassium chloride brine or any other type of brine.

[0031] In another embodiment, the hydraulic fluid includes a mixture comprising deionized water providing the fluid pressure with a syringe pump.

[0032] In another embodiment, iteratively measuring permeability of the core sample while saturating the core sample includes, at selected times up to a stop value, iteratively measure permeability of the core sample with respective pressure decay measurements; and at the selected times up to the stop value, numerically calculate, with a computer, permeability of the core sample by solving a pressure diffusion equation.

[0033] In another embodiment, the core sample includes irregularly shaped edges, and numerically calculating the pressure diffusion equation comprises obtaining a geometric profile of the core sample with an imaging device.

[0034] In another embodiment, the method includes selecting the permeability value from a measured permeability and a numerically calculated permeability, averages thereof, or statistically weighted combinations thereof.

[0035] In another embodiment, the method further includes using a computer for numerically solving a pressure diffusion equation for the core sample with a finite difference method or a finite element method with a respective pressure.

[0036] In another embodiment, the method further includes using at least one pressure transducer and measuring a respective pressure at the selected times and software stored on the computer to minimize the difference between the numerically estimated and measured pressure values to determine permeability and / or relative permeability of the core sample.

[0037] In another embodiment, iteratively measuring saturation level of the core sample further includes performing gravimetric measurements on the core sample at the selected times and performing NMR measurements of the core sample at the selected times until a stop criterion is met.

[0038] In another embodiment, iteratively measuring saturation level of the core sample further includes averaging the gravimetric measurements and the NMR measurements or selected a saturation level of the core sample from statistically weighted combinations of the gravimetric measurements and the NMR measurements.BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Reference will now be made to the accompanying drawings, which are not necessarily drawn to scale.

[0040] FIG. 1 illustrates aspects of a system for saturating core samples according to aspects the present disclosure.

[0041] FIG. 2 illustrates example shapes of core samples used in implementing aspects of the present disclosure.

[0042] FIG. 3 illustrates saturation test results for a first core sample according to one embodiment of the present disclosure.

[0043] FIG. 4 illustrates porosity of the core sample of FIG. 3.

[0044] FIG. 5 illustrates saturation test results for a second core sample according to one embodiment of the present disclosure.

[0045] FIG. 6 illustrates porosity of the second core sample of FIG. 5.

[0046] FIG. 7 illustrates saturation test results for a third core sample according to one embodiment of the present disclosure.

[0047] FIG. 8 illustrates a comparison of saturation test results for the second and third core samples of respective FIG. 5 and FIG. 7.

[0048] FIG. 9 illustrates another comparison of saturation test results for the second and third core samples of respective FIG. 5 and FIG. 7.

[0049] FIG. 10 illustrates a combination of a saturation system and a pressure-decay setup for to perform permeability and saturation dependent relative permeability measurements.

[0050] FIG. 11 Experimental setup used for pressure decay measurements to estimate permeability.

[0051] FIG. 12A Workflow for enhanced saturation of irregular- shaped tight rock samples and for quantifying the saturation level at each saturation stage.

[0052] FIG. 12B Workflow for assessment of saturation and saturation dependent relative permeability using the measured pressure-decay measurements stage.

[0053] FIG. 12C. Workflow for assessment of permeability using the measured pressure-decay measurements.

[0054] FIG. 13 illustrates Table 1 according to this disclosure for assumed parameters to perform NMR T2 measurements.

[0055] FIG. 14 illustrates Table 2 according to this disclosure for estimated gas permeability for Sample 1 at different saturation levels.

[0056] FIG. 15A shows a volume of injected brine inside Sample 1 estimated using (a) gravimetric (blue line) and (b) NMR T2 (red line) measurements.

[0057] FIG. 15B shows a volume of injected brine inside Sample 1 estimated using (a) gravimetric (blue line) and (b) NMR T2 (red line) measurements.

[0058] FIG. 16A shows, for Sample 1: The pressure-decay measurement recorded over time (blue dots) and the fitted numerical solution (red line) to the pressure decay measurement at (a) initial state, when S«=0%, (b) S«=17.2%, (c) S«=28.9%, (d) S«=37.3%, (e) S«=52.6%, and (f) S„=65.1%.

[0059] FIG. 16B shows, for Sample 1: The pressure-decay measurement recorded over time (blue dots) and the fitted numerical solution (red line) to the pressure decay measurement at (a) initial state, when S«=0%, (b) S«=17.2%, (c) S«=28.9%, (d) S«=37.3%, (e) S«=52.6%, and (f) S„=65.1%.

[0060] FIG. 16C shows, for Sample 1: The pressure-decay measurement recorded over time (blue dots) and the fitted numerical solution (red line) to the pressure decay measurement at (a) initial state, when S«=0%, (b) S«=17.2%, (c) S«=28.9%, (d) S«=37.3%, (e) S«=52.6%, and (f) S»=65.1%.

[0061] FIG. 16D shows, for Sample 1: The pressure-decay measurement recorded over time (blue dots) and the fitted numerical solution (red line) to the pressure decay measurement at (a) initial state, when S«=0%, (b) S«=17.2%, (c) S«=28.9%, (d) S«=37.3%, (e) S«=52.6%, and (f) S„=65.1%.

[0062] FIG. 16E shows, for Sample 1: The pressure-decay measurement recorded over time (blue dots) and the fitted numerical solution (red line) to the pressure decay measurement at (a) initial state, when S«=0%, (b) S«=17.2%, (c) S«=28.9%, (d) S«=37.3%, (e) S«=52.6%, and (f) S„=65.1%.

[0063] FIG. 16F shows, for Sample 1: The pressure-decay measurement recorded over time (blue dots) and the fitted numerical solution (red line) to the pressure decay measurement at (a) initial state, when S«=0%, (b) S«=17.2%, (c) S«=28.9%, (d) S«=37.3%, (e) S«=52.6%, and (f) S„=65.1%.

[0064] FIG. 17 illustrates gas relative permeability measurements acquired using the Helium pressure-decay setup for Sample 1.

[0065] FIG. 18 shows, for Sample 1: NMR saturation profile along the length of the sample after accomplishment of the saturation process using the developed method.

[0066] FIG. 19 illustrates Table 3 showing properties of Samples 1, 2, 3, 4, 5, and 6 documented in this paper.

[0067] FIG. 20A illustrates 3D images of (a) Sample 1 obtained from CT-scan imaging, (b) Sample 2 obtained from CT-scan imaging, and (c) Sample 3.

[0068] FIG. 20B illustrates 3D images of (a) Sample 1 obtained from CT-scan imaging, (b) Sample 2 obtained from CT-scan imaging, and (c) Sample 3.

[0069] FIG. 20C illustrates 3D images of (a) Sample 1 obtained from CT-scan imaging, (b) Sample 2 obtained from CT-scan imaging, and (c) Sample 3.

[0070] FIG. 21 A shows, for Sample 1: The volume of injected brine, estimated using gravimetric measurements recorded over (a) 3 days while applying a pressure on the piston at1000 psi (blue region) and 1500 psi (red region) and (b) 1 day with detailed demonstration of hour-by-hour measurements.

[0071] FIG. 21B shows, for Sample 1: The volume of injected brine, estimated using gravimetric measurements recorded over (a) 3 days while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi (red region) and (b) 1 day with detailed demonstration of hour-by-hour measurements.

[0072] FIG. 22A shows, for Sample 1: The volume of injected brine, estimated using NMR T2 measurements recorded over (a) 3 days while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi (red region and (b) 1 day with detailed demonstration of hour-by-hour measurements.

[0073] FIG. 22B shows, for Sample 1: The volume of injected brine, estimated using NMR T2 measurements recorded over (a) 3 days while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi (red region and (b) 1 day with detailed demonstration of hour-by-hour measurements.

[0074] FIG. 23A shows, for Sample 2: The volume of injected brine, estimated using (a) gravimetric and (b) NMR T2 measurements with vacuum saturation process (green region) and the developed saturation technique while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi. The dotted line represents the predicted extension of the vacuum saturation process.

[0075] FIG. 23B shows, for Sample 2: The volume of injected brine, estimated using (a) gravimetric and (b) NMR T2 measurements with vacuum saturation process (green region) and the developed saturation technique while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi. The dotted line represents the predicted extension of the vacuum saturation process.

[0076] FIG. 24A shows, for Sample 3 The volume of injected brine, estimated using (a) gravimetric and (b) NMR T measurements with the developed saturation technique while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi.

[0077] FIG. 24B shows, for Sample 3 The volume of injected brine, estimated using (a) gravimetric and (b) NMR T measurements with the developed saturation technique while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi.

[0078] FIG. 25A shows, for Sample 4: The volume of injected brine, estimated using (a) gravimetric and (b) NMR T measurements with the developed saturation technique while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi.

[0079] FIG. 25B shows, for Sample 4: The volume of injected brine, estimated using (a) gravimetric and (b) NMR T measurements with the developed saturation technique while applying a pressure on the piston at 1000 psi (blue region) and 1500 psi.

[0080] FIG. 26A shows, for Sample 5: The volume of injected brine, estimated using (a) gravimetric and (b) NMR T2measurements recorded over time.

[0081] FIG. 26B shows, for Sample 5: The volume of injected brine, estimated using (a) gravimetric and (b) NMR T2measurements recorded over time.

[0082] FIG. 27 shows, for Sample 6: The volume of injected brine, estimated using (a) gravimetric and (b) NMR T measurements recorded over time.

[0083] FIG. 28 illustrates a comparison of the time taken to reach 20% water saturation level for Sample 1 (using the enhanced saturation method), Sample 2 (using vacuum saturation method), Sample 3 (using the enhanced saturation method), Sample 4 (using the enhanced saturation method), Sample 5 (using spontaneous imbibition method), and Sample 6 (using vacuum saturation method).

[0084] FIG. 29 illustrates a computer environment in which aspects of this disclosure may be practiced.DETAILED DESCRIPTION

[0085] Although example embodiments of the present disclosure are explained in detail herein, it is to be understood that other embodiments are contemplated. Accordingly, it is not intended that the present disclosure be limited in its scope to the details of construction and arrangement of components set forth in the following description or illustrated in the drawings. The present disclosure is capable of other embodiments and of being practiced or carried out in various ways.

[0086] It must also be noted that, as used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” or “approximately” one particular value and / or to “about” or “approximately” another particularvalue. When such a range is expressed, other exemplary embodiments include from the one particular value and / or to the other particular value.

[0087] By “comprising” or “containing” or “including” is meant that at least the named compound, element, particle, or method step is present in the composition or article or method, but does not exclude the presence of other compounds, materials, particles, method steps, even if the other such compounds, material, particles, method steps have the same function as what is named.

[0088] In describing example embodiments, terminology will be resorted to for the sake of clarity. It is intended that each term contemplates its broadest meaning as understood by those skilled in the art and includes all technical equivalents that operate in a similar manner to accomplish a similar purpose. It is also to be understood that the mention of one or more steps of a method does not preclude the presence of additional method steps or intervening method steps between those steps expressly identified. Steps of a method may be performed in a different order than those described herein without departing from the scope of the present disclosure. Similarly, it is also to be understood that the mention of one or more components in a device or system does not preclude the presence of additional components or intervening components between those components expressly identified.

[0089] A detailed description of aspects of the present disclosure, in accordance with various example embodiments, will now be provided with reference to the accompanying drawings. The drawings form a part hereof and show, by way of illustration, specific embodiments and examples. In referring to the drawings, like numerals represent like elements throughout the several figures. Some experimental data are presented herein for purposes of illustration and should not be construed as limiting the scope of the present disclosure in any way or excluding any alternative or additional embodiments.

[0090] Descriptions of this disclosure includes use of words that are known in the arts of geology as well as hydrocarbon and water extraction from geological formations. For example, a core sample can be any portion of any kind of solid geological formation that is subject to testing as described herein. For example, and without limiting this disclosure, the core sample can be a portion of a rock formation under investigation as a source of hydrocarbons, water, or other useful substances. This disclosure refers to organic rich mud rocks, including but not limited to Qz, Ca, Py, Pl II, Ch, Ka, Ke, Bi, PYb.

[0091] This project develops a new system and method that enables fast saturation of tight core samples, while maintaining a uniform distribution of water or other saturating fluid along the length of the core samples. The setup comprises of two primary parts. The first part is the experimental setup fixture with a syringe injection pump, piston, and a sample cell. The second part is the alteration of the core sample to increase the exposed surface.

[0092] Unconventional reservoirs are playing a big role in today’s race for meeting the energy demands. Successful exploitation of these tight, dense, low permeability reservoirs require enhanced formation evaluation efforts including experiments on core samples to understand the flow of multi-phase fluids. Experimental measurements on core samples for multi-phase fluids require saturating the core sample in laboratory. In the case of conventional reservoir samples, saturating the core is done using a core flood setup where brine is injected into a core holder containing the core at high pressure under confining stress until achieving a steady-state at the outlet. Numerous authors (Jones and Owens, 1980; Chowdiah, 1987; Firoozabadi and Aziz, 1991) have documented the use of core flooding setup for saturating core samples with a particular fluid phase. In the case of unconventional core samples, using the common core-flood setup for saturating the sample can be time consuming and unreliable. The saturation profile can be uneven along the axis of the core due to capillary-end effects (Heavyside et al., 1983). Several authors have experimented with tight core samples for measuring permeability by saturating or desaturating the samples.Centrifuge desaturation has been documented in the publication of Slobod et al. (1951). Ward and Morrow (1987) have also reported the use of ultracentrifuge and long stabilization times for desaturating core samples. The existing saturating methods take significant time (e.g. months), which make the measurements following the saturation process expensive and in some cases not feasible. Maintaining a uniform distribution of water in the sample can also be challenging.

[0093] Many of the current experimental set-ups used in the field require high back pressure systems which require additional safety features to be built in adding to the complexity of the setup. Even with the safety features and the pressure system added in, the efficiency of the setup is not optimal. Therefore, there is a need for a fast and reliable saturation technique for organic -rich mud rock and other tighter rock samples. In this work we introduce an experimental setup along with an alteration to the core sample shape for achieving fast saturation of core samples. The characteristics of the proposed method is faster and better saturation process in tight core samples such organic-rich mud rocks whose porethroat can be significantly small (i.e., in the range of few nanometers) which would require high entry pressure for brine injection. The biggest advantage of the setup is it can be built in the laboratory with existing setups without requiring any specialized equipment.

[0094] The proposed method is primarily intended to be used for saturating tight core samples 125, 130 (i.e., core samples having a density above an average value), but can also be used for conventional core samples or any porous solid. It can then be used for different saturation-dependent measurements such as electrical, fluid-flow, relative permeability, and capillary pressure. The proposed method is comprised of two parts: (a) the experimental setup and equipment and (b) alteration of cylindrical core samples to increase the surface area exposed to fluids. Combining both parts of the proposed method, the setup and the core sample shape, increases the surface area exposed to brine which will help in better injection and saturation of brine. As the setup doesn’t have any confining pressure, the outer surface of the cylindrical shape is also exposed to the brine along with both the axial faces compared to core flood setup where there is confining pressure and the brine is injected into only one of the axial faces. The inner surface of the hollowed cylindrical shape is also exposed to the brine.

[0095] Experimental setup and equipment

[0096] FIG. 1 shows an overview of the setup to saturate core samples 125, 130. The base of the setup is a 1.5 in matrix cup, or vessel, or sample cell 100 where the core sample will reside. There will be a piston 115 with 3 O-ring grooves on it. The piston 115 will separate the chamber of the matrix cup into two parts. The lower chamber 118 will carry the brine or other saturating fluid that will saturate the sample. The O-ring setup and O-rings 116 therein will prevent the fluid from the upper chamber 117 from mixing with the brine, or saturating fluid 127, in the lower chamber. The piston will facilitate compressing the saturating fluid in the chamber to penetrate the pore throats of the core sample. The upper part will carry the fluid, i.e., hydraulic fluid, from the syringe pump which will compress the piston. The piston is displaced within the matrix cup using the fluid from a syringe pump. The pump provides a pressure of approximately 2500 psi on the piston. The whole matrix cup will be isolated from the atmosphere with a top cover consisting of another O-ring setup with only the syringe pump fluid entering the setup through connecting lines. Once the experiment is completed, the pump fluid will be retracted into the syringe pump and the piston will be removed to retrieve the core sample.

[0097] Alteration of cylindrical core samples to increase the surface area exposed to fluids.

[0098] To increase the surface area of the core sample exposed to the brine, this disclosure may use a 1.5 in diameter cylindrical core sample 125 with a 1.5 in length and cut out a concentric cylinder in the middle of the core to create a hollow space. As the setup doesn’t have any confining pressure the outer face of the cylindrical core sample is also exposed to the brine. With the new core sample architecture, the inner face also is exposed to brine for saturation. The size of the core sample as well as the number of holes created in the sample can vary.

[0099] Combining both the alterations, the setup and the core sample shape, increases the surface area exposed to brine which will help in better injection and saturation of brine. As the setup doesn’t have any confining pressure, the outer surface of the cylindrical shape is also exposed to the brine along with both the axial faces compared to core flood setup where there is confining pressure and the brine is injected into only one of the axial faces. The inner surface of the hollowed cylindrical shape is also exposed to the brine.

[0100] To increase the surface area of the core sample exposed to the brine, this disclosure uses a 1.5 in diameter cylindrical core sample with 1.5 in length and cut out a concentric cylinder in the middle of the core to create a hollow space. As the setup doesn’t have any confining pressure the outer face of the cylindrical core sample is also exposed to the brine. With the new core sample architecture, the inner face also is exposed to brine for saturation. The size of the core sample as well as the number of holes created in the sample can vary.

[0101] Combining both the alterations, the setup and the core sample shape, increases the surface area exposed to brine which will help in better injection and saturation of brine. As the setup does not have any confining pressure, the outer surface of the cylindrical shape is also exposed to the brine along with both the axial faces compared to core flood setup where there is confining pressure and the brine is injected into only one of the axial faces. The inner surface of the hollowed cylindrical shape is also exposed to the brine.

[0102] PRELIMINARY RESULTS

[0103] This disclosure used a 1.5-in diameter core sample from an organic-rich mud rock formation. This disclosure included cutting the core sample into two samples to maintain two relatively similar 1.5-in diameter core samples, Sample 1 and Sample 2. Theprocess used Sample 1 for the saturation step. The process modified the Sample 2 into a hollowed-out cylindrical shape. The diameter of the cut-out was 0.5-in diameter along the axis of the core at the center. Once the core was modified into the new form, the process used the modified core sample for the saturation step. Before initiating the saturation step, the process recorded NMR T2 measurement on the dry core sample (Sample 1 and Sample 2) to obtain the T2 distribution of the dry sample. This disclosure also recorded the weight of the core sample for reference. The process then used 3% KC1 brine solution as the saturating fluid in the new injection setup for saturating the core sample. The process applied a pressure of 2500 psi on the movable piston in the injection fixture using a syringe pump. After finishing the saturation process, we again recorded the NMR T2 and the NMR saturationprofile measurement along the core sample. We also recorded the weight of the saturated core sample using a weighing balance.

[0104] Table A documents the porosity, the weight of the samples before and after the saturation process.Table A. Properties of Sample 1 and Sample 2 documented before and after the saturation process.Sample Porosity (%) Weight before saturation (g) Weight after saturation (g)Sample 1 4.2 39.451 39.647Sample 2 4.4 32.889 33.105

[0105] It should be understood that embodiments of the present disclosure are illustrated in further detail in FIGS. 1 - 29. FIG. 1 shows an experimental setup fixture 90 for fast saturation of tight core sample: (a) the sample reference cell 100 and pump setup fixture 110 connected via a valve, (b) the movable piston sample reference cell setup, and (c) the altered design of the core sample to be used in the saturation setup. FIG. 1 further shows the diagrammatic description of the proposed setup / method. Figure 1 shows the overall setup of the fixture for performing the saturation experiment. It consists of the sample reference cell connected to a syringe pump via a value and pressure transducer setup. Figure 1 shows the detailed description of the fixture within the sample reference cell. A movable piston fits snugly into the sample reference cell for pressurizing the saturating fluid into the core sample. Figure 1c shows the diagrammatic description of the altered cylindrical core sample to increase the exposed surface area to the saturating fluid.

[0106] FIG. 2 shows three different samples that were tested according to this disclosure. Sample 1 is a first core sample exposed to a pressure of 2500 psi in the setup of FIG. 1. The illustration shows that in one non-limiting embodiment, the sample was damaged during testing. Sample 2 was a second core sample that included a bored hole through the length of the core sample. The dimensions of the bore are illustrated in the third panel of FIG. 1. The bore allows more surface area of the second core sample to be exposed to fluid pressure for saturation.Sample 3 of FIG. 2 shows a third core sample that did not have a bore but exposed saturation methods as disclosed herein.

[0107] FIG. 3 shows the NMR T2 distributions obtained for Sample 1 before and after the saturation process. FIG. 4 shows the saturation profile along the Sample 1 after the saturation process. Sample 1 was exposed to 2500 psi. FIG. 5 shows the NMR T2 distributions obtained for Sample 2 at 1500 psi before and after the saturation process. FIG. 6 shows the saturation profile along the Sample 2 after the saturation process. The absolute increase in bulk water volume for Sample 1 (intact sample) was 1.4% compared to 1.66% for the case of Sample 2 (hollowed sample). The initial saturation level for the case of Sample 1 was higher compared to Sample 2. The initial saturation was measured using NMR after heating the samples at 45°C for 1 day. The increase in exposed surface area for Sample 2 allowed for the heating process to effectively dry the sample. Due to the uniformity of the exposed surface to the saturating brine from the outer as well as the inner axial walls of the core sample, the saturation profile measured along the length of the sample is uniform. This is advantageous when we perform saturation-dependent measurements on the core sample, such as capillary pressure, relative permeability, and electrical measurements. FIG. 7 shows the NMR T2 distributions obtained for Sample 3 before and after the saturation process. Sample 3 was also an intact sample but only exposed to 1500 psi. FIGS. 8 and 9 show the saturation comparison of Sample 2 and Sample 3.

[0108] Laboratory-based assessment of petrophysical properties (e.g., permeability, saturation-dependent relative permeability and capillary pressure, water saturation) of tight formations such as organic-rich mud rocks has always been a challenge in the petroleum industry. Main reasons for these challenging core evaluation processes are (a) uncertainties associated with saturating the samples with water and (b) the extensively long times requires for saturating the samples with water. The existing saturating methods take significant time (e.g. months), which make the measurements following the saturation process expensive andin some cases not feasible. Maintaining a uniform distribution of water in the sample can also be challenging. The benefits of this new method are listed as follows:

[0109] Saturating tight samples with water can be performed in significantly shorter times compared to conventional methods.

[0110] It requires less expensive and specialized equipment compared to conventional methods such as ultra-high-speed centrifuge.

[0111] It can produce a relatively uniform water saturation profile along the core sample.

[0112] It includes a procedure for verifying the saturation profile along the core sample.

[0113] The saturating process has minimal impact on properties of core samples under analysis compared to methods such as centrifuge.

[0114] Different water saturation levels can be achieved faster compared to conventional methods.

[0115] Fluid flow in the pore network depends on the preferential movement of different fluid phases. To understand the preferential movement of different fluids in the reservoir, saturation-dependent petrophysical properties such as relative permeability are critical. Therefore, saturating the core samples forms the basis for such experimental measurements. Conventional laboratory-based methods for saturating tight core samples take significant time, making the process expensive and not feasible. Even with high back pressure systems added in, the efficiency of the setup is not optimal. This disclosure further includes a new method that enables fast saturation of tight cylindrical core samples and irregular- shaped cutting samples while maintaining a uniform water distribution along the length of the core samples.

[0116] The experimental fixture is comprised of a sample cell of 1.5-in diameter with a movable piston with three O-ring grooves on the outer surface of the piston. The piston is moved into the sample cell chamber with the help of a syringe pump, separating the chamber into lower and upper parts. The lower part contains the core sample sitting in the saturating fluid isolated from the upper part, where the injection fluid from the syringe pump pushes the piston into the chamber. The saturating fluid used in our study is 3wt% KC1 brine solution to reduce the impact of clay swelling. The core samples were subjected to a constant chamberpressure of 1500 psi using the syringe pump-piston setup to saturate the core samples. This disclosure used NMR T2 measurements to track the change of saturation in the samples.

[0117] This disclosure tested the introduced workflow on core samples (Sample 4, intact, and Sample 5, cylindrical cavity of 0.5-in diameter in the center) from the Eagle Ford formation and cutting samples (Sample 6) from another organic-rich mudrock formation. The water saturation increased by 30%, relatively, when sample shape was modified from Case 4 to 5. This disclosure also observed a uniform water saturation profile along the length of these two samples, which could be challenging to obtain using conventional saturation methods. The saturation profile was uniform due to the uniformity of the exposed surface to the saturating brine, both for Sample 4 and Sample 5. In the case of Sample 6, the water saturation increased to 45% in 12 hours and to 75% in 36 hours. Saturating irregular- shaped samples can potentially lead to moving away from coring of samples for fluid-flow measurements.

[0118] Saturating tight core samples took 3 days using the new tool compared to approximately 25 days using the conventional core flooding technique. The novelties of this method for saturating tight rock samples include (a) significantly shorter times compared to conventional methods, (b) less expensive and specialized equipment compared to conventional methods such as ultra-high-speed centrifuge, (c) relatively uniform water saturation profile along the length of the core sample, (d) minimal impact on petrophysical properties of core samples during the saturation process compared to methods such as centrifuge, and (e) shape of the sample does not impact the saturation process. The experimental fixture and procedure described in this paper can also be used for conventional core samples.

[0119] Reliable and fast core saturation process forms the basis for many saturationdependent measurements of petrophysical properties such as relative permeability and capillary pressure. Conventional laboratory-based methods for saturating tight core samples take significant time, making the process expensive and not feasible. The conventional experimental setups used in the laboratory require high back pressure systems, which mandates additional safety features to be built, adding to the complexity of the setup. Such methods can lead to multiple months of experiments, including the saturation process and the permeability measurements, for measuring a single relative permeability data point. Highspeed centrifuge is another option used for saturating core samples, but it leads to a non- uniform saturation profile along the length of the core sample. In this paper, we introduce anew method that enables fast saturation of tight core samples while maintaining a uniform water distribution along the length of the core samples.

[0120] The experimental fixture and procedure described in this paper are primarily intended for saturating tight core samples but can also be used for conventional core samples. We start with a core sample cell of 1.5-in diameter with a movable piston with three O-ring grooves on the outer surface of the piston. The piston is moved into the sample cell chamber with the help of a syringe pump, separating the chamber into lower and upper parts. The lower part contains the core sample sitting in the saturating fluid isolated from the upper part, where the injection fluid from the syringe pump pushes the piston into the chamber. The saturating fluid used in our study is 3wt% KC1 brine solution to reduce the impact of clay swelling during the saturation process. We used cylindrical core samples as well as altered core samples, with a cavity of 0.5-in diameter at the center, for the saturation process. The core samples were subjected to a pressure of 1500 psi using the syringe pump-piston setup. We performed NMR T2 measurements before and after the saturation process to monitor the total water saturation. We also performed NMR saturation-profile measurements to confirm the uniformity of the water saturation along the length of the core sample.

[0121] We tested the aforementioned workflows, including the new tool and the altered core sample on outcrop samples from the Eagle Ford formation. This disclosure will cut the cylindrical core into two equivalent parts, Sample 7 and Sample 8. This disclosure modified the Sample 8 into a hollowed-out cylindrical shape. The absolute increase in bulk water volume for Sample 7 (intact sample) was 1.4% compared to 1.66% for the case of Sample 8 (hollowed sample). The initial saturation level for the case of Sample 7 was higher compared to Sample 8. The initial saturation was measured using NMR after heating the samples at 45°C for one day. The increased exposed surface area for Sample 2 allowed the heating process to dry the sample effectively. The measured NMR saturation profile was uniform due to the uniformity of the exposed surface to the saturating brine. The uniform saturation profile is advantageous when we perform saturation-dependent measurements on the core sample, such as capillary pressure, relative permeability, and electrical measurements. Saturating tight core samples took 3 days using the new tool compared to approximately 25 days using the conventional core flooding technique. The novelties of this method for saturating tight rock samples include (a) significantly shorter times compared to conventional methods, (b) less expensive and specialized equipment compared to conventional methods such as ultra-high-speed centrifuge, (c) relatively uniform watersaturation profile, and (d) minimal impact on petrophysical properties of core samples during the saturation process compared to methods such as centrifuge.

[0122] Another embodiment of this disclosure utilizes the Pressure-Diffusion Equation for more accuracy in determining exactly the extent to which certain core samples can be saturated. For regular shaped cores, permeability may be estimated using the pressure diffusion equation, and for irregular shaped cores, permeability may be defined more closely with the pressure-diffusion equation. The pressure-diffusion equation follows: dP / dt = D x V2P

[0123] In the above expression, the differential of pressure versus change in time is equal to a sample’s diffusivity parameter (D) multiplied by the LaPlace transform (of the gradient) multiplied by the pressure value at a particular point.

[0124] Understanding the fluid-flow characteristics in reservoir rocks requires a reliable assessment of permeability and saturation-dependent relative permeability. It is also essential for quantifying the primary recovery mechanisms and enhancing the ability to exploit reserves successfully. This paper introduces new methods to perform reliable permeability and saturation-dependent relative permeability measurements in organic -rich mudrock core samples using a pressure-decay setup. This disclosure also designed an experimental fixture to saturate the tight core samples in a fast, uniform, and reliable manner. The introduced method is applicable to samples of any shape (i.e. intact or hollowed cylindrical core samples, irregular- shaped samples such as cuttings.)

[0125] FIG. 10 illustrates the setup for the pressure-decay experiment comprises of a reference gas cell 155, a sample cell 100, pressure valves, pressure transducer 105 to record the pressure decay, and a vacuum pump. The sample 125, 130 is placed in the sample chamber and the whole setup is vacuumed for 1 hr. Helium (He) is filled into the reference cell at a pressure of 210 psi. Next, the upstream valve is opened to allow the He into the sample chamber. The pressure decay is recorded using a pressure transducer in the reference cell. This disclosure numerically solve the pressure diffusion equation for either an intact or hollowed cylinder shape using the finite difference method, or for the irregular shape using the finite element method. This disclosure estimate the permeability by minimizing the difference between the numerically estimated and the measured pressure values.

[0126] This disclosure shows permeability measurements using the pressure-decay setup on 1.5-in diameter cylindrical core samples from the Eagle Ford Formation. The matrix permeability of the sample at dry condition was 10 nD. The relative permeability of the sample at 35% saturation decreased to 6.5 nD. This disclosure also estimated the permeability of the sample using a pulse-decay setup for the purpose of comparison. As the conventional pulse decay happens in the range of 10-12 psi, in the case of low permeability samples, the nano-leak in the system impacted the measurements. This disclosure also tested a hollowed-out cylindrical core sample for permeability measurement. Saturating the hollowed samples using the new method was approximately 5 times faster compared to conventional methods and 1.5 times faster compared to cylindrical samples, which led to faster relative permeability measurements.

[0127] Coupling the saturation method with the pressure-decay setup reduced the experimental duration and increased the reliability of the measurement. The introduced workflow enables (a) relative permeability and absolute permeability measurements performed in significantly shorter times compared to conventional techniques, (b) fluid-flow measurements in tight rock samples without the need for specialized and expensive equipment, and (c) making fluid flow measurements in unconventional core shapes such as hollowed cylindrical samples and potentially in other irregular- shaped samples such as cuttings or chipped core samples. Use of irregular- shaped sample can eliminate the need for coring which can introduce induced fractures in organic-rich samples, affecting the reliability of the measurements.

[0128] This disclosure start with a core sample cell of 1.5-in diameter with a movable piston with three O-ring grooves on the outer surface of the piston. The piston is moved into the sample cell chamber with the help of a syringe pump, separating the chamber into lower and upper parts. The lower part contains the core sample sitting in the saturating fluid isolated from the upper part, where the injection fluid from the syringe pump pushes the piston into the chamber. The saturating fluid used in our study is 3wt% KC1 brine solution to reduce the impact of clay swelling during the saturation process. This disclosure used cylindrical core samples as well as altered core samples, with a cavity of 0.5-in diameter at the center, for the saturation process. The core samples were subjected to a pressure of 1500 psi using the syringe pump-piston setup. This disclosure performed NMR T2 measurements before and after the saturation process to monitor the total water saturation. This disclosure alsoperformed NMR saturation-profile measurements to confirm the uniformity of the water saturation along the length of the core sample.

[0129] This disclosure tested the aforementioned workflows, including the new tool and the altered core sample on outcrop samples from the Eagle Ford formation. This disclosure cut the cylindrical core into two equivalent parts, Sample 1 and Sample 2. This disclosure modified the Sample 2 into a hollowed-out cylindrical shape. The absolute increase in bulk water volume for Sample 1 (intact sample) was 1.4% compared to 1.66% for the case of Sample 2 (hollowed sample). The initial saturation level for the case of Sample 1 was higher compared to Sample 2. The initial saturation was measured using NMR after heating the samples at 45°C for one day. The increased exposed surface area for Sample 2 allowed the heating process to dry the sample effectively. The measured NMR saturation profile was uniform due to the uniformity of the exposed surface to the saturating brine. The uniform saturation profile is advantageous when This disclosure perform saturationdependent measurements on the core sample, such as capillary pressure, relative permeability, and electrical measurements. Saturating tight core samples took 3 days using the new tool compared to approximately 25 days using the conventional core flooding technique. The novelties of this method for saturating tight rock samples include (a) significantly shorter times compared to conventional methods, (b) less expensive and specialized equipment compared to conventional methods such as ultra-high-speed centrifuge, (c) relatively uniform water saturation profile, and (d) minimal impact on petrophysical properties of core samples during the saturation process compared to methods such as centrifuge.

[0130] Example A

[0131] The measurement of fluid flow in organic-rich mudrock samples is performed using a pressure-decay experimental setup. This disclosure uses Helium as the penetrating gas instead of nitrogen due to the smaller molecule size of Helium. The core samples are first placed in the reference sample chamber, and then the chamber is vacuumed for one hour till the vacuum gauge pressure stabilizes. Then, Helium is filled into a reference cell at a pressure of 210 psi. Next, the upstream valve is opened to allow the helium gas into the sample chamber, which expands across the sample chamber. The expansion in the sample chamber occurs in an unconfined manner. The pressure decay is recorded using a pressure transducer in the reference cell. This disclosure numerically solved the pressure diffusion equation for a cylindrical core to estimate the permeability values. The permeability estimation uses aminimization routine to minimize the squared difference between the numerically derived pressure solution and the recorded pressure values from the experiment. Next, This disclosure partially saturate the core sample using the enhanced saturation setup recently developed by our team which expedites the saturation process at least four times in a cylindrical core plug. This disclosure will repeat the pressure decay experiment using the partially saturated core sample. This disclosure finally applied the introduced method to a modified core sample with a hollowed cavity at the center of the sample to accelerate the saturation as well as permeability measurement process. This disclosure will estimate the permeability in the altered sample using the pressure diffusion equation with modified boundary conditions.

[0132] Example B

[0133] This disclosure performed permeability and saturation-dependent relative permeability measurements on outcrop samples from the Eagle Ford Formation. This disclosure used a 1.5-in diameter core sample from an organic-rich mudrock formation. This disclosure cut the cylindrical core into two parts, Sample 1 and Sample 2. This disclosure used Sample 1 for the permeability and saturation-dependent permeability measurements. This disclosure modified Sample 2 into a hollowed-out cylindrical shape with a 0.5-in diameter of the cavity at the center of the core. This disclosure then used Sample 2 for the permeability measurements. The numerical solution of the pressure decay provided the absolute gas permeability. This disclosure estimated the matrix permeability of Sample 1 before saturation to be 0.6 nD. The relative permeability of Sample 1 at 35% saturation decreased to 0.4 nD. This disclosure also estimated the matrix permeability of Sample 2 before saturation to be 1.1 nD. The relative permeability of Sample 2 at 45% saturation decreased to 0.75 nD. The introduced workflow enables (a) saturation-dependent relative permeability and absolute permeability measurements performed in significantly shorter times compared to conventional techniques and (b) fluid-flow measurements in tight rock samples without the need for specialized and expensive equipment.

[0134] Figure 11 shows the experimental workflow to measure permeability and saturation-dependent relative permeability integrated with a recently developed experimental setup for saturating tight core samples. The sample cell 100 holds the sample 125, 130 for saturating with fluid such as brine and conducting permeability analyses with a computer or data logger 300 while the system conducts both pressure decay measurements and numerically calculated permeability valuation. The workflow includes a recently developed experiment setup for fast saturation of tight core samples (Dash and Heidari 2024) and apressure decay setup for estimation permeability. The proposed workflow starts with preparing the core samples for the permeability estimation process, which includes extracting cylindrical core plugs from whole-core samples and cleaning the extracted plugs. The plugs are extracted using a low rotational speed of 65 RPM for the coring process compared to the typically used rotational speed of 900 RPM in the case of conventional sandstone core plugs. The extracted core plug is cleaned using toluene in a Soxhlet apparatus. This disclosure will estimate the pore volume of the sample using the Helium porosimeter after drying in an oven at 45°C for three days. This disclosure will then perform gravimetric and NMR T2 measurements on the sample in its initial state. This disclosure will make pressure decay measurements on the sample to estimate the gas permeability of the sample in its initial state. This disclosure will saturate the sample using the introduced method and repeat the pressure decay measurements after each saturation step to estimate the permeability.

[0135] This disclosure will also perform gravimetric and NMR T2 measurements after each saturation step to monitor the water saturation level corresponding to the estimated permeability. The outcome of this workflow is the estimated permeability at each water saturation level and the saturation-dependent relative permeability of the sample. This disclosure will describe the process of permeability assessment in detail in the subsequent subsections. This disclosure will stop the experiments when the stopping criterion is fulfilled. The stopping criterion is defined asVi - Vi-1 / Vp < e

[0136] where Vi is the volume of injected brine into the sample estimated using the NMR T2 measurement at the ith saturation step, Vp is the estimated pore volume at the initial state of the sample, and epsilon is the threshold parameter defined for stopping the experiment. In this paper, a value of 2% is used for the stopping criterion

[0137] Experimental Setup for Assessment of Permeability

[0138] Figure 12 shows the experimental setup for the pressure-decay measurements. The setup comprises of a reference chamber connected to a sample chamber via a pressure valve and a pressure transducer to record the pressure data. The reference chamber is connected to an upstream line with a vacuum pump and a helium gas tank. Helium can easily penetrate small pores and pore throats present in organic-rich mudrocks compared to nitrogen due to the small size of Helium molecules. Helium as the pore fluid can be more stable with minimal Joule-Thomson effect (Hannon 2020; Jia et al. 2020; Wang et al. 2021) compared tonitrogen. Therefore, Helium as a pore fluid can be advantageous for estimating permeability in tight rocks such as organic-rich mudrocks. The core sample is first placed in the sample chamber. The reference and sample chambers are vacuumed until the pressure stabilizes. The reference chamber and the sample chamber are then disconnected using the valve. Helium gas is filled into the reference chamber at a pressure of approximately 200 psig. The sample chamber is still under vacuum. The valve connecting the reference and the sample chamber is opened to allow helium gas to expand into the sample chamber. The expansion in the sample chamber occurs in an unconfined manner. The pressure decay is recorded using a pressure transducer in the reference cell. This disclosure will then numerically solve the pressure diffusion equation for unconfined cylindrical core samples. The pressure diffusion equation is defined as dP / dt = D x V2P where P is the pressure, t is the time, and V is the Laplacian operator. D is the diffusivity coefficient, defined where k is the permeability of the sample, LI is the viscosity of the gas, G is the compressibility of the gas, and (p is the porosity of the sample. The numerical solution to Equation 2 provides the absolute gas permeability of the sample.Figure 13 shows the minimization workflow employed to estimate the permeability using the measured pressure decay measurements. This disclosure will use the finite difference method to numerically solve the pressure diffusion equation. This disclosure will start with an initial guess of the permeability value to calculate the diffusivity coefficient. This disclosure will then calculate the pressure change with time through solving the pressure diffusion equation. This disclosure will update the value of permeability after each iteration. This disclosure will continue to update the permeability value to minimize a cost function, a, based on the L2 norm between the measured pressure and calculated pressure. The cost function, a, is defined as a = 1 / n HPmeasured - Pcalculatedlh , where n is the number of measured data points, Pmeasured is the measured pressure change from the pressure decay measurement, and Peculated is the calculated pressure change from the pressure diffusion equation. The optimization process stops when a is less than a pre-defined threshold. The value of d assumed in this paper is 10'4.

[0139] Enhanced Saturation of Core Samples

[0140] To estimate relative permeability, this disclosure will need to saturate the core samples in a wide range of saturation levels. This disclosure will partially saturate the coresample using a newly developed experimental setup (Dash and Heidari 2024). The experimental setup comprises of an injection setup consisting of a reference sample chamber 1.5-inch in diameter connected to a syringe pump via a connecting line, a valve, and a pressure transducer.

[0141] A cylindrical piston fits snugly inside the reference chamber and consists of three O-rings. Once the core sample is placed inside the chamber along with the saturating fluid, the piston is placed inside the chamber and sealed. The piston is movable within the chamber, dividing it into upper and lower parts. The core sample is placed in the saturating fluid in the lower part. The upper part is where the fluid from the syringe pump pushes the piston into the chamber. The pump can provide a maximum pressure of 3700 psi on the piston. However, in the experiments documented in this paper, this disclosure will use 1000 psi to saturate the core samples to prevent cracking of the samples. This disclosure will use 3wt% KC1 brine solution as the saturating fluid to prevent swelling of the clay minerals in the sample (Wysocki et al. 2016; Chen et al. 2020).

[0142] Gravimetric and NMR Measurements for Saturation Monitoring

[0143] This disclosure will use gravimetric and NMR measurements to track the variation in water saturation within the core samples. In the case of gravimetric measurements, this disclosure will use a weight balance with 0.1 mg accuracy. The measured weight is then converted to the volume of injected brine using the density of the 3wt% KC1 brine solution (1.031 g / cc). The change in the volume of injected brine after each saturation step provides an estimate of the water saturation level achieved after each saturation step. Similarly, this disclosure will perform NMR measurements to track the change in water saturation within the core samples. The NMR measurements are performed using a 2 MHz Magritek NMR spectrometer. Table 1 documents the parameters used for recording the NMR T2 measurements. This disclosure will calibrate the NMR spectrometer using a 10 cc 3wt% KC1 brine solution and apply background corrections to obtain a calibrated NMR T2 response. The inversion of the magnetization decay is done using Lawson and Hansons nonnegative least square regression method (Lawson and Hanson 1995; Aster et al. 2005) to obtain the NMR T2 distribution. This disclosure will record the NMR T2 distribution of the core samples in their initial state and after each saturation step to track the water saturation level.

[0144] Assessment of Saturation-dependent Relative Permeability

[0145] In this section, this disclosure will discuss the estimation of relative permeability to gas for the core samples, which is considered the relative permeability measurements to the non- wetting phase. While estimating gas relative permeability for tight rock samples such as organic -rich mudrocks is possible, measuring water relative permeability is challenging, time-consuming, and often unreliable. To estimate the gas relative permeability of the core samples, this disclosure will start with the gas permeability of the samples in the initial state, assumed to be the dry state (Sw=0). This disclosure will then partially saturate the samples using the developed saturation technique and repeat the gas permeability measurement. This disclosure will repeat the saturation and the measurement step until the estimated gas permeability at a particular saturation level is less than 1% of the gas permeability of the initial state of the sample. This disclosure will then normalize the recorded gas permeability values at each saturation level to the gas permeability measured at the initial state. The normalized values provide the gas relative permeability of the sample.

[0146] Results

[0147] In this paper, this disclosure used a whole-core sample from Lower Eagle Ford formation to assess permeability and saturation-dependent relative permeability. This disclosure extracted a cylindrical core plug sample (Sample 1) measuring 1.5-inch diameter and 1.25-inch in length. Sample 1 was dried in the oven at 45 °C until the loss in weight from gravimetric measurements reached an asymptotic value. The estimated porosity of Sample 1 at the initial state was 6.1% using the Helium porosimeter. This disclosure recorded the pressure-decay data over time for Sample 1 using the Helium pressure-decay setup. The initial pressure of Helium was set at approximately 200 psig in the reference chamber. The pressure decay was recorded when Helium was introduced into the vacuumed sample chamber containing the sample. The pressure of Helium decayed when it penetrated the sample.

[0148] Figure 14 shows the water saturation levels achieved for Sample 1 at the end of each saturation stage. The pressure decay data was recorded after each saturation stage, and the permeability value was estimated.

[0149] Figure 15 shows the recorded pressure decay data and the numerical solution of the pressure diffusion equation. The pressure data is recorded at a time interval of 0.15seconds. However, this disclosure discareded the data before 1 second due to the Joule- Thomson effect, which leads to a cooldown of the gas within the system.

[0150] The theoretical initial pressure when Helium is introduced into the sample chamber (i.e., no gas has penetrated the sample) was calculated to be 97.1 psi. However, this disclosure will observed that the pressure decay starts at 94.8 psi (Figure 5a). This gap in pressure is attributed to the presence of natural fractures, which amount to 1.9% of the total estimated porosity. The matrix porosity corresponds to 3.8% of the total estimated porosity. The presence of natural fractures leads to a rapid decay of the pressure data before 1.5 seconds. The slower decay corresponds to the matrix permeability. The matrix permeability of the sample in its initial state was estimated to be 60 nD. Table 2 documents the estimated permeability values at the initial state and after each saturation stage for Sample 1.

[0151] Figure 16 shows the measured gas relative permeability values against the water saturation values for Sample 1. The water saturation was estimated using the volume of injected brine using gravimetric measurements. Relative permeability was calculated using the estimated matrix permeability at a particular water saturation value and then normalized to the matrix permeability of the sample at its initial state.

[0152] The estimated gas relative permeability for Sample 1 demonstrates a sharp decrease of gas permeability as the water saturation of the sample increases. The gas relative permeability of Sample 1 at 28% water saturation level was 10%. This value decreased further and dipped below 1% at 65% water saturation level. The time taken for saturation alone of the sample from 0% to 65% was 2.6 hours. A comparison of the saturation of tight samples cored from the same whole-core sample revealed that the maximum saturation that could be achieved using a vacuum saturation process was 25% after 7 days of saturation (Dash and Heidari 2024). A 20% water saturation level was achieved after 15 minutes of saturation process using the developed saturation technique. This disclosure also compared the saturation outcomes reported in previous publications for making relative permeability measurements. Researchers have documented saturating samples from the Eagle Ford, Barnett, and Wolfcamp formations (Peng et al. 2019) using the spontaneous imbibition process where the sample is saturated by exposing only the bottom of the sample to brine. In the case of the Eagle Ford formation, the samples could take up to 35 hours to saturate to 30% maximum water saturation. For the case of Barnett, it took 3.6 hours to reach 29%, and for the Wolfcamp formation, the mudrock sample reached 56% saturation in 6.2 hours. This comparison shows that using conventional saturation techniques, the maximum saturationlevel which can be achieved will vary and can depend on the pore-size distribution of the sample. The total time taken to reach maximum saturation for Sample 1 was 2.6 hours. For a similar sample going under the vacuum saturation and spontaneous imbibition processes (Dash and Heidari 2024), it took 7 days to reach the maximum attainable saturation level. This observation suggests that performing relative permeability measurements with 5 different saturation levels using conventional saturation methods would take at least 12 days to complete. In comparison, the total time taken to perform relative permeability measurements using the proposed saturation method was 5 days. Moreover, the relative permeability curve using conventional saturation methods would not be complete as the maximum attainable saturation level was low (-20%) compared to the maximum attainable saturation level using the proposed saturation method (-65%). Figures 17A and 17B show the saturation profile along the length of Sample 1. This saturation profile is obtained using NMR measurements and shows a relatively uniform distribution of brine within the sample. This uniform saturation profile enables enhanced assessment of relative permeability.

[0153] In this paper, this disclosure introduced a workflow for the assessment of permeability and saturation-dependent relative permeability in organic-rich mudrock samples by integrating the permeability measurements with a fast and reliable saturation process. Using the new setup for saturating core samples enabled us to fast track the saturationdependent relative permeability measurement. This, coupled with the pressure-decay setup, considerably reduced the duration of each experimental measurement of saturationdependent relative permeability. The sample used in this paper could be saturated from 0% to 65% in 2.6 hours. Including the time taken for the permeability measurement, the total experiment was completed in 5 days. The estimated permeability of the sample was 60 nD at the initial state and dropped to 0.4 nD at 65% water saturation level. The NMR saturation profile measurement confirmed that the brine distribution within the saturated sample was uniform. The uniform saturation profile is essential for reliable saturation-dependent relative permeability measurements.

[0154] The novelties and contributions of the developed technique for saturating tight rock samples and estimating relative permeability include but are not limited to fluid-flow measurements, especially saturation-dependent relative permeability measurements, which can be performed in shorter times compared to conventional techniques such as vacuum saturation and spontaneous imbibition processes; the proposed method enables fluid-flow measurements in tight rock samples without the need for specialized equipment; thesaturation process has minimal impact on the properties of the sample under analysis compared to techniques such as saturation or desaturation using the centrifuge; and control over the water saturation level using the pressure that is applied to the piston setup and the time duration of the saturation to have reliable relative permeability measurement.

[0155] The developed workflow documented in this paper has the capability of assessment of relative permeability in tight rock samples such as organic -rich mudrocks with absolute permeability in the range of nano-darcies.

[0156] The minimum estimated gas permeability using the pressure-decay setup documented in this paper was 0.4 nD. The authors anticipate that the setup can also be used for samples with higher permeability ranging from 100 nD to 100 pD. The developed workflow and setup can provide an enhanced understanding of the reservoir characteristics by making petrophysical measurements in a timely and reliable manner. However, a larger number of tests on rock samples with a wide range of permeability values belonging to different formations needs to be performed to further define the limitations and the range of applicability of the proposed method.

[0157] Acronyms

[0158] JBN = Johnson-Bossier-Naumann

[0159] LH = Lawson and Hanson

[0160] NMR = Nuclear Magnetic Resonance

[0161] SNR = Signal-to-Noise Rati

[0162] Nomenclature

[0163] Tn = transverse or spin-spin relaxation, ms

[0164] Vi= volume of injected brine at z* step, cc

[0165] VP= connected pore volume, cc

[0166] s = saturation experiment threshold, %

[0167] a = stopping criterion for the permeability optimization routine

[0168] V = laplacian operator

[0169] P = pressure decay recorded over time, psi

[0170] k = permeability of the sample, mD[oi7i] Ct = compressibility of the gas, psi i

[0172] p = viscosity of the gas, cP

[0173] tp = porosity of the sample, %

[0174] Saturation Method

[0175] Figure 18 describes the proposed experimental workflow for saturating irregular- shaped rock samples using the newly developed experimental setup (Dash and Heidari 2024). The irregular- shaped rock samples can include cuttings, broken core samples, and outcrop samples. The developed workflow facilitates the fast and reliable saturation of tight rock samples. The proposed setup comprises a combination of a piston and a syringe pump. The setup works by exposing the surface area of the rock samples to the saturating fluid and enforcing the samples to a uniform and faster fluid penetration compared to conventional saturation methods such as vacuum saturation and spontaneous imbibition processes. The proposed workflow starts with drying the samples in an oven at 45° C until the decrease in this disclosure willight stops. This disclosure will then use the CT-scan technique to estimate the bulk volume of the samples. This disclosure will then use the estimates of grain volume from a Helium porosimeter and the estimated bulk volume to calculate the pore volume of the samples. This disclosure will also perform gravimetric and NMR Tn measurements on the samples in their initial state. Next, this disclosure will saturate the samples using the newly developed technique. This disclosure will then repeat the gravimetric and NMR T2 measurements on the saturated samples. This disclosure will continue with the saturation process until a stopping criterion is fulfilled. The stopping criterion is defined as where Vi is the volume of the injected brine estimated using the NMR T2 measurements at the z* saturation process step, V?is the estimated pore volume of the sample, and s is the threshold parameter, assumed to be 2% for the experiments documented in this paper. Lastly, this disclosure will compare the results of the water saturation levels achieved using the newly developed technique against the water saturation levels achieved using vacuum saturation and spontaneous imbibition processes. This disclosure will also document the time to reach the maximum saturation level for each saturation process.

[0176] Experimental Setup for the Fast and Enhanced Saturation Process

[0177] In this section, this disclosure will describe the experimental setup and the developed technique for saturating tight rock samples, such as organic-rich mudrocks. Theexperimental setup consists of a sample chamber as a base where the samples to be saturated can be placed. The next component of the setup is a movable piston comprising of three O- rings, separating the sample chamber into two parts. The lower part consists of the saturating fluid and the sample, and the upper part carries the injection fluid from a syringe pump. The piston is moved into the sample chamber using the fluid from the syringe pump. The movement of the piston into the sample chamber forces the saturating fluid into the exposed surface area of the samples. The top of the sample chamber is isolated using a top cover consisting of another o-ring fixture and connecting lines to the syringe pump. The syringe pump can retract the injection fluid after the saturation process. Dash and Heidari (2024) described this experiment setup for saturating tight rock samples in detail.

[0178] Assessment of Bulk Volume using CT-scan Imaging

[0179] This disclosure will use CT imaging to determine the bulk volume of the irregular- shaped samples. The rock sample is first scanned using High-Resolution X-ray Computed Tomography equipment. A total of 1546 image slices, with a voxel size of 35were acquired. The volume of each voxel was calculated, and the total bulk volume was estimated by counting the total number of voxels and the volume of each voxel.

[0180] Assessment of Pore Volume using Helium Poroshnetry

[0181] This disclosure will use Helium porosimetry to estimate the pore volume of the irregular- shaped samples. The Helium porosimetery is based on the Boyle-Marriote Gas Law (Ernest 1926; Luffel and Guidry 1992). The irregular- shaped sample is first placed in a sample chamber of known volume. A second known volume reference chamber is connected to the sample chamber via a valve and connecting lines. Both the sample and the reference chamber are vacuumed along with the sample. The sample chamber is then disconnected from the reference chamber. Helium gas is introduced into the reference chamber at an initial pressure. Lastly, the valve between the reference chamber and the sample chamber is opened to let Helium expand into the sample chamber. The final equilibrium pressure can provide the grain volume of the sample. This disclosure will calculate the pore volume and porosity of the sample using the estimated bulk volume estimated from the CT-scan imaging.

[0182] Assessment of Water Saturation using Gravimetric and NMR Measurements

[0183] This disclosure will use a high-accuracy (0.1 mg) Mettler- Loredo weighing machine for gravimetric measurements. The samples are weighed before and after each saturation step. The measured weights are converted to the volume of injected brine into thesamples using the density of 3wt% KC1 brine solution. This disclosure will also use a 2 MHz Magritek NMR spectrometer to record the NMR T2 response in the saturated samples. The response is recorded for the samples in their initial state and after each saturation step. This disclosure will calibrate the NMR system using a lOcc 3wt% KC1 brine solution and apply background corrections. This disclosure will record the magnetization decay until a minimum signal-to-noise ratio (SNR) of 100 is achieved. This disclosure will then invert the magnetization decay signal to NMR T2 distribution using Lawson and Hanson’ s (LH) nonnegative least square regression approach (Lawson and Hanson 1995; Aster et al. 2005). This disclosure will use both gravimetric and NMR measurements to track the changes in the volume of injected brine and the saturation levels in the samples.

[0184] Vacuum Saturation and Spontaneous Imbibition Process for Comparison of Saturation Efficacy

[0185] This disclosure will saturate the samples using vacuum saturation and spontaneous imbibition methods to compare the results of saturation levels achieved using different saturation processes. In the case of the vacuum saturation process, this disclosure will place the rock sample in a sealed chamber, which is then vacuumed for 24 hours. Next, this disclosure will inject the brine solution (3wt% KC1 brine) into the vacuumed chamber so that the sample is submerged in the brine. This disclosure will vacuum the chamber again and maintain the vacuum pressure. This disclosure weighs the samples before and after the saturation process to record the volume of injected brine into the samples. This disclosure will also make NMR measurements before and after the saturation process. In the case of the spontaneous imbibition process, this disclosure will place the samples in a sealed glass container along with the brine solution (3wt% KC1 brine). The sealed glass container prevents any evaporation of the brine solution, which is required for avoiding any change in salt concentration. This disclosure will make gravimetric and NMR measurements before and after the saturation process.

[0186] Results

[0187] This disclosure used a whole-core sample taken from the Lower Eagle Formation for the analysis. The Lower Eagle Formation is a predominantly organic -rich mudrock formation with the dominant presence of quartz and calcite. This disclosure cut two irregular- shaped samples from the whole-core samples, named Sample 1 and Sample 2. This disclosure also cored four cylindrical plug samples (Samples 3, 4, 5, and 6), each with adiameter of 1.5 inches. The cylindrical plug samples were cored along the formation's horizontal bedding. This disclosure modified Sample 4 into a hollow cylindrical core sample with the hollowed out diameter being 0.5 inches along the length of the core sample. Samples 3, 4, 5, and 6 have been documented in a previous publication by Dash and Heidari (2024). This disclosure will bring the results of these samples for comparison. Figure 20A - 20C shows the 3D rendition of the irregular- shaped Samples 1 and 2, and the regular cylindricalshaped Sample 3.

[0188] Table 1 of Figure 19 summarizes the properties of the samples documented in this paper.

[0189] Sample 1: Irregular- shaped Sample, Enhanced Saturation

[0190] Figure 21 showcases the volume of injected brine into Sample 1 over time. The volume of injected brine is estimated using gravimetric measurements. The initial pressure applied on the piston to saturate the sample was 1000 psi, which was then increased to 1500 psi. Increasing the pressure to 1500 psi increased the volume of injected brine before reaching an asymptotic value. The volume of injected brine was normalized to water saturation using the estimated pore volume of the sample. Figure 22 shows the volume of injected brine into Sample 1 over time, estimated using NMR measurements. The water saturation level, monitored using gravimetric measurements, increased to 37%, 42%, and 43% at the end of days 1, 2, and 3, respectively. The water saturation level, monitored using NMR measurements, increased to 41%, 44%, and 47% at the end of days 1, 2, and 3, respectively.

[0191] Sample 2: Irregular- shaped Sample, Enhanced Saturation

[0192] Figure 23 shows the volume of injected brine into Sample 2 over time, which was estimated using gravimetric and NMR measurements. Sample 2 was initially saturated using the vacuum saturation process for 3 days. The water saturation increased to 37% and plateaued after 3 days. Sample 2 was then saturated using the developed technique. The water saturation increased to 65% at 1000 psi pressure and 68% at 1500 psi pressure.

[0193] Sample 3: Regular- shaped Sample, Enhanced Saturation

[0194] Figure 24 shows the volume of injected brine into Sample 3 over time, which was estimated using gravimetric and NMR measurements. The initial pressure applied on the piston to saturate the sample was 1000 psi, which was then increased to 1500 psi. The water saturation levels, monitored using gravimetric measurements, increased to 45%, 60%, and69% at the end of days 1, 2, and 3, respectively. The water saturation levels, monitored using NMR measurements, increased to 40%, 57%, and 66% at the end of days 1, 2, and 3, respectively.

[0195] Sample 4: Hollowed Core Sample, Enhanced Saturation

[0196] Figure 25 shows the volume of injected brine into hollowed Sample 4 over time, which was estimated using gravimetric and NMR measurements. The water saturation level, monitored using gravimetric measurements, increased to 33%, 47%, and 54% at the end of days 1, 2, and 3, respectively. The water saturation level, monitored using NMR measurements, increased to 36%, 51%, and 61% at the end of days 1, 2, and 3, respectively.

[0197] Sample 5: Regular- shaped Sample, Spontaneous Imbibition

[0198] Sample 5 was saturated using the spontaneous imbibition process. The water saturation level achieved for Sample 5 was 13% and 18% after 3 and 7 days of saturation, respectively. The water saturation was estimated using NMR measurements. Figure 26 shows the volume of injected brine into Sample 5 over time, which was estimated using gravimetric and NMR measurements.

[0199] Sample 6: Regular- shaped Sample, Vacuum Saturation

[0200] Sample 6 was saturated using the vacuum saturation process. Figure 27 shows the volume of injected brine into Sample 6 over time, which was estimated using gravimetric and NMR measurements. The water saturation level achieved for Sample 6 was 15% and 25% after 3 and 7 days of saturation, respectively. The water saturation was estimated using NMR measurements.

[0201] Figure 28 shows the time taken by different saturation processes, such as the developed saturation technique, spontaneous imbibition process, and vacuum saturation process, to reach a 20% water saturation level using brine as the saturating fluid. Sample 1 took 3 hours to reach a water saturation level of 20% using the introduced saturation method. Sample 2 took 24 hours to reach the same water saturation level using the vacuum saturation process. However, in the case of Sample 2, the water saturation value plateaued at 37%, and further saturation of the sample was possible after using the introduced saturation method. Samples 3 and 4 reached a water saturation level of 20% within 2 hours of saturation process using the introduced saturation method. Sample 5 never reached a water saturation level of 20%. For the case of Sample 6, it took 120 hours to reach a water saturation level of 20% using the vacuum saturation process.

[0202] The maximum water saturation level achieved using the developed technique was 43% and 66% for Samples 1 and 2, respectively. Sample 3 reached a maximum water saturation level of 66% using the introduced saturation method after 3 days of saturation. Similarly, Sample 4 reached a maximum water saturation level of 55% using the introduced saturation method. The maximum water saturation level achieved using the spontaneous imbibition process alone was 13% for Sample 5, and the vacuum saturation process alone was 21% for Sample 6. The aforementioned volumes are estimated using gravimetric measurements.

[0203] This disclosure developed a new saturation method for irregular- shaped rock samples for the purpose of fast and reliable saturation process. This disclosure will compared water saturation results against conventional saturation techniques, such as vacuum saturation and spontaneous imbibition methods. The maximum saturation level achieved for an irregular- shaped rock sample was 47% for Sample 1 and 68% for Sample 2 using the introduced method. The developed technique also demonstrated that a water saturation level of 45% - 60% can be achieved in 3 days compared to a 20% - 30% water saturation level in 7 days in the case of conventional saturation processes.

[0204] The novelties of the developed saturation method include but are not limited to saturating tight rock samples with brine can be performed in shorter time intervals compared to conventional saturation processes such as vacuum saturation and spontaneous imbibition processes; the introduced method uses less expensive and specialized equipment compared to methods such as ultra-high-speed centrifuge; the process of saturating the rock samples using the new method has minimal impacts on the properties of the rock samples compared to methods such as forced imbibition; the introduced saturation process has more control over the different water saturation levels that can be achieved, which can be beneficial in making saturation-dependent petrophysical measurements such as relative permeability.

[0205] Results demonstrated that the shape of the rock sample has minimal impact on the water saturation level, which can be achieved using the developed method. This can result in using irregular- shaped rock samples such as broken core samples, cuttings, and outcrop samples for saturation and further making saturation dependent measurements. The successful use of such irregular- shaped samples for laboratory measurements can save money and reduce the wastage of these samples. In the case of organic -rich mudrock samples, coring a perfectly shaped sample is difficult. The coring process can fracture the samples, break up the samples. Cuttings can also be beneficial as they are often discarded without much use.The authors believe that the developed saturation method has the potential to provide a universal technique for saturating rock samples in a fast, uniform, and reliable way. The introduced method can be invariably applied to tight and conventional rock samples. It can also be applied to perfectly- shaped core samples and irregular- shaped rock samples.

[0206] Acronyms

[0207] CT = Computed Tomography

[0208] LH = Lawson and Hanson

[0209] NMR = Nuclear Magnetic Resonance

[0210] SNR = Signal-to-Noise Rati

[0211] Nomenclature

[0212] Tn = transverse or spin-spin relaxation, ms

[0213] Vi= volume of injected brine at z* step, cc

[0214] VP= connected pore volume, cc

[0215] s = saturation experiment threshold, %

[0216] FIG. 29 is a computer architecture diagram showing a computing system capable of implementing aspects of the present disclosure in accordance with one or more embodiments described herein. A computer 300 may be configured to perform one or more specific steps of a method and / or specific functions for a system. The computer may be configured to perform one or more functions associated with embodiments illustrated in one or more of the figures herein. For example, the computer 300 may be configured to perform aspects described herein for implementing the pulse sequences shown and for various aspects of magnetic resonance imaging and related signal and temperature monitoring shown in the figures. It should be appreciated that the computer 300 may be implemented within a single computing device or a computing system formed with multiple connected computing devices. The computer 300 may be configured to perform various distributed computing tasks, in which processing and / or storage resources may be distributed among the multiple devices.

[0217] As shown, the computer 300 includes a processing unit 302 (“CPU”), a system memory 304, and a system bus 306 that couples the memory 304 to the CPU 302. The computer 300 further includes a mass storage device 312 for storing program modules 314. The program modules 314 may be operable to perform functions associated with one or moreembodiments described herein. For example, when executed, the program modules can cause one or more medical imaging devices, localized energy producing devices, and / or computers to perform functions described herein for implementing the pulse sequence shown in FIG. 3, the method shown in FIG. 1, and for various aspects of magnetic resonance imaging and related signal and temperature monitoring and analysis shown in the figures herein. The program modules 314 may include an imaging application 318 for performing data acquisition and / or processing functions as described herein, for example to acquire and / or process image data corresponding to magnetic resonance imaging of an area of interest. The computer 300 can include a data store 320 for storing data that may include imaging-related data 322 such as acquired data from the implementation of magnetic resonance imaging pulse sequences in accordance with various embodiments of the present disclosure.

[0218] The mass storage device 312 is connected to the CPU 302 through a mass storage controller (not shown) connected to the bus 306. The mass storage device 312 and its associated computer- storage media provide non-volatile storage for the computer 300.Although the description of computer-storage media contained herein refers to a mass storage device, such as a hard disk, it should be appreciated by those skilled in the art that computerstorage media can be any available computer storage media that can be accessed by the computer 300.

[0219] By way of example and not limitation, computer storage media (also referred to herein as “computer-readable storage medium” or “computer-readable storage media”) may include volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer- storage instructions, data structures, program modules, or other data. For example, computer storage media includes, but is not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, digital versatile disks (“DVD”), HD-DVD, BLU-RAY, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computer 300. “Computer storage media”, “computer-readable storage medium” or “computer-readable storage media” as described herein do not include transitory signals.

[0220] According to various embodiments, the computer 300 may operate in a networked environment using connections to other local or remote computers through a network 316 via a network interface unit 310 connected to the bus 306. The networkinterface unit 310 may facilitate connection of the computing device inputs and outputs to one or more suitable networks and / or connections such as a local area network (LAN), a wide area network (WAN), the Internet, a cellular network, a radio frequency (RF) network, a Bluetooth-enabled network, a Wi-Fi enabled network, a satellite-based network, or other wired and / or wireless networks for communication with external devices and / or systems.

[0221] The computer 300 may also include an input / output controller 308 for receiving and processing input from any of a number of input devices. Input devices may include one or more of keyboards, mice, stylus, touchscreens, microphones, audio capturing devices, and image / video capturing devices. An end user may utilize the input devices to interact with a user interface, for example a graphical user interface, for managing various functions performed by the computer 300. The input / output controller 308 may be configured to manage output to one or more display devices for displaying visually representations of data, such as display monitors / screens that are integral with other components of the computer 300 or are remote displays.

[0222] The bus 306 may enable the processing unit 302 to read code and / or data to / from the mass storage device 312 or other computer-storage media. The computer-storage media may represent apparatus in the form of storage elements that are implemented using any suitable technology, including but not limited to semiconductors, magnetic materials, optics, or the like. The computer-storage media may represent memory components, whether characterized as RAM, ROM, flash, or other types of technology. The computer storage media may also represent secondary storage, whether implemented as hard drives or otherwise. Hard drive implementations may be characterized as solid state, or may include rotating media storing magnetically-encoded information. The program modules 314, which include the imaging application 318, may include instructions that, when loaded into the processing unit 302 and executed, cause the computer 300 to provide functions associated with one or more embodiments illustrated in the figures. The program modules 314 may also provide various tools or techniques by which the computer 300 may participate within the overall systems or operating environments using the components, flows, and data structures discussed throughout this description.

[0223] Example Embodiments

[0224] In a non-limiting embodiment, a computer implemented method of calculating saturation dependent permeability of a core sample having pores therein includes estimatingpore volume 225 of the core sample prior to saturation 290; estimating permeability of the core sample prior to saturation 365, 370; saturating the core sample within a chamber of a sample cell 290; while saturating the core sample, iteratively measuring permeability of the core sample at selected times over a time interval; while saturating the core sample, iteratively measuring saturation levels of the core sample at the selected times; and saving, in computer memory 300, paired data comprising values for a permeability of the core sample and saturation level of the core sample at the selected times.

[0225] In another embodiment, estimating pore volume prior to saturation includes using computed tomography (CT) scans 380 to estimate bulk volume of the core sample.

[0226] In another embodiment, estimating pore volume prior to saturation includes gravimetric measurements 225.

[0227] In another embodiment, estimating pore volume prior to saturation further includes nuclear magnetic resonance (NMR) measurements 215.

[0228] In another embodiment, estimating pore volume prior to saturation further includes calculating grain volumes of the core samples with a helium porosimeter.

[0229] In another embodiment, estimating pore volume prior to saturation includes selecting an estimated pore volume from gravimetric measurements of the core sample, NMR measurements of the core sample, grain volumes of the core samples, or an average of the gravimetric measurements of the core sample, NMR measurements of the core sample, and grain volumes of the core samples, or a statistically weighted combination of the gravimetric measurements of the core sample, NMR measurements of the core sample, and grain volumes of the core samples relative to a bulk volume of the core sample.

[0230] In another embodiment, saturating the core sample includes establishing saturation fluid pressure within a chamber that holds the core sample and a saturation fluid therein, wherein a saturation fluid pressure is exerted by the saturation fluid on surfaces within the core sample and on exterior surfaces of the core sample 275.

[0231] In another embodiment, the method further includes maintaining the saturation fluid pressure with a syringe pump moving a hydraulic fluid onto a piston sealing the chamber.

[0232] In another embodiment, saturating the core sample includes maintaining the saturation fluid pressure at 2500 psi.

[0233] In another embodiment, saturating the core sample includes maintaining the saturation fluid pressure at a value from 1500 psi to 2500 psi, inclusive.

[0234] In another embodiment, the saturation fluid includes a mixture comprising potassium chloride brine or any other type of brine.

[0235] In another embodiment, the hydraulic fluid includes a mixture comprising deionized water providing the fluid pressure with a syringe pump.

[0236] In another embodiment, iteratively measuring permeability of the core sample while saturating 270, 272, 274 the core sample includes, at selected times up to a stop value, iteratively measure permeability of the core sample with respective pressure decay measurements; and at the selected times up to the stop value, numerically calculate, with a computer, permeability of the core sample by solving a pressure diffusion equation.

[0237] In another embodiment, the core sample includes irregularly shaped edges, and numerically calculating the pressure diffusion equation comprises obtaining a geometric profile of the core sample with an imaging device.

[0238] In another embodiment, the method includes selecting the permeability value from a measured permeability and a numerically calculated permeability, averages thereof, or statistically weighted combinations thereof.

[0239] In another embodiment, the method further includes using a computer for numerically solving a pressure diffusion equation for the core sample with a finite difference method or a finite element method with a respective pressure.

[0240] In another embodiment, the method further includes using at least one pressure transducer and measuring a respective pressure at the selected times and software stored on the computer to minimize the difference between the numerically estimated and measured pressure values to determine permeability and / or relative permeability of the core sample.

[0241] In another embodiment, iteratively measuring saturation level of the core sample further includes performing gravimetric measurements on the core sample at the selected times and performing NMR measurements of the core sample at the selected times until a stop criterion is met.

[0242] In another embodiment, iteratively measuring saturation level of the core sample further includes averaging the gravimetric measurements and the NMR measurementsor selected a saturation level of the core sample from statistically weighted combinations of the gravimetric measurements and the NMR measurements.

[0243] In another non-limiting embodiment, a method of saturating a core sample for saturation-dependent measurements includes forming a cavity within the core sample, wherein the cavity provides a saturation fluid with access to surfaces within the core sample; establishing saturation fluid pressure within a chamber that holds the core sample and the saturation fluid therein, wherein the saturation fluid pressure is exerted by the saturation fluid on the surfaces within the core sample and on exterior surfaces of the core sample; and maintaining the saturation fluid pressure with a syringe pump moving a hydraulic fluid onto a piston sealing the chamber.

[0244] In another embodiment, the cavity extends through opposite surfaces of the core sample.

[0245] In another embodiment, the cavity extends through an entire length of the core sample.

[0246] In another embodiment, the cavity comprises a bored hole extending through the core sample.

[0247] In another embodiment, the bored hole comprises a consistent diameter through the core sample.

[0248] In another embodiment, the bored hole comprises a plurality of diameters through the core sample.

[0249] In another embodiment, the saturation fluid comprises a mixture comprising potassium chloride brine or any other type of brine.

[0250] In another embodiment, the hydraulic fluid comprises a mixture comprising deionized water providing the fluid pressure with a syringe pump.

[0251] In another embodiment, the method further includes calculating a saturation of the core sample with nuclear magnetic resonance spectroscopy.

[0252] In another embodiment, a system for saturating a core sample for saturationdependent measurements includes a vessel comprising an inner surface defining a receptacle that receives and holds a core sample and a saturating fluid, the vessel defining an opening into the receptacle at a first end of the vessel; a piston configured to fit within the opening and the receptacle and so dimensioned as to travel along the inner surface to seal the vessel;and a pump directing hydraulic fluid to the piston, wherein the pump pushes the hydraulic fluid against the piston to maintain a saturation pressure within the receptacle to accommodate the saturating fluid filling pore throats within the core sample.

[0253] In another embodiment, the piston further includes sealing elements connected to the piston and configured to engage the inner surface of the vessel to seal the receptacle.

[0254] In another embodiment, the piston travels to a position along the inner surface of the vessel to divide the vessel into a lower chamber and an upper chamber, wherein the lower chamber holds the saturating fluid and the core sample, and the upper chamber holds the hydraulic fluid applying pressure to the piston.

[0255] In another embodiment, the system includes a lid for the vessel that defines an inlet for the hydraulic fluid and to close the upper chamber.

[0256] In one non-limiting example, the hydraulic pressure is 2500 psi.

[0257] In another non-limiting example, the hydraulic pressure is between 1500 psi and 2500 psi.

[0258] In another non-limiting example, the core sample comprises a shape and the receptacle comprises a corresponding shape to exert the saturation pressure on the core sample with an effective saturation of exposed surfaces on the core sample.

[0259] In another non-limiting example, the piston is configured to travel to a plurality of positions along the inner surface by being pushed by the hydraulic fluid.

[0260] In another non-limiting embodiment, a system for saturating a core sample for saturation-dependent measurements and determining permeability and / or relative permeability, includes a vessel having an inner surface defining a receptacle that receives and holds a core sample and a saturating fluid, the vessel defining an opening into the receptacle at a first end of the vessel; a piston configured to fit within the opening and the receptacle and so dimensioned as to travel along the inner surface to seal the vessel; and a pump directing hydraulic fluid to the piston, wherein the pump pushes the hydraulic fluid against the piston to maintain a saturation pressure within the receptacle to accommodate the saturating fluid filling pore throats within the core sample before pumping the saturating fluid out of the vessel; a vacuum pump applying a vacuum to the vessel; a reference gas cell holding a reference gas at a pressure; at least one valve controlling transferring the reference gas into the vessel at the pressure.

[0261] In another embodiment, the system includes a computer numerically solving a pressure diffusion equation for the core sample with a finite difference method or a finite element method with a respective pressure.

[0262] In another embodiment, at least one pressure transducer is positioned for measuring the respective pressure and software is stored on the computer to minimize the difference between the numerically estimated and measured pressure values to determine permeability and / or relative permeability of the core sample.

[0263] CONCLUSION

[0264] The specific configurations, choice of materials and the size and shape of various elements can be varied according to particular design specifications or constraints requiring a system or method constructed according to the principles of the present disclosure. Such changes are intended to be embraced within the scope of the present disclosure. The presently disclosed embodiments, therefore, are considered in all respects to be illustrative and not restrictive. The patentable scope of certain embodiments of the present disclosure is indicated by the appended claims, rather than the foregoing description.

[0265] REFERENCES

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Claims

CLAIMS1. A computer implemented method of calculating saturation dependent permeability of a core sample having pores therein, the method comprising: estimating pore volume of the core sample prior to saturation; estimating permeability of the core sample prior to saturation; saturating the core sample within a chamber of a sample cell; while saturating the core sample, iteratively measuring permeability of the core sample at selected times over a time interval; while saturating the core sample, iteratively measuring saturation levels of the core sample at the selected times; and save, in computer memory, paired data comprising values for a permeability of the core sample and saturation level of the core sample at the selected times.

2. The computer implemented method of Claim 1, wherein estimating pore volume prior to saturation comprises using computed tomography (CT) scans to estimate bulk volume of the core sample.

3. The computer implemented method of Claim 1, wherein estimating pore volume prior to saturation comprises gravimetric measurements.

4. The computer implemented method of Claim 3, wherein estimating pore volume prior to saturation further comprises nuclear magnetic resonance (NMR) measurements.

5. The computer implemented method of Claim 3, wherein estimating pore volume prior to saturation further comprises calculating grain volumes of the core samples with a helium porisometer.

6. The computer implemented method of Claim 1, wherein estimating pore volume prior to saturation comprises selecting an estimated pore volume from gravimetric measurements of the core sample, NMR measurements of the core sample, grain volumes of the core samples, or an average of the gravimetric measurements of the core sample, NMR measurements of the core sample, and grain volumes of the core samples, or a statistically weighted combination of the gravimetric measurements of the core sample, NMR measurements of the core sample, and grain volumes of the core samples relative to a bulk volume of the core sample.

7. The computer implemented method of Claim 1, wherein saturating the core sample comprises establishing saturation fluid pressure within a chamber that holds the core sample and a saturation fluid therein, wherein a saturation fluid pressure is exerted by the saturation fluid on surfaces within the core sample and on exterior surfaces of the core sample.

8. The computer implemented method of Claim 7, further comprising maintaining the saturation fluid pressure with a syringe pump moving a hydraulic fluid onto a piston sealing the chamber.

9. The computer implemented method of Claim 8, wherein saturating the core sample comprises maintaining the saturation fluid pressure at 2500 psi.

10. The computer implemented method of Claim 8, wherein saturating the core sample comprises maintaining the saturation fluid pressure at a value from 1500 psi to 2500 psi, inclusive.

11. The computer implemented method of Claim 8, wherein the saturation fluid comprises a mixture comprising potassium chloride brine or any other type of brine.

12. The computer implemented method of Claim 8, wherein the hydraulic fluid comprises a mixture comprising deionized water providing the fluid pressure with a syringe pump.

13. The computer implemented method of Claim 1, wherein iteratively measuring permeability of the core sample while saturating the core sample comprises: at selected times up to a stop value, iteratively measure permeability of the core sample with respective pressure decay measurements; and at the selected times up to a stop value, numerically calculate, with a computer, permeability of the core sample by solving a pressure diffusion equation.

14. The computer implemented method of Claim 13, wherein the core sample comprises irregularly shaped edges, and numerically calculating the pressure diffusion equation comprises obtaining a geometric profile of the core sample with an imaging device.

15. The computer implemented method of Claim 13, selecting the permeability value from a measured permeability and a numerically calculated permeability, averages thereof, or statistically weighted combinations thereof.

16. The computer implemented method of Claim 13, further comprising a computer numerically solving a pressure diffusion equation for the core sample with a finite difference method or a finite element method with a respective pressure.

17. The method of Claim 13, further comprising using at least one pressure transducer and measuring a respective pressure at the selected times and software stored on the computer to minimize the difference between the numerically estimated and measured pressure values to determine permeability and / or relative permeability of the core sample.

18. The method of Claim 13, wherein iteratively measuring saturation level of the core sample comprises performing gravimetric measurements on the core sample at the selected times and performing NMR measurements of the core sample at the selected times until a stop criterion is met.

19. The method of Claim 18, wherein iteratively measuring saturation level of the core sample comprises averaging the gravimetric measurements and the NMR measurements or selected a saturation level of the core sample from statistically weighted combinations of the gravimetric measurements and the NMR measurements.

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