A method and apparatus for predicting pressure in a horizontal well with multiple horizontal fractures

Abstract

The present application relates to the technical field of horizontal well, in particular to a horizontal well pressure prediction method and device with multiple horizontal fractures.A horizontal well pressure prediction method with multiple horizontal fractures comprises the following steps: collecting horizontal well environment data, obtaining geological data and experimental data; constructing a model according to the geological data and the experimental data, obtaining a multi-fracture horizontal well pressure prediction mathematical model; calculating and solving according to the multi-fracture horizontal well pressure prediction mathematical model, obtaining a multi-fracture horizontal well pressure prediction model pressure solution; collecting to-be-predicted horizontal well environment data, predicting and drawing according to the multi-fracture horizontal well pressure prediction model pressure solution, and obtaining a multi-fracture horizontal well pressure prediction curve.The present application is a horizontal well pressure prediction method with multiple horizontal fractures of arbitrary shape.

Description

Technical Field

[0001] This invention relates to the field of horizontal well technology, and in particular to a method and apparatus for predicting pressure in horizontal wells with multiple horizontal fractures. Background Technology

[0002] With the development of the times and the progress of society, the demand for oil resources in various countries is increasing day by day. Under these circumstances, we are required to extract oil resources more economically and efficiently than ever before. Extensive domestic and international practice has proven that hydraulic fracturing is an important engineering method for increasing oil well production. Hydraulic fracturing technology has the advantages of mature technology, complete equipment, and more economical extraction of shale oil reservoirs. It can reduce the price of oil resources and create a large number of new jobs, thus having significant social benefits.

[0003] Shale reservoirs contain abundant oil resources. In shale oil reservoirs, hydraulic fracturing-induced fractures sometimes result in vertical stresses exceeding horizontal stresses, leading to fractures primarily located horizontally rather than vertically. The combined use of hydraulic fracturing technology and horizontal well technology has gradually become a highly effective method and means for developing these energy sources and increasing production. However, to date, our predictions have mainly focused on the pressure behavior of horizontal wells with single horizontal fractures, neglecting the impact of multiple horizontal fractures on the pressure behavior of horizontal wells.

[0004] In the existing technology, there is a lack of a method for predicting the pressure of horizontal wells with multiple horizontal fractures of arbitrary shapes. Summary of the Invention

[0005] This invention provides a method and apparatus for predicting pressure in horizontal wells with multiple horizontal fractures. The technical solution is as follows:

[0006] On the one hand, a method for predicting pressure in horizontal wells with multiple horizontal fractures is provided. This method is implemented by electronic devices and includes:

[0007] Collect environmental data from horizontal wells to obtain geological and experimental data;

[0008] Based on the geological and experimental data, a mathematical model for predicting pressure in multi-fracture horizontal wells was constructed.

[0009] The pressure solution of the multi-fractured horizontal well pressure prediction model is obtained by calculating and solving the mathematical model of pressure prediction of multi-fractured horizontal well.

[0010] Collect environmental data of the horizontal well to be predicted, and predict and plot the pressure curve of the multi-fracture horizontal well based on the pressure solution of the multi-fracture horizontal well pressure prediction model.

[0011] Optionally, the step of constructing a model based on the geological data and experimental data to obtain a mathematical model for predicting pressure in multi-fracture horizontal wells includes:

[0012] Based on the geological and experimental data, a physical model for predicting pressure in multi-fracture horizontal wells was constructed.

[0013] Based on the physical model for pressure prediction in multi-fractured horizontal wells and the preset physical conditions, a mathematical model for pressure prediction in multi-fractured horizontal wells is constructed to obtain the model.

[0014] Optionally, the step of calculating and solving the pressure prediction mathematical model for multi-fractured horizontal wells to obtain the pressure solution of the multi-fractured horizontal well pressure prediction model includes:

[0015] Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the point source solution for the pressure prediction model in single-fractured horizontal wells is obtained by calculation and solution using the mirror reflection method and the Poisson summation method.

[0016] By performing double integration on the point source solution of the single-fractured horizontal well pressure prediction model, the fundamental solution of the single-fractured horizontal well pressure is obtained.

[0017] Based on the fundamental pressure solution of a single-fractured horizontal well, the pressure solution of the two-dimensional fractured segment of a multi-fractured horizontal well is obtained by superposition principle.

[0018] The pressure solution of the two-dimensional fractured section of the multi-fractured horizontal well is obtained by using Gaussian elimination and Stehfest numerical inversion to obtain the pressure prediction model solution of the multi-fractured horizontal well.

[0019] Optionally, the step of calculating and solving the pressure prediction mathematical model for a single-fractured horizontal well using the mirror reflection method and the Poisson summation method to obtain the point source solution for the pressure prediction model for a multi-fractured horizontal well includes:

[0020] Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the seepage equation, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well are obtained.

[0021] The Laplace transform is applied to the seepage equations, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well to obtain the mathematical model equations for horizontal well pressure prediction.

[0022] The equations of the horizontal well pressure prediction mathematical model are calculated and solved using the mirror reflection method and the Poisson summation method to obtain the point source solution of the single-fracture horizontal well pressure prediction model.

[0023] Optionally, the step of performing double integration on the point source solution of the single-fractured horizontal well pressure prediction model to obtain the fundamental solution of the single-fractured horizontal well pressure includes:

[0024] The point source solution of the single-fracture horizontal well pressure prediction model is double-integrated to obtain the two-dimensional space equation of the point source solution.

[0025] Based on geological and experimental data, reservoir and fracture data were obtained.

[0026] Substituting the reservoir data and fracture data into the two-dimensional spatial equation of the point source solution, the basic solution of pressure in a single-fracture horizontal well is obtained.

[0027] Optionally, the step of calculating the two-dimensional fracture segment pressure solution of a multi-fractured horizontal well based on the fundamental pressure solution of the single-fractured horizontal well using the superposition principle includes:

[0028] Based on the fundamental solution of the single-fracture horizontal well pressure, the pressure response equation of a single horizontal fracture is obtained by calculation using the superposition principle.

[0029] The pressure response equation of the single horizontal fracture is calculated and solved to obtain the pressure solution of the horizontal well with the single horizontal fracture.

[0030] Based on the pressure solution of a single horizontal fracture well and the horizontal well fracture matrix, the two-dimensional fracture segment pressure solution of a multi-fracture horizontal well is obtained.

[0031] On the other hand, a horizontal well pressure prediction device with multiple horizontal fractures is provided. This device is applied to a horizontal well pressure prediction method with multiple horizontal fractures. The device includes:

[0032] The data acquisition module is used to collect environmental data from horizontal wells, and to obtain geological and experimental data.

[0033] The model building module is used to build a model based on the geological data and experimental data to obtain a mathematical model for predicting pressure in multi-fracture horizontal wells.

[0034] The pressure solution calculation module is used to calculate and solve the pressure prediction mathematical model of the multi-fractured horizontal well to obtain the pressure solution of the multi-fractured horizontal well pressure prediction model.

[0035] The pressure curve prediction module is used to collect environmental data of the horizontal well to be predicted, and to predict and plot the pressure curve of the multi-fracture horizontal well based on the pressure solution of the multi-fracture horizontal well pressure prediction model.

[0036] Optionally, the model building module is further used for:

[0037] Based on the geological and experimental data, a physical model for predicting pressure in multi-fracture horizontal wells was constructed.

[0038] Based on the physical model for pressure prediction in multi-fractured horizontal wells and the preset physical conditions, a mathematical model for pressure prediction in multi-fractured horizontal wells is constructed to obtain the model.

[0039] Optionally, the pressure solution calculation module is further configured to:

[0040] Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the point source solution for the pressure prediction model in single-fractured horizontal wells is obtained by calculation and solution using the mirror reflection method and the Poisson summation method.

[0041] By performing double integration on the point source solution of the single-fractured horizontal well pressure prediction model, the fundamental solution of the single-fractured horizontal well pressure is obtained.

[0042] Based on the fundamental pressure solution of a single-fractured horizontal well, the pressure solution of the two-dimensional fractured segment of a multi-fractured horizontal well is obtained by superposition principle.

[0043] The pressure solution of the two-dimensional fractured section of the multi-fractured horizontal well is obtained by using Gaussian elimination and Stehfest numerical inversion to obtain the pressure prediction model solution of the multi-fractured horizontal well.

[0044] Optionally, the pressure solution calculation module is further configured to:

[0045] Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the seepage equation, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well are obtained.

[0046] The Laplace transform is applied to the seepage equations, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well to obtain the mathematical model equations for horizontal well pressure prediction.

[0047] The equations of the horizontal well pressure prediction mathematical model are calculated and solved using the mirror reflection method and the Poisson summation method to obtain the point source solution of the single-fracture horizontal well pressure prediction model.

[0048] Optionally, the pressure solution calculation module is further configured to:

[0049] The point source solution of the single-fracture horizontal well pressure prediction model is double-integrated to obtain the two-dimensional space equation of the point source solution.

[0050] Based on geological and experimental data, reservoir and fracture data were obtained.

[0051] Substituting the reservoir data and fracture data into the two-dimensional spatial equation of the point source solution, the basic solution of pressure in a single-fracture horizontal well is obtained.

[0052] Optionally, the pressure solution calculation module is further configured to:

[0053] Based on the fundamental solution of the single-fracture horizontal well pressure, the pressure response equation of a single horizontal fracture is obtained by calculation using the superposition principle.

[0054] The pressure response equation of the single horizontal fracture is calculated and solved to obtain the pressure solution of the horizontal well with the single horizontal fracture.

[0055] Based on the pressure solution of a single horizontal fracture well and the horizontal well fracture matrix, the two-dimensional fracture segment pressure solution of a multi-fracture horizontal well is obtained.

[0056] On the other hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the above-described method for predicting pressure in a horizontal well with multiple horizontal fractures.

[0057] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, the at least one instruction being loaded and executed by a processor to implement the above-described method for predicting pressure in a horizontal well with multiple horizontal fractures.

[0058] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0059] This invention proposes a method for predicting the pressure of horizontal wells with multiple horizontal fractures. By solving a constructed mathematical model for predicting the pressure of multi-fractured horizontal wells, a pressure solution for the multi-fractured horizontal well pressure prediction model is obtained. Based on the pressure solution of the multi-fractured horizontal well pressure prediction model, a precise mathematical model for predicting the pressure of horizontal wells with multiple horizontal fractures of arbitrary shapes can be constructed, and pressure prediction curves can be plotted. Predicting the impact of multiple horizontal fractures on the pressure of horizontal wells during oil and gas extraction helps to improve oil and gas production. This invention is a method for predicting the pressure of horizontal wells with multiple horizontal fractures of arbitrary shapes. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0061] Figure 1 This is a flowchart of a method for predicting pressure in a horizontal well with multiple horizontal fractures, provided by an embodiment of the present invention.

[0062] Figure 2 This is a schematic diagram of a physical model for predicting pressure in a horizontal well with multiple horizontal fractures of arbitrary shapes, provided in an embodiment of the present invention.

[0063] Figure 3 This is a schematic diagram of a discrete multi-level fracture model for a horizontal well provided in an embodiment of the present invention;

[0064] Figure 4 This is a schematic diagram of a pressure prediction curve provided in an embodiment of the present invention;

[0065] Figure 5 This is a block diagram of a horizontal well pressure prediction device with multiple horizontal fractures provided in an embodiment of the present invention;

[0066] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0067] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0068] This invention provides a method for predicting pressure in horizontal wells with multiple horizontal fractures. This method can be implemented using electronic equipment, such as a terminal or a server. Figure 1 The flowchart shown is a method for predicting pressure in a horizontal well with multiple horizontal fractures. The processing flow of this method may include the following steps:

[0069] S1. Collect environmental data from horizontal wells to obtain geological and experimental data.

[0070] In one feasible implementation, the horizontal well environmental data involved in this invention refers to horizontal wells located in the Ordos Basin in central and northern China, where the sedimentary microfacies in the shale oil reservoir are mainly composed of sandy clastic flow deposits.

[0071] The lithology is mainly fine-grained and very fine-grained lithic sandstone; the reservoir thickness is 10m, and the comprehensive compressibility coefficient is 1.1436×10⁻⁶. -4 MPa -1 The reservoir depth is 700 m, the fluid viscosity is 1.1 mPa·s, and the fluid density is 876.3 kg / m³. 3 The fluid compressibility coefficient is 1.109 × 10⁻⁶. -3 MPa -1 The volume factor is 1, the number of fractures is 4, the well radius is 0.1m, and the production rate is 1m³. 3 / d, the well length is 600m.

[0072] S2. Based on geological and experimental data, a model is constructed to obtain a mathematical model for predicting pressure in multi-fracture horizontal wells.

[0073] In one feasible implementation, the horizontal well in the pressure prediction mathematical model of a horizontal well with multiple horizontal fractures of arbitrary shapes is discretized into multiple horizontal fractures. Simultaneously, seepage equations are established for each horizontal fracture, and dimensionless variables are defined. These may include dimensionless time, dimensionless length, dimensionless fracture distance, etc.

[0074] The mathematical expression for dimensionless time is shown in equation (1) below:

[0075]

[0076] Where k refers to permeability, in mD; t refers to time, in h; and μ refers to gas viscosity, in mPa·s. Porosity; C t The overall compressibility factor is expressed in MPa. -1 L refers to the reference length, in meters (m).

[0077] The mathematical expression for dimensionless distance is shown in equation (2) below:

[0078]

[0079] Where x and y refer to the distance in the rectangular coordinate system, in meters; r refers to the radial distance, in meters; and L refers to the reference length, in meters.

[0080] The mathematical expression for the half-length of the dimensionless horizontal crack along the y-axis is shown in equation (3) below:

[0081]

[0082] Where L refers to the reference length, in meters (m); L f The half-length of the hydraulic fracture along the y-axis is measured in meters (m).

[0083] The mathematical expression for the half-length of the dimensionless horizontal crack along the x-axis is shown in equation (4) below:

[0084]

[0085] Where L refers to the reference length, in meters; w f The length of the hydraulic fracture along the x-axis is measured in meters (m).

[0086] The mathematical expression for dimensionless reservoir thickness is shown in equation (5) below:

[0087]

[0088] Where h refers to reservoir thickness in meters (m) and L refers to reference length in meters (m).

[0089] The mathematical expression for the dimensionless spacing between multiple horizontal cracks is shown in equation (6) below:

[0090]

[0091] Where I refers to the crack spacing in meters (m) and L refers to the reference length in meters (m).

[0092] The mathematical expression for the dimensionless vertical distance of a horizontal crack is shown in equation (7) below:

[0093]

[0094] Where z refers to the distance in a rectangular coordinate system, in meters; and h refers to the reservoir thickness, in meters.

[0095] In the mathematical model of pressure analysis of horizontal fractures with multiple arbitrary shapes, the horizontal well is discretized into multiple horizontal fractures. The mathematical expression of the seepage equation of the horizontal fractures is shown in the following equation (8):

[0096]

[0097] Where η refers to the diffusivity, in mD·MPa / mPa·s; p refers to the pressure, in MPa; r refers to the radial distance, in m; and k refers to the reservoir permeability, in mD. Porosity; μ refers to fluid viscosity, measured in mPa·s; C t The overall compressibility factor is expressed in MPa. -1 .

[0098] The initial conditions, inner boundary conditions, and outer boundary conditions of the horizontal well are defined.

[0099] The mathematical expression for the initial conditions of a horizontal well is shown in equation (9) below:

[0100] p| t＝0 =p i (9)

[0101] The mathematical expression for the external boundary conditions of the horizontal well is shown in equation (10) below:

[0102] p| r→∞ =p i (10)

[0103] For a spherical point source in the three-dimensional space of a horizontal well, the mathematical expression for the internal boundary conditions is as shown in equation (11):

[0104]

[0105] Where q refers to flow rate, in meters (m). 3 / d; r refers to radial distance, in meters; p refers to pressure, in MPa; t refers to time, in hours; B refers to volume coefficient; k refers to permeability, in mD; μ refers to viscosity, in mPa·s.

[0106] Optionally, a mathematical model for predicting pressure in multi-fracture horizontal wells is constructed based on geological and experimental data, including:

[0107] A physical model for predicting pressure in multi-fracture horizontal wells was obtained by constructing a model based on geological and experimental data.

[0108] Based on the physical model for pressure prediction in multi-fractured horizontal wells and the preset physical conditions, a mathematical model for pressure prediction in multi-fractured horizontal wells is constructed to obtain the model.

[0109] In one feasible implementation, the pre-defined physical conditions for constructing the mathematical model for predicting pressure in multi-fractured horizontal wells in this invention include: the reservoir is homogeneous and isotropic, with uniform initial pressure and temperature; only single-phase, slightly compressible fluid exists; the horizontal fractures are parallel to the top and bottom boundaries of the reservoir; for convenience, the spacing between adjacent horizontal fractures is equal; due to the small aspect ratio of thickness to length, the fluid flow in the horizontal fractures is two-dimensional; the well in the model produces at a constant rate; the effects of gravity and temperature on the flow are ignored; the fluid flow satisfies Darcy's law; and the horizontal fractures have infinite conductivity.

[0110] The physical model for predicting pressure in horizontal wells with multiple horizontal fractures of arbitrary shapes constructed in this invention is as follows: Figure 2 As shown.

[0111] S3. Calculate and solve the pressure prediction mathematical model for multi-fractured horizontal wells to obtain the pressure solution of the multi-fractured horizontal well pressure prediction model.

[0112] Optionally, step S3 may further include the following steps S31-S34;

[0113] S31. Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the point source solution of the pressure prediction model for single-fractured horizontal wells is obtained by calculation and solution using the mirror reflection method and the Poisson summation method.

[0114] Optionally, based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the point source solution for the pressure prediction model in single-fractured horizontal wells is obtained by calculating and solving using the mirror reflection method and the Poisson summation method, including:

[0115] Based on the mathematical model for pressure prediction in multi-fracture horizontal wells, the seepage equation, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well are obtained.

[0116] The Laplace transform of the seepage equations, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well yields the mathematical model equations for horizontal well pressure prediction.

[0117] The mathematical model equations for horizontal well pressure prediction were solved using the mirror reflection method and the Poisson summation method to obtain the point source solution for the single-fracture horizontal well pressure prediction model.

[0118] In one feasible implementation, the above seepage equation (8), initial condition (9), inner boundary condition (11), and outer boundary condition (10) are rewritten using the Laplace transform:

[0119] Using the relevant dimensionless variable t D and r D According to formulas (8), (9), (10), and (11), they can be rewritten as formulas (12), (13), (14), and (15):

[0120]

[0121]

[0122]

[0123]

[0124] in, The values ​​are: r (radial distance, in meters), L (reference length, in meters), k (permeability, in mD), μ (viscosity, in mPa·s), B (volume factor), and q (flow rate, in cubic meters per second). 3 / d.

[0125] In this invention, the fracture half-length along the x-axis is selected as the reference length. The q on the right-hand side of equation (15) is the cumulative rate term, which is equal to the fundamental point source. The cumulative value over a certain period of time.

[0126] Using the δ(t) function, formula (15) can be transformed into formula (16):

[0127]

[0128] Where L refers to the reference length, in meters (m); k refers to the permeability, in mD; r D The value is a dimensionless radial distance; μ refers to viscosity, measured in mPa·s; B refers to the volume index. It is the fundamental point source.

[0129] The mathematical expression for δ(t) is shown in equation (17) below:

[0130]

[0131] Formula (17) transforms the mathematical model into one with t D The relevant Lagrangian domain. Because... The internal boundary conditions become:

[0132]

[0133] Where L refers to the reference length, in meters (m); k refers to the permeability, in mD; r D Dimensionless radial distance; The pressure difference in Laplace space; r D The value is a dimensionless radial distance; μ refers to viscosity, measured in mPa·s; B refers to the volume index. Point sources in Laplace space; Porosity; C t The overall compressibility factor is expressed in MPa. -1 .

[0134] Simplifying the equations, we set the point source to unit intensity. Equation (18) can be rewritten as Equation (19):

[0135]

[0136] Where L refers to the reference length, in meters; r D Dimensionless radial distance; The pressure difference in Laplace space; B refers to the volume coefficient. Porosity; C t The overall compressibility factor is expressed in MPa. -1 .

[0137] The seepage equations, initial conditions, and internal and external boundary conditions after the Laplace transformation can be rewritten as formulas (20) and (21):

[0138]

[0139]

[0140]

[0141] Where, r D Dimensionless radial distance; The pressure difference in Laplace space; s refers to the Laplace variable; L refers to the reference length in meters; B refers to the volume coefficient. Porosity; C t The overall compressibility factor is expressed in MPa. -1 .

[0142] Use formula Equation (20) can be simplified to Equation (22) as follows:

[0143]

[0144] Based on the above equation (22), the general solution to equation (22) can be obtained, as shown in equations (23) and (24) below:

[0145]

[0146]

[0147] To satisfy the mathematical relationship between equations (19) and (21), the coefficients M and N can be determined as shown in equations (25) and (26) below:

[0148]

[0149] N = 0 (26)

[0150] Therefore, the pressure response caused by the point source can be expressed as shown in equation (27):

[0151]

[0152] Considering the continuous change of the point source, equation (27) can be transformed into equation (28) as follows:

[0153]

[0154] in, The pressure difference in Lagrange space refers to the pressure difference; B refers to the volume coefficient; μ refers to the viscosity, with the unit being mPa·s. The point source in the Laplace space; s refers to the Laplace variable; r D The value refers to the dimensionless radial distance; k refers to the permeability, in mD; and L refers to the reference length, in meters.

[0155] The boundary conditions in the vertical direction can be expressed as:

[0156]

[0157]

[0158] Using the mirror reflection method and Poisson summation, a pressure analysis is performed on a mathematical model of a single horizontal crack of arbitrary shape with impermeable top and bottom boundaries. The point source solution in the Lagrange domain can then be expressed as shown in equation (31):

[0159]

[0160] in, The pressure difference in Laplace space; B refers to the volume coefficient. The term refers to a point source in Laplace space; μ refers to viscosity, measured in mPa·s; k refers to permeability, measured in mD; L refers to the reference length, measured in m; h D The dimensionless reservoir thickness refers to s; the Laplace variable refers to s; and K0 refers to the zeroth-order Bessel function of the first kind. The dimensionless radial distance; n refers to the summation number; z D This refers to dimensionless vertical distance.

[0161] S32. Double integration is performed on the point source solution of the single-fractured horizontal well pressure prediction model to obtain the basic solution of the single-fractured horizontal well pressure.

[0162] Optionally, the point source solution of the single-fractured horizontal well pressure prediction model is double-integrated to obtain the fundamental solution of the single-fractured horizontal well pressure, including:

[0163] The point source solution of the single-fracture horizontal well pressure prediction model is double-integrated to obtain the two-dimensional space equation of the point source solution.

[0164] Based on geological and experimental data, reservoir and fracture data were obtained.

[0165] By substituting reservoir data and fracture data into the two-dimensional spatial equation of the point source solution, the basic solution of pressure in a single-fracture horizontal well is obtained.

[0166] In one feasible implementation, the discrete multi-level crack model involved in this invention is as follows: Figure 3 Since the boundary is regarded as an impermeable top and bottom boundary, the point source solution of the pressure prediction mathematical model for a single horizontal crack of arbitrary shape obtained above is double-integrated in the Lagrange domain, and its mathematical expression is shown in the following equation (32):

[0167]

[0168] in, The pressure difference in Laplace space; B refers to the volume coefficient. The term refers to a point source in Laplace space; μ refers to viscosity, measured in mPa·s; k refers to permeability, measured in mD; L refers to the reference length, measured in m; h D y refers to the dimensionless reservoir thickness; s refers to the dimensionless Laplace variable; n refers to the summation number; y wD The x-axis refers to the origin of the dimensionless coordinate system. wD The origin of the dimensionless coordinate system in the x-direction; L fD The dimensionless half-length of the hydraulic fracture along the y-axis; w fD The dimensionless half-length of the hydraulic fracture along the x-axis; K0 refers to the zeroth-order Bessel function of the first kind; rD z refers to dimensionless radial distance; D This refers to dimensionless vertical distance.

[0169] S33. Based on the basic pressure solution of a single-fractured horizontal well, the pressure solution of the two-dimensional fractured section of a multi-fractured horizontal well is obtained by superposition principle.

[0170] Optionally, based on the fundamental pressure solution of a single-fractured horizontal well, the pressure solution of the two-dimensional fractured section of a multi-fractured horizontal well is obtained by calculation using the superposition principle, including:

[0171] Based on the fundamental solution of pressure in a single-fractured horizontal well, the pressure response equation for a single horizontal fracture is obtained by superposition principle.

[0172] The pressure response equation for a single horizontal fracture is calculated and solved to obtain the pressure solution for a horizontal well with a single horizontal fracture.

[0173] Based on the pressure solution of a single horizontal fracture well and the horizontal well fracture matrix, the two-dimensional fracture segment pressure solution of a multi-fracture horizontal well is obtained.

[0174] In one feasible implementation, since the present invention is for pressure prediction in horizontal wells with multiple horizontal fractures, pressure superposition is used for calculation to calculate the pressure solution in one fracture segment caused by the flow rate of another fracture segment.

[0175] According to equation (32) above, the pressure solution in one fracture segment caused by the flow rate in another fracture segment can be obtained. Considering that there are n horizontal fractures in a horizontal well, the pressure response equation is as follows (33):

[0176]

[0177] in, This represents the pressure response of the l-th segment of the k-th horizontal crack, which is caused by the flow rate of the s-th segment of the i-th horizontal crack.

[0178] The term is shown in equation (34):

[0179]

[0180] in, This represents the pressure response of the l-th segment of the k-th horizontal fracture, caused by the flow rate of the s-th segment of the i-th horizontal fracture; B refers to the volume coefficient; μ refers to the viscosity in mPa·s; k refers to the permeability in mD; L refers to the reference length in m; h D y refers to the dimensionless reservoir thickness; s refers to the dimensionless Laplace variable; n refers to the summation number; y wD The origin of the dimensionless coordinate system in the y-direction; vwD The origin of the dimensionless coordinate system in the x-direction; L fD The dimensionless half-length of the hydraulic fracture along the y-axis; w fD The dimensionless half-length of the hydraulic fracture along the x-axis; x Dk，l The x-th dimensionless coordinate origin is the k-th line in the x-direction; y Dk，l The k-th dimensionless coordinate origin in the y-direction; K0 refers to the zeroth-order Bessel function of the first kind; z D This refers to dimensionless vertical distance.

[0181] Equations (32), (33), and (34) represent the pressure response of all two-dimensional fracture segments under the influence of flow rate. For a single horizontal fracture, the pressure response of all fracture segments can be expressed as N. i The mathematical expression for a square matrix of order is shown in equation (35):

[0182]

[0183] Among them, A l，f Let represent the pressure response of each fracture segment on the l-th fracture, which is a result of the flow rate from the f-th fracture. Therefore, for n horizontal fractures, the mathematical matrix expression for the final two-dimensional fracture segment pressure solution of a multi-fractured horizontal well is shown in equation (36) below:

[0184]

[0185] S34. The pressure solution of the two-dimensional fractured section of the multi-fractured horizontal well is obtained by Gaussian elimination and Stehfest numerical inversion method to obtain the pressure prediction model of the multi-fractured horizontal well.

[0186] In one feasible implementation, based on the pressure solution of the two-dimensional fracture segment of all fracture segments in n horizontal fractures under the influence of flow rate obtained above, the matrices of (35) and (36) are solved by Gaussian elimination method, and finally the bottom hole pressure solution in the time domain is obtained by Stehfest numerical inversion algorithm.

[0187] When a horizontal well produces at a constant flow rate, there is a flow rate assumption for all fracture segments. The production of the horizontal well is equal to the total flow rate of each fracture segment, and its mathematical expression is shown in equation (37) below:

[0188]

[0189] Equation (38) is used to consider the influence of the wellbore storage coefficient and skin coefficient on the bottom hole pressure. Then, the pressure solution in the time domain is obtained through the Stehfest numerical inversion algorithm, and equation (38) is shown below:

[0190]

[0191] Where, p w C refers to the bottom hole pressure. D S refers to the energy storage coefficient, S refers to the skin coefficient, and s refers to the Laplace variable.

[0192] The system checks whether the set time t matches the total simulation time. If the time comparison does not match, the system will execute the command t = t + Δt and solve the mathematical model for predicting pressure in a horizontal well with multiple horizontal fractures of arbitrary shapes again. The system will continue to the next step until the set time t matches the total simulation time.

[0193] Output the solution of the mathematical model for predicting pressure in a horizontal well with multiple horizontal fractures of arbitrary shapes. Obtain the bottom hole pressure solution of the mathematical model for predicting pressure in a horizontal well with multiple horizontal fractures of arbitrary shapes in the time domain, and use it as the pressure solution of the mathematical model for predicting pressure in a horizontal well with multiple horizontal fractures of arbitrary shapes.

[0194] S4. Collect environmental data of the horizontal well to be predicted, and predict and plot the pressure based on the pressure solution of the multi-fracture horizontal well pressure prediction model to obtain the multi-fracture horizontal well pressure prediction curve.

[0195] In one feasible implementation, the present invention uses actual data and, based on the pressure solution of the multi-fracture horizontal well pressure prediction model obtained in the above steps, plots pressure curves and pressure derivative curves as follows: Figure 4 , Figure 4 The pressure prediction curves for a horizontal well with four horizontal fractures of arbitrary shape are shown, where the vertical axis is set to dimensionless pressure and the horizontal axis is set to dimensionless time.

[0196] This invention proposes a method for predicting the pressure of horizontal wells with multiple horizontal fractures. By solving a constructed mathematical model for predicting the pressure of multi-fractured horizontal wells, a pressure solution for the multi-fractured horizontal well pressure prediction model is obtained. Based on the pressure solution of the multi-fractured horizontal well pressure prediction model, a precise mathematical model for predicting the pressure of horizontal wells with multiple horizontal fractures of arbitrary shapes can be constructed, and pressure prediction curves can be plotted. Predicting the impact of multiple horizontal fractures on the pressure of horizontal wells during oil and gas extraction helps to improve oil and gas production. This invention is a method for predicting the pressure of horizontal wells with multiple horizontal fractures of arbitrary shapes.

[0197] Figure 5 This is a block diagram illustrating a horizontal well pressure prediction device with multiple horizontal fractures according to an exemplary embodiment. (Refer to...) Figure 5 The device includes:

[0198] The data acquisition module 510 is used to acquire environmental data of horizontal wells, and obtain geological data and experimental data.

[0199] The model building module 520 is used to build a model based on the geological data and experimental data to obtain a mathematical model for predicting pressure in multi-fracture horizontal wells.

[0200] The pressure solution calculation module 530 is used to calculate and solve the pressure prediction mathematical model of the multi-fractured horizontal well to obtain the pressure solution of the multi-fractured horizontal well pressure prediction model.

[0201] The pressure curve prediction module 540 is used to collect environmental data of the horizontal well to be predicted, and to predict and draw the pressure curve of the multi-fracture horizontal well based on the pressure solution of the multi-fracture horizontal well pressure prediction model.

[0202] Optionally, the model building module 520 is further configured to:

[0203] Based on the geological and experimental data, a physical model for predicting pressure in multi-fracture horizontal wells was constructed.

[0204] Based on the physical model for pressure prediction in multi-fractured horizontal wells and the preset physical conditions, a mathematical model for pressure prediction in multi-fractured horizontal wells is constructed to obtain the model.

[0205] Optionally, the pressure solution calculation module 530 is further configured to:

[0206] Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the point source solution for the pressure prediction model in single-fractured horizontal wells is obtained by calculation and solution using the mirror reflection method and the Poisson summation method.

[0207] By performing double integration on the point source solution of the single-fractured horizontal well pressure prediction model, the fundamental solution of the single-fractured horizontal well pressure is obtained.

[0208] Based on the fundamental pressure solution of a single-fractured horizontal well, the pressure solution of the two-dimensional fractured segment of a multi-fractured horizontal well is obtained by superposition principle.

[0209] The pressure solution of the two-dimensional fractured section of the multi-fractured horizontal well is obtained by using Gaussian elimination and Stehfest numerical inversion to obtain the pressure prediction model solution of the multi-fractured horizontal well.

[0210] Optionally, the pressure solution calculation module 530 is further configured to:

[0211] Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the seepage equation, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well are obtained.

[0212] The Laplace transform is applied to the seepage equations, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well to obtain the mathematical model equations for horizontal well pressure prediction.

[0213] The equations of the horizontal well pressure prediction mathematical model are calculated and solved using the mirror reflection method and the Poisson summation method to obtain the point source solution of the single-fracture horizontal well pressure prediction model.

[0214] Optionally, the pressure solution calculation module 530 is further configured to:

[0215] The point source solution of the single-fracture horizontal well pressure prediction model is double-integrated to obtain the two-dimensional space equation of the point source solution.

[0216] Based on geological and experimental data, reservoir and fracture data were obtained.

[0217] Substituting the reservoir data and fracture data into the two-dimensional spatial equation of the point source solution, the basic solution of pressure in a single-fracture horizontal well is obtained.

[0218] Optionally, the pressure solution calculation module 530 is further configured to:

[0219] Based on the fundamental solution of pressure in a single-fractured horizontal well, the pressure response equation for a single horizontal fracture is obtained by superposition principle.

[0220] The pressure response equation for a single horizontal fracture is calculated and solved to obtain the pressure solution for a horizontal well with a single horizontal fracture.

[0221] Based on the pressure solution of a single horizontal fracture well and the horizontal well fracture matrix, the two-dimensional fracture segment pressure solution of a multi-fracture horizontal well is obtained.

[0222] This invention proposes a method for predicting the pressure of horizontal wells with multiple horizontal fractures. By solving a constructed mathematical model for predicting the pressure of multi-fractured horizontal wells, a pressure solution for the multi-fractured horizontal well pressure prediction model is obtained. Based on the pressure solution of the multi-fractured horizontal well pressure prediction model, a precise mathematical model for predicting the pressure of horizontal wells with multiple horizontal fractures of arbitrary shapes can be constructed, and pressure prediction curves can be plotted. Predicting the impact of multiple horizontal fractures on the pressure of horizontal wells during oil and gas extraction helps to improve oil and gas production. This invention is a method for predicting the pressure of horizontal wells with multiple horizontal fractures of arbitrary shapes.

[0223] Figure 6 This is a schematic diagram of the structure of an electronic device 600 provided in an embodiment of the present invention. The electronic device 600 may vary considerably due to different configurations or performance. It may include one or more central processing units (CPUs) 601 and one or more memories 602. The memory 602 stores at least one instruction, which is loaded and executed by the processor 601 to implement the steps of the above-mentioned method for predicting pressure in a horizontal well with multiple horizontal fractures.

[0224] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions that can be executed by a processor in a terminal to complete the aforementioned method for predicting pressure in a horizontal well with multiple horizontal fractures. For example, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, or optical data storage device.

[0225] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0226] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting pressure in a horizontal well with multiple horizontal fractures, comprising: The method includes: Collect environmental data from horizontal wells to obtain geological and experimental data; Based on the geological and experimental data, a mathematical model for predicting pressure in multi-fracture horizontal wells was constructed. The pressure solution for the multi-fractured horizontal well pressure prediction model is obtained by calculating and solving the mathematical model based on the aforementioned model, including: Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the point source solution for the pressure prediction model in single-fractured horizontal wells is obtained by calculation and solution using the mirror reflection method and the Poisson summation method. By performing double integration on the point source solution of the single-fractured horizontal well pressure prediction model, the fundamental solution of the single-fractured horizontal well pressure is obtained. Based on the fundamental pressure solution of a single-fractured horizontal well, the pressure solution of the two-dimensional fractured segment of a multi-fractured horizontal well is obtained by superposition principle. The pressure solution of the two-dimensional fractured section of the multi-fractured horizontal well is obtained by Gaussian elimination and Stehfest numerical inversion method to obtain the pressure solution of the multi-fractured horizontal well pressure prediction model. The step of calculating and solving the pressure prediction mathematical model for a single-fractured horizontal well using the mirror reflection method and the Poisson summation method, based on the multi-fractured horizontal well pressure prediction mathematical model, includes: Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the seepage equation, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well are obtained. The Laplace transform is applied to the seepage equations, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well to obtain the mathematical model equations for horizontal well pressure prediction. The equations of the horizontal well pressure prediction mathematical model are calculated and solved using the mirror reflection method and the Poisson summation method to obtain the point source solution of the single-fracture horizontal well pressure prediction model. The step of performing double integration on the point source solution of the single-fractured horizontal well pressure prediction model to obtain the fundamental solution of the single-fractured horizontal well pressure includes: The point source solution of the single-fracture horizontal well pressure prediction model is double-integrated to obtain the two-dimensional space equation of the point source solution. Based on geological and experimental data, reservoir and fracture data were obtained. Substitute the reservoir data and fracture data into the two-dimensional spatial equation of the point source solution for calculation and solution to obtain the basic solution of pressure in a single-fracture horizontal well. The step of calculating the pressure solution of a multi-fractured horizontal well based on the fundamental pressure solution of the single-fractured horizontal well using the superposition principle includes: Based on the fundamental solution of the single-fracture horizontal well pressure, the pressure response equation of a single horizontal fracture is obtained by calculation using the superposition principle. The pressure response equation of the single horizontal fracture is calculated and solved to obtain the pressure solution of the horizontal well with the single horizontal fracture. Based on the pressure solution of a single horizontal fracture well and the horizontal well fracture matrix, the two-dimensional fracture segment pressure solution of a multi-fracture horizontal well is obtained. Collect environmental data of the horizontal well to be predicted, and predict and plot the pressure curve of the multi-fracture horizontal well based on the pressure solution of the multi-fracture horizontal well pressure prediction model.

2. The method of predicting pressure in a horizontal well with multiple horizontal fractures of claim 1, wherein, The process of constructing a model based on the geological and experimental data to obtain a mathematical model for predicting pressure in multi-fracture horizontal wells includes: Based on the geological and experimental data, a physical model for predicting pressure in multi-fracture horizontal wells was constructed. Based on the physical model for pressure prediction in multi-fractured horizontal wells and the preset physical conditions, a mathematical model for pressure prediction in multi-fractured horizontal wells is constructed to obtain the model.

3. A horizontal well pressure prediction device with multiple horizontal fractures, characterized by, The device includes: The data acquisition module is used to collect environmental data from horizontal wells, and to obtain geological and experimental data. The model building module is used to build a model based on the geological data and experimental data to obtain a mathematical model for predicting pressure in multi-fracture horizontal wells. The pressure solution calculation module is used to calculate and solve the pressure prediction mathematical model of the multi-fractured horizontal well to obtain the pressure solution of the multi-fractured horizontal well pressure prediction model: The pressure solution calculation module is further used for: Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the point source solution for the pressure prediction model in single-fractured horizontal wells is obtained by calculation and solution using the mirror reflection method and the Poisson summation method. The point source solution of the single-fractured horizontal well pressure prediction model is double-integrated to obtain the basic solution of the single-fractured horizontal well pressure. Based on the fundamental pressure solution of a single-fractured horizontal well, the pressure solution of a two-dimensional fractured segment in a multi-fractured horizontal well is obtained by superposition principle. The pressure solution of the two-dimensional fractured section of the multi-fractured horizontal well is obtained by Gaussian elimination and Stehfest numerical inversion method to obtain the pressure solution of the multi-fractured horizontal well pressure prediction model. The pressure solution calculation module is further used for: Based on the mathematical model for pressure prediction in multi-fractured horizontal wells, the seepage equation, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well are obtained. The Laplace transform is applied to the seepage equations, initial parameters, and internal and external boundary conditions in the three-dimensional space of the horizontal well to obtain the mathematical model equations for horizontal well pressure prediction. The equations of the horizontal well pressure prediction mathematical model are calculated and solved using the mirror reflection method and the Poisson summation method to obtain the point source solution of the single-fracture horizontal well pressure prediction model. The pressure solution calculation module is further used for: The point source solution of the single-fracture horizontal well pressure prediction model is double-integrated to obtain the two-dimensional space equation of the point source solution. Based on geological and experimental data, reservoir and fracture data were obtained. Substitute the reservoir data and fracture data into the two-dimensional spatial equation of the point source solution for calculation and solution to obtain the basic solution of pressure in a single-fracture horizontal well. The pressure solution calculation module is further used for: Based on the fundamental solution of the single-fracture horizontal well pressure, the pressure response equation of a single horizontal fracture is obtained by calculation using the superposition principle. The pressure response equation of the single horizontal fracture is calculated and solved to obtain the pressure solution of the horizontal well with the single horizontal fracture. Based on the pressure solution of a single horizontal fracture well and the horizontal well fracture matrix, the two-dimensional fracture segment pressure solution of a multi-fracture horizontal well is obtained. The pressure curve prediction module is used to collect environmental data of the horizontal well to be predicted, and to predict and plot the pressure curve of the multi-fracture horizontal well based on the pressure solution of the multi-fracture horizontal well pressure prediction model.

4. The apparatus of claim 3, wherein, The model building module is further used for: According to the geological data and experimental data, a model is constructed to obtain a physical model for predicting pressure in the multi-fractured horizontal well; According to the physical model for predicting pressure in the multi-fractured horizontal well and preset physical conditions, a model is constructed to obtain a mathematical model for predicting pressure in the multi-fractured horizontal well.

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