Characterization of formation fractures based on acoustic and pressure decay after shut-in using three-zone model

Abstract

A method for determining the characteristics of hydraulic fracturing based on downhole pressure measurements taken after stopping the pumping of fracturing fluid into the well (shutdown) includes determining a first time after shutdown, where the pressure drop is measured to be caused by fluid leakage in the fracture. A second time after shutdown is determined, where the pressure drop is caused by fluid leakage, fracture growth, and fluid pressure equilibrium in the fracture. A third time after shutdown is determined, where the pressure drop is caused by fluid leakage, fracture growth, fluid pressure equilibrium in the fracture, and pressure drop in the near-wellbore region. The determined values ​​for fluid efficiency, minimum stress, and net pressure are such that the calculated pressure relative to time matches the measured pressure values ​​within predetermined thresholds.

Description

Background Technology

[0001] Pressure decay analysis is sometimes used to analyze hydraulic fracturing in subsurface formations penetrated by a well. Pressure decay analysis captures pressure data over a period of time after fluid injection into the formation. This fluid injection can be hydraulic fracturing, where proppant is injected to maintain fracture propagation, thereby allowing for subsequent increases in hydrocarbon production. Various models and methods are known in the prior art. This invention significantly improves upon the prior art by considering the separate contribution of the near-borehole zone to pressure decay and by using direct acoustic measurements of the conductivity of the near-borehole zone to constrain fracture and pressure decay models. This allows for a more accurate determination of the fracture system and its characteristics. Summary of the Invention

[0002] According to one aspect of this disclosure, a method for determining the characteristics of hydraulic fracturing based on downhole pressure measurements taken after stopping the pumping of fracturing fluid into the well (shutdown) includes determining a first time after shutdown, wherein the pressure reduction is caused by fluid leakage in the fracture. A second time after shutdown is determined, wherein the pressure reduction is caused by fluid leakage, fracture growth, and fluid pressure balancing in the fracture. A third time after shutdown is determined, wherein the pressure reduction is caused by fluid leakage, fracture growth, fluid pressure balancing in the fracture, and pressure drop in the near-wellbore region. The determined values ​​of fluid efficiency, minimum stress, and net pressure are such that the calculated pressure relative to time matches the measured pressure values ​​within predetermined thresholds. Based on the causes of pressure reduction in a segment, a time-dependent pressure is calculated, the segment corresponding to: (i) the third and second times, (ii) the second and first times, and (iii) after the first time.

[0003] According to another aspect of this disclosure, a computer program is stored in a non-transitory computer-readable medium and includes operable logic that causes the computer to perform operations corresponding to the methods of the preceding aspect of this disclosure.

[0004] In some embodiments, the pressure calculation that begins at the first moment includes calculating the Carter leakoff.

[0005] In some embodiments, the pressure of the calculation that begins at a second time and ends at a third time includes computation.

[0006]

[0007] Where ξ f = Local efficiency or fracture growth ratio at shut-in, η av = Average efficiency from the start of pumping fluid to well shut-in, p av = Average net pressure in the crack, p * = Crack propagation pressure, p-n = Average net pressure, p n 0 = Initial net pressure, t inj =Injection time, t =Time for pressure calculation, and Smin -Minimum principal stress.

[0008] In some embodiments, the pressure calculated from the start of the third time to the end of the second time includes calculating Darcy equation flow for an axisymmetric biplane crack with a cylindrical cross-section.

[0009] In some embodiments, the pressure calculation from the start of the third time period to the end of the second time period includes analyzing reflections in pressure or pressure-time derivative measurements in response to acoustic pulses emitted into the well, thereby calculating near-field conductivity. The acoustic pulses induce tubular waves in the well. The near-field conductivity index is used to limit the calculation of near-wellbore pressure drop.

[0010] Some embodiments also include using determined values ​​for fluid efficiency, minimum stress, and net pressure, and values ​​for Young's modulus, Poisson's ratio, fracturing fluid viscosity, fracturing fluid pumping volume, pumped fracturing fluid volume fraction, and the number of well perforation clusters through which the pumped fracturing fluid passes, to determine fracture length, width, height, and leakage parameters.

[0011] In some embodiments, the determined length, width, height, and leakage parameters are used to estimate the fluid productivity of the fracturing process phases in and throughout the well.

[0012] In some embodiments, determining the length, width, and height of the crack includes using a Perkins-Kern-Nordgren model of the crack geometry.

[0013] In some embodiments, the third time occurs after the water hammer caused by the cessation of pumping has ended.

[0014] In some embodiments, the second time is determined when the rate of change of the pressure measurement value with respect to time is less than a predetermined threshold.

[0015] In some embodiments, a first time is determined when the pressure measurement value is lower than the fracturing pressure of the rock formation into which the fracturing fluid is pumped.

[0016] In some embodiments, the determined minimum stress is also used to estimate the fluid pressure in the formation penetrated by the fracture.

[0017] In some embodiments, efficiency includes the fraction of fracture volume relative to the volume of fracturing fluid pumped into the fracture.

[0018] In some embodiments, the method also includes determining the fracture conductivity relative to time after well shut-in.

[0019] In some embodiments, the method further includes determining the conductivity of the proppant filling when the conductivity of the fracture stops changing over time after the well is shut in.

[0020] In some embodiments, the method further includes changing at least one of the following: the viscosity of the fracturing fluid, the pumping volume of the fracturing fluid, the volume fraction of the pumped fracturing fluid, or the concentration of proppant in the fracturing fluid, in order to pump the fracturing fluid to different stages or different wells.

[0021] Other aspects and potential advantages of this disclosure will become apparent from the following description and claims. Attached Figure Description

[0022] Figure 1A Exemplary embodiments of data acquisition and recording used in conjunction with the methods according to this disclosure are shown.

[0023] Figure 1 illustrates the flow of fluid into the fracture during hydraulic fracturing pumping and shut-in.

[0024] Figure 2 Three distinct hydraulic zones are shown as the distance from the wellbore increases.

[0025] Figure 3 The pressure decay after shut-in is shown as decomposed into three main segments.

[0026] Figure 4 Some assumptions used in the analysis according to this disclosure are shown during staged pumping.

[0027] Figure 5 The crack propagation ratio ξ is shown. f and average efficiency η f The relationship between them.

[0028] Figure 6 The geometry of the PKN (Perkins-Kern-Nordgren, see Perkins and Kern (1961); Nordgren (1972)) crack is shown.

[0029] Figure 7 The pressure distribution and fluid hysteresis in the fracture are shown (see Vahab and Khalili, 2001).

[0030] Figure 8 The relationship between pressures in the crack is shown.

[0031] Figure 9A flowchart is shown of the process of implementing a three-segment model to obtain crack characteristics; a flowchart is also shown (optional) of implementing a three-segment model to obtain crack characteristics by calculating the NWB pressure drop using acoustic measurement limitation (NFCI).

[0032] Figure 10 The calculation results for p* are shown.

[0033] Figure 11 It shows β s Instances of values ​​(see Economides and Nolte, 1983).

[0034] Figure 12 The diagram shows how, using the PKN assumption, the pressure in the fracture is simplified to a function of the wellbore distance.

[0035] Figure 13 The volume V that should be moved to achieve equilibrium is shown. * .

[0036] Figure 14 The volumetric flow rate variation with fracture location (x) is shown in three different time periods: during injection, shortly after shut-in, and longer after shut-in.

[0037] Figure 15 The possible pressure distributions when the NWB pressure drop is large or small are shown (see Weijers et al., 1994; Weijers et al., 2000).

[0038] Figure 16 Two extreme cases of near-bore width and permeability as a function of pressure are shown (see Weijers et al., 2004; Weng et al., 1993).

[0039] Figure 17 p is shown NWBPL effect.

[0040] Figure 18 The stress state of the rock in the strata is shown (see Economides and Nolte, 1983).

[0041] Figure 19 The relationship between minimum stress, reservoir pressure, and Poisson's ratio is shown.

[0042] Figure 20 The diagram shows the NWB voltage drop and the NWB cylindrical cross-section.

[0043] Figure 21 The graph shows the pressure decay after well shut-in.

[0044] Figure 22A block diagram is shown illustrating the use of acoustic measurements and pressure decay measurements to estimate fracture size after well shut-in.

[0045] Definitions used in the following description

[0046] The following are the names, symbols, and abbreviations arranged alphabetically for detailed explanation below:

[0047] • A = Surface area (For an ellipse, A = πHw / 4)

[0048] ·E'=E / (1-ν)

[0049] E = Young's modulus

[0050] ·f T =Total friction force

[0051] ·f 管道 = Pipe friction

[0052] ·f perf =Perforation friction

[0053] H = Crack height

[0054] ·k = permeability (for an elliptical cross section, k = w) 2 / 16)

[0055] ·L = Crack length

[0056] ·N 簇 =Number of perforated clusters in each stage of well casing or liner

[0057] ·Q inj =Average injection volume ratio

[0058] ·q T = Total volume ratio entering the crack

[0059] ·q l =Leakage volume ratio

[0060] ·q fg =Water loss caused by crack growth and natural cracks

[0061] ·q fc =Volume fraction related to crack compressibility coefficient

[0062] ·q NWB =Volume fraction from NWB to FF region

[0063] ·q = fluid volume fraction in the crack

[0064] ·ξ f = Local efficiency or fracture growth ratio at shut-in (η) f =q fg / q T )·ηav = Average efficiency from pumping start to well shut-in (η av =V fr / V inj )·p M =Net pressure at the crack

[0065] ·p w =Pressure near the wellbore and fracture

[0066] ·p ave = Average net pressure in the crack

[0067] ·p n =Net pressure

[0068] ·p- n = Average net pressure

[0069] ·p n M =Net pressure at the crack

[0070] ·p 尖端 = Pressure at the crack tip

[0071] ·p NWBPL = Pressure loss near the wellbore

[0072] ·p * = Crack propagation pressure (below this pressure, cracks will not propagate)

[0073] ·p n 0 = Initial net pressure (assuming infinite permeability)

[0074] ·p f = Total pressure in the crack (assuming infinite permeability)

[0075] ·β s =(p- n ) / (p n M )

[0076] ·t inj =Injection time (pumping phase)

[0077] •t = decay time (calculated from the time the well is shut in)

[0078] ·S min =Minimum principal stress

[0079] μ = fluid viscosity

[0080] ·ν=Poisson's ratio

[0081] ·β = compressibility factor

[0082] ·t mat =Time to match the pressure fitting curve with the pressure data points

[0083] ·u leak =Leakage rate per unit length

[0084] ·V fr = Crack volume (volume penetrated by proppant: main crack and large natural crack)

[0085] ·V inj =Injected fluid volume (V) inj =Q inj t inj )

[0086] ·w = crack width (for cracks where l is much larger than H, w = (2H / E')p) n )

[0087] NFCI = Near-field Connectivity (Conductivity) Index Detailed Implementation

[0088] This disclosure relates to the determination of fracture characteristics, such as fracture length, width, height, fracture conductivity, formation fluid (pore) pressure, and reservoir / completion quality. Input data used for determination can be obtained from available data measured during the pumping phase of the hydraulic fracturing process, such as fracturing fluid injection rate, injection volume, fracturing fluid composition, etc. Other data may include measured pressures after fracturing pumping has ended, which gradually decrease after well shut-in (after fracturing fluid pumping has ended).

[0089] Figure 1AThis is a schematic diagram of an exemplary well data acquisition system, which may be used in some embodiments. System 100 includes well-related components, including a fluid pump 101, sensors (e.g., hydrophones or pressure sensors 102), data acquisition and processing equipment 103, a casing well or open well 104, a plug or wellbore bottom 106, a fracture network 107, and a perforation 108. Nearby wells 109 (vertical or horizontal) may exist in the relevant area. Water hammer pulses 105 may be generated by pump 101, for example, by changing the pumping rate, or pressure pulses may be generated by other devices, such as a pressure pulse generator 110. Some pressure pulses are inherently generated as part of the fluid pumping. Since no additional pressure pulse source is required, such pulses can be considered "passive" and are generally considered a preferred metric. The pressure pulses will propagate along the well and reflect. Non-invasive sensors, such as pressure sensors, accelerometers, and hydrophones, can be positioned at or near the wellhead (e.g., the wellhead) to continuously measure pressure, pressure-time derivative, and / or particle motion data before, during, and after pumping during the fracturing process. Similar measurements can be performed at other points along the well and surface equipment where pressure pulses or pumping noise can be detected.

[0090] Figure 1B The diagram illustrates typical fluid flow (generally designated "q" with varying subscripts) during and after a 111-pump hydraulic fracturing procedure, or more broadly, the injection of any fluid into a subsurface fracture system. During injection, the flow velocity q... inj =q T >0. After the injection stops, q inj =0 and qT~0 (no fluid enters the crack, fluid only leaks).

[0091] In this example, signals such as pressure (p) and pressure-time derivative (dp / dt) can be recorded and processed according to the detailed description below. Pressure pulses can induce tubular waves in the well; pressure or pressure-time derivative signals can be processed to extract available resonances and other events, thereby detecting anomalies in fractured-wellbore systems. In particular, according to U.S. Patent Application No. 10,641,090 granted to Felkl et al., some pulses and their reflections can be used to determine the near-field or near-wellbore (NWB) connectivity index (NFCI).

[0092] According to the method disclosed herein, a model is used to analyze fracturing characteristics from fracturing pumping and pressure decay data, assuming that hydraulic fracturing caused by fluid pumping has three regions: 1) wellbore region, 2) near-wellbore (NWB) region and 3) far-field (FF) region. Figure 2These three regions are shown in 201, 202, and 203, respectively. In fracture analyses known in the prior art prior to this disclosure, the influence of NWB region 202 is generally ignored. However, it has been determined that NWB region 202 may have a significant impact on the initial (early) portion of pressure decay after shut-in. Note that the term "shut-in" is used in the art to refer to the time following pump shutdown (or hydraulic function equivalent) and cessation of fluid injection.

[0093] In the method according to this disclosure, the properties of the improved model used take into account that the pressure decay after initial shut-in comprises three stages, each of which can be attributed to one of three different causes of pressure decay. Figure 3 The graph shows the well pressure versus time after a phase of pumping (fracturing fluid injection) has ended. Ignoring the instantaneous water hammer after shut-in (shown by the dashed line on the far left of the graph), the subsequent pressure decay can be divided into three distinct segments. These segments are highlighted and correspond to... Figure 3 Segments 301, 302, and 303 are shown in the table. There are some based on... Figure 3 The calculated values ​​are shown by the method described. These three segments correspond to three sources of pressure decay; these sources include pressure drop after shut-in in the NWB region, pressure drop due to fracture growth, and pressure drop due to leakage. Each of the three pressure decay segments 301, 302, and 303 illustrates its respective primary pressure drop source, which contributes to pressure decay in each region. For example, segment 3 is primarily due to leakage, while segment 1 is primarily due to NWB pressure loss.

[0094] During the fracturing pumping stage, the variations in pressure and injection rate are complex. However, for the purposes of this disclosure, it can be assumed that fluid pressure and injection rate are constant during fracturing pumping and during PKN (Perkins-Kern-Nordgren, Perkins and Kern (1961); Nordgren (1972)) type fracturing growth. The PKN model is a classic two-dimensional (plane strain) fracture growth model that assumes long fracture lengths (hundreds of feet), finite but constant heights (tens to hundreds of feet), and small widths (measurable in millimeters) propagating in an infinitely homogeneous, isotropic, linear elastic formation, characterized by Young's modulus E and Poisson's ratio ν (Kovalyshen, 2010). These assumptions lead to a constant fracture height during fracture growth, with the fracture width linearly dependent on both fracture height and net pressure. In summary, the assumptions for analyzing pressure during the fracturing pumping stage are as follows: Figure 4 As shown:

[0095] 1. Throughout the entire pumping phase at 401, from start to finish, the fluid pressure remains constant;

[0096] 2. Throughout the entire pumping phase at 402, from start to finish, the fluid injection rate remained constant;

[0097] 3. Throughout the pumping process at location 403, the crack height remained constant during crack propagation; and

[0098] 4. The fracture width is linearly related to the fracture height and net pressure (the difference between fracturing fluid pressure and closure pressure), and is independent of the fracture length.

[0099] Calculate the average efficiency as a function of local efficiency.

[0100] Fluid efficiency (or simply efficiency) is the fraction of the amount of fluid present in a fracture compared to the total volume of injected fluid. Efficiency is an important parameter for determining fracture size. Typically, fracturing stages with higher efficiency have larger fracture lengths and higher net pressures. The efficiency of pumped fracturing fluid varies across different formations, and even between different fracturing stages within the same formation. This variation can be caused by a variety of factors, such as the presence of naturally formed fractures, fissures, faults, and variations in fracturing fluid injection design. Therefore, according to this disclosure, efficiency values ​​are calculated for each fracturing stage, without assuming that the efficiency is constant across all stages. This paper considers two types of efficiency: local efficiency and average efficiency. Local efficiency is the volumetric rate q of fracture growth. fg With the injected volume ratio q inj Correspondingly, it can be observed that its value is not constant during fracturing fluid injection. The average efficiency correlates the fracturing volume at the end of the pumping phase with the total injected volume of the same pumping phase, and it is a unique value for each phase. It should be mentioned that the average efficiency can be calculated by averaging the local efficiency values ​​during injection. To calculate the average efficiency, one can start with the mass conservation equation, such as... Figure 1B As shown at point 111:

[0101] q inj =q fg +q leak (1)

[0102] The crack growth ratio (local efficiency) ξ can be defined as:

[0103]

[0104] Where, q fg (t) = Crack growth volume rate Related to crack growth, and q inj =Fluid injection volume ratio Please note that ξ(t) is a function of time. Carter (1957) derived the leakage equation. The leakage equation is widely used in hydraulic fracturing modeling. The Caterpillar leakage equation is derived based on one-dimensional fluid flow in porous media, which is also an applicable assumption of this disclosure. Therefore, it is assumed that the leakage rate (1-ξ) can be calculated using the Caterpillar leakage equation:

[0105]

[0106] Among them, c leak =Carter's leakage parameter, t eq = Equivalent leakage time and crack surface area, A fs = 2HL (area of ​​one slit wing). Assume t eq =a eq t represents The result is:

[0107]

[0108]

[0109] Crack growth can be calculated as follows:

[0110]

[0111] in, It is the average crack cross section (a non-zero constant is not important, as it will cancel out in the later derivation).

[0112]

[0113]

[0114] express:

[0115]

[0116] The differential equation 9 above can be solved using the initial condition L(t=0)=0. The solution is:

[0117]

[0118] Two extreme cases can be considered: one is a very large leakage, and the other is the opposite, a very small leakage. For the case of a large leakage (c... eq If t is large (or t is large), the exponential term in equation 10 can be ignored, and the result is:

[0119]

[0120] In the second extreme case, the leakage is negligible. eq →0. In this case, the limitation is:

[0121]

[0122] Please note that both of these extreme cases are similar to those in the Nordgren derivation.

[0123] The L value at the end of the injection period can be calculated as L. f =L(t=t) f ):

[0124]

[0125] Since the crack height and crack width are constant, the average efficiency can be defined as the ratio of the crack length to the length of a leak-free crack.

[0126]

[0127] Where L f η＝1 Defined as the length of a leak-free crack, it is calculated as follows:

[0128]

[0129] The result is

[0130]

[0131] by This indicates that an expression is provided:

[0132]

[0133] t = t f The local efficiency value at that time can be calculated as follows (using equations 5, 14, and 15):

[0134]

[0135] ξ f =1-γη av (19)

[0136] therefore

[0137] γ=(1-ξ f ) / η av (20)

[0138] Substituting equation 19 into equation 17 yields the expression:

[0139]

[0140] Equation 21 cannot be solved by analytical methods, but it can be solved by numerical methods. Figure 5It shows ξ f and η av The calculation relationship between them (the solution to equation 21). Figure 5 The study also compared the effects of using Caterpillar leakage with using constant leakage (a non-time function) on ξ. f and η av The relationship between them.

[0141] Calculate the pressure distribution at the end of the pumping phase.

[0142] To calculate the pressure distribution at the end of the pumping phase, the same assumptions mentioned earlier can be used, and additionally, reference can be made to... Figure 6 Assume the crack cross-section at the end of the pumping stage is elliptical:

[0143] ξ(t=t f )=η f L(t=t) f ) = L f (twenty two)

[0144] Assuming the leakage rate is constant across the entire surface of the crack, the volume fraction within the crack can be calculated as follows:

[0145] q(x,t) f )=q inj -q leak (x, t) f ) (twenty three)

[0146] Where, q leak (x) is the sum of the leakage rate increments from the crack opening to point x. Using Caterpillar Leakage, we obtain:

[0147]

[0148] Here, t' is the time it takes for the crack front to reach a certain point in the crack and for leakage to begin. To calculate t', the length extension equation (Equation 10) can be used, and the time required to reach a specific fracture length can be calculated. However, from an analytical perspective, it is impossible to inverse Equation 10. Therefore, this calculation can be performed numerically. However, for extreme cases with large leakage volumes, the following expression can be used:

[0149]

[0150] therefore:

[0151]

[0152] At the end of the pumping phase, t = t f , and thus

[0153]

[0154] Therefore, it can be written as follows:

[0155]

[0156] Calculate t = t using the relationship described in Equation 28. f Leakage amount at time:

[0157]

[0158] The volume fraction in the crack can be written as:

[0159]

[0160] Assuming the water flow in the crack is linear, the volumetric flow rate obtained using Darcy's law is provided by the following formula:

[0161]

[0162] Where, p n Net pressure (pressure p in the crack) f With minimum principal stress p n =p f -S min (difference between them), k abs The absolute permeability (depending on the cross-sectional shape) is given by A, the cross-sectional area by μ, and the viscosity of the fracturing fluid in the fracture by k. r This is the permeability reduction factor, resulting from the influence of proppant, tortuosity, saturation, and other factors that reduce permeability. Furthermore, note that the viscosity values ​​in the cracks differ substantially from those calculated in laboratory tests. The main reasons are the effects of shear rate, proppant, and temperature on viscosity.

[0163] Because of k r Since both μ and y are unknowns, equation 31 can be rewritten as:

[0164]

[0165] To write the equation in this form, only one unknown parameter μ is needed. ap This can be expressed as apparent viscosity. Details regarding the calculation of this unknown parameter will be discussed below.

[0166] For elliptical cross-sections:

[0167]

[0168] Where w is the crack width and H is the crack height. Also based on classical theory (see Sneddon and Elliot (1946)), the width of a pressure crack can be calculated as follows:

[0169]

[0170] Where p n For clean Pressure, substituting equations 33 and 34 into equation 31, yields the expression:

[0171]

[0172]

[0173] Combining equations 23 and 35:

[0174]

[0175] Relate equation 37 to condition p n (x=0)=p M The integral yields:

[0176]

[0177] Note that p n (x=L f ) = p 尖端 Classical fracture mechanics predicts p 尖端 Very small (about 10 psi), however, observational data usually indicate p 尖端 The values ​​are significantly large (approximately 100-400 psi) [see Economides 1989; Chen, 2018; Jeffrey 1989, Vahab 2018]. The following derivation will explain how to calculate p. 尖端 Value. An important and long-standingly accepted consideration is that fracturing fluid never fully reaches the fracture tip; that is, there is a "fluid hysteresis" region at the fracture tip, which increases apparent toughness and tip pressure. Figure 7 The pressure distribution and fluid hysteresis in the fracture are shown (see Vahab and Khalili, 2001).

[0178] The equation describing the pressure difference between the crack opening pressure and the crack tip pressure can be written as:

[0179]

[0180] Using equation 36, we obtain:

[0181]

[0182] therefore:

[0183]

[0184] The observed effect of each parameter matched the expected behavior:

[0185] The longer the crack, the greater the pressure drop.

[0186] • The higher the viscosity, the greater the pressure difference.

[0187] • The higher the altitude, the higher the permeability and the lower the pressure difference.

[0188] Higher efficiency results in lower leakage and higher pressure at the crack opening.

[0189] Post-well shut-in stage

[0190] As is known in the art, shut-in (cessation of pumping) following an instantaneous shut-in (ISIP) can cause water hammer. In this disclosure, pressure data obtained after water hammer is considered. Furthermore, in the method of this disclosure, the fracture is considered to be divided into three zones. See again. Figure 2 These regions are wellbore region 201, near-wellbore (NWB) region 202, and far-field (FF) region 203. NWB region 202 has a complex shape, often exhibiting fracture turning, twisting, branching, and splitting. Furthermore, NWB region 202 typically has a smaller width and much lower permeability than FF region 203. The size of NWB region 202 can vary from several well diameters to approximately 30 feet from the well. Due to the lower permeability in NWB region 202, and the fact that fracture initiation directions in NWB region 202 can differ from the preferred direction (perpendicular to the minimum principal stress), a pressure differential often occurs between wellbore region 201 and FF region 203 after ISIP. This pressure differential causes a rapid drop in pressure after shut-in. This pressure drop is sometimes referred to as the pressure drop due to wellbore tortuosity; however, in this disclosure, the direct pressure drop after shut-in is referred to as near-wellbore (NWB) pressure loss (NWBPL), i.e., pressure loss attributable to the NWB region, such as... Figure 2 As shown in Figure 202.

[0191] According to the method of this disclosure, one novel aspect is that the pressure decay after ISIP (Instantaneous Shut-in Pressure) is divided into three stages based on the main sources of pressure decay in each stage. The sources of pressure decay are:

[0192] 1. Leakage: Consider that it exists in all three segments.

[0193] 2. Pressure Equilibrium: Pressure equilibrium in the fracture begins immediately after ISIP and is almost negligible in segment 3, as the pressure in the entire fracture area will begin to equalize after a few minutes.

[0194] 3. Crack growth: Crack growth may be a significant source of pressure decay after ISIP. However, its impact on the pressure decay trend diminishes rapidly and can be completely ignored in section 3.

[0195] 4. Near-bore pressure loss (NWBPL): The pressure loss is significant in the first few minutes after shut-in. However, this effect quickly diminishes, and its impact on pressure decay is negligible in the latter half of stages 3 and 2.

[0196] As a hint, Figure 3 The sources of pressure decay in each segment are explained. In segment 301, NWBPL is the primary source of pressure decay; in segment 302 (NWB), all pressure decay sources contribute comparablely; while in segment 303 (FF), leakage is the primary source of pressure decay. Before the analysis, the significance of fluid friction should also be considered. The effects of two fluid friction components will be considered below: friction within the wellbore (pipeline) and friction caused by perforation. It should be noted that the effects of these two friction sources are negligible in this analysis because both depend on the wellbore volume fraction, which rapidly becomes very small after ISIP.

[0197] Figure 8 A graph showing the relationship between pressures in the NWB and FF regions within the fracture is presented. The fracture orifice pressure on the wellside in the NWB region is represented by p. w The calculation equation is as follows:

[0198]

[0199] Where p wh = Wellhead pressure. Typically, p wh This is the only available pressure measurement data. Please note again that a few minutes after the ISIP ends, p wh (t)≈p w (t). Next, observe p. w The relationship between p and the pressure at the FF region inlet M (t) = p(x = 0, t). The difference between these two pressures is NWBPL. The result is:

[0200] p M (t)=p w (t)-p NWBPL (t) (43)

[0201] Pressure decay caused by crack growth and leakage (paragraph 2)

[0202] The focus of this section is the attenuation of the mean pressure (FF region) in section 2, such as... Figure 2As shown in section 203. It should be noted that in section 2, the pressure in the FF region is uneven, and there is an effect of pressure balance. The average pressure in the FF region can be represented by p. av (t) represents:

[0203]

[0204] Please note that p f (x,t) represents the pressure within the crack, which is a function of time and location (the pressure within the crack is not uniform). The mass conservation expression for the FF region can be written as:

[0205] q fc -q f =-q fg -q l (45)

[0206] Where q f From the NWB region ( Figure 2 The volume fraction from 202) to the FF region, q fg = Volume ratio associated with crack growth, q l Leakage-related volume fraction, q fe = The volume fraction related to the crack compressibility coefficient. To make this relationship complete, it is necessary to express each of the above volume fractions with an equation. Since the volume fraction generated by crack growth depends primarily on the crack propagation pressure p prop The following can be calculated:

[0207]

[0208] in It is the mean net pressure (expanded pressure), p * The unknown pressure determines the minimum net pressure required for crack growth. The steps for calculating the minimum required pressure will be explained at the end of this section. The average net pressure can be calculated as follows:

[0209]

[0210] According to literature (Weijers 2000, Economides 1989), the crack growth rate u fg Depends on the extended pressure p prop As shown below:

[0211]

[0212] Where c fg Here, r is an unknown parameter, and r is an unknown power, based on the literature 0.6 < r < 1.6. For simplicity, we can set r = 1 here. Therefore, the volume fraction associated with crack growth can be calculated as follows:

[0213] q fg =u fg A fg (49)

[0214] Where A fg This is the volume associated with crack growth. This volume is also related to pressure, therefore A fg ∝p prop (Height is assumed to be constant, width is assumed to be related to pressure). Therefore, due to

[0215]

[0216] And due to the calculation of q fg Other required parameters are unknown, so q can be added after each ISIP. fg With q fg The values ​​before well shut-in were compared. The results using this method are as follows:

[0217]

[0218] Where q inj fg It is the volume fraction associated with fracture growth at the end of the injection period. This is based on the fracture growth ratio ξ. f The definition of q allows us to calculate q. inj fg for

[0219]

[0220] Therefore, q fg The following can be calculated:

[0221]

[0222] Please note that in p prop When q < 0, i.e., when the pressure is below the minimum stress, fg =0. Note that this is a very simplified crack growth relationship; other relationships can also be used. Various other crack growth relationships do not significantly change the results. Observe the leakage volume fraction q. l Because the existing section of the fracture involves both fracture extension and a decrease in leakage rate, leakage calculations in this segment are complex. During fracture extension, the fracture grows slowly (leakage increases), while the leakage rate of the existing section decreases (leakage decreases). For simplicity, it is assumed that the increase in leakage due to fracture growth cancels out the decrease in leakage due to reservoir pressurization, leaving a constant leakage rate equal to the value at the end of the pumping phase.

[0223] q l =(1-ξ f )qinj (54)

[0224] Determine q f The value (i.e., the flow from the NWB region to the FF region) can be interpreted as follows. For example... Figure 3 As shown in 301, this flow rate is large during segment 1; however, it quickly becomes negligible and is negligible in segment 2, as... Figure 3 As shown in 302 of section 2. Note that at 302 in section 2,

[0225] Due to β fr >>β w and V fr >>V w Therefore, this flow rate can be ignored. Here, β = compressibility coefficient. V fr = Crack volume, V w = Wellbore volume.

[0226] The last volume fraction to be defined is the volume fraction associated with the crack compressibility coefficient. This can be calculated as follows:

[0227]

[0228] β fr This is the compressibility coefficient of the crack. The average compressibility coefficient used here is the same as the average pressure used previously. The compressibility coefficient β of the crack. fr It consists of three parts: the compressibility coefficient of the fracturing fluid, the change in fracturing area caused by pressure changes, and the change in proppant content caused by pressure changes. Of these three parts, the change in fracturing area caused by pressure changes is dominant. In this case:

[0229]

[0230] Assuming the fracture surface is elliptical, the fracturing area is:

[0231]

[0232] Where w = crack width, H = crack height. According to Sneddon and Elliot (1946), the average width is given by, where S... min Minimum principal stress:

[0233]

[0234] Assuming that H remains essentially constant during pressure decay, the average crack compressibility coefficient can be calculated as follows:

[0235]

[0236] Please note that S is assumedmin This is a time-dependent constant. Now all volume fractions are equationd, and the mass conservation equation 45 can be written as:

[0237]

[0238] Where β fr V fr It is essentially a constant because V fr ∝p- n And β fr ∝1 / (p- n Therefore, β fr V fr =β 0fr V 0fr The following relationship can be derived:

[0239]

[0240] Equation 61 can be simplified to (V fr =η av V inj ):

[0241]

[0242] Utilizing injection time The definition yields the expression

[0243]

[0244] The above differential equation (Equation 63) can be solved analytically. The initial condition is p- n (t=0)=-p n0 After solving this differential equation, p- n The final equation can be written as:

[0245]

[0246] therefore,

[0247]

[0248] The only unknown here is p. * The value of . This pressure can be called the crack propagation pressure, because below this pressure, cracks will not grow. To calculate the crack propagation pressure p * The value of this value can be found at a point in the pressure data after which further pressure decay is primarily due to leakage. To address this, the Caterpillar leakage function can be fitted to the end portion of the pressure data (measured relative to the final portion of the pressure decay time after shut-in) and the point at which the pressure decay deviates from the Caterpillar leakage can be calculated. The Caterpillar leakage rate depends on time, as follows:

[0249]

[0250] Define Carter time as The pressure drop caused by leakage has a linear relationship with τ. This line can be defined as:

[0251]

[0252]

[0253] Pressure decay data deviates from p Carter The point is (t) * ,p * ). Figure 10 It shows the target p * An example of this calculation. Note that due to p * The pressure is p, under which no crack will grow; therefore, the pressure at the crack tip can be assumed to be p. 尖端 =p * This assumption will reduce a previously unknown parameter.

[0254] Pressure decay due to leakage (segment 3, no crack growth)

[0255] This section shows Figure 3 The pressure decay relationship of the average pressure in segment 3, shown at point 303, is where the sole source of pressure decay is leakage (no crack growth). Recall... Figure 3 The diagram shows a superimposed fit of a set of measurement data and model data. Since crack growth is not considered, the reduction in leakage rate should be taken into account. Therefore, the leakage rate can be written as:

[0256]

[0257] The last two items were added to account for the pressure-related Caterpillar leakage effect.

[0258] The differential equation for pressure can be written as:

[0259]

[0260] In section 2 ( Figure 3 In the 302nd position), assuming β fr V fr The value of remains unchanged, equal to its initial value. This assumption is correct if the proppant in the crack does not affect the crack compressibility. However, when the net pressure decreases, it means the width decreases, so the proppant can change the compressibility. The parameter c can be used... pr Let's consider the effect of the proppant on the compressibility coefficient. Therefore...

[0261]

[0262] When the width is much larger than the proppant width (proppant particle diameter or size), c pr =1. However, when the width is close to the width of the proppant filling, c pr >1. To calculate c pr The value of V can be used to... pr Let c be the volume of the injected proppant. Furthermore, it is assumed that all proppant remains within the fracture. The volume of the fracture can now be compared to the volume of the proppant, and an empirical equation can be defined to calculate c. pr The value of V. Suppose if V fr >c v V pr If the proppant has no effect, then c pr =1. When c v When the information is unknown, assume c v =2. Furthermore, to calculate the increase in the compressibility factor, it can be assumed that the compressibility factor increases linearly from the initial compressibility factor to the compressibility factor of the proppant-filled section as the volume decreases. The volume of the crack depends on the net pressure (assuming length and height remain constant, width is variable). Therefore:

[0263]

[0264]

[0265] Where c pr max It is C pr The maximum value occurs when the crack closes at p- n When p = 0, cr n is V fr =c v V pr The critical net pressure. pr max The value can be used to determine β when the crack closes. fr V fr Calculate the value

[0266]

[0267]

[0268] β pr It is the compressibility coefficient of the proppant filling. According to the literature, we can use β. pr = 0.011 / MPa. Equations 72-75 can be used to calculate c. pr .

[0269] The pressure decay equation for the average pressure in segment 3 is:

[0270]

[0271] Simplified to:

[0272]

[0273]

[0274] in

[0275]

[0276] Solving the differential equation (78), we obtain the expression.

[0277]

[0278] Here, c and ψ are two fitting parameters. The parameter ψ can be used to calculate efficiency, as shown below.

[0279]

[0280] Pressure balance in the crack

[0281] Calculating the average pressure decay in the FF region after well shut-in requires using the equations currently in use (equations 64, 65, 80, and 81). Additionally, the pressure p at the FF region inlet needs to be calculated. M The relationship between mean net pressure and maximum net pressure (orifice pressure) is usually defined by the parameter βs:

[0282]

[0283] The value of βs during the pumping phase depends on several parameters. According to Nolte (1979, 1991), the value of βs mainly depends on the decrease in fracturing fluid viscosity from the well to the fracture tip due to thermal degradation and shear degradation. The relationship between net pressure and fracture length (X) is as follows: Figure 11 As shown in Part A. The decrease in fracturing fluid viscosity depends primarily on the fluid type, fracture length, and formation temperature. Figure 11 Part B adopts Smith and Montgomery (2015) and shows some numerically calculated values ​​of βs.

[0284] The value of βs indicates that the pressure in the fracture is not uniform upon shut-in. According to the method of this disclosure, determining the time required for pressure equilibrium to be reached in the fracture is very useful. The previous assumption was that pressure equilibrium is very rapid, and that a substantially uniform pressure appears shortly after shut-in (within a few seconds). In the analysis below, it is assumed that the pressure equation for the fracture is very simplified. For example, it can be obtained using p...尖端 The pressure equation is derived from the PKN fracture growth model with a coefficient of 0. Further assumptions are made that the fracturing fluid is a Newtonian fluid and there is no leakage. The net pressure can be written as:

[0285]

[0286] Therefore, the average net pressure can be calculated as follows:

[0287]

[0288] Figure 12 The net pressure curve p is shown. n Its functional relationship with wellbore distance (x) and average net pressure.

[0289] To calculate the volume of material that needs to be moved in to reach crack equilibrium, refer to... Figure 13 Volume V * The shaded area (at 1301, the pressure is higher than the average net pressure p) n ave Volume V * The same volume V at 1302 below the average net pressure * (Phase equilibrium). The volume of a crack depends on the net pressure. This is because the height and length of the crack are constant, while the crack width depends linearly on the net pressure. A crack can be divided into two parts: a part with pressure above the average pressure and a part with pressure below the average pressure. av The net pressure along the crack length reaches the average pressure p. n ave The points can be calculated as follows:

[0290]

[0291] To achieve uniform (balanced) pressure, the volume V * It should start from the first part of the crack (x>x) ave Part 1) moves to the second part (x) <x ave (partial). This volume can be calculated as follows:

[0292]

[0293] Finally, to calculate the time required to move this volume, the volume fraction needs to be known. This volume fraction is initially equal to q. inj However, this volume fraction decreases as the pressure in the crack reaches equilibrium. Figure 14 The relationship between volume fraction and fracture length was described at different times (e.g., during injection, shortly after injection, and longer after injection). Assume q = q inj Calculate the lower limit to determine the time required for equilibrium:

[0294]

[0295] This is the shortest time required for equilibration (not considering leakage); the actual equilibration time will be longer. The same calculation method can be used for leakage scenarios. Assuming the fluid leakage from fracturing to the formation is very simple and constant, the equation in this case is:

[0296]

[0297] Therefore, the minimum time required for equilibration depends on the injection time, and equilibration requires at least 8% of the injection time (see Equation 87). Typically, the injection time is approximately 2 hours. Therefore, the minimum required time is 8% of two hours, or approximately 10 minutes, while the actual required time will be longer. Therefore, the effect of pressure balance cannot be ignored and should be considered in the equation. Developing such pressure balance is very difficult because it depends on several unknown properties, such as fluid rheology, fracture permeability, and fluid degradation under temperature and shear stress. Even with these parameters, the analysis will be numerical because there is no analytical solution for the volume fraction after shut-in. Therefore, for the integrity of the model, some reasonable assumptions can be made to derive a relatively simple pressure balance equation. Assume the flow rate between the two parts ( Figure 13 The linearity depends on the pressure difference between the two average pressures. Therefore, by using this assumption, the time equation can be written as:

[0298]

[0299] In equation 89, the last term on the right-hand side represents the difference between the average pressure and the fracture pressure. It can be seen that this pressure difference is greatest at shut-in and decreases over time. eq This is the unknown parameter that determines the rate at which this equilibrium occurs. Assuming that at the end of segment 2, the pressure in the crack is almost uniform, then it can be achieved at time t = t * (At the end of paragraph 2) set c eq =4, which means that at the end of segment 2, the initial pressure difference is only 2%.

[0300] Near-borehole pressure loss

[0301] Finally, the pressure loss to consider is NWB ( Figure 2 Pressure loss in the 201 area. This pressure loss leads to a rapid drop in pressure in the near-wellbore area. Figure 15 The pressure curves that may appear with large, small, and zero NWB pressure loss are shown. The NWB pressure loss is calculated as follows:

[0302]

[0303] Among them, a NWBIt is a parameter, which will be discussed further below, β NWB = Unknown index, which depends on the characteristics of the NWB region, q NWB This refers to the flow from the NWB region to the FF region. The key point is flow calculation:

[0304]

[0305] Where kNWB = NWB permeability, ANWB = NWB area, and μNWB = viscosity of the fluid in the NWB. Due to the highly complex shape of the NWB and the difficulty in calculating the pressure distribution in this region, the calculation of this flow rate is extremely complex. Furthermore, the relationship between permeability and the area of ​​the NWB with pressure is unclear. According to the literature, there are two extreme cases regarding the relationship between area and permeability with pressure in the NWB region. The first extreme case is that permeability and area remain constant (kNWBANWB ∝ pNWB0), and the second extreme case is that width and permeability depend entirely on pressure. In the second extreme case, the relationship is cubic kNWBANWB ∝ pNWB3. The value of βNWB also depends on the relationship between permeability and width with pressure. Weijers et al. (2004) assumed that the exponent βNWB should be limited between 0.25 and 1. The lower limit of 0.25 is derived from the flow in the fracture, whose width depends on the fluid pressure in the fracture (Perkins and Kern, 1961). The upper limit of 1 is based on the flow between parallel plates of fixed width. Figure 16 These two extreme cases are shown.

[0306] This stress correlation is usually assumed to be the general case in the literature, and β is used. NWB =0.5. For this exponent, k NWB A NWB ∝p NWB 2 If β NWB =0.5, and using the average pressure gradient between the wellbore region and the FF region instead of the pressure gradient, we get:

[0307]

[0308] Where q 0 NWB The initial flow rate at well shut-in is almost equal to the injection flow rate q. 0 NWB ≈q inj p NWB The average net pressure in the near-wellbore region can be calculated as follows:

[0309]

[0310] Where σ NWBThe average pressure when the NWB is open can be calculated as follows:

[0311]

[0312] Where σ max = Maximum horizontal stress, σ min =Minimum horizontal stress. σ max The value can be estimated by the pressure at the end of the first segment (in the time domain). Figure 3 The time point between section 301 and section 302 (approximately 700 seconds) is a good estimate of the maximum horizontal stress. This is because when the pressure drops to the maximum horizontal stress pressure (maximum horizontal stress, σ... max When the crack is below σ, the crack mainly runs along the direction perpendicular to σ. min The preferred direction of growth is given. Therefore, the pressure at the end of segment 1 should be a good estimate of the pressure above which cracks may appear in other directions besides the preferred direction. Thus, this pressure can be used as a rough estimate of the maximum horizontal stress.

[0313] p NWBPL The value can be calculated as follows:

[0314]

[0315] The only unknown is a NWB The value can be obtained by using a point p after the well is shut in. w and p M It is calculated from the pressure difference between them. Knowing p NWBPL The value can be derived as follows:

[0316] p w =p M +p NWBPL (96)

[0317] To calculate a NWB The value is the pressure difference between the wellbore pressure and the wellhead pressure at the midpoint of segment 1. Figure 17 Here are examples, where curve 1701 shows the pressure decay but does not account for the NWB pressure drop; curve 1702 includes the NWB pressure drop.

[0318] Relationship between reservoir pressure and minimum principal stress

[0319] For a long time, the theoretical relationship between formation fluid (pore) pressure and stress has been used to constrain the minimum horizontal stress (fracture gradient). The "classical" lateral confinement model assumes that in a fully relaxed geological basin, the effective horizontal stress can be calculated from the vertical stress. This calculation assumes that the Earth can be simulated as being instantaneously subjected to a vertical load of gravity under uniaxial strain. This implies that, under the conditions of laboratory rock mechanics tests, there is no lateral strain (ε).xx ,=ε yy =0). Assuming the Biot coefficient (rock properties, typically between 0.6 and 0.8) is approximately equal to 1, and the horizontal stresses are equal (S min =S xx =S yy See also Figure 18 :

[0320]

[0321] Where ν = Poisson's ratio, E = Young's modulus, and S V =Vertical stress, S min =Minimum principal stress. Using Equation 97, we obtain:

[0322]

[0323] Equation (98) is derived under the assumption of complete basin relaxation. However, due to the influence of tectonic pressure, the equation can be modified as follows:

[0324]

[0325] Where S T This refers to tectonic stress. The value of tectonic stress is unknown and can be calculated based on the pressure value of stage 1 of the well, which is the hydraulic enhancement stage. Additionally, vertical stress is typically between 1 and 1.2 psi / ft. In this disclosure, S is used. V = 1.1 psi / ft. Equation 99 can be used to relate the change in minimum stress to changes in reservoir pressure and Poisson's ratio. Typically, S min Any change in S can be explained by a change in Poisson's ratio, a change in reservoir pressure, or a change in either of these parameters. Since experiments show that the value of Poisson's ratio varies within the formation, it is reasonable to consider S... min The primary cause of the variation is attributed to changes in Poisson's ratio. However, experiments typically also show that the value of Poisson's ratio does not vary by more than a few percentage points over a distance of several hundred feet, which corresponds to the typical stage length between hydraulic fracturing "stages," separated during stage pumping by impermeable "bridge" plugs in the well. Therefore, setting an empirical limit (e.g., 10%) for such variation is consistent with observations.

[0326] Therefore, S min Any further changes could be attributed to alterations in reservoir pore fluid pressure. Finally, this method requires an initial value for the reservoir pore pressure (Stage 1). Such a value can be guessed, estimated, or calculated based on pumping information from the first pumping fracturing stage (Stage 1). Figure 19 Equation 99 is shown as the explanation for S. minExamples of the results of change. It can be seen that S varies between stages. min Changes can usually be explained by a 10% variation in Poisson's ratio, with only a few stages requiring larger variations in Poisson's ratio or reservoir pressure. Therefore, since the variation in Poisson's ratio is limited to within 10%, S min The additional changes are attributed to p res The changes in reservoir pressure and Poisson's ratio are significant. There may be other methods or models that can more realistically represent changes in reservoir pressure and Poisson's ratio, but the method presented here is simple and effective.

[0327] Calculate crack size

[0328] To calculate the actual crack size, the crack shape can be assumed to resemble the shape used in the PKN model, for example, as described in U.S. Patent Application Publication No. 2020 / 0319007 filed by Moos et al.:

[0329]

[0330] Among them, w f L f , and H f These represent the width, length, and height of the crack at the end of the pumping stage, respectively. Additionally, n is a shape factor used to account for the effect of reduced PKN crack width. For p 尖端 The normal value for n is approximately 0.1. In the determined final size, the effect on n is negligible (<1%). According to the Sneddon relation, w f The following can be calculated:

[0331]

[0332] Next, we use the definition of average efficiency:

[0333]

[0334] Using equation 41, we can obtain:

[0335]

[0336] Pressure-related leaks

[0337] Pressure-related leakage (PDL) is a type of leakage in which fracturing fluid can penetrate into the surrounding matrix, pre-existing natural fractures, and fissures. Increasing the treatment pressure along the main fracture can induce the expansion of natural fractures and fissures, significantly increasing leakage. PDL was also included in the model to further improve the results.

[0338] The pressure at which a natural crack begins to expand is called the reactivation pressure, p. actIf the well fluid pressure exceeds this level, a higher leakage rate may occur. Therefore, the simplest calculation equation is as follows:

[0339]

[0340] Among them, C leak It is the pressure-related leakage coefficient; C form It is the inherent leakage coefficient related to the formation; Is p = p 0 The leakage coefficient, and p 0 It is the initial pressure in the fracture when the well is shut in.

[0341] In a PDL relation, there are two new unknowns, namely p act and C form To calculate these parameters, we used the pressure derivative from segment 3 (leakage segment only). If the PDL does not exist, segment 3 should have a constant slope. However, typically, the slope of this segment decreases over time, indicating the presence of the PDL, and this change in slope can be used to calculate the unknown parameters in the PDL relationship.

[0342] Additional limitations are provided for NWB voltage drop in NWB acoustic measurements.

[0343] This part of the disclosure presents the observation that the NWB pressure loss (NWBPL) is due to flow through a finite region with low permeability. The relationship between pressure loss and flow rate is shown in Equation 108, and the relationship for all fractures is shown in Equation 109.

[0344] To further improve the results, additional restrictions can be imposed on the pressure attenuation analysis using active acoustic pulses. This pulsed method is described in Dunham 2017, where the conductivity of hydraulic fracturing is estimated by analyzing tube wave reflections. The following describes how to use the conductivity measurements of hydraulic fracturing obtained thereby.

[0345] The near-field connectivity index (NFCI) is determined (see Equation 107, which can be determined using, for example, the method disclosed in U.S. Patent Application No. 10,641,090, granted to Felkl et al.). NFCI is a measurement of the hydraulic conductivity of the near-bore (NWB) region. Therefore, NFCI can be used to estimate the pressure drop in the NWB region. Figure 20 The pressure drop and cylindrical cross-section of the NWB region are shown. It should be noted that the pressure loss in the NWB region (p...) NWBPL The initial pressure drop (at shut-in) is a significant component of the overall pressure drop, and determining the value of the NWB pressure loss helps to better identify other sources of the pressure drop (see [link]). Figure 20(Part A). To calculate the pressure loss in the NWB region, the flow equation (Darcy's law) in the biplane cracked NWB region must first be calculated:

[0346]

[0347] Where, k NWB It is the penetration rate of the NWB region, and A NWB This is the cross-section of the NWB region. For simplicity, we can assume the NWB region is axisymmetric and then use an idealized cylindrical cross-section for growth (see [link]). Figure 20 (Part B). Therefore, A NWB =2πxw NWB Furthermore, please note that the total flow rate in all fractures during a fracturing stage can be calculated as follows:

[0348]

[0349] Where, N frac It refers to the number of cracks in a given stage.

[0350] The definition of NFCI

[0351]

[0352] Therefore, according to the NFCI definition, the traffic in the NWB area can be calculated as follows:

[0353]

[0354] During fluid injection, Q NWB The pressure remains almost constant throughout the entire NWB region. Therefore, by integrating the flow relationship, the initial NWB pressure loss can be calculated.

[0355]

[0356] Note that this relationship provides the initial value for the NWB pressure loss (synonymous with pressure drop); after shut-in, the pressure in the NWB region will continue to decrease, therefore p NWBPL Not constant (see Figure 21 Furthermore, since we know that the only time for the flow is before the well is shut down, the flow Q before shutting down is... inj Used to calculate the initial pressure drop in the NWB. A typical pressure decay curve after shut-in is shown below. Figure 21 As shown.

[0357] Obtaining the correct value of the NWB pressure drop helps the model better distinguish pressure drops from different sources, thus enabling more accurate calculation of crack size and efficiency. Figure 22An integrated NF-FF model is shown, in which the NFCI value calculated using least misfit inversions is used in the 3-segment FF model to calculate fracture size and efficiency. At 2210, an acoustic pulse is emitted into the well to induce tubular waves in the well and in the connected fractures; and pressure or pressure-time derivative is measured in response to the emitted acoustic pulse. At 2212, the detected pressure or pressure-time derivative measurements are processed to obtain NCFI. At 2214, the NFCI can be combined with the time-varying well pressure measurement shown at 2218 to constrain the 3-segment model as interpreted herein. At 2216, the pressure decay measurement curve is curve-fitted to the simulated pressure decay curve based on the 3-segment model. At 2222, if the curve fit is not within the predetermined error or misfit range, the parameters of the 3-segment model are adjusted and a new model curve is generated. Returning to 2216, the measured pressure decay is compared with the simulated pressure decay. If the curve fit is within the predetermined error or mismatch range, the fracture size is calculated at 2220 using the model parameters from the most recent iteration of the 3-segment model.

[0358] Development proxies are used to determine the production potential of each stage and wellbore.

[0359] This section will develop indicators to determine the fluid production potential at each stage of the well and across all stages throughout the well. The first indicator is called well potential, Γ. 井 The value of each stage is called the stage potential, Γ 阶段 The following can be calculated:

[0360] Γ 阶段 =1-η ave (110)

[0361] Where η ave = Average efficiency at each stage (calculated by fitting a pressure decay curve). Γ 阶段 This method effectively determines the ease or difficulty of producing oil or gas at each stage because it indicates the ease or difficulty of fluid loss at each stage. In other words, if the reservoir has high conductivity within a stage, resulting in low efficiency, then it can be expected that high conductivity will also lead to high fluid productivity. To calculate the well potential, the stage potential Γ... 阶段 The weighted average of the values ​​is:

[0362]

[0363] in L i = Stage crack length, H i = Stage crack height. Γ 井This should be a rough indicator for determining the overall well productivity. Specifically, Γ 开 It can be used to compare the productivity of adjacent wells.

[0364] While well potential is an easily measurable indicator, its drawback is that it is highly dependent on the pumping design. Specifically, well potential is heavily dependent on the injection rate during fracturing pumping. This is because when the injection rate is low, the injected fluid has more time to leak, thus resulting in lower efficiency compared to a higher injection rate. However, this low efficiency (and therefore high well potential) is not due to higher reservoir permeability, but simply due to the low injection rate. Therefore, well potential is a good indicator for comparing the production of wells with similar pumping designs. To address this issue, it is necessary to define reservoir potential, Θ. Res The reservoir potential value at each stage is called the stage reservoir potential, Θ. 阶段 To calculate Θ 阶段 First, we use Equation 3 to calculate the Caterpillar leakage coefficient, as shown below:

[0365]

[0366] Where A fs = Crack surface area, ξ = Crack growth ratio (local efficiency), q inj = Injection rate, and t eq = Equivalent leakage time. The equation for calculating the Caterpillar leakage coefficient can be further simplified and written as:

[0367]

[0368] in and t inj =Injection time. The Carter leakage coefficient can be calculated using reservoir characteristics (Carter, 1957):

[0369]

[0370] Where k r =Reservoir formation permeability, c r = Total compressibility coefficient of the reservoir, φ = Reservoir porosity (fraction of pore volume in reservoir rock), μ r = Reservoir fluid viscosity, and Δp dr =The driving force of the leak can be calculated as follows:

[0371] Δp dr =S min +p n -p res (115)

[0372] Where S min =Minimum horizontal stress, p n =Net pressure, and pres =Reservoir pore pressure. As shown in Equation 115. It is to determine the reservoir's liquidity A very good indicator, therefore the stage reservoir potential can be defined as:

[0373]

[0374] Due to Θ 阶段 It depends entirely on the formation's conductivity, therefore it is a good indicator for determining the reservoir's potential production at each stage. Furthermore, similar to well potential, reservoir potential can be expressed as a weighted average Θ. 阶段 The calculation is as follows:

[0375]

[0376] Implement the disclosed three-stage pressure decay steps

[0377] Figure 9 This is a flowchart of an exemplary implementation of the method according to the present disclosure. Figure 9 An exemplary workflow is illustrated, in which, in some embodiments, a determined NFCI from pulsed acoustic measurements is used to estimate or limit the NWB voltage drop, thereby improving the estimation of crack size. Using the NFCI determined by the acoustic pulses is an option and may be omitted in some embodiments.

[0378] At point 910, measure the pressure in the well undergoing fracturing treatment. Record the pressure after stopping pumping and shutting in the well. The pressure measured in the well may decrease over time after shut-in. Typically, pressure measurements should be recorded for at least 10 minutes after shut-in.

[0379] At 920, fracture conductivity can be calculated by analyzing the acoustic pulses emitted within the well after shut-in, and the response of pressure or pressure-time derivative to these pulses. Conductivity is defined as permeability multiplied by the fracture width. A method for performing and analyzing acoustic pulse measurements disclosed in U.S. Patent Application No. 10,641,090, granted to Felkl et al., can be used to provide such calculations. This step is optional if one wishes to perform only pressure attenuation analysis using the proposed three-stage method.

[0380] At location 930, reservoir rock formation characteristics can be obtained. For specific geological and geographical locations, formation characteristics can be understood through well logging, seismic surveys, and other geological exploration sources.

[0381] At 940, the wellhead pressure of the first pumped fracturing stage (Stage 1) is used to calculate the reservoir pressure. Wellhead pressure refers to the pressure within the wellbore after the initial pressure test and before the injection of fracturing fluid in the first stage. At this point, the wellbore is effectively "open," meaning it is not under external pressure, and the pressure within the well represents the reservoir pressure connected to it at the bottom of the well. The wellhead pressure of Stage 1 can be used as an indicator of reservoir pressure. The three-stage model can be used later to validate reservoir pressure values ​​and modify them as necessary. In horizontal fracturing operations, i.e., multiple stages along a horizontal well, only the values ​​from Stage 1 before hydraulic fracturing can be used. For vertical well fracturing, the reservoir pressure may differ in each stage; therefore, the wellhead pressure of each stage can be used.

[0382] At 950, fracturing pumping data was measured and recorded. Pumping data, such as mud volume, number of clusters, proppant volume, injection rate, and fracturing fluid phase type, were collected and input into the model used in this method.

[0383] At 960 (an optional step in the 3-stage pressure decay measurement), an acoustic NFCI measurement at 920 can be used to calculate near-wellbore pressure drop, thereby more accurately determining fracture characteristics.

[0384] At 970, the above three-stage model (Equation 22-103) can be used to analyze the pressure decay data and calculate the pressure characteristics of each stage (all previously collected data can be used in this element of the method).

[0385] At 980, calculate the efficiency and fracturing size for each fracturing stage. For fracturing geometry calculations, refer to Equations 101-103, and for efficiency calculations, refer to Equation 1-21.

[0386] At 990, the reservoir pressure and reservoir quality for each stage are calculated, and the productivity for each stage is estimated.

[0387] At point 991, the conductivity of the fracture and its variation over time was calculated (the conductivity of the proppant-filled area was also calculated). This differs from point 920, where the near-bore zone (NWB, e.g.) was calculated. Figure 2 The crack conductivity (as shown in Figure 202) is calculated. At 910, the far-field region FF (as shown in Figure 202) is calculated. Figure 2 The conductivity (shown in Figure 203) is as follows. Due to leakage, fluid is lost from the fracture after well shut-in, and the volume decreases. At 990, the conductivity changes over time. Over time (after well shut-in), the fracture conductivity in the FF region decreases. When the fracture is hydraulically sealed and its volume is maintained solely by the proppant in the fracture, the fracture volume stops decreasing; the conductivity at this point is called "proppant-filled conductivity".

[0388] At point 992, calculated values ​​of NFCI, stress shadowing, and any measured off-well interactions are used to assess potential interactions between different fracturing stages and adjacent wells. Off-well interactions require simultaneous pressure measurements in at least two nearby wells. See, for example, International Application Publication No. WO2021 / 087233 filed by Moos et al. This publication describes interactions ranging from stress shadowing effects to direct fracture-fracture interactions, intersecting, or merging wells.

[0389] At point 993, adjustments required for handling subsequent fracture stages can be determined. This can be done based on the determined fracture geometry to maximize the production-enhancing reservoir area, or based on other determined parameters that can be used to inform the fracturing treatment design. Well operators may want to leave as little unproductive reservoir space as possible between nearby wells to prevent overlapping of nearby fracture systems and cannibalization of each other's production. Several factors can be considered when assessing expected changes in fracture geometry for subsequent stages: 1) the spacing between the well and the intact formation portion.

[0390] 2) Based on fracture height and compared with formation thickness; 3) Based on stress shadowing effect between stages;

[0391] 4) Based on potential interactions between adjacent wells. Leakage parameters can be used to estimate productivity. Higher leakage parameters indicate higher formation productivity (i.e., easier extraction of hydrocarbons).

[0392] It should be understood that the methods according to this disclosure can be executed on any general-purpose or special-purpose computer or computer system. Such a computer or computer system may include a reader for reading information stored on a non-transitory computer-readable medium such as a disk or solid-state storage. Such a computer-readable medium may include operable logic that causes the computer or computer system to perform actions corresponding to those described in this disclosure. Such a computer system may, for example, but not limited to, be configured with… Figure 1A In the data processing device shown in 103.

[0393] Although only a few examples have been described in detail above, those skilled in the art will readily understand that many modifications are possible in these examples. Therefore, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.

[0394] References cited in this disclosure

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Claims

1. A method for determining hydraulic fracturing characteristics based on well pressure measurements after stopping the pumping of fracturing fluid into the well, comprising: The immediate after shut-in was determined to be caused by fluid leakage from the fracture; The second time after well shut-in was determined, during which the pressure drop was caused by fluid leakage in the fracture, fracture growth, and fluid pressure balance. The third time point after well shut-in was determined, during which the pressure drop was caused by fluid leakage in the fractures, fracture growth, fluid pressure balance, and pressure drop in the near-wellbore region; and The values ​​of fluid efficiency, minimum stress, and net pressure are determined such that the calculated value of time-related pressure matches the pressure measurement results within a predetermined threshold, wherein the time-related pressure is calculated based on the cause of pressure reduction in a segment corresponding to the following times: (i) between the third time and the second time, (ii) between the second time and the first time, and (iii) after the first time.

2. The method according to claim 1, wherein, The pressure calculations that begin immediately include the calculation of Caterpillar leaks.

3. The method according to claim 1, wherein, The computational pressure, which begins at the second time and ends at the third time, includes computational... Where ξ f = Local efficiency or fracture growth ratio during well shut-in, η av = Average efficiency from the start of pumping fluid to well shut-in, p av = Average net pressure in the crack, p ∗ = Crack propagation pressure, p¯ n = Average net pressure, p n 0 = Initial net pressure, t inj = Injection time, t = time for pressure calculation, and Smin - minimum principal stress.

4. The method according to claim 1, wherein, The pressure calculations from the start of the third time period to the end of the second time period include the near-bore pressure drop calculations for axisymmetric biplane fractures with cylindrical cross-sections, based on Darcy's equations of flow.

5. The method according to claim 1, wherein, The calculated pressure from the start of the third time period to the end of the second time period includes the analysis of reflection events in pressure or pressure time derivative measurements in response to acoustic pulses emitted into the well, which induce tubular waves in the well to determine the near-field conductivity index, thereby constraining the calculation of near-wellbore pressure drop.

6. The method according to claim 1, further comprising: Use the determined values ​​for fluid efficiency, minimum stress, and net pressure; and The length, width, height, and leakage parameters of the fracture are determined using values ​​of Young's modulus, Poisson's ratio, fracturing fluid viscosity, fracturing fluid pumping volume, pumped fracturing fluid volume fraction, and the number of well perforation clusters through which the pumped fracturing fluid passes.

7. The method according to claim 6, wherein, Determining the length, width, and height of the cracks involves using the Perkins–Kern–Nordgren model of crack geometry.

8. The method according to claim 6, wherein, The determined fracture length, fracture width, fracture height, and leakage parameters are used to estimate the fluid productivity of each fracturing stage and the entire well.

9. The method according to claim 1, wherein, The third time was determined after the water hammer caused by the cessation of pumping ended.

10. The method according to claim 1, wherein, The second time is determined when the rate of change of the pressure measurement value relative to time is lower than a predetermined threshold.

11. The method according to claim 1, wherein, The first time was determined when the pressure measurement value was lower than the fracturing pressure of the rock formation into which the fracturing fluid was pumped.

12. The method of claim 1, further comprising using the determined minimum stress to estimate the fluid pressure in the formation penetrated by the fracture.

13. The method according to claim 1, wherein, Efficiency includes the fraction of fracture volume relative to the volume of fracturing fluid pumped into the fracture.

14. The method of claim 1, further comprising determining the fracture conductivity relative to time after well shut-in.

15. The method of claim 14, further comprising determining the conductivity of the proppant filling when the conductivity of the fracture stops changing over time after the well is shut in.

16. The method of claim 1, further comprising changing at least one of the viscosity of the fracturing fluid, the pumping volume of the fracturing fluid, the volume fraction of the pumped fracturing fluid, or the concentration of proppant in the fracturing fluid, so as to pump the fracturing fluid to different stages or different wells.

17. A computer program stored in a computer-readable medium, the program including operable logic that causes a programmable computer to perform operations based on pressure measurements in the well after stopping the pumping of fracturing agent into the well, said operations including: The immediate after well shut-in was determined to be caused by fluid leakage from the fracture. The second time after well shut-in was determined, during which the pressure drop was caused by fluid leakage in the fracture, fracture growth, and fluid pressure balance. The third time point after well shut-in was determined, during which the pressure drop was caused by fluid leakage in the fractures, fracture growth, fluid pressure balance, and pressure drop in the near-wellbore region; and The values ​​of fluid efficiency, minimum stress, and net pressure are determined such that the calculated value of time-related pressure matches the pressure measurement results within a predetermined threshold, wherein the time-related pressure is calculated based on the cause of pressure reduction in a segment corresponding to the following times: (i) between the third time and the second time, (ii) between the second time and the first time, and (iii) after the first time.

18. The computer program according to claim 17, wherein, The pressure calculations that begin immediately include the calculation of Caterpillar leaks.

19. The computer program according to claim 17, wherein, The computational pressure, which begins at the second time and ends at the third time, includes computational... Where ξ f = Local efficiency or fracture growth ratio during well shut-in, η av = Average efficiency from the start of pumping fluid to well shut-in, p av = Average net pressure in the crack, p ∗ = Crack propagation pressure, p¯ n = Average net pressure, p n 0 = Initial net pressure, t inj = Injection time, t = time for pressure calculation, and Smin - minimum principal stress.

20. The computer program according to claim 17, wherein, The pressure calculations from the start of the third time period to the end of the second time period include the near-bore pressure drop calculations for axisymmetric biplane fractures with cylindrical cross-sections, based on Darcy's equations of flow.

21. The computer program of claim 17, wherein the pressure calculated from the start of the third time to the end of the second time includes, in response to an acoustic pulse emitted into the well, analyzing reflection events in a pressure or pressure time derivative measurement, the acoustic pulse inducing tubular waves within the well to determine a near-field conductivity index, thereby constraining the calculation of near-wellbore pressure drop.

22. The computer program according to claim 17, wherein, The logic also includes logic that enables the computer to perform the following operations: Use determined values ​​for fluid efficiency, minimum stress, and net pressure; and The length, width, height, and leakage parameters of the fracture are determined using values ​​of Young's modulus, Poisson's ratio, fracturing fluid viscosity, fracturing fluid pumping volume, pumped fracturing fluid volume fraction, and the number of well perforation clusters through which the pumped fracturing fluid passes.

23. The computer program according to claim 22, wherein, Determining the length, width, and height of the cracks involves using the Perkins–Kern–Nordgren model of crack geometry.

24. The computer program according to claim 22, wherein, The determined fracture length, fracture width, fracture height, and leakage parameters are used to estimate the fluid productivity of each fracturing stage and the entire well.

25. The computer program according to claim 17, wherein, The third time was determined after the water hammer caused by the cessation of pumping ended.

26. The computer program according to claim 17, wherein, The second time is determined when the rate of change of the pressure measurement value relative to time is lower than a predetermined threshold.

27. The computer program according to claim 17, wherein, The first time was determined when the pressure measurement value was lower than the fracturing pressure of the rock formation into which the fracturing fluid was pumped.

28. The computer program according to claim 17, wherein, It also includes instructions that enable the computer to perform the following operation: using the determined minimum stress to estimate the fluid pressure in the formation penetrated by the fracture.

29. The computer program according to claim 17, wherein, Efficiency includes the fraction of fracture volume relative to the volume of fracturing fluid pumped into the fracture.

30. The computer program of claim 17, further comprising operable instructions for causing the computer to perform a determination of fracture conductivity relative to time after well shut-in.

31. The computer program of claim 30 further includes determining the conductivity of the proppant filling when the conductivity of the fracture stops changing over time after the well is shut in.

32. The computer program of claim 17 further includes logic that enables the computer to execute at least one of the following: the viscosity of the fracturing fluid, the pumping volume of the fracturing fluid, the volume fraction of the pumped fracturing fluid, or the concentration of proppant in the fracturing fluid, so as to pump the fracturing fluid to different stages or different wells.

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