Well test interpretation method of linear composite oil reservoir fractured well analytical model

Abstract

The invention belongs to the technical field of well testing, particularly relates to a well testing interpretation method for an analytical model of a fractured well of a linear composite oil reservoir, and aims to solve the problems that in the prior art, unit division needs to be carried out on a reservoir, the process is tedious, the speed is low, and the precision is prone to being influenced by the number and size of grid units. The method comprises the steps that a linear composite oil reservoir fractured well analysis well testing model is established according to an unstable seepage theory; the linear composite reservoir fractured well analytical well testing model is transformed through a Laplace integral transformation method and a Fourier transformation method, after transformation, superposition integration is carried out in the fracture direction by combining the symmetry of fractures, and a bottom hole pressure solution is obtained; and drawing a well testing theoretical curve and an actually-measured double logarithmic curve, and fitting the actually-measured double logarithmic curve and the well testing theoretical curve to obtain reservoir parameters. According to the method, reservoir unit subdivision is not needed, the curve fitting speed and precision are improved, and the method can be used for reservoir parameter inversion, yield or pressure simulation and prediction and the like.

Description

Background Art

[0002] Unconventional oil and gas reservoirs such as shale oil and tight oil have become the focus of development. Such reservoirs have low permeability, and fracturing transformation measures are often required during development. The degree of reservoir transformation can be understood through reservoir parameter evaluation, and well testing is one of the important means to obtain reservoir parameters. By monitoring the bottom-hole pressure data to master the dynamic changes of the reservoir and conducting well test interpretation, the reservoir properties can be evaluated. At present, the application of well testing technology has covered most reservoir types.

[0003] The linear composite reservoir is one of the common reservoir characteristics and is of great significance for reservoir development. Most of the well test model studies for such reservoirs are mainly based on the straight well circular composite model. For the bottom-hole pressure simulation of fractured wells in linear composite reservoirs, numerical models are basically used, which requires unit subdivision of the reservoir, with a cumbersome process, slow speed, and the accuracy is easily affected by the number and size of grid units. Based on this, the present invention proposes a well test interpretation method for the analytical model of fractured wells in linear composite reservoirs, establishes an analytical model of fractured wells in linear composite reservoirs, solves it through Laplace and Fourier transforms, obtains the change of bottom-hole pressure. Compared with the numerical solution, it does not require grid subdivision, can greatly improve the interpretation accuracy, and the calculation is convenient and simple, improving the fitting efficiency of well test data for fractured wells in linear composite reservoirs, providing a theoretical basis for evaluating the reservoir properties of such reservoirs and guiding subsequent development. Summary of the Invention

[0004] To solve the above problems in the prior art, that is, the prior art requires unit subdivision of the reservoir, with a cumbersome process, slow speed, and the accuracy is easily affected by the number and size of grid units, that is, the problems of low efficiency and accuracy. In the first aspect of the present invention, a well test interpretation method for the analytical model of fractured wells in linear composite reservoirs is provided, which is used to conduct well test interpretation and analysis on the continuously monitored bottom-hole pressure data of fractured wells in linear composite reservoirs to obtain relevant reservoir parameters, including:

[0005] Step S1, construct a physical model of a fractured well in a linear composite reservoir; based on the physical model of the fractured well in the linear composite reservoir, establish an analytical well test model of the fractured well in the linear composite reservoir according to the unstable seepage theory;

[0006] Step S2, transform the analytical well test model of the fractured well in the linear composite reservoir by the Laplace integral transform method and the Fourier transform method. After the transformation, combined with the symmetry of the fracture, perform superposition integration along the fracture direction to obtain the bottom-hole pressure solution;

[0007] Step S3: Based on the given time and model parameters, obtain a set of bottom-hole pressure solutions through the methods of Step S1 and Step S2, and combine with the dimensionless definition to plot the well test theoretical curve; use the pressure build-up data to plot the measured double-logarithmic curve; fit the measured double-logarithmic curve with the well test theoretical curve to obtain the reservoir parameters.

[0008] In some preferred embodiments, the assumptions of the physical model of the fractured well in a linear composite reservoir are as follows:

[0009] The linear composite reservoir is divided into two semi-infinite regions, designated as Region 1 and Region 2 respectively. The rock and fluid properties of the two regions are different. The reservoir is homogeneous and isotropic within the same region; the fractured well is located at the center of a strip in one of the regions, maintaining a constant production rate; the fluid is single-phase and weakly compressible; the fracture has finite conductivity, penetrates the entire linear composite reservoir, and is symmetric about the wellbore; the wellbore storage effect and skin effect are considered; the fluid obeys Darcy's law, and the effects of capillary force and gravity are ignored.

[0010] In some preferred embodiments, for the analytical well test model of the fractured well in a linear composite reservoir, its construction method is as follows:

[0011] Establish a mathematical model by defining dimensionless variables. The dimensionless variables are defined as:

[0012]

[0013] Based on the physical model and assumption conditions of the fractured well in a linear composite reservoir, establish the dimensionless seepage equations for Region 1 and Region 2, namely the reservoir model:

[0014]

[0015]

[0016] Interface conditions between the two regions:

[0017] p 1D =p 2D ,x D =0 (3)

[0018]

[0019] Boundary conditions:

[0020] p 1D (x D →∞)=0 (5)

[0021] p 2D (x D →-∞)=0 (6)

[0022] Initial conditions:

[0023] p 1D (t D = 0)= p 2D (t D = 0)= 0 (7)

[0024] The governing equation of the fracture model is:

[0025]

[0026] Inner boundary condition at the wellbore:

[0027]

[0028] Closed condition at the fracture tip:

[0029]

[0030] Flow normalization condition:

[0031]

[0032] Where p is the reservoir pressure, MPa; p i is the original formation pressure, MPa; t is the production time, h; q is the oil well production rate, m 3 / d; q i is the linear density flow rate, m 2 / d; B is the volume factor, m 3 / m 3 ; h is the effective thickness, m; w f is the fracture width, m; x f is the half-length of the fracture, m; a, b are the wellbore position coordinates, m; ω is the strip width, m; L is the reference length, m; is the porosity, %; k is the reservoir permeability, μm 2 ; K F is the fracture permeability, μm 2 ; μ is the fluid viscosity, mPa·s; C t is the comprehensive compressibility, MPa -1 ; C is the wellbore storage coefficient, m 3 / MPa; S is the skin factor, dimensionless; b D represents the dimensionless wellbore position coordinate of b; subscripts 1 and 2 represent Zone 1 and Zone 2 respectively.

[0033] In some preferred embodiments, step S2 is specifically:

[0034] Based on t D 、y DTaking the Laplace transform and Fourier transform of equations (1) and (2) gives:

[0035]

[0036]

[0037] where a D represents the dimensionless wellbore position coordinate of a;

[0038] Combining the two-zone interface conditions of equations (3) and (4), the boundary conditions of equations (5) and (6), and the initial condition of equation (7), the pressure response caused by the linear density can be obtained as:

[0039]

[0040] Taking the Laplace transform and solving equations (8) to (10) gives:

[0041]

[0042] Considering the symmetry of the fracture, dividing the single side of the fracture into N units, the discrete form of equation (15) is:

[0043]

[0044] At the fracture wall, the reservoir pressure is equal to the fracture pressure. Therefore, according to the superposition principle, the pressure response at each unit in the fracture is:

[0045]

[0046] where:

[0047]

[0048] Substituting equation (17) into equation (16), combining with the flow rate normalization condition of equation (11), and solving the matrix equation, the bottom-hole pressure solution can be obtained. Considering the well storage and skin effect, the bottom-hole pressure can be expressed as:

[0049]

[0050] In the formula, s is the dimensionless time t D corresponding Laplace variable; m is the dimensionless distance y D corresponding Fourier variable;

[0051] Performing the inverse Fourier transform and the Stehfest numerical inversion technique on the bottom-hole pressure solution in sequence, the real-time spatial bottom-hole pressure solution can be obtained. According to the inverse transform of the finite Fourier cosine transform:

[0052]

[0053] The Stehfest numerical inversion technique is an approximate algorithm that inverses the Laplace space solution into the real-time space solution, and its specific expression is:

[0054]

[0055] In the formula, is the Laplace transform corresponding to P(t); N is an even number; The accuracy of the approximate calculation mainly depends on the selection of V i which is determined by N according to the following formula

[0056] where! represents the factorial symbol.

[0057] In some preferred embodiments, the theoretical well test curve is plotted, and the method is as follows:

[0058] Given a set of time and model parameters, a set of corresponding dimensionless bottom-hole pressure solutions of a fractured well in a linear composite reservoir can be obtained. Combining with the dimensionless definition, the dimensional pressure difference can be obtained; when the well is shut in, according to the superposition principle, there is:

[0059]

[0060] The discrete form is:

[0061]

[0062] where p wf represents the bottom-hole pressure at any time, MPa;

[0063] From this, the change of the bottom-hole pressure at any time after the well is shut in is obtained, and then the double-logarithmic curve of the pressure difference and the pressure difference derivative with respect to time is plotted, that is, the theoretical well test curve.

[0064] In some preferred embodiments, the measured double-logarithmic curve is plotted using the pressure build-up data, and the method is as follows:

[0065] The pressure difference is: Δp = p - p ws

[0066] The pressure derivative is the derivative of the logarithm of the pressure difference with respect to the time function, and the time function is:

[0067] Therefore, the pressure derivative is defined as:

[0068] where p ws represents the bottom-hole pressure when the well is shut in, MPa; t pIt represents the shut-in time, h; Δt represents the time elapsed after shut-in, h;

[0069] From this, a measured double logarithmic curve of pressure difference and pressure derivative with respect to time can be plotted.

[0070] In the second aspect of the present invention, a well test interpretation system for an analytical model of a fractured well in a linear composite reservoir is proposed, which is used to perform well test interpretation and analysis on the bottom hole pressure data of a fractured well in a continuously monitored linear composite reservoir to obtain relevant reservoir parameters. The system includes:

[0071] A model construction module configured to construct a physical model of a fractured well in a linear composite reservoir; based on the physical model of the fractured well in the linear composite reservoir, an analytical well test model of the fractured well in the linear composite reservoir is established according to the theory of unsteady seepage;

[0072] A transformation module configured to transform the analytical well test model of the fractured well in the linear composite reservoir by means of Laplace integral transformation method and Fourier transformation method. After transformation, combined with the symmetry of the fracture, superposition integration is carried out along the fracture direction to obtain the bottom hole pressure solution;

[0073] A fitting module configured to obtain a set of bottom hole pressure solutions through the methods of the model construction module and the transformation module based on the given time and model parameters, and combined with dimensionless definitions, plot a well test theoretical curve; use the pressure build-up data to plot a measured double logarithmic curve; fit the measured double logarithmic curve with the well test theoretical curve to obtain reservoir parameters.

[0074] In the third aspect of the present invention, an electronic device is proposed, including:

[0075] At least one processor; and a memory communicatively connected to at least one of the processors; wherein, the memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the above-mentioned well test interpretation method for an analytical model of a fractured well in a linear composite reservoir.

[0076] In the fourth aspect of the present invention, a computer-readable storage medium is proposed, and the computer-readable storage medium stores computer instructions, and the computer instructions are used to be executed by the computer to implement the above-mentioned well test interpretation method for an analytical model of a fractured well in a linear composite reservoir.

[0077] Advantages of the present invention:

[0078] The present invention can perform well test interpretation and analysis on the bottom hole pressure data of a fractured well in a linear composite reservoir under continuous monitoring to obtain relevant reservoir parameters. Compared with the numerical simulation method of this model, it is not necessary to perform reservoir unit subdivision, and the method is more simple and practical. By performing analytical solution, the curve fitting speed and accuracy are improved, the model is more in line with the actual situation, and it can be used for reservoir parameter inversion, simulation and prediction of production or pressure, etc., which helps to understand the reservoir more clearly and provides theoretical guidance for subsequent oil well production. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Other features, objects, and advantages of the present application will become more apparent by reading the detailed description of the non-limiting embodiments with reference to the following drawings:

[0080] Figure 1 is a schematic flow chart of a well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to an embodiment of the present invention;

[0081] Figure 2 is a schematic framework diagram of a well test interpretation system for an analytical model of a fractured well in a linear composite reservoir according to an embodiment of the present invention;

[0082] Figure 3 is a schematic diagram of a physical model of a fractured well in a linear composite reservoir according to an embodiment of the present invention;

[0083] Figure 4 is a schematic diagram of a fracture unit according to an embodiment of the present invention;

[0084] Figure 5 is a schematic diagram of measured curves and fitting curves according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0085] The following further describes the present application in detail with reference to the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the related invention, rather than limiting the invention. In addition, it should be noted that for the sake of description, only parts related to the relevant invention are shown in the drawings.

[0086] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the drawings and embodiments.

[0087] A well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to the first embodiment of the present invention is used to perform well test interpretation and analysis on the bottom hole pressure data of a fractured well in a linear composite reservoir under continuous monitoring to obtain relevant reservoir parameters, such as Figure 1 shown, including:

[0088] Step S1, construct a physical model of a fractured well in a linear composite reservoir; based on the physical model of the fractured well in the linear composite reservoir, establish an analytical well test model for the fractured well in the linear composite reservoir according to the unsteady seepage theory;

[0089] Step S2, transform the analytical well test model for the fractured well in the linear composite reservoir by using the Laplace integral transform method and the Fourier transform method. After the transformation, combined with the symmetry of the fracture, perform a superposition integral along the fracture direction to obtain the bottom-hole pressure solution;

[0090] Step S3, based on the given time and model parameters, obtain a set of bottom-hole pressure solutions by the methods of Step S1 and Step S2, and combined with the dimensionless definition, plot the theoretical well test curve; use the pressure build-up data to plot the measured double-logarithmic curve; fit the measured double-logarithmic curve with the theoretical well test curve, and then obtain the reservoir parameters.

[0091] To more clearly illustrate the well test interpretation method of the analytical model of the fractured well in the linear composite reservoir of the present invention, each step in the method embodiment of the present invention will be described in detail below with reference to the drawings.

[0092] Step S1, construct a physical model of a fractured well in a linear composite reservoir; based on the physical model of the fractured well in the linear composite reservoir, establish an analytical well test model for the fractured well in the linear composite reservoir according to the unsteady seepage theory;

[0012] In this embodiment, as Figure 3 shown, the assumptions of the physical model of the fractured well in the linear composite reservoir are:

[0093] The linear composite reservoir is divided into two semi-infinite large regions, which are respectively taken as Region 1 and Region 2. The rock and fluid properties of the two regions are different. The reservoir is homogeneous and isotropic within the same region; the fractured well is located at the center of the strip in one of the regions, and the production rate is kept constant; the fluid is single-phase and weakly compressible; the fracture has finite conductivity, penetrates the entire linear composite reservoir, and is symmetric about the wellbore; consider the wellbore storage effect and the skin effect; the fluid obeys Darcy's law, and the influence of capillary force and gravity is ignored.

[0094] Based on the physical model of the fractured well in the linear composite reservoir, establish an analytical well test model for the fractured well in the linear composite reservoir according to the unsteady seepage theory, specifically:

[0013] Establish a mathematical model by defining dimensionless variables. The dimensionless variables are defined as:

[0095]

[0096] Build a reservoir model and establish the dimensionless seepage equations for Region 1 and Region 2 based on the physical model of the fractured well in the linear composite reservoir and the assumed conditions:

[0097]

[0098]

[0099] Interface conditions between the two regions:

[0100] p 1D = p 2D , x D = 0 (3)

[0101]

[0102] Boundary conditions:

[0103] p 1D (x D → ∞) = 0 (5)

[0104] p 2D (x D → -∞) = 0 (6)

[0105] Initial conditions:

[0106] p 1D (t D = 0) = p 2D (t D = 0) = 0 (7)

[0107] The fracture model is similar to the reservoir model, and its governing equation is:

[0108]

[0109] Inner boundary conditions at the wellbore:

[0110]

[0111] Closed conditions at the fracture tip:

[0112]

[0113] Flow rate normalization condition:

[0114]

[0115] where p is the reservoir pressure, MPa; p i is the original formation pressure, MPa; t is the production time, h; q is the oil well production rate, m 3 / d; q i is the linear density flow rate, m 2 / d; B is the volume coefficient, m 3 / m 3 ; h is the effective thickness, m; w f is the fracture width, m; x f is the half-length of the fracture, m; a, b are the wellbore position coordinates, m; ω is the strip width, m; L is the reference length, m; is the porosity, %; k is the reservoir permeability, μm 2 ; K F is the fracture permeability, μm 2 ; μ is the fluid viscosity, mPa·s; C t is the comprehensive compressibility, MPa -1 ; C is the wellbore storage coefficient, m 3 / MPa; S is the skin factor, dimensionless; b D represents the dimensionless wellbore position coordinate of b; the subscripts 1 and 2 represent Zone 1 and Zone 2 respectively.

[0116] Step S2, transform the analytical well test model of the fractured well in the linear composite reservoir by the Laplace integral transform method and the Fourier transform method. After transformation, combined with the symmetry of the fracture, perform superposition integration along the fracture direction to obtain the bottom hole pressure solution;

[0117] In this embodiment, based on t D 、y D Performing Laplace transform and Fourier transform on Equations (1) and (2) gives:

[0118]

[0119]

[0120] where, a D represents the dimensionless wellbore position coordinate of a;

[0121] Combined with the two-zone interface conditions of Equations (3) and (4), the boundary conditions of Equations (5) and (6), and the initial condition of Equation (7), the pressure response caused by the line density can be obtained as:

[0122]

[0123] Performing Laplace transform and solving on Equations (8) to (10) gives:

[0124]

[0125] Considering the symmetry of the fracture, divide the single side of the fracture into N units, as Figure 4 shown, then the discrete form of Equation (15) is:

[0126]

[0127] At the fracture wall, the reservoir pressure is equal to the fracture pressure. Therefore, according to the superposition principle, the pressure response at each unit in the fracture is:

[0128]

[0129] Where:

[0130]

[0131] Substitute Equation (17) into Equation (16), combine with the flow rate normalization condition Equation (11), and the bottom-hole pressure solution can be obtained by solving the matrix equation. After considering the well storage and skin effect, the bottom-hole pressure can be expressed as:

[0132]

[0133] In the formula, s is the dimensionless time t D corresponding Laplace variable; m is the dimensionless distance y D corresponding Fourier variable;

[0134] Performing the inverse Fourier transform and Stehfest numerical inversion technique on the bottom-hole pressure solution in sequence can obtain the real-time spatial bottom-hole pressure solution. According to the inverse transform of the finite Fourier cosine transform, there is:

[0135]

[0136] The Stehfest numerical inversion technique is an approximate algorithm for inverting the Laplace space solution into the real-time space solution. The specific expression is:

[0137]

[0138] In the formula, is the Laplace transform corresponding to P(t); in this embodiment, it is preferably 4 ≤ N ≤ 16, and N is an even number; The accuracy of the approximate calculation mainly depends on V i selection, which is determined by N according to the following formula

[0139] where,! represents the factorial symbol.

[0140] Step S3, based on the given time and model parameters, obtain a set of bottom-hole pressure solutions by the methods of Step S1 and Step S2, and combine with the dimensionless definition to draw the well test theoretical curve; use the pressure build-up data to draw the measured double logarithmic curve; fit the measured double logarithmic curve with the well test theoretical curve, and then obtain the reservoir parameters.

[0141] In this embodiment, the measured double logarithmic curve is plotted using the pressure recovery data, and the method is as follows:

[0142] The pressure difference is: Δp = p - p ws

[0143] The pressure derivative is the derivative of the pressure difference with respect to the logarithm of the time function, and the time function is:

[0144] Therefore, the pressure derivative is defined as:

[0145] where p ws represents the bottom-hole pressure at shut-in, MPa; t p represents the shut-in time, h; Δt represents the time elapsed after shut-in, h;

[0146] From this, the measured double logarithmic curves of the pressure difference and the pressure derivative with respect to time can be plotted.

[0147] When plotting the theoretical curve, given a set of time and model parameters, a set of corresponding dimensionless bottom-hole pressure solutions for a fractured well in a linear composite reservoir can be obtained. Combining with the dimensionless definition, the dimensional pressure difference can be obtained; when shut-in, according to the superposition principle, there is:

[0148]

[0149] The discrete form is:

[0150]

[0151] where p wf represents the bottom-hole pressure at any time, MPa;

[0152] From this, the change in the bottom-hole pressure at any time after shut-in is obtained, and then the double logarithmic curves of the pressure difference and the pressure difference derivative with respect to time are plotted, which is the well test theoretical curve.

[0153] The model parameters such as the fracture conductivity, fracture half-length, and reservoir permeability are repeatedly adjusted until the theoretical curve coincides with the measured curve, so as to obtain the correct reservoir parameters and realize the evaluation of reservoir parameters.

[0154] When conducting pressure well test interpretation, the basic parameters used are shown in Table 1:

[0155] Table 1

[0156] In the present invention, the shut-in section in the pressure history is selected for pressure well test interpretation, and the well test curve fitting results are shown in Figure 5 . It can be seen from the figure that the theoretical and measured curves basically coincide. Through fitting, the fracture half-length is 20.02 m and the conductivity is 0.35 μm2 ·m, and the reservoir permeability is 0.7 md.

[0157] The well test interpretation system of the linear composite reservoir fracturing well in the second embodiment of the present invention is used to perform well test interpretation and analysis on the continuously monitored bottom hole pressure data of the linear composite reservoir fracturing well to obtain relevant reservoir parameters, such as Figure 2 As shown, the system includes:

[0158] The model construction module 100 is configured to construct a physical model of the linear composite reservoir fracturing well; based on the physical model of the linear composite reservoir fracturing well, an analytical well test model of the linear composite reservoir fracturing well is established according to the unsteady seepage theory;

[0159] The transformation module 200 is configured to transform the analytical well test model of the linear composite reservoir fracturing well by the Laplace integral transformation method and the Fourier transformation method. After transformation, combined with the symmetry of the fracture, superposition integration is performed along the fracture direction to obtain the bottom hole pressure solution;

[0160] The fitting module 300 is configured to obtain a set of bottom hole pressure solutions through the methods of the model construction module and the transformation module based on the given time and model parameters, and draw a well test theoretical curve in combination with the dimensionless definition; draw a measured double logarithm curve using the pressure build-up data; fit the measured double logarithm curve with the well test theoretical curve to obtain the reservoir parameters.

[0161] Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process and related descriptions of the above-described system can refer to the corresponding process in the foregoing method embodiment, and will not be repeated here.

[0162] It should be noted that the well test interpretation system of the linear composite reservoir fracturing well provided in the above embodiment is only illustrated by the division of the above functional modules. In actual applications, the above functions can be allocated to different functional modules according to needs, that is, the modules or steps in the embodiments of the present invention can be further decomposed or combined. For example, the modules in the above embodiment can be combined into one module, or further split into multiple sub-modules to complete all or part of the functions described above. For the names of the modules and steps involved in the embodiments of the present invention, they are only used to distinguish each module or step, and are not regarded as an improper limitation of the present invention.

[0163] An electronic device according to the third embodiment of the present invention includes at least one processor; and a memory communicatively connected to at least one of the processors; wherein, the memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the above-mentioned well test interpretation method of the linear composite reservoir fracturing well analytical model.

[0164] A computer-readable storage medium according to a fourth embodiment of the present invention, wherein the computer-readable storage medium stores computer instructions for being executed by a computer to implement the above-mentioned well test interpretation method for the analytical model of a fractured well in a linear composite reservoir.

[0165] Those skilled in the art can clearly understand that for the convenience and conciseness of description, the specific working processes and related descriptions of the above-described well test interpretation equipment and computer-readable storage medium for the analytical model of a fractured well in a linear composite reservoir can refer to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0166] Those skilled in the art should be able to realize that the modules and method steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. The programs corresponding to the software modules and method steps can be placed in a random access memory (RAM), memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art. To clearly illustrate the interchangeability of electronic hardware and software, the components and steps of each example have been generally described according to their functions in the above description. Whether these functions are executed in the form of electronic hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0167] The term "comprising" or any other similar term is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus / device comprising a series of elements includes not only those elements but also other elements not expressly listed, or also includes elements inherent to those processes, methods, articles, or apparatus / device.

[0168] So far, the technical solution of the present invention has been described in conjunction with the preferred embodiments shown in the drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A well test interpretation method for an analytical model of a fractured well in a linear composite reservoir, which is used to perform well test interpretation and analysis on the bottom hole pressure data of a fractured well in a continuously monitored linear composite reservoir to obtain relevant reservoir parameters. Characterized in that: This method includes the following steps: Step S1, construct a physical model of a fractured well in a linear composite reservoir; based on the physical model of the fractured well in the linear composite reservoir, establish an analytical well test model of the fractured well in the linear composite reservoir according to the theory of unsteady seepage. Step S2, transform the analytical well test model of the fractured well in the linear composite reservoir by using the Laplace integral transform method and the Fourier transform method. After the transformation, combined with the symmetry of the fracture, perform a superposition integral along the fracture direction to obtain the bottom hole pressure solution. Step S3, based on the given time and model parameters, obtain a set of bottom hole pressure solutions by the methods of Step S1 and Step S2, and draw a well test theoretical curve in combination with the dimensionless definition; draw a measured double logarithm curve by using the pressure build-up data; fit the measured double logarithm curve with the well test theoretical curve to obtain the reservoir parameters.

2. A well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to claim 1. Characterized in that: The assumptions of the physical model of the fractured well in the linear composite reservoir are as follows: The linear composite reservoir is divided into two semi-infinite large regions, which are respectively taken as Region 1 and Region 2. The rock and fluid properties of the two regions are different. The reservoir in the same region is homogeneous and isotropic; the fractured well is located at the center of a strip in one of the regions, and the production rate is kept constant; the fluid is single-phase and weakly compressible; the fracture has finite conductivity, penetrates the entire linear composite reservoir, and is symmetric about the wellbore; the wellbore storage effect and skin effect are considered; the fluid obeys Darcy's law, and the influence of capillary force and gravity is ignored.

3. A well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to claim 2. Characterized in that: The construction method of the analytical well test model of the fractured well in the linear composite reservoir is as follows: Establish a mathematical model by defining dimensionless variables. The dimensionless variables are defined as: Establish dimensionless seepage equations for Region 1 and Region 2 according to the physical model and assumption conditions of the fractured well in the linear composite reservoir, that is, the reservoir model: Interface conditions between the two regions: p 1D = p 2D , x D = 0 (3) Boundary conditions: p 1D (x D →∞) = 0 (5) p 2D (x D → -∞) = 0 (6) Initial conditions: p 1D (t D = 0) = p 2D (t D = 0) = 0 (7) The control equation of the fracture model is: Inner boundary conditions at the wellbore: Closed conditions at the fracture tip: Flow normalization conditions: Among them, p is the reservoir pressure, MPa; p i is the original formation pressure, MPa; t is the production time, h; q is the oil well production rate, m 3 / d; q i is the linear density flow rate, m 2 / d; B is the volume factor, m 3 / m 3 ; h is the effective thickness, m; w f is the fracture width, m; x f is the fracture half-length, m; a, b are the wellbore location coordinates, m; ω is the strip width, m; L is the reference length, m; is the porosity, %; k is the reservoir permeability, μm 2 ; K F is the fracture permeability, μm 2 ; μ is the fluid viscosity, mPa·s; C t is the comprehensive compressibility, MPa -1 ; C is the wellbore storage coefficient, m 3 / MPa; S is the skin factor, dimensionless; b D represents the dimensionless wellbore location coordinate of b; subscripts 1 and 2 represent Zone 1 and Zone 2 respectively.

4. A well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to claim 3. Characterized in that: The specific content of Step S2 is as follows: Based on t D and y D Taking the Laplace transform and Fourier transform of equations (1) and (2) gives: where a D represents the dimensionless wellbore position coordinate of a; Combined with the interface conditions of the two regions, equations (3) and (4), the boundary conditions, equations (5) and (6), and the initial conditions, equation (7), the pressure response caused by the line density can be obtained as: Perform Laplace transform on equations (8) to (10) and solve to obtain: Considering the symmetry of the fracture, divide one side of the fracture into N units, then the discrete form of equation (15) is: At the fracture wall, the reservoir pressure is equal to the fracture pressure. Therefore, according to the superposition principle, the pressure response at each unit in the fracture is: Where: Substitute Equation (17) into Equation (16), and combine with the flow rate normalization condition Equation (11). The bottom-hole pressure solution can be obtained by solving the matrix equation. After considering the well storage and skin effect, the bottom-hole pressure can be expressed as: where s is the dimensionless time t D and the corresponding Laplace variable; m is the dimensionless distance y D and the corresponding Fourier variable; Performing the inverse Fourier transform and Stehfest numerical inversion technique on the bottom-hole pressure solution in sequence can obtain the real-time spatial bottom-hole pressure solution. According to the inverse transform of the finite Fourier cosine transform, we have: The Stehfest numerical inversion technique is an approximate algorithm for inverting the Laplace space solution into the real-time space solution, and the specific expression is: In the formula, is the Laplace transform corresponding to P(t); N is an even number; The accuracy of the approximate calculation mainly depends on V i The selection of which is determined by N according to the following formula where,! represents the factorial symbol.

5. A well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to claim 4, characterized in that, Drawing the well test theoretical curve, and the method is: Given a set of time and model parameters, a set of corresponding dimensionless bottom-hole pressure solutions of the fractured well in the linear composite reservoir can be obtained. Combining with the dimensionless definition, the dimensional pressure difference can be obtained. When shutting in the well, according to the superposition principle, we have: The discrete form is: Among them, p wf represents the bottom-hole pressure at any time, MPa; Thus, the change of the bottom-hole pressure at any time after shutting in the well is obtained, and then the double logarithmic curves of the pressure difference and the pressure difference derivative with respect to time are drawn, that is, the well test theoretical curve.

6. A well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to claim 5, characterized in that, Using the pressure build-up data to draw the measured double logarithmic curve, and the method is: The pressure difference is: Δp = p - p ws The pressure derivative is the derivative of the logarithm of the pressure difference with respect to time, and the time function is: Therefore, the pressure derivative is defined as: where p ws represents the bottom hole pressure at shut-in, MPa; t p represents the shut-in time, h; Δt represents the time elapsed after shut-in, h; Thus, the measured double logarithmic curves of the pressure difference and the pressure derivative with respect to time can be drawn.

7. A well test interpretation system for an analytical model of a fractured well in a linear composite reservoir, which is used to perform well test interpretation and analysis on the continuously monitored bottom-hole pressure data of the fractured well in the linear composite reservoir to obtain relevant reservoir parameters, characterized in that, this system includes: A model construction module configured to construct a physical model of a fractured well in a linear composite reservoir; based on the physical model of the fractured well in the linear composite reservoir, an analytical well test model of the fractured well in the linear composite reservoir is established according to the unsteady seepage theory; A transformation module configured to transform the analytical well test model of the fractured well in the linear composite reservoir by the Laplace integral transformation method and the Fourier transformation method. After transformation, combined with the symmetry of the fracture, the superposition integral is performed along the fracture direction to obtain the bottom-hole pressure solution; A fitting module configured to obtain a set of bottom-hole pressure solutions based on the given time and model parameters by the methods of the model construction module and the transformation module, and combine with the dimensionless definition to draw the well test theoretical curve; use the pressure build-up data to draw the measured double logarithmic curve; fit the measured double logarithmic curve with the well test theoretical curve, and then obtain the reservoir parameters.

8. An electronic device, characterized in that, including: At least one processor; And a memory communicatively connected to at least one of the processors; wherein, the memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement a well test interpretation method for an analytical model of a fractured well in a linear composite reservoir according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for being executed by the computer to implement the well test interpretation method of a linear composite reservoir fracturing well analysis model according to any one of claims 1-6.

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