A method and system for determining permeability sensitivity coefficients for a solution-filled cavern reservoir
Patent Information
- Application Number
- CN202311146884.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-09-06
- Publication Date
- 2026-09-08
- Estimated Expiration
- 2043-09-06
AI Technical Summary
但是目前压力试井法所依赖的模型存在2方面的不足:一是没有考虑填充溶洞的介质变形特征,不适用于生产井钻遇填充溶洞型油藏的生产过程;二是目前裂缝储层中流动均为平面径向流,没有考虑填充溶洞的空间特征引起的空间径向流特征,难以表征真实的流动特征
[0063] The beneficial effects of this invention are as follows: This invention obtains the permeability parameters of drilled caverns and the physical properties of the surrounding reservoir by testing pressure data. It takes into account the deformation coefficient of the cavern reservoir medium and the spherical concentric flow characteristics, which is more consistent with the actual production conditions of production wells that have drilled caverns. It solves the problem that existing seepage models and interpretation methods are not applicable to cavern reservoirs and cannot obtain the permeability parameters of cavern reservoirs, thus enriching the existing theories and interpretation methods of oil and gas seepage in fractured reservoirs.
Smart Images

Figure CN117307142B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of oil and gas field development technology, and in particular to a method and system for determining the permeability sensitivity coefficient of a cavernous reservoir. Background Technology
[0002] In recent years, China's marine carbonate rock oil reserves have been mainly distributed in the Tarim Basin, primarily in fracture-vuggy reservoirs. In these reservoirs, oil is mainly stored in the pores between natural fractures, natural caverns, and cavern fillings. Cavern-filled spaces within the rock provide excellent storage space and are locations easily encountered and completed during drilling. Due to differences in cementation and diagenesis between the fillings and the surrounding reservoir, cavern fillings often exhibit significant pressure sensitivity. During production, pressure reductions can easily cause changes in near-wellbore permeability, thus affecting the production capacity of wells. Accurate reservoir permeability is crucial for subsequent production capacity evaluation during oilfield development. However, due to the discontinuous and highly heterogeneous nature of the medium in these reservoirs, conventional sampling and testing methods are insufficient to obtain reservoir permeability-related physical parameters. The main reason is that the presence of natural fractures in the rock makes core sampling extremely prone to breakage, making it difficult to obtain complete fractured rock samples under laboratory conditions, thus preventing the acquisition of rock parameters and permeability parameters through testing.
[0003] Therefore, compared to conventional mean sandstone reservoirs, the use of test pressure during production to obtain reservoir permeability (pressure well testing) is widely used in fractured-vuggy reservoirs. However, the models currently used in pressure well testing have two shortcomings: first, they do not consider the deformation characteristics of the medium filled with caverns, making them unsuitable for production wells encountering cavern-filled reservoirs; second, current flow patterns in fractured reservoirs are all planar radial flow, failing to consider the spatial radial flow characteristics caused by the spatial features of the caverns, making it difficult to characterize the true flow patterns. Summary of the Invention
[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.
[0005] In view of the aforementioned existing problems, the present invention is proposed.
[0006] Therefore, this invention provides a method and system for determining the permeability sensitivity coefficient of a cavernous reservoir, solving the problem that existing seepage models and interpretation methods are not applicable to drilling into cavernous reservoirs and cannot obtain the permeability parameters of cavernous reservoirs.
[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:
[0008] In a first aspect, the present invention provides a method for determining the permeability sensitivity coefficient of a cavernous reservoir, comprising: measuring pressure changes over time during well shut-in period;
[0009] A mathematical model of bottom hole pressure in fractured reservoirs filled with karst caves was established, and the theoretical bottom hole pressure solution was obtained by solving the established mathematical model.
[0010] The actual pressure measurement data is fitted to obtain the fitting parameters.
[0011] As a preferred embodiment of the method for determining the permeability sensitivity coefficient of a cavernous reservoir according to the present invention, it further includes the following steps:
[0012] Lower the pressure gauge to the bottom of the test well and measure the pressure change over time during the well shut-in period.
[0013] Based on the basic data, the bottom pressure of the well was solved by using a mathematical model of the bottom pressure of a fractured oil reservoir filled with karst caves.
[0014] Set the initial parameters of the model, which will serve as the initial values for the fitting parameters;
[0015] Set the fitting error and calculate the difference between the measured bottom hole pressure and the pressure in the mathematical model;
[0016] If the difference between the calculated value and the actual value is less than the fitting error, then output the initial parameters;
[0017] If the difference between the calculated value and the actual value is not less than the fitting error, then the parameters to be fitted are corrected.
[0018] The fitting parameters are output only after both parameters are within the fitting error range.
[0019] As a preferred embodiment of the method for determining the permeability sensitivity coefficient of a cavern-filled reservoir as described in this invention, wherein: the establishment of a mathematical model of the bottom-hole pressure of a fractured reservoir encountering cavern-filled areas divides the entire reservoir flow system into two parts: a cavern-filled region and a peripheral reservoir region. The dimensionless form of the seepage equation for the cavern-filled region is expressed as:
[0020]
[0021] The dimensionless form of the flow equation for the outer reservoir region is expressed as:
[0022]
[0023] As a preferred embodiment of the method for determining the permeability sensitivity coefficient of a cavern-filled reservoir according to the present invention, wherein: a mathematical model of the bottom-hole pressure of a fractured reservoir encountering cavern-filled areas is established, and the established mathematical model is solved, the seepage equation of the cavern-filled region is transformed by perturbation into:
[0024]
[0025] Where, r D For an infinite distance, t D Time is dimensionless;
[0026] Dimensionless perturbation pressure ζ D With dimensionless pressure p D The relationship is represented as:
[0027]
[0028] Wherein, γ is the stress sensitivity coefficient;
[0029] The seepage equation filling the karst region, after perturbation transformation and then Laplace transformation, becomes:
[0030]
[0031] Where u is a Laplace space variable.
[0032] As a preferred embodiment of the method for determining the permeability sensitivity coefficient of a cavern-filled reservoir according to the present invention, wherein: a mathematical model of the bottom-hole pressure of a fractured reservoir encountering cavern-filled reservoir is established, and the established mathematical model is solved, the pressure solution of the filled region is expressed as:
[0033]
[0034] A1 and B1 are the parameters to be determined.
[0035] After the Laplace transform, the flow equation of the outer reservoir becomes:
[0036]
[0037] The pressure solution of the outer reservoir is expressed as:
[0038]
[0039] A2 and B2 are the parameters to be determined.
[0040] As a preferred embodiment of the method for determining the permeability sensitivity coefficient of a cavern-filled reservoir according to the present invention, the method involves: establishing a mathematical model of the bottom-hole pressure of a fractured reservoir encountering cavern-filled areas; solving the established mathematical model; and, after perturbation and Laplace transformations, obtaining the pressure and flow conditions at the wellbore location for the cavern-filled region:
[0041]
[0042] The pressure and flow conditions at the boundary between the inner and outer zones of the pressure solution in the cavity-filled region and the pressure solution in the surrounding reservoir are as follows:
[0043]
[0044] The flow condition at the reservoir boundary for the pressure solution of the outer reservoir is:
[0045]
[0046] Substituting the pressure solutions of the cavity-filling region and the surrounding reservoir into the boundary equations, we obtain the following system of equations for the unknown coefficients A1, A2, B1, and B2:
[0047]
[0048] According to Cramer's rule, solving the system of equations A1, A2, B1, and B2 yields A1 and B1 as follows:
[0049]
[0050] Where Δ is matrix a in the system of equations A1, A2, B1, B2. ij The determinant of .
[0051] Substituting A1 and B1 into the pressure solution of the karst region, the dimensionless bottom hole perturbation pressure at the wellbore is:
[0052]
[0053] According to the perturbation transformation relationship, the dimensionless bottom-hole pressure solution in real space is:
[0054]
[0055] Where Ln is the natural logarithm function, L -1 This is the inverse Laplace transform function.
[0056] Secondly, the present invention provides a system suitable for determining the permeability sensitivity coefficient of a cavernous reservoir, comprising: a measurement module for measuring pressure changes over time during well shut-in period;
[0057] A module was established to create a mathematical model of the bottom hole pressure in a fractured reservoir filled with karst caves. The theoretical bottom hole pressure solution was obtained by solving the established mathematical model.
[0058] The fitting module fits the actual pressure measurement data to obtain the fitting parameters.
[0059] Thirdly, the present invention provides a computing device, comprising:
[0060] Memory, used to store programs;
[0061] A processor for executing the computer-executable instructions, which, when executed by the processor, implement the steps of the method for determining the permeability sensitivity coefficient of a cavernous reservoir.
[0062] Fourthly, the present invention provides a computer-readable storage medium comprising: when the program is executed by a processor, implementing the steps of the method for determining the permeability sensitivity coefficient of a cavernous reservoir.
[0063] The beneficial effects of this invention are as follows: This invention obtains the permeability parameters of drilled caverns and the physical properties of the surrounding reservoir by testing pressure data. It takes into account the deformation coefficient of the cavern reservoir medium and the spherical concentric flow characteristics, which is more consistent with the actual production conditions of production wells that have drilled caverns. It solves the problem that existing seepage models and interpretation methods are not applicable to cavern reservoirs and cannot obtain the permeability parameters of cavern reservoirs, thus enriching the existing theories and interpretation methods of oil and gas seepage in fractured reservoirs. Attached Figure Description
[0064] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:
[0065] Figure 1 This is a basic flowchart illustrating a method for determining the permeability sensitivity coefficient of a cavernous reservoir according to an embodiment of the present invention.
[0066] Figure 2 A schematic diagram of a production well encountering a filled cavern, illustrating a method for determining the permeability sensitivity coefficient of a cavern-filled reservoir according to an embodiment of the present invention.
[0067] Figure 3 A flowchart of the test pressure data fitting process for a method of determining the permeability sensitivity coefficient of a cavernous reservoir, provided in one embodiment of the present invention;
[0068] Figure 4 A test pressure data fitting effect diagram for a method of determining the permeability sensitivity coefficient of a cavern reservoir according to an embodiment of the present invention; Detailed Implementation
[0069] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.
[0070] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.
[0071] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.
[0072] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.
[0073] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.
[0074] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0075] Example 1
[0076] Reference Figure 1-2 As one embodiment of the present invention, a method for determining the permeability sensitivity coefficient of a cavernous reservoir is provided, such as... Figure 1 As shown, it includes the following steps:
[0077] S1: Measurement data on pressure changes over time during well shut-in period;
[0078] Furthermore, the pressure gauge is lowered to the target well bottom position to monitor the pressure change value after the well is shut in in real time, and the actual test time and actual test pressure value are recorded.
[0079] S2: Establish a mathematical model of the bottom hole pressure in a fractured reservoir filled with karst caves. Solve the established mathematical model to obtain the theoretical bottom hole pressure solution.
[0080] Furthermore, the entire reservoir flow system is divided into two parts: a cavern-filled zone and a peripheral reservoir zone. The wellbore encounters the cavern-filled zone, and the peripheral reservoir is a fractured reservoir. Considering the deformation characteristics of the cavern-filled medium and the fracture development characteristics of the peripheral reservoir, a mathematical model of "bottom hole pressure in a fractured reservoir encountering a cavern-filled zone" is established. The established mathematical model is solved to obtain the theoretical bottom hole pressure, preparing for subsequent fitting.
[0081] Furthermore, the physical model and explanation:
[0082] like Figure 2 As shown, a production well encountered a cavern-filled area. The inner region is the cavern-filled area, with a porosity of [missing information]. The permeability is k1, and the overall compressibility is c. t1 The distance between the region boundaries is r f The outer zone is a fractured peripheral reservoir with a porosity of [missing information]. The permeability is k2, and the overall compressibility is c. t2 The distance from the outer reservoir boundary is r e The inner reservoir zone exhibits strong medium deformation characteristics, while the outer reservoir zone shows obvious fracture characteristics. The bottom of the wellbore is located at the center of the inner reservoir zone, and the fluid in the inner zone flows radially towards the bottom of the wellbore. The fluid in the outer reservoir zone flows radially towards the interface between the inner and outer zones.
[0083] Furthermore, the process of building a digital model:
[0084] The relationship between dimensional and dimensionless parameters is shown in Table 1.
[0085] Table 1. Relationship between dimensional and dimensionless parameters
[0086]
[0087]
[0088] In the table: Porosity, %; Porosity of the filled region, %; Porosity of the outer reservoir region, %; The value represents the crack porosity, in percentages (%). t The overall compression factor is Pa. -1 c t1 The overall compressibility coefficient of the filled region is Pa. -1 c t2 The comprehensive compressibility coefficient of the outer reservoir region is given in Pa. -1 ;c tf Pa is the crack compressibility coefficient. -1 k is the permeability, m 2 k1 is the permeability of the filling area, m 2 k2 represents the permeability of the outer reservoir region, m 2 ;k m m is the permeability of the rock matrix. 2 ;k f m represents the rock fracture permeability. 2 q is the wellhead flow rate, m 3 / s; μ is the fluid viscosity, Pa·s; B is the fluid volume coefficient; α is the shape factor, m. -2 ;α k Pa is the permeability sensitivity coefficient. -1 r is the distance from the center of the wellbore, in meters (m). w r is the radius of the wellbore, in meters (m). f r is the radius of the filled region, m; e t is the boundary distance of the outer reservoir, in meters (m). t is time, in seconds (s). p is pressure, in Pa. i p1 is the original reservoir pressure, Pa; p2 is the pressure in the filling region, Pa; p3 is the pressure in the outer reservoir region, Pa.
[0089] Furthermore, the region filled with karst caves exhibits medium deformation characteristics, and its dimensionless seepage equation is as follows:
[0090]
[0091] The peripheral reservoir region exhibits fracture characteristics, and its dimensionless flow equation is as follows:
[0092]
[0093] Digital model solution process:
[0094] The seepage equation (1) for filling the karst region becomes, after perturbation transformation:
[0095]
[0096] Dimensionless perturbation pressure ζ D With dimensionless pressure p D The relationship is represented as:
[0097]
[0098] Equation (3) becomes the following after the Laplace transform:
[0099]
[0100] Where u is a Laplace space variable.
[0101] The solution to equation (5) is in the form of:
[0102]
[0103] A1 and B1 are the parameters to be determined.
[0104] After the Laplace transform, the flow equation (2) of the outer reservoir becomes:
[0105]
[0106] The solution to equation (7) is in the form of:
[0107]
[0108] A2 and B2 are the parameters to be determined.
[0109] After perturbation and Laplace transformation, the pressure solution (6) for the karst region has the following pressure and flow conditions at the wellbore location:
[0110]
[0111] The pressure and flow conditions at the boundary between the inner and outer zones of the pressure solution (6) for the filling cavern region and the pressure solution (8) for the outer reservoir are as follows:
[0112]
[0113] The flow condition at the reservoir boundary for the pressure solution (8) of the outer reservoir is:
[0114]
[0115] Substituting the solutions to equations (6) and (8) into the boundary equations (9-11), we obtain a system of equations concerning the unknown coefficients A1, A2, B1, and B2:
[0116]
[0117] The elements within the matrix are,
[0118]
[0119] According to Cramer's rule, solving equation (12) yields A1 and B1 as follows:
[0120]
[0121] Where Δ is matrix a in equation (12). ij The determinant of .
[0122] Substituting (14) into equation (6), the dimensionless bottom hole perturbation pressure at the wellbore is:
[0123]
[0124] According to the perturbation transformation (4), the dimensionless bottom pressure solution in real space is:
[0125]
[0126] Where Ln is the natural logarithm function, L -1 This is the inverse Laplace transform function.
[0127] S3: Fit the actual pressure measurement data to obtain the fitting parameters.
[0128] Furthermore, based on the theoretical bottom-hole pressure values calculated by the model, the actual test pressure data is fitted using the least squares method. The fitted parameters include: the radius of the cavity-filled area, the radius of the outer reservoir, the permeability of the cavity-filled area, the permeability of the outer reservoir area, the permeability sensitivity coefficient of the cavity-filled area, the fracture channeling coefficient of the outer reservoir area, and the fracture storage ratio of the outer reservoir area.
[0129] It should be noted that this invention is particularly effective for production wells in fracture-vuggy reservoirs that encounter caverns, and is also applicable to reservoir conditions of various complex carbonate oil and gas reservoirs, such as porous reservoirs, fracture-vuggy reservoirs, cavernous reservoirs, and fractured reservoirs.
[0130] This embodiment also provides a system suitable for determining the permeability sensitivity coefficient of a cavernous reservoir, including: a measurement module for measuring the pressure change data over time during well shut-in period;
[0131] A module was established to create a mathematical model of the bottom hole pressure in a fractured reservoir filled with karst caves. The theoretical bottom hole pressure solution was obtained by solving the established mathematical model.
[0132] The fitting module fits the actual pressure measurement data to obtain the fitting parameters.
[0133] Furthermore, this also includes:
[0134] Memory, used to store programs;
[0135] A processor is used to load the program to execute the method applicable to determining the permeability sensitivity coefficient of a cavernous reservoir.
[0136] This embodiment also provides a computer-readable storage medium storing a program that, when executed by a processor, implements the method for determining the permeability sensitivity coefficient of a cavernous reservoir.
[0137] The storage medium proposed in this embodiment and the method for determining the permeability sensitivity coefficient of filled cavern reservoirs proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.
[0138] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.
[0139] Example 2
[0140] Refer to Table 1 and Figure 3-4 This invention provides a method for determining the permeability sensitivity coefficient of a cavernous reservoir. To verify the beneficial effects of this invention, specific implementation methods and their effects are scientifically demonstrated.
[0141] The specific details of this embodiment are as follows:
[0142] (1) Lower the pressure gauge to the bottom of the test well and measure the pressure change data (t, P) over time during the well shut-in period. to ).
[0143] (2) Determine the basic parameters of the model (original formation pressure p) based on well logging and geological data. i Wellhead flow rate q, fluid viscosity μ, volume factor B, wellbore radius r w reservoir porosity Overall compression coefficient c t1 c t2 Given the initial values of the fitting parameters M0(r) f0 r e0 k 10 k 20 α k0 , λ m0 ω f0 Using the mathematical model of this invention, the change in bottom hole pressure with shut-in time (t, P) is calculated. t ).
[0144] (3) Set the accuracy error e, and calculate the pressure by fitting the test pressure and mathematical model using the least squares method. Calculate the measured bottom hole pressure P. to The difference between the mathematically calculated pressure Pt and |P t -P to |;If the pressure difference is |Pt-P to If the parameter is less than the accuracy error e, then the parameter corresponding to the initial parameter M0 is used as the final fitted parameter M; if they are not equal, then the parameter M to be fitted is corrected until both are within the accuracy error e, and finally the fitted parameter M(r) is output. f r e k1, k2, α k , λ m ω f The specific fitting process is as follows: Figure 3 As shown, the fitting effect is as follows: Figure 4 As shown.
[0145] (4) Based on the output fitting parameters M(r) f r e k1, k2, α k , λ m ω f The explanatory parameter is obtained as: the radius r of the area filled with the karst cave. f The outer reservoir radius r ePermeability k1 in the cavity-filled area, permeability k2 in the surrounding reservoir area, and permeability sensitivity coefficient α in the cavity-filled area. k Fracture channeling coefficient λ in the outer reservoir region m Fracture capacity ratio ω in the outer reservoir region f The parameters are explained in Table 1.
[0146] Table 1 Explanation of Example Parameters
[0147] Region radius rf = 28.6m re = 2.7km <![CDATA[Permeability m 2 > <![CDATA[k1=1.7×10 -17 m 2 ]]> <![CDATA[k2=4.8×10 -17 m 2 ]]> Permeability Sensitivity <![CDATA[α k =3.6×10 -5 Well -1 ]]> / Crossflow coefficient / <![CDATA[λm=5.8×10 -9 ]]> Storage ratio of fractures / ωf=0.261
[0148] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A method for determining the permeability sensitivity coefficient of a cavernous reservoir, characterized in that, include: Measure the pressure change over time during the well shut-in period; A mathematical model of bottom hole pressure in fractured reservoirs filled with karst caves was established, and the theoretical bottom hole pressure solution was obtained by solving the established mathematical model. The actual pressure measurement data is fitted to obtain the fitting parameters; The mathematical model for bottom-hole pressure in fractured reservoirs encountering cavernous areas divides the entire reservoir flow system into two parts: the cavernous area and the surrounding reservoir area. The dimensionless form of the seepage equation for the cavernous area is expressed as follows: in, Pressure in the dimensionless filling region; The dimensionless form of the flow equation for the outer reservoir region is expressed as: in, The pressure is a dimensionless peripheral reservoir pressure. For cracks, The ratio of the filling region to the surrounding reservoir capacity. The ratio of the mobility of the filling region to that of the surrounding reservoir. The storage capacity ratio of the fracture. As a matrix; The method involves establishing a mathematical model of the bottom-hole pressure in a fractured reservoir filled with karst caves. Solving this model yields the following flow equation for the karst cave region, which, after perturbation transformation, becomes: in, For an infinite distance, Time is dimensionless; Dimensionless perturbation pressure ζ D With dimensionless pressure The relationship is represented as: in, This is the stress sensitivity coefficient; The seepage equation filling the karst region, after perturbation transformation and then Laplace transformation, becomes: Where u is a Laplace space variable; The actual pressure measurement data is fitted to obtain fitting parameters. Based on the theoretical bottom hole pressure value calculated by the model, the actual measured pressure data is fitted using the least squares method. The fitting parameters include: radius of the cavity-filled area, radius of the outer reservoir, permeability of the cavity-filled reservoir, permeability of the outer reservoir area, permeability sensitivity coefficient of the cavity-filled area, fracture channeling coefficient of the outer reservoir area, and fracture storage ratio of the outer reservoir area.
2. The method for determining the permeability sensitivity coefficient of a cavernous reservoir as described in claim 1, characterized in that: It also includes the following steps: Lower the pressure gauge to the bottom of the test well and measure the pressure change over time during the well shut-in period. Based on the basic data, the bottom pressure of the well was solved by using a mathematical model of the bottom pressure of a fractured oil reservoir filled with karst caves. Set the initial parameters of the model, which will serve as the initial values for the fitting parameters; Set the fitting error and calculate the difference between the measured bottom hole pressure and the pressure in the mathematical model; If the difference between the calculated value and the actual value is less than the fitting error, then output the initial parameters; If the difference between the calculated value and the actual value is not less than the fitting error, then the parameters to be fitted are corrected. The fitting parameters are output only after both parameters are within the fitting error range.
3. The method for determining the permeability sensitivity coefficient of a cavernous reservoir as described in claim 2, characterized in that: The method involves establishing a mathematical model of the bottom-hole pressure in a fractured reservoir filled with karst caverns. Solving this model yields the pressure solution for the filled region as follows: Where A1 and B1 are the parameters to be determined; After the Laplace transform, the flow equation of the outer reservoir becomes: The pressure solution of the outer reservoir is expressed as: A2 and B2 are the parameters to be determined.
4. The method for determining the permeability sensitivity coefficient of a cavernous reservoir as described in claim 3, characterized in that: The method establishes a mathematical model of bottomhole pressure in fractured reservoirs filled with karst caverns. Solving this model, after perturbation and Laplace transformations, yields the following pressure and flow conditions at the wellbore location: The pressure and flow conditions at the boundary between the inner and outer zones of the pressure solution in the cavity-filled region and the pressure solution in the surrounding reservoir are as follows: The flow condition at the reservoir boundary for the pressure solution of the outer reservoir is: Substituting the pressure solutions of the cavity-filling region and the surrounding reservoir into the boundary equations, we obtain the following system of equations for the unknown coefficients A1, A2, B1, and B2: According to Cramer's rule, solving the system of equations A1, A2, B1, and B2 yields A1 and B1 as follows: Where Δ is matrix a in the system of equations A1, A2, B1, B2. ij The determinant of; Substituting A1 and B1 into the pressure solution of the karst region, the dimensionless bottom hole perturbation pressure at the wellbore is: According to the perturbation transformation relationship, the dimensionless bottom-hole pressure solution in real space is: in, It is the natural logarithm function. This is the inverse Laplace transform function.
5. A system for determining the permeability sensitivity coefficient of a cavernous reservoir, characterized in that, The method described in claim 1 includes: The measurement module measures the pressure change over time during the well shut-in period. A module was established to create a mathematical model of the bottom hole pressure in a fractured reservoir filled with karst caves. The theoretical bottom hole pressure solution was obtained by solving the established mathematical model. The fitting module fits the actual pressure measurement data to obtain the fitting parameters.
6. An electronic device, characterized in that, include: Memory, used to store programs; A processor for loading the program to perform the steps of the method for determining the permeability sensitivity coefficient of a cavernous reservoir as described in any one of claims 1-4.
7. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the steps of the method for determining the permeability sensitivity coefficient of a cavernous reservoir as described in any one of claims 1-4.
Citation Information
Patent Citations
Method and system for determining fracture-cavern space structure of fault-karst commingled production reservoir
CN115017841A