Method and device for determining limit saturation through rock core oil displacement experiment data
Through the fitting function relationship of core displacement experimental data, the maximum water saturation is calculated using an optimization algorithm, which solves the problem of lack of basis for determining residual oil saturation errors and extrapolation in the existing technology, and achieves more accurate reservoir recovery Rate prediction.
Patent Information
- Application Number
- CN202310714750.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-15
- Publication Date
- 2024-12-17
AI Technical Summary
The prior art cannot accurately determine the residual oil saturation in the core, resulting in errors in the results of the phase permeability experiment. The extrapolation method lacks theoretical basis and cannot be unified.
By obtaining core displacement experimental data, the average water saturation and injection multiple of the core are determined, the fitting functional relationship is established, and the maximum water saturation is calculated using an optimization algorithm program to determine the residual oil saturation.
It improves the accuracy of residual oil saturation in the phase permeability curve, provides more reliable data support for reservoir recovery calculation, and avoids the uncertainty caused by artificial extrapolation.
Smart Images
Figure CN119149882A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of oil reservoir engineering, and in particular to a method and a device for determining limiting saturation from core oil displacement experimental data. Background Art
[0002] At present, the conventional method for obtaining phase permeability curves is mainly indoor experimental testing. The current industry standard for phase permeability experiments stipulates that the cutoff condition for water-driven oil phase permeability experiments is "water content reaches 99.95% or water injection is 30 times the pore volume". At this time, the oil saturation in the core is regarded as residual oil saturation. This method has simple conditions and is easy to master in the laboratory. However, when the experiment stops, there is still a part of movable oil in the core that has not been produced and is regarded as "residual oil", resulting in a large residual oil saturation.
[0003] The physical meaning of residual oil saturation is the core oil saturation when the water content is 100%. During the phase permeability test, the water content starts to increase slowly after reaching 95% to 98%, and it will take a long time to reach 100% water content. During this process, the cumulative oil production will gradually increase. In theory, the time required for the water content to reach 100% tends to infinity, so the real residual oil saturation cannot be directly measured in indoor experiments.
[0004] Therefore, experimenters often extrapolate part of the maximum water saturation curve to compensate for experimental errors, but the extrapolation method usually lacks theoretical basis and cannot be unified. Summary of the invention
[0005] The present invention proposes a method and device for determining the limiting saturation from core flooding experimental data, so as to solve the problem that in the past, when conducting phase permeability tests, the residual oil saturation could not be accurately measured in indoor experiments, and the experimental error was compensated by extrapolating the water saturation curve, but this method lacks theoretical basis and the extrapolation method cannot be unified.
[0006] According to one aspect of the present invention, there is provided a method for determining limiting saturation from core flooding experimental data, comprising: acquiring core flooding experimental data;
[0007] According to the core displacement experimental data, determine the average water saturation and injection multiple of the core at each timing point;
[0008] Determine a fitting function relationship between the average water saturation and the inverse of the injection multiple according to the average water saturation of the core and the core displacement experimental data;
[0009] According to the fitting function relationship and the core displacement experimental data, the maximum water saturation of the core is determined by an optimization algorithm program;
[0010] The residual oil saturation of the core is determined according to the maximum water saturation, and the residual oil saturation is the limiting saturation.
[0011] Preferably, the core flooding experiment data at least includes: core pore volume, irreducible water saturation, time of each timing point, cumulative oil production and injection volume.
[0012] Preferably, the method for determining the average water saturation of the core at each timing point based on the core displacement experimental data comprises:
[0013] The average water saturation calculation formula is used to determine the average water saturation of the core at each timing point;
[0014] The average water saturation calculation formula is:
[0015]
[0016] Where: S wc is the bound water saturation, O cp is the cumulative oil output, V pcw is the total pore volume.
[0017] Preferably, the method for determining the injection multiple at each timing point based on core flooding experimental data includes:
[0018] Use the injection multiple calculation formula to determine the injection multiple corresponding to each timing point;
[0019] The injection multiple calculation formula is:
[0020]
[0021] Where: W ci is the cumulative injection volume, V pcw is the total pore volume.
[0022] Preferably, the fitting function relationship between the average water saturation and the inverse of the injection multiple is:
[0023]
[0024] Where: f w ' e is the inverse of the injection multiple, is the average water saturation, a 1 、a 2 、a 3 、a 4 are the coefficients of the fitting function.
[0025] Preferably, the method for determining the maximum water saturation of the core by optimizing the algorithm program according to the fitting function relationship and the core displacement experimental data includes:
[0026] According to the average water saturation and injection multiple corresponding to each timing point of the core displacement experimental data, the fitting function coefficient a in the fitting function relationship is solved by an optimization algorithm program. 1 、a 3 The value of
[0027] According to the fitting function coefficient a 1 、a 3 The value of is used to determine the maximum water saturation of the core.
[0028] Preferably, the optimization algorithm program is: local minimization algorithm L-BFGS-B.
[0029] Preferably, the method for determining the residual oil saturation of the core according to the maximum water saturation comprises:
[0030] The residual oil saturation = 1 - maximum water saturation.
[0031] According to one aspect of the present invention, there is provided a device for determining limiting saturation from core flooding experimental data, comprising:
[0032] An acquisition unit, used to acquire core flooding experimental data;
[0033] An average water saturation and injection multiple determination unit, used to determine the average water saturation and injection multiple of the core at each timing point according to the core displacement experimental data;
[0034] A fitting function determination unit, used to determine a fitting function relationship between the average water saturation and the inverse of the injection multiple according to the average water saturation of the core and the core displacement experimental data;
[0035] A maximum water saturation determination unit is used to determine the maximum water saturation of the core through an optimization algorithm program according to the fitting function relationship and the core displacement experimental data;
[0036] The limiting saturation determination unit is used to determine the residual oil saturation of the core according to the maximum water saturation, and the residual oil saturation is the limiting saturation.
[0037] The present invention has at least the following beneficial effects:
[0038] The present invention proposes a method and device for determining the limiting saturation from core flooding experimental data, regressing the fitting function relationship between the average water saturation and the injection multiple through the data obtained from the original core displacement experiment, and obtaining the maximum water saturation, i.e., the residual oil saturation, by finding the mathematical limit. The residual oil saturation of the phase permeability curve obtained by the method of the present invention is more accurate, has a theoretical basis, and can provide more accurate data support for calculating the ultimate recovery rate of the oil reservoir. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] The accompanying drawings herein are incorporated into and constitute a part of the specification. These drawings illustrate embodiments consistent with the present invention and, together with the specification, are used to explain the technical solutions of the present invention.
[0040] Figure 1 A flow chart showing a method for determining limiting saturation from core flooding experimental data according to an embodiment of the present invention. DETAILED DESCRIPTION
[0041] Various exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.
[0042] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.
[0043] The term "and / or" herein is only a description of the association relationship of the associated objects, indicating that there may be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the term "at least one" herein represents any combination of at least two of any one or more of a plurality of. For example, including at least one of A, B, and C can represent including any one or more elements selected from the set consisting of A, B, and C.
[0044] In addition, in order to better illustrate the present invention, numerous specific details are provided in the following specific embodiments. It should be understood by those skilled in the art that the present invention can be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the subject matter of the present invention.
[0045] Figure 1 A flow chart showing a method for determining the limiting saturation from core flooding experimental data according to an embodiment of the present invention is shown. Figure 1As shown, a method for determining the limiting saturation from core flooding experimental data comprises: step S01: acquiring core displacement experimental data; step S02: obtaining the core average water saturation and injection multiple at each timing point according to the core displacement experimental data; step S03: determining the fitting function relationship between the average water saturation and the inverse of the injection multiple according to the core average water saturation and the core displacement experimental data; step S04: determining the maximum water saturation of the core through an optimization algorithm program according to the fitting function relationship and the core displacement experimental data; step S05: determining the residual oil saturation of the core according to the maximum water saturation, and the residual oil saturation is the limiting saturation.
[0046] The method for determining the limiting saturation from core flooding experimental data provided by the embodiment of the present invention specifically comprises the following steps:
[0047] Step S01: obtaining core flooding experimental data;
[0048] In the present invention, the core flooding experimental data at least include: core pore volume, irreducible water saturation, time of each timing point, cumulative oil production and injection volume.
[0049] In the embodiment of the present invention, the core displacement experiment data can be the original data of the non-steady-state method of oil-water relative permeability detection, that is, time, water volume and oil volume, specifically including the core pore volume, bound water saturation, time at each timing point, cumulative oil production, and injection multiples.
[0050] Step S02: According to the core displacement experimental data, the average water saturation of the core at each timing point is obtained.
[0051] In the present invention, the method for determining the average water saturation of the core at each timing point according to the core displacement experimental data comprises: determining the average water saturation of the core at each timing point using the average water saturation calculation formula;
[0052] The average water saturation calculation formula is:
[0053]
[0054] Where: S wc is the bound water saturation, O cp is the cumulative oil output, V pcw is the total pore volume.
[0055] In the embodiment of the present invention, the cumulative oil production corresponding to each timing point in the core flooding experiment, as well as the total pore volume and irreducible water saturation of the core are substituted into formula (1) to determine the average water saturation corresponding to each timing point.
[0056] In the present invention, the method for determining the injection multiple at each timing point according to the core displacement experimental data includes: using the injection multiple calculation formula to determine the injection multiple corresponding to each timing point;
[0057] The injection multiple calculation formula is:
[0058]
[0059] Where: W ci is the cumulative injection volume, V pcw is the total pore volume.
[0060] In the embodiment of the present invention, the cumulative injection volume corresponding to each timing point in the core displacement experiment and the total pore volume of the core are substituted into formula (2) to determine the injection multiple corresponding to each timing point.
[0061] Step S03: According to the average water saturation of the core and the core displacement experimental data, a fitting function relationship between the average water saturation and the inverse of the injection multiple is determined.
[0062] In the present invention, the fitting function relationship between the average water saturation and the inverse of the injection multiple is:
[0063]
[0064] Where: f w ' e is the inverse of the injection multiple, is the average water saturation, a 1 、a 2 、a 3 、a 4 are the coefficients of the fitting function.
[0065] In the embodiment of the present invention, the reciprocal of the injection multiple is 1 / PV. The analytical expression (fitting function) is obtained by fitting the displacement data (average water saturation and injection multiple) corresponding to each timing point in the experimental process. This analytical expression can fit the displacement data, and the analytical expression has a limit. After fitting, the exact value of the residual oil saturation can be obtained.
[0066] Step S04: According to the fitting function relationship and the core displacement experimental data, the maximum water saturation of the core is determined by an optimization algorithm program.
[0067] In the present invention, the method for determining the maximum water saturation of the core by optimizing the algorithm program according to the fitting function relationship and the core displacement experimental data includes: solving the fitting function coefficient a in the fitting function relationship by optimizing the algorithm program according to the average water saturation and injection multiple corresponding to each timing point of the core displacement experimental data.1 、a 3 The value of the fitting function coefficient a 1 、a 3 The value of is used to determine the maximum water saturation of the core.
[0068] In the present invention, the optimization algorithm program is: local minimization algorithm L-BFGS-B.
[0069] In the embodiment of the present invention, after calculating the binary sequence of the PV number (injection multiple) and the average water saturation at each timing point, the optimization algorithm L-BFGS-B can be used to calculate a 1 、a 2 、a 3 、a 4 The optimization algorithm is the limited memory BFGS algorithm, which is a local minimization algorithm.
[0070] Step S05: Determine the residual oil saturation of the core according to the maximum water saturation, and the residual oil saturation is the limit saturation.
[0071] In the present invention, the method for determining the residual oil saturation of the core according to the maximum water saturation includes: the residual oil saturation = 1-maximum water saturation.
[0072] In the embodiment of the present invention, since the residual oil saturation = 1-maximum water saturation, and the maximum water saturation is the saturation when the PV (injection multiple) is the maximum, that is, the PV takes the maximum limit, then f w ' e Close to 0, that is, f w ' e = 0, according to the fitting function (3), the maximum water saturation is: a 1 +a 3 , the residual oil saturation is: 1-(a 1 +a 3 ).
[0073] In the embodiment of the present invention, the original data of the non-steady-state oil-water relative permeability test of a core is: the total pore volume of the core is 11.34cm 2 , bound water saturation: 0.3078, the cumulative oil output and injection multiples at each timing point (cumulative time) are shown in Table 1 below.
[0074] Table 1: Original data table of oil-water relative permeability test using non-steady-state core method
[0075]
[0076]
[0077] According to the core irreducible water saturation S wc , total pore volume V pcw As well as the cumulative oil output in Table 1, the average water saturation corresponding to each timing point is calculated using formula (1):
[0078]
[0079] According to the total pore volume V pcw And the cumulative injection volume in Table 1, use formula (2) to calculate the PV number corresponding to each timing point:
[0080]
[0081] The final calculation results are shown in Table 2 below.
[0082] Table 2: Calculation table of average water saturation of core
[0083]
[0084] According to the analytical expression, that is, the fitting function (3), a is calculated 1 、a 2 、a 3 、a 4 The value of f w ' e is the inverse of the injection multiple, The average water saturation is obtained by reading the injection multiple PV and average water saturation in Table 2 through the program. The two columns are calculated by the optimization algorithm L-BFGS-B to obtain a 1 =0.774817, a 2 =-0.0282568, a 3 =0.0573529, a 4 =4.04084; R^2=0.995914, indicating a good fit.
[0085] According to the analytical formula, the water saturation at the limit is taken as the maximum water saturation, and the maximum water saturation is: a 1 +a 3 =0.8321699; then the residual oil saturation is: 1-(a 1 +a 3 )=0.167830.
[0086] The residual oil saturation calculated by the method of the present invention is 0.167830, which is 0.03947 less than the residual oil saturation of 0.2073 of the original phase permeability curve. The residual oil saturation obtained by this method is more accurate and reasonable than the result of the original experimental data.
[0087] It can be understood that the above-mentioned various method embodiments mentioned in the present invention can be combined with each other to form a combined embodiment without violating the principle logic. Due to space limitations, the present invention will not go into details.
[0088] The execution subject of the method for determining the limit saturation from the core flooding oil experiment data may be a device for determining the limit saturation from the core flooding oil experiment data. For example, the method for determining the limit saturation from the core flooding oil experiment data may be executed by a terminal device or a server or other processing device, wherein the terminal device may be a user equipment (UE), a mobile device, a user terminal, a terminal, a cellular phone, a cordless phone, a personal digital assistant (PDA), a handheld device, a computing device, a vehicle-mounted device, a wearable device, etc. In some possible implementations, the method for determining the limit saturation from the core flooding oil experiment data may be implemented by a processor calling a computer-readable instruction stored in a memory. "
[0089] Those skilled in the art will appreciate that, in the above method of specific implementation, the order in which the steps are written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of the steps should be determined by their functions and possible internal logic.
[0090] The present invention also provides a device for determining the limiting saturation from core flooding experimental data, comprising:
[0091] An acquisition unit is used to acquire core displacement experimental data; an average water saturation and injection multiple determination unit is used to obtain the average water saturation and injection multiple of the core at each timing point according to the core displacement experimental data; a fitting function determination unit is used to determine the fitting function relationship between the average water saturation and the inverse of the injection multiple according to the average water saturation of the core and the core displacement experimental data; a maximum water saturation determination unit is used to determine the maximum water saturation of the core through an optimization algorithm program according to the fitting function relationship and the core displacement experimental data; a limit saturation determination unit is used to determine the residual oil saturation of the core according to the maximum water saturation, and the residual oil saturation is the limit saturation.
[0092] In some embodiments, the functions or modules and units included in the device provided by the embodiment of the present invention can be used to execute the method described in the above method embodiment. Its specific implementation can refer to the description of the above method embodiment. For the sake of brevity, it will not be repeated here.
[0093] Water injection development is the main development method for oil reservoirs at home and abroad, and the oil-water relative permeability curve is an indispensable data for water injection development of oil reservoirs. The application of relative permeability curves can be used to carry out research work in reservoir engineering parameter calculation, dynamic analysis, numerical simulation, etc., which is of great significance for guiding oil field development. At present, the residual oil saturation of the relative permeability curve given by the non-steady-state relative permeability method has artificial factors. Some are based on 98% water content, but the water content cannot be directly measured and points must be taken manually; if it is based on PV numbers, it is not uniform and is often artificially taken, so the uncertainty is too large. These values are often larger than the theoretical residual oil saturation, which will cause errors in production prediction.
[0094] In view of the shortcomings of the conventional phase permeability test method for determining residual oil saturation, the present invention proposes a method for regressing the relationship between average saturation and injection multiple through the original displacement data, and obtaining the maximum water saturation, i.e., residual oil saturation, by finding the mathematical limit. That is, by reading the injection volume and cumulative oil output corresponding to each timing point in the core displacement test data, calculating the average water saturation SW and injection multiple PV data, and cyclically calling the L-BFGS-B calculation library subroutine to obtain the fitting function coefficient a 1 、a 2 、a 3 、a 4 The value of 1 +a 3 ) Calculate the residual oil saturation SOR and calculate the regression correlation coefficient R 2 Determine the regression effect. This method can solve the problem that the actual residual oil saturation cannot be determined experimentally and there is no theoretical basis for artificially extrapolating the relative permeability curve.
[0095] The present invention uses direct data from core displacement experiments to obtain theoretical residual oil saturation through mathematical methods, and provides a unified method for calculating residual oil saturation. In addition to phase permeability experiments, there are a large number of core experiments to evaluate the effects of water flooding, polymer flooding, composite flooding, foam flooding, and adjustment and displacement effects, but the cutoff conditions for the final recovery rate are not unified. The residual oil saturation of the phase permeability curve obtained by this method is more accurate, and can provide more accurate data support for calculating the final recovery rate of the oil reservoir.
[0096] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.
Claims
1. A method for determining limiting saturation from core flooding experimental data, characterized in that: include: Obtain core flooding experimental data; According to the core displacement experimental data, determine the average water saturation and injection multiple of the core at each timing point; Determine a fitting function relationship between the average water saturation and the inverse of the injection multiple according to the average water saturation of the core and the core displacement experimental data; According to the fitting function relationship and the core displacement experimental data, the maximum water saturation of the core is determined by an optimization algorithm program; The residual oil saturation of the core is determined according to the maximum water saturation, and the residual oil saturation is the limiting saturation.
2. The method for determining limiting saturation from core flooding experimental data according to claim 1, characterized in that: The core displacement experiment data at least include: core pore volume, irreducible water saturation, time of each timing point, cumulative oil output and injection volume.
3. The method for determining limiting saturation from core flooding experimental data according to claim 1, characterized in that: The method for determining the average water saturation of the core at each timing point based on the core displacement experimental data includes: The average water saturation calculation formula is used to determine the average water saturation of the core at each timing point; The average water saturation calculation formula is: Where: S wc is the bound water saturation, O cp is the cumulative oil output, V pcw is the total pore volume.
4. The method for determining limiting saturation from core flooding experimental data according to claim 1, characterized in that: The method for determining the injection multiple at each timing point according to the core displacement experimental data includes: Use the injection multiple calculation formula to determine the injection multiple corresponding to each timing point; The injection multiple calculation formula is: Where: W ci is the cumulative injection volume, V pcw is the total pore volume.
5. The method for determining limiting saturation from core flooding experimental data according to claim 1, characterized in that: The fitting function relationship between the average water saturation and the inverse of the injection multiple is: Where: f w ' e is the reciprocal of the injection multiple, is the average water saturation, a1, a2, a3, and a4 are the fitting function coefficients.
6. The method for determining limiting saturation from core flooding experimental data according to claim 5, characterized in that: The method for determining the maximum water saturation of the core by optimizing the algorithm program based on the fitting function relationship and the core displacement experimental data includes: According to the average water saturation and injection multiple corresponding to each timing point of the core displacement experimental data, the values of the fitting function coefficients a1 and a3 in the fitting function relationship are solved by an optimization algorithm program; The maximum water saturation of the core is determined according to the values of the fitting function coefficients a1 and a3.
7. The method for determining limiting saturation from core flooding experimental data according to claim 6, characterized in that: The optimization algorithm program is: local minimization algorithm L-BFGS-B.
8. The method for determining limiting saturation from core flooding experimental data according to any one of claims 1 to 7, characterized in that: The method for determining the residual oil saturation of the core according to the maximum water saturation comprises: The residual oil saturation = 1 - maximum water saturation.
9. A device for determining limiting saturation from core flooding experimental data, characterized in that: include: An acquisition unit, used to acquire core flooding experimental data; An average water saturation and injection multiple determination unit, used to determine the average water saturation and injection multiple of the core at each timing point according to the core displacement experimental data; A fitting function determination unit, used to determine a fitting function relationship between the average water saturation and the inverse of the injection multiple according to the average water saturation of the core and the core displacement experimental data; A maximum water saturation determination unit is used to determine the maximum water saturation of the core through an optimization algorithm program according to the fitting function relationship and the core displacement experimental data; The limiting saturation determination unit is used to determine the residual oil saturation of the core according to the maximum water saturation, and the residual oil saturation is the limiting saturation.