Method and system for determining relative permeability of fractured-vuggy carbonate reservoir

Abstract

The invention provides a method and system for determining the relative permeability of a fractured-vuggy carbonate reservoir, and belongs to the technical field of oil and gas resource development. The method comprises the following steps: calculating the relationship between the water content of a to-be-analyzed oil well and the recovery degree; the method comprises the following steps: collecting relative permeability calculation parameters of each oil well to be analyzed, determining an objective function for calculation optimization, determining a calculation formula for inversely calculating the moisture content fw of the oil well to be analyzed, calculating to obtain an inversely calculating moisture content result, substituting the inversely calculating moisture content result into the formula to obtain a calculation error, and calculating the relative permeability of the oil well to be analyzed according to the numerical value of the calculation error. And judging the accuracy of oil-phase relative permeability and water-phase relative permeability results. Compared with the prior art, the reservoir body relative permeability is calculated through inversion of actual oil well production data, the blank of the relative permeability curve of the fractured-vuggy carbonate reservoir is filled up, and the accuracy of numerical simulation of the fractured-vuggy reservoir is improved.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas resource development technology, and provides a method and system for determining the relative permeability of carbonate fractured-vuggy reservoirs. Background Technology

[0002] Carbonate rocks exhibit significant lithological variations, diverse reservoir space types, marked secondary alterations, and strong heterogeneity. The complexity of diagenesis further amplifies the heterogeneity of carbonate reservoirs, making the distribution of porosity and permeability difficult to predict. The distribution patterns of fractures are also complex, making the study of fractures and cavities in carbonate rocks a major challenge in this field.

[0003] In actual carbonate reservoirs, two or more fluids exist, such as oil-gas, oil-water, or oil-gas-water, especially in water-injected oilfields where oil and water co-flow and coexistence are common. When the reservoir pressure drops below the saturation pressure, three-phase coexistence and co-flow of oil, gas, and water can also occur. Under these multiphase flow conditions, due to the different wettability of each phase of the rock, interfaces exist between the fluids, resulting in capillary forces in porous rocks; this, in turn, affects the permeability of each phase. In this field, absolute permeability and relative permeability are commonly used for evaluation.

[0004] Absolute permeability refers to the amount of fluid passing through a segment of porous media with a cross-sectional area of ​​A, length of L, and pressure difference of ΔP in a laminar flow pattern, where the fluid viscosity is μ. The equation is: Q = KΔPA / μL. Effective permeability is the ability of a rock to allow each phase of fluid to pass through when multiple fluids coexist. The effective permeability of oil and water is always lower than the absolute permeability of the rock. Relative permeability is the ratio of the effective permeability to the absolute permeability of each phase when multiple fluids coexist. Therefore, accurate assessment of relative permeability is crucial for reservoir engineering, oil production engineering, and flow mechanics.

[0005] Patent application CN114036774A provides a method, calculation method, and determination system for determining the pseudo-relative permeability of semi-filled fractured-vuggy reservoirs, belonging to the field of unconventional reservoir development technology in the petroleum industry. The determination method includes: constructing a proxy model of the oil-water two-phase flow process of the fractured-vuggy reservoir for the target oilfield; predicting the relative permeability parameters and fractured-vuggy reservoir indices of the target oilfield based on the proxy model; substituting the predicted values ​​of the fractured-vuggy reservoir indices, the measured values ​​of the fractured-vuggy reservoir indices, and the predicted values ​​of the relative permeability parameters of the target oilfield into a calculable error objective function; employing a genetic algorithm, iterating multiple times until the objective function calculation result reaches its minimum, and outputting the corresponding predicted relative permeability parameter value at this point; and substituting the relative permeability parameter value into the pseudo-relative permeability expression to obtain the pseudo-relative permeability of the semi-filled fractured-vuggy reservoir in the target oilfield.

[0006] However, the aforementioned patent applications only apply to semi-filled fracture-vuggy reservoirs and lack applicability to fracture-type, fracture-void, and cavern-type reservoirs.

[0007] Patent application CN109933747A discloses a pseudo-phase permeability calculation method for the fracture-vuggy model, which includes the following steps: first, collecting basic data of selected typical fracture-vuggy models and establishing a two-dimensional model; simulating the water-driven oil flow process according to the Navier-Stokes equations to obtain flow parameters at different time steps; using the instability method to obtain the initial value of pseudo-phase permeability under this model based on the simulation results; and substituting the initial value of phase permeability into commercial simulation software based on Darcy's formula for fitting to obtain a relatively accurate pseudo-phase permeability for the fracture-vuggy model.

[0008] However, the data used in the aforementioned patents are basic data on typical slot patterns, lacking consideration of actual production and making it difficult to provide targeted guidance for production.

[0009] Meanwhile, carbonate fractured-vuggy reservoirs are highly heterogeneous, and most wells encountering the reservoir experience venting and leakage, resulting in a lack of relative permeability test data. Furthermore, the reservoirs are characterized by well-developed caverns and fractures, with multiple flow patterns coexisting, making it impossible to determine the relative permeability. Consequently, the accuracy of relative permeability values ​​during numerical simulation is poor, leading to strong ambiguity in numerical simulations of fractured-vuggy reservoirs.

[0010] Therefore, how to provide a method for determining the relative permeability of fractured-vuggy carbonate reservoirs is a problem that those skilled in the art hope to solve. Summary of the Invention

[0011] This invention addresses the lack of a method in the existing technology for determining the relative permeability of fractured-vuggy reservoirs that can simultaneously determine the missing relative permeability curve of the leaking and venting reservoir. It provides a method and system for determining the relative permeability of carbonate fractured-vuggy reservoirs, effectively calculating the relative permeability of the reservoir.

[0012] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0013] A method for determining the relative permeability of fractured-vuggy carbonate reservoirs includes the following steps:

[0014] S1. Collect production data, reserve data and physical property data of the oil wells involved in the fractured-vuggy unit to be analyzed, and calculate the relationship between the water cut and the degree of recovery of the oil wells to be analyzed.

[0015] S2. Collect the relative permeability calculation parameters for each oil well to be analyzed;

[0016] S3. Determine the objective function for the optimization calculation, as shown in the formula:

[0017]

[0018] Where E is the calculation error, fw is the inverted calculated moisture content, fw* is the actual moisture content, and n is the number of data points involved in the calculation.

[0019] S4. Determine the formula for calculating the water cut fw of the oil well to be analyzed. The formula is:

[0020]

[0021] Where fw is the water content calculated by inversion, and ρ w ρ is the density of the aqueous phase, ρo is the density of the oil phase, Krw is the relative permeability of the aqueous phase, Kro is the relative permeability of the oil phase, μw is the viscosity of the aqueous phase, μo is the viscosity of the oil phase, Bw is the volume coefficient of the aqueous phase, and Bo is the volume coefficient of the oil phase.

[0022] S5. Calculate the relative permeability of the oil phase and the relative permeability of the water phase in the well to be analyzed, using the following formula:

[0023]

[0024] Among them, K rw K represents the relative permeability of the aqueous phase. ro is the relative permeability of the oil phase, Sw is the water saturation, Swi is the bound water saturation, Sor is the residual oil saturation, nw and no are randomly generated correction parameters, Krwe is the relative permeability of the water phase calculated in the previous cycle, and Kroe is the relative permeability of the oil phase calculated in the previous cycle.

[0025] S6. Substitute the oil phase relative permeability and water phase relative permeability calculated in step S5 into formula (2) to obtain the inversion calculation water content result, and then substitute the inversion calculation water content result into formula (1) to obtain the calculation error;

[0026] S7. Repeat steps S5 and S6. Based on the magnitude of the calculation error, determine the accuracy of the oil phase relative permeability and water phase relative permeability results, and output the optimal oil phase relative permeability and water phase relative permeability.

[0027] Preferably, the production data in step S1 includes daily oil production, daily water production, water content, cumulative oil production, and cumulative water production.

[0028] Preferably, the reserve data in step S1 includes static sculpted reserves and dynamic reserves.

[0029] Preferably, the physical property data in step S1 includes crude oil volume factor, crude oil density, and crude oil viscosity data.

[0030] More preferably, the method for calculating the relationship between the water cut of the oil well to be analyzed and the degree of recovery in step S1 is as follows: calculate the change in the degree of recovery at different times based on the daily oil production, cumulative oil production and reserves data.

[0031] More preferably, the method for calculating the relationship between the water cut and the recovery degree of the oil well to be analyzed in step S1 further includes: calculating the water cut change at the corresponding time based on the daily water production.

[0032] Preferably, the relative permeability calculation parameters in step S2 include bound water saturation and residual oil saturation.

[0033] More preferably, the calculation results of the bound water saturation and residual oil saturation are obtained based on physical property parameters and phase permeability parameters.

[0034] More preferably, the physical property parameters and relative permeability parameters on which the calculation results of the bound water saturation and residual oil saturation are based include:

[0035] Oil phase viscosity, water phase viscosity, oil phase density, water phase density, oil phase volume index, and water phase volume index.

[0036] Most preferably, the physical property parameters and relative permeability parameters on which the calculation results of the bound water saturation and residual oil saturation are based further include:

[0037] The range of variation of the oil phase interpenetration endpoint, the range of variation of the water phase interpenetration endpoint, the range of variation of the oil phase interpenetration index, and the range of variation of the water phase interpenetration index.

[0038] In some embodiments, the oil phase interpenetration endpoint varies in the range of 0.01-0.2.

[0039] In some embodiments, the variation range of the aqueous phase infiltration endpoint is 0.01-0.2.

[0040] In some embodiments, the oil phase interpenetration index varies from 0 to 3.

[0041] In some embodiments, the aqueous phase interpermeability index varies from 0 to 3.

[0042] Preferably, the method for judging the accuracy of the relative permeability of the oil phase and the relative permeability of the water phase in step S7 is as follows: the smaller the calculation error, the better the accuracy.

[0043] The present invention also provides a system for determining the relative permeability of carbonate fracture-vuggy reservoirs, comprising a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for determining the relative permeability of carbonate fracture-vuggy reservoirs.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] This invention calculates the relative permeability of reservoirs by inverting actual oil well production data, filling the gap in the lack of relative permeability curves for lost and vented reservoirs in carbonate fractured-vuggy reservoirs. It can be applied to fractured, fracture-vuggy, and cavernous reservoirs, has a wider range of applicability, and effectively improves the accuracy of numerical simulation of fractured-vuggy reservoirs. Attached Figure Description

[0046] Figure 1 This is a graph showing the relationship between moisture content and recovery rate according to an embodiment of the present invention;

[0047] Figure 2 This is a graph of the relative permeability inversion objective function according to an embodiment of the present invention;

[0048] Figure 3 This is a diagram showing the relative permeability inversion results of an unfilled cavern type according to an embodiment of the present invention;

[0049] Figure 4 This is a graph showing the relative permeability inversion results of fractured and porous reservoirs according to embodiments of this disclosure;

[0050] Figure 5 This is a diagram showing the relative permeability inversion results of a fractured reservoir according to an embodiment of the present invention. Detailed Implementation

[0051] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly used in the field to which this invention pertains. For the purposes of interpreting this specification, the following definitions will apply, and where appropriate, terms used in the singular will also include the plural forms, and vice versa.

[0052] Unless the context clearly indicates otherwise, the terms “a” and “an” as used herein include plural references.

[0053] As used herein, the term "about" indicates a range of ±20% of the following value. In some embodiments, the term "about" indicates a range of ±10% of the following value. In some embodiments, the term "about" indicates a range of ±5% of the following value.

[0054] The numerical ranges used in this article should be understood as including all numbers within that range. For example, the range 1 to 20 should be understood to include any number, combination of numbers, or subrange from the following group: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20.

[0055] As used herein, the terms “comprises” or “comprising” mean “including, but not limited to”. This term is intended to be open-ended to specify the presence of any of the stated features, elements, integers, steps, or components, but does not exclude the presence or addition of one or more other features, elements, integers, steps, components, or groups thereof. Therefore, the term “comprising” includes the more restrictive terms “consisting of” and “substantially consisting of”. In one embodiment, the term “comprising” as used throughout the application, particularly in the claims, may be replaced by the term “consisting of”.

[0056] As used herein, the terms “optional,” “any,” “arbitrary,” or “any one” mean that the event or situation described below may, but does not have to, occur, including the circumstances in which the event or situation occurs or does not occur. As used herein, “an” and “a” refer to one or more grammatical objects.

[0057] The term “and / or” as used herein should be understood to mean any one of the options or any combination of two or more of the options.

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. Unless otherwise specified in the embodiments, conventional conditions or conditions recommended by the manufacturer shall apply. All reagents or instruments without specified manufacturers are commercially available conventional products. Numerous specific details are provided in the following detailed embodiments to better illustrate the invention. The specific embodiments described herein are for illustrative purposes only and are not intended to constitute any limitation on the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention. Such structures and techniques have also been described in many publications.

[0059] Example: A method for determining the relative permeability of fractured-vuggy carbonate reservoirs.

[0060] In step S1, production data, reserve data, and physical property data of all oil wells in the target fractured unit are obtained. The production data includes daily oil production, daily water production, water cut, cumulative oil production, and cumulative water production. The reserve data includes static carved reserves and dynamic reserves. The physical property data includes crude oil volume coefficient, crude oil density, and crude oil viscosity data.

[0061] Specifically, Figure 1 Table 1 shows the actual data on moisture content and extraction degree according to the embodiments of this disclosure.

[0062] The changes in recovery rate at different times were calculated based on daily oil production, cumulative oil production, and reserves data. The changes in water cut at corresponding times were calculated based on daily water production, thus obtaining the relationship between water cut and recovery rate, as shown in Table 1. Figure 1 As shown.

[0063] Table 1 shows the actual data of water content fw and extraction degree R according to the embodiments of this disclosure.

[0064] R fw 2.6758 2.478 3.7495 5.312 4.7446 7.33 5.861 9.708 7.0469 14.1 8.0859 16.4 9.4985 22.1 11.4919 29.3 13.2263 36.2 14.9699 42.1 16.5664 50.2 18.2302 56.1 19.7915 65.164 21.1784 70.583 22.5643 76.2 23.8297 79.603 24.6785 82.217 25.5961 83.1 26.4272 86.532 27.1713 87.966

[0065] Next, proceed to step S2.

[0066] In step S2, the key parameters of relative permeability for each oil well are determined. These key parameters include bound water saturation, residual oil saturation, relative permeability of the water phase, and relative permeability of the oil phase. The data are obtained from conventional laboratory tests.

[0067] Input physical property data and phase permeability parameters, i.e., the key parameters, including oil phase viscosity of 52 mPa·s, water phase viscosity of 2.9 mPa·s, and oil phase density of 0.86 kg / m³. 3 The density of the aqueous phase is 1 kg / m³ 3The oil phase volume factor is 1.12, the water phase volume factor is 1, the input range for the oil phase interpenetration endpoint is 0.01-0.2, the input range for the water phase interpenetration endpoint is 0.01-0.2, the input range for the oil phase interpenetration index is 0-3, and the input range for the water phase interpenetration index is 0-3. Calculate the bound water saturation and residual oil saturation.

[0068] Next, proceed to step S3.

[0069] In step S3, the objective function for calculation optimization is determined. The objective function is the difference between the inverted calculated moisture content fw and the actual moisture content fw*, and the formula is:

[0070]

[0071] Where E is the calculation error, fw is the inversion calculation moisture content, fw* is the actual moisture content, and n is the number of data points involved in the calculation.

[0072] Next, proceed to step S4.

[0073] In step S4, the inversion calculation of the water cut fw of the oil well is performed using the following formula:

[0074]

[0075] Where fw is the water content calculated by inversion, ρw is the density of the aqueous phase, ρo is the density of the oil phase, Krw is the relative permeability of the aqueous phase, Kro is the relative permeability of the oil phase, μw is the viscosity of the aqueous phase, μo is the viscosity of the oil phase, Bw is the volume factor of the aqueous phase, and Bo is the volume factor of the oil phase.

[0076] Next, proceed to step S5.

[0077] In step S5, the relative permeability of the oil phase and the relative permeability of the water phase in the oil well are calculated. Correction parameters are randomly generated, and the relative permeability of the oil phase and the relative permeability of the water phase in the oil well are calculated. The formulas for calculating the relative permeability of the water phase and the relative permeability of the oil phase are as follows:

[0078]

[0079] Where Krw is the relative permeability of the aqueous phase, Kro is the relative permeability of the oil phase, Sw is the water saturation, Swi is the bound water saturation, Sor is the residual oil saturation, nw and no are randomly generated correction parameters, Krwe is the relative permeability of the aqueous phase calculated in the previous cycle, and Kroe is the relative permeability of the oil phase calculated in the previous cycle.

[0080] The calculation process and Python code for implementation are as follows:

[0081] Step 1: Input extraction level and moisture content

[0082] R=np.array([2.6758,3.7495,4.7446,5.861,7.0469,8.0859,9.4985,11.4919])

[0083] fwr=np.array([2.478,5.312,7.33,9.708,14.1,16.4,22.1,29.3])

[0084] Step 2: Define the objective equation

[0085] def obj(a):

[0086] krwe,nw,kroe,no=a

[0087] Sw_a=R*(1-Swr) / 100+swr

[0088] krw=krwe*((Sw_a-Swr) / (1-Swr-Sor))**nw

[0089] kro=kroe*((1-Sw_a-Sor) / (1-Swr-Sor))**no

[0090] fw=denw*krw / (muw*Bw) / (denw*krw / (muw*Bw)+deno*kro / (muo*Bo))

[0091] error = np.sum((fw-fwr)**2)

[0092] Step 3: Iterative Solution

[0093] varbound=np.array([[0.001,1],[0.01,10],[0.001,1][0.01,10]])

[0094] model=ga(function=obj,dimesion=4,variable_type='real',variable_varbound)

[0095] model.run

[0096] Next, proceed to step S6.

[0097] In step S6, the calculated relative permeability of the oil phase and the relative permeability of the water phase of the oil well are substituted into formula (2) to calculate the water cut, and the calculated water cut is substituted into the objective function calculation formula (1).

[0098] Next, proceed to step S7.

[0099] In step S7, it is determined whether the objective function value is the minimum value, including:

[0100] If the objective function value is the minimum, then the parameter values ​​corresponding to the last generation of individuals are output to obtain the relative permeability of the water phase and the relative permeability of the oil phase.

[0101] If the objective function value is not the minimum, proceed to steps S5 and S6 to recalculate in sequence until the minimum objective function value is obtained, and then output the relative permeability of the water phase and the relative permeability of the oil phase.

[0102] Figure 2 and Figure 3 The diagram shows the objective function and inversion result of relative permeability inversion according to an embodiment of the present invention. Figure 4 and Figure 5 The diagram shows the inversion results for different storage group types according to embodiments of this disclosure. For example... Figure 2 and Figure 3 The calculation results output relative permeability curves. Based on these curves, relative permeability curves for different fractured-vuggy reservoir types are calculated. The calculation results are consistent with the flow patterns of different reservoir types. Vuggy reservoirs have strong initial flow capacity, but after water exposure, the bottom water coning is weaker than that of fractured-vuggy reservoirs. Figure 4 ), fractured reservoirs ( Figure 5 The phase permeation curve shows a typical cross-flow pattern, indicating that the method disclosed in this invention patent is highly reliable.

[0103] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A method for determining the relative permeability of fractured-vuggy carbonate reservoirs, characterized in that, Includes the following steps: S1. Collect production data, reserve data and physical property data of the oil wells involved in the fractured-vuggy unit to be analyzed, and calculate the relationship between the water cut and the degree of recovery of the oil wells to be analyzed. S2. Collect the relative permeability calculation parameters for each oil well to be analyzed; S3. Determine the objective function for the optimization calculation, as shown in the formula: Where E is the calculation error, fw is the inverted calculated moisture content, fw* is the actual moisture content, and n is the number of data points involved in the calculation. S4. Determine the formula for calculating the water cut fw of the oil well to be analyzed. The formula is: Where fw is the water content calculated by inversion, and ρ w ρ is the density of the aqueous phase, ρo is the density of the oil phase, Krw is the relative permeability of the aqueous phase, Kro is the relative permeability of the oil phase, μw is the viscosity of the aqueous phase, μo is the viscosity of the oil phase, Bw is the volume coefficient of the aqueous phase, and Bo is the volume coefficient of the oil phase. S5. Calculate the relative permeability of the oil phase and the relative permeability of the water phase in the well to be analyzed, using the following formula: Among them, K rw K represents the relative permeability of the aqueous phase. ro is the relative permeability of the oil phase, Sw is the water saturation, Swi is the bound water saturation, Sor is the residual oil saturation, nw and no are randomly generated correction parameters, Krwe is the relative permeability of the water phase calculated in the previous cycle, and Kroe is the relative permeability of the oil phase calculated in the previous cycle. S6. Substitute the oil phase relative permeability and water phase relative permeability calculated in step S5 into formula (2) to obtain the inversion calculation water content result, and then substitute the inversion calculation water content result into formula (1) to obtain the calculation error; S7. Repeat steps S5 and S6. Based on the magnitude of the calculation error, determine the accuracy of the oil phase relative permeability and water phase relative permeability results, and output the optimal oil phase relative permeability and water phase relative permeability.

2. The method according to claim 1, characterized in that, The production data mentioned in step S1 includes daily oil production, daily water production, water content, cumulative oil production, and cumulative water production.

3. The method according to claim 1, characterized in that, The reserve data mentioned in step S1 includes static sculpted reserves and dynamic reserves.

4. The method according to claim 1, characterized in that, The physical property data mentioned in step S1 includes crude oil volume factor, crude oil density, and crude oil viscosity data.

5. The method according to claim 4, characterized in that, The method for calculating the relationship between the water cut and the recovery degree of the oil well to be analyzed in step S1 is as follows: calculate the changes in the recovery degree at different times based on the daily oil production, cumulative oil production and reserves data.

6. The method according to claim 5, characterized in that, The method for calculating the relationship between the water cut and the recovery rate of the oil well to be analyzed in step S1 also includes: calculating the water cut change at the corresponding time based on the daily water production.

7. The method according to claim 1, characterized in that, The relative permeability calculation parameters mentioned in step S2 include bound water saturation and residual oil saturation.

8. The method according to claim 7, characterized in that, The calculation results of the bound water saturation and residual oil saturation are obtained based on the physical property parameters and the relative permeability parameters.

9. The method according to claim 8, characterized in that, The physical properties and relative permeability parameters on which the calculation results of the bound water saturation and residual oil saturation are based include: Oil phase viscosity, water phase viscosity, oil phase density, water phase density, oil phase volume index, and water phase volume index.

10. The method according to claim 9, characterized in that, The physical property parameters and relative permeability parameters on which the calculation results of the bound water saturation and residual oil saturation are based also include: The range of variation of the oil phase interpenetration endpoint, the range of variation of the water phase interpenetration endpoint, the range of variation of the oil phase interpenetration index, and the range of variation of the water phase interpenetration index.

11. The method according to claim 10, characterized in that, The variation range of the oil phase permeability endpoint is 0.01-0.2; The variation range of the aqueous phase infiltration endpoint is 0.01-0.2; The oil phase permeability index varies from 0 to 3. The water phase interpenetration index varies from 0 to 3.

12. A system for determining the relative permeability of fractured-vuggy carbonate reservoirs, comprising a computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for determining the relative permeability of a carbonate fracture-vuggy reservoir as described in any one of claims 1-11.

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