A heterogeneous seal formation pressure determination method, device, equipment and medium

Abstract

The application discloses a heterogeneous sealing stratum pressure determination method, device, equipment and medium. The method comprises the following steps: carrying out regional division on a target region in a heterogeneous sealing stratum; determining a time-domain pressure change expression of each coordinate position in each sub-region at each moment according to a wellbore and an interface involved by each sub-region; determining a complex frequency-domain pressure change expression of each coordinate position in each sub-region at each moment according to the time-domain pressure change expression and a pre-defined source function; and determining a stratum pressure of a target point in the heterogeneous sealing stratum according to a pre-determined constraint condition and the complex frequency-domain pressure change expression, wherein the constraint condition comprises a multi-region coupling constraint, a pressure and flow continuity constraint, a variable production constraint and a gas flow constraint. The technical scheme solves the problems of low calculation efficiency and poor accuracy of the heterogeneous stratum pressure, and can improve the calculation efficiency while improving the calculation accuracy of the heterogeneous stratum pressure.

Description

Technical Field

[0001] This invention relates to the field of geophysics, and in particular to a method, apparatus, equipment and medium for determining pressure in heterogeneous sealed formations. Background Technology

[0002] Geological storage of carbon dioxide in saline aquifers is an effective means of reducing greenhouse gas emissions, and its utilization can effectively mitigate these emissions. The most critical issue to consider with saline aquifer storage is formation leakage. Leakage of stored carbon dioxide can cause severe climate change and threaten the survival of organisms. Formation leakage can be directly reflected by changes in formation pressure between wells.

[0003] Methods for calculating formation pressure in heterogeneous saline aquifers for carbon dioxide sequestration mainly include reservoir engineering methods and numerical simulation methods. Reservoir engineering methods, based on analytical methods to solve the seepage equations, offer high computational efficiency but struggle to account for complex formation heterogeneity. Numerical simulation methods, based on numerical methods to solve the seepage equations, require a complex modeling process. For highly heterogeneous formations, existing formation pressure calculation methods have significant limitations, making it difficult to simultaneously improve computational efficiency and maintain accurate formation description. Summary of the Invention

[0004] This invention provides a method, apparatus, equipment, and medium for determining pressure in heterogeneous formations, which solves the problems of low calculation efficiency and poor accuracy in heterogeneous formation pressure calculation. It can improve the calculation efficiency while improving the accuracy of heterogeneous formation pressure calculation.

[0005] According to one aspect of the present invention, a method for determining the pressure of a heterogeneous storage formation is provided, the method comprising:

[0006] The target area in the heterogeneous storage strata is divided into regions to obtain sub-regions;

[0007] Based on the wellbore and interface involved in each sub-region, determine the time-domain pressure change expression for each coordinate position in each sub-region at each moment;

[0008] Based on the time-domain pressure change expression for each coordinate position in each sub-region at each time step and the predefined source function, determine the complex frequency domain pressure change expression for each coordinate position in each sub-region at each time step;

[0009] Based on predetermined constraints and the complex frequency domain pressure variation expression, the formation pressure at the target point in the heterogeneous storage formation is determined; wherein, the constraints include multi-region coupling constraints, pressure and flow continuity constraints, variable production constraints, and gas flow constraints.

[0010] According to another aspect of the present invention, a pressure determination apparatus for heterogeneous storage formations is provided, the apparatus comprising:

[0011] The sub-region division module is used to divide the target area in heterogeneous deposited strata into sub-regions.

[0012] The time-domain expression determination module is used to determine the time-domain pressure change expression for each coordinate position in each sub-region at each time step, based on the wellbore and interface involved in each sub-region.

[0013] The complex frequency domain expression determination module is used to determine the complex frequency domain pressure change expression for each coordinate position in each sub-region at each time step, based on the time-domain pressure change expression for each coordinate position in each sub-region at each time step and the predefined source function.

[0014] The formation pressure determination module is used to determine the formation pressure at a target point in a heterogeneous storage formation based on predetermined constraints and a complex frequency domain pressure variation expression; wherein the constraints include multi-region coupling constraints, pressure and flow continuity constraints, variable production constraints, and gas flow constraints.

[0015] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising:

[0016] At least one processor; and

[0017] A memory communicatively connected to the at least one processor; wherein,

[0018] The memory stores a computer program that can be executed by the at least one processor, which enables the at least one processor to perform the method for determining the pressure of heterogeneous sealed formations according to any embodiment of the present invention.

[0019] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to execute and implement the method for determining the pressure of heterogeneous sealed formations according to any embodiment of the present invention.

[0020] The technical solution of this invention involves dividing the target area in a heterogeneous storage formation into sub-regions; determining the time-domain pressure change expression for each coordinate position in each sub-region at each time step based on the wellbore and interface involved in each sub-region; determining the complex frequency domain pressure change expression for each coordinate position in each sub-region at each time step based on the time-domain pressure change expression for each coordinate position in each sub-region at each time step and a predefined source function; and determining the formation pressure at the target point in the heterogeneous storage formation based on pre-determined constraints and the complex frequency domain pressure change expression. This technical solution solves the problems of low calculation efficiency and poor accuracy in heterogeneous formation pressure calculation, and can improve both the accuracy and efficiency of heterogeneous formation pressure calculation.

[0021] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0022] 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.

[0023] Figure 1 This is a flowchart of a method for determining the pressure of a heterogeneous storage formation according to Embodiment 1 of the present invention;

[0024] Figure 2A This is a formation pressure distribution map provided according to Embodiment 2 of the present invention;

[0025] Figure 2B This is a comparison chart of calculated and measured values ​​of inter-well pressure provided in Embodiment 2 of the present invention;

[0026] Figure 3 This is a schematic diagram of a heterogeneous formation pressure determination device according to Embodiment 3 of the present invention;

[0027] Figure 4 This is a schematic diagram of the structure of an electronic device for implementing the method for determining the pressure of heterogeneous storage formations according to embodiments of the present invention. Detailed Implementation

[0028] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0029] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be used interchangeably where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices. The acquisition, storage, use, and processing of data in the technical solutions of this application all comply with the relevant provisions of national laws and regulations.

[0030] Example 1

[0031] Figure 1 This is a flowchart illustrating a method for determining the pressure of a heterogeneous formation in carbon dioxide sequestration, as provided in Embodiment 1 of the present invention. This embodiment is applicable to formation pressure detection scenarios in heterogeneous saline aquifers with carbon dioxide sequestration. The method can be executed by a device for determining the pressure of a heterogeneous formation in sequestration. This device can be implemented in hardware and / or software and can be configured in an electronic device. Figure 1 As shown, the method includes:

[0032] S110. Divide the target area in the heterogeneous strata into sub-regions.

[0033] For heterogeneous storage formations, carbon dioxide is typically injected through multiple wells at varying flow rates. This approach uses a heterogeneous storage formation as a numerical model for pressure analysis. Specifically, the numerical module for heterogeneous formations can possess the following characteristics:

[0034] (1) The entire seepage area is closed, the strata are heterogeneous and anisotropic, and have a single or dual seepage medium;

[0035] (2) Carbon dioxide fluid and rock are compressible, seepage follows Darcy's law, and is a single-phase isothermal process;

[0036] (3) When the well is injected at a constant flow rate, the friction and pressure changes in the wellbore can be ignored.

[0037] To describe the heterogeneity of formation properties, the boundary element method is used as a model. Each sub-layer is divided into multiple sub-regions on a plane, and each sub-region is considered homogeneous and anisotropic, represented by a rectangular hexahedron. Each sub-region has different formation parameters, requiring a separate pressure distribution calculation model, which is then coupled together using the condition of equal pressure and flow at the interface. The target region can be any sub-layer within a heterogeneous stratum.

[0038] S120. Based on the wellbore and interface involved in each sub-region, determine the time-domain pressure change expression for each coordinate position in each sub-region at each moment.

[0039] Consider a single subregion traversed by a well. For this subregion, since fluid flows in or out through the wellbore and the interface, the wellbore and the interface can be considered as line sources B, respectively. w and surface source B e Source B w and surface source B e The fluid intensities are denoted as follows: and According to the superposition principle and Duhamel convolution, t D At any point M in this sub-region at any time D (x D ,y D ,z D The pressure change at point () can be expressed as:

[0040]

[0041] Among them, t D M represents dimensionless time. D M' represents the location of the target point in the sub-region. D Indicates t D The position of the point source in the sub-region at time, G(·) is the Green's function, B w B represents the wire source determined based on the wellbore. e This indicates a surface source determined based on the interface. Indicates the fluid intensity of the line source. Let τ represent the fluid intensity of the surface source, τ represent the integration time, and M' represent the integration position.

[0042] S130. Based on the time-domain pressure change expression for each coordinate position in each sub-region at each time step and the predefined source function, determine the complex frequency domain pressure change expression for each coordinate position in each sub-region at each time step.

[0043] To facilitate the solution, the line source B can be... w and surface source B eDiscretize them separately, and then process the line source B. w Discretized into n segments, surface source B e Discretize into m segments, and we get:

[0044] Since the source intensity is equal across each segment, the source function can be defined as: Source B w and surface source B e The discrete results and the defined source function are substituted into the time-domain pressure change expression for each coordinate position in each sub-region at each time step, and a Laplace transform is performed to obtain the complex frequency domain pressure change expression for each coordinate position in each sub-region at each time step. The complex frequency domain pressure change expression is:

[0045]

[0046] Among them, t D M represents dimensionless time. D M' represents the location of the target point in the sub-region. D Indicates t D The position of the point source in the sub-region at time, where G(·) is the Green's function. B w Or B e , This represents the fluid intensity in the complex frequency domain of line source segment i. Let s represent the complex frequency domain fluid intensity of the surface source segment j, and s represent the Laplace variable. This represents the source function obtained by spatial integration along the source of the Green's function. Let represent the source function obtained by spatial integration of the Green's function along the surface source, where n represents the number of line source segments and m represents the number of surface source segments.

[0047] S140. Determine the formation pressure at the target point in the heterogeneous storage formation based on the predetermined constraints and the complex frequency domain pressure change expression.

[0048] Based on the complex frequency domain pressure variation expression and predetermined preset conditions, the formation pressure at a target point in a heterogeneous stratum can be solved. These constraints include multi-region coupling constraints, pressure and flow continuity constraints, variable production constraints, and gas flow constraints.

[0049] In this scheme, for a rectangular hexahedron, based on the mirror reflection method and according to the expression for pressure change in the complex frequency domain, the expression for the Green's function can be obtained as follows:

[0050]

[0051] in,

[0052] x ′ D The z-axis represents the dimensionless distance of a point source along the X-axis. ′ D This represents the dimensionless distance of the point source along the Z-axis. This represents the dimensionless distance of the first point source along the Y-axis. x represents the dimensionless distance of the second point source along the Y-axis. eD y eD and z eD Let represent the dimensionless length, width, and height of the rectangular hexahedron, respectively; let u represent the Laplace variable; u = s represent a single medium; and u = sf(s) = [sω(1-ω) + λ] / [s(1-ω) + λ] represent a matrix-fracture dual medium. k represents the characteristic length. r ξ represents the equivalent permeability of anisotropic formations, μ represents fluid viscosity, and ξ represents the fluid viscosity. ′ D ξ represents the dimensionless distance of the point source in the direction of the target. ′ eD This represents the dimensionless distance of a point source along the target direction of a rectangular hexahedron, where the target direction is any one of the X-axis, Y-axis, or Z-axis.

[0053] Green's function Source B along the line wi and surface source B ej The corresponding source function can be obtained by performing spatial integration. and Given the position coordinates M of the target point D Then, the pressure change at the target point can be calculated.

[0054] Specifically, based on the Green's function expression derived from the complex frequency domain pressure change expression, multi-region coupling constraints, pressure and flow continuity constraints, variable production constraints, and gas flow constraints can be used to heterogeneously seal the formation pressure at a target point in the formation. The multi-region coupling constraints include formation pressure change constraints and wellbore pressure change constraints; the formation pressure change constraints are as follows: The wellbore pressure variation constraint is: Where b represents the sub-region index; k represents the interface segment index, k = 1, 2, ..., m; This represents the pressure change at interface segment k; s represents the wellbore segment index, s = 1, 2, ..., n; This indicates the pressure change in wellbore section s; This represents the source function of wellbore segment i at interface segment k. This represents the source function of interface segment j in interface segment k. This represents the source function of wellbore segment i in wellbore segment s. This represents the source function of interface segment j in wellbore segment s. This represents the complex frequency domain fluid intensity of wellbore segment i in subregion b. denoted by , where represents the complex frequency domain fluid intensity of interface segment j in subregion b, n represents the number of wellbore segments, and m represents the number of interface segments.

[0055] Based on the Green's function expression and multi-region coupling constraints, the unknown quantity can be determined as follows: and By combining the continuity conditions at the wellbore and the interface, a closed and solvable system of equations can be formed.

[0056] In this scheme, the pressure and flow continuity constraints may include:

[0057]

[0058]

[0059]

[0060]

[0061] Where b' represents the neighboring region of subregion b, This represents the pressure change at interface segment k in subregion b. This represents the pressure change at the interface segment k of subregion b'. This represents the complex frequency domain fluid intensity at interface segment k in subregion b. Let represent the complex frequency domain fluid intensity of the interface segment k in subregion b', w1, w2, ..., wn represent the segment indices of well w within the same region b, and b1, b2, ..., bn represent the region indices traversed by well w; b w represents the number of wells in sub-region b, n represents the number of wellbore sections, The complex frequency domain fluid intensity of well section i in subregion b is represented by l. hi Let represent the length of wellbore section i, t represent the production time, q(t) represent the well production, and L[·] represent the Laplace transform function.

[0062] Based on the above scheme, the variable production constraint may include:

[0063]

[0064] Where i represents the wellbore segment index, u(tt) i-1 ) represents the unit step function, c i This represents the intercept of the output change function at the zero point.

[0065] After obtaining the well production expression, the production can be transformed to the complex frequency domain to obtain the well production expression in the complex frequency domain:

[0066] Where δ represents the Dirac function, a i This indicates the rate of change in output.

[0067] Understandably, compared to liquids, gases have high compressibility and low viscosity, and the compressibility of gases leads to a strongly nonlinear flow control equation. To account for the changes in gas properties with pressure, this embodiment proposes pseudo-pressure and pseudo-time for the gas. Using pseudo-pressure and pseudo-function, the gas flow control equation can be formally equivalent to that of a microcompressible fluid, thus utilizing the solution of the microcompressible fluid flow control equation when solving gas flow problems.

[0068] Specifically, the gas flow constraint includes:

[0069]

[0070]

[0071] Where, μ g z represents the viscosity of natural gas g c represents the natural gas compressibility factor. t p represents the compression factor. ref t represents the reference pressure. ps Let m(p) represent the pseudo-time and m(p) represent the pseudo-pressure.

[0072] It should be noted that the instantaneous point source function of a single sub-region is based on the dimensionless time t. D The instantaneous point source function obtained by performing the Laplace transform. The Laplace variable s in the equation corresponds to the dimensionless time t. D However, for heterogeneous stratigraphic models, the rock parameters differ in each sub-region, resulting in different dimensionless time t. D Furthermore, the conditions for equal pressure and flow rate at the interface between adjacent regions need to be met within the Laplace space. Therefore, it is necessary to transform it to the same time scale. This scheme is based on the similarity properties of the Laplace transform. Will be on t D The Laplace space solution is transformed into a Laplace space solution with respect to time t. Due to similarity properties, the source function of time can still be calculated using the source function of dimensionless time, only requiring a time scale factor transformation of the source function and related parameters.

[0073] Based on the pressure change expressions for each sub-region, multi-region coupling constraints, pressure and flow continuity constraints, variable production constraints, and gas flow constraints, intermediate variables are eliminated to obtain the block algebraic matrix expression:

[0074]

[0075] Among them, A RR A represents the coefficients of the formation pressure equation. WW A represents the coefficients of the wellbore pressure equation. RW A WR L represents the coefficients of the formation and wellbore coupling equations, respectively. WR Represents the coefficients of the normalized equation for wellbore production. The wellbore linear source intensity and the regional interface source intensity at any time t. and and corresponding pressure changes and Will and Back to The pressure change at any point M in the stratum can be calculated, thus obtaining the pressure distribution Δp(M,t) of the entire buried stratum.

[0076] Through the establishment and solution process of the heterogeneous formation model, it is evident that the proposed method for calculating formation pressure between wells in saline aquifer storage requires only daily carbon dioxide injection data, without needing well shut-in testing or affecting operations. Furthermore, it can calculate formation pressure at different times, strata, and distances. The model has few assumptions and a wide range of applicability, greatly facilitating real-time prediction, monitoring, and rapid assessment of formation spatial pressure fluctuations and carbon dioxide leakage risks.

[0077] This technical solution divides the target area in a heterogeneous storage formation into sub-regions. Based on the wellbore and interface involved in each sub-region, it determines the time-domain pressure variation expression for each coordinate position in each sub-region at each time step. Using the time-domain pressure variation expression and a predefined source function, it determines the complex frequency domain pressure variation expression for each coordinate position in each sub-region at each time step. Finally, based on pre-determined constraints and the complex frequency domain pressure variation expression, it determines the formation pressure at the target point in the heterogeneous storage formation. This technical solution solves the problems of low calculation efficiency and poor accuracy in heterogeneous formation pressure calculation, improving both accuracy and efficiency.

[0078] Example 2

[0079] This embodiment is a specific implementation based on the above embodiment. This scheme selects the M1 formation in the target saline water layer of oilfield A for pressure monitoring. The saline water layer is highly heterogeneous, with uneven regional development. The strata are deltaic deposits, with an elevation depth of -830 to 920 m. The sand bodies are stable and contiguous, with dip angles of 0.2° to 1.3°. The caprock above the layer is 17.5 meters thick, exhibiting overall high porosity and high permeability characteristics (porosity 28%–33%, permeability 400 mD–11034 mD). The water layer is a normal temperature and pressure system (temperature: 52℃–67℃; pressure 8.4 MPa–11.6 MPa), indicating abundant formation energy. Multiple reservoir-caprock assemblages exist above (mudstone caprock permeability less than 0.2 mD). Although internal faults develop in the east-west direction, the sealing performance is good (SGR ≥ 20%).

[0080] The target area of ​​the heterogeneous storage formation was divided into grids of 100×100×1. The formation porosity was 0.12, the fluid viscosity was 0.6 mPa·s, and the overall compressibility was 1.15×10⁻⁶. -3 MPa -1 The wellbore radius is 0.07m, and the carbon dioxide injection rate is 2m³. 3 / day, injection time 10a.

[0081] Formation pressure calculations need to consider the changes in gas properties with pressure and temperature. Based on full gas chromatography-mass spectrometry (GC-MS) data, the gas deviation factor z and viscosity μ are calculated using industry standards throughout the injection process. g and volume factor B g As the pressure changes, the system can switch between pressure and simulated pressure, and between time and simulated time.

[0082] Given the actual daily carbon dioxide injection rate at a given formation, the bottom hole flowing pressure and pressure changes at any point in the formation can be calculated at different production times. Figure 2A According to the formation pressure distribution map provided in Embodiment 2 of the present invention, points are uniformly distributed in the formation, and the formation pressure at each point is calculated to obtain the following: Figure 2A The diagram shows the formation pressure distribution between wells. (See diagram for example.) Figure 2A As shown, the ring mark indicates a well, and the average formation pressure in the main gas-bearing area of ​​layer M1 is less than 10 MPa.

[0083] Since the formation pressure between wells cannot be directly measured, in order to verify the accuracy of the formation pressure prediction in this scheme, the calculated formation pressure results at different times are compared with the measured static pressure data of the formation before injection. Figure 2B This is a comparison chart of calculated and measured values ​​of inter-well pressure provided in Embodiment 2 of the present invention. Figure 2B Dark rectangles represent calculated values, and light rectangles represent measured values. For example... Figure 2BAs shown, the calculated and measured values ​​of formation pressure for each well are in good agreement, with an average error of 0.6 MPa and a maximum error of 3.8 MPa. Only a few wells show significant differences, and the overall accuracy meets the engineering requirements.

[0084] The computational accuracy of this method is comparable to that of numerical simulation methods. The heterogeneous formation model in this method is solved in Laplace space, allowing direct calculation of formation pressure values ​​at any given time without iterative steps, significantly accelerating the computation. Furthermore, the computational accuracy of this method is minimally affected by grid scale, being only related to the heterogeneity of the reservoir.

[0085] This technical solution divides the target area in a heterogeneous storage formation into sub-regions. Based on the wellbore and interface involved in each sub-region, it determines the time-domain pressure variation expression for each coordinate position in each sub-region at each time step. Using the time-domain pressure variation expression and a predefined source function, it determines the complex frequency domain pressure variation expression for each coordinate position in each sub-region at each time step. Finally, based on pre-determined constraints and the complex frequency domain pressure variation expression, it determines the formation pressure at the target point in the heterogeneous storage formation. This technical solution solves the problems of low calculation efficiency and poor accuracy in heterogeneous formation pressure calculation, improving both accuracy and efficiency.

[0086] Example 3

[0087] Figure 3 This is a schematic diagram of a device for determining the pressure of a heterogeneous formation in a storage site, provided in Embodiment 3 of the present invention. Figure 3 As shown, the device includes:

[0088] The sub-region division module 310 is used to divide the target region in the heterogeneous deposited strata into sub-regions;

[0089] The time-domain expression determination module 320 is used to determine the time-domain pressure change expression for each coordinate position in each sub-region at each time step, based on the wellbore and interface involved in each sub-region.

[0090] The complex frequency domain expression determination module 330 is used to determine the complex frequency domain pressure change expression for each coordinate position in each sub-region at each time step based on the time-domain pressure change expression for each coordinate position in each sub-region at each time step and the predefined source function.

[0091] The formation pressure determination module 340 is used to determine the formation pressure at a target point in a heterogeneous storage formation based on predetermined constraints and a complex frequency domain pressure change expression; wherein the constraints include multi-region coupling constraints, pressure and flow continuity constraints, variable production constraints, and gas flow constraints.

[0092] In this scheme, optionally, the expression for the time-domain pressure change is:

[0093]

[0094] Among them, t D M represents dimensionless time. D M' represents the location of the target point in the sub-region. D Indicates t D The position of the point source in the sub-region at time, G(·) is the Green's function, B w B represents the wire source determined based on the wellbore. e This indicates a surface source determined based on the interface. Indicates the fluid intensity of the line source. Let τ represent the fluid intensity of the surface source, τ represent the integration time, and M' represent the integration position.

[0095] Based on the above scheme, optionally, the source function can be represented as:

[0096]

[0097] The expression for the pressure change in the complex frequency domain is:

[0098]

[0099] Among them, t D M represents dimensionless time. D M' represents the location of the target point in the sub-region. D Indicates t D The position of the point source in the sub-region at time, where G(·) is the Green's function. B w Or B e , This represents the fluid intensity in the complex frequency domain of line source segment i. Let s represent the complex frequency domain fluid intensity of the surface source segment j, and s represent the Laplace variable. This represents the source function obtained by spatial integration along the source of the Green's function. Let represent the source function obtained by spatial integration of the Green's function along the surface source, where n represents the number of line source segments and m represents the number of surface source segments.

[0100] In a feasible scheme, the multi-region coupling constraint includes formation pressure variation constraint and wellbore pressure variation constraint; the formation pressure variation constraint is as follows:

[0101] The wellbore pressure variation constraint is:

[0102]

[0103] Where b represents the sub-region index; k represents the interface segment index, k = 1, 2, ..., m; This represents the pressure change at interface segment k; s represents the wellbore segment index, s = 1, 2, ..., n; This indicates the pressure change in wellbore section s; This represents the source function of wellbore segment i at interface segment k. This represents the source function of interface segment j in interface segment k. This represents the source function of wellbore segment i in wellbore segment s. This represents the source function of interface segment j in wellbore segment s. This represents the complex frequency domain fluid intensity of wellbore segment i in subregion b. denoted by , where represents the complex frequency domain fluid intensity of interface segment j in subregion b, n represents the number of wellbore segments, and m represents the number of interface segments.

[0104] In this scheme, optionally, the pressure and flow continuity constraints include:

[0105]

[0106]

[0107]

[0108]

[0109] Where b' represents the neighboring region of subregion b, This represents the pressure change at interface segment k in subregion b. This represents the pressure change at the interface segment k of subregion b'. This represents the complex frequency domain fluid intensity at interface segment k in subregion b. Let represent the complex frequency domain fluid intensity of the interface segment k in subregion b', w1, w2, ..., wn represent the segment indices of well w within the same region b, and b1, b2, ..., bn represent the region indices traversed by well w; b w represents the number of wells in sub-region b, n represents the number of wellbore sections, The complex frequency domain fluid intensity of well section i in subregion b is represented by l. hi Let represent the length of wellbore section i, t represent the production time, q(t) represent the well production, and L[·] represent the Laplace transform function.

[0110] Based on the above scheme, optionally, the variable production constraint includes:

[0111]

[0112] Where i represents the wellbore segment index, u(tt) i-1 ) represents the unit step function, c i This represents the intercept of the output change function at the zero point.

[0113] In a preferred embodiment, the gas flow constraint includes:

[0114]

[0115]

[0116] Where, μ g z represents the viscosity of natural gas g c represents the natural gas compressibility factor. t p represents the compression factor. ref t represents the reference pressure. ps Let m(p) represent the pseudo-time and m(p) represent the pseudo-pressure.

[0117] The heterogeneous formation pressure determination device provided in this embodiment of the invention can execute the heterogeneous formation pressure determination method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method.

[0118] Example 4

[0119] Figure 4 A schematic diagram of an electronic device 410 that can be used to implement embodiments of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0120] like Figure 4As shown, the electronic device 410 includes at least one processor 411 and a memory, such as a read-only memory (ROM) 412 or a random access memory (RAM) 413, communicatively connected to the at least one processor 411. The memory stores computer programs executable by the at least one processor. The processor 411 can perform various appropriate actions and processes based on the computer program stored in the ROM 412 or loaded from storage unit 418 into the RAM 413. The RAM 413 may also store various programs and data required for the operation of the electronic device 410. The processor 411, ROM 412, and RAM 413 are interconnected via a bus 414. An input / output (I / O) interface 415 is also connected to the bus 414.

[0121] Multiple components in electronic device 410 are connected to I / O interface 415, including: input unit 416, such as keyboard, mouse, etc.; output unit 417, such as various types of displays, speakers, etc.; storage unit 418, such as disk, optical disk, etc.; and communication unit 419, such as network card, modem, wireless transceiver, etc. Communication unit 419 allows electronic device 410 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0122] Processor 411 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 411 include, but are not limited to, central processing unit (CPU), graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any suitable processor, controller, microcontroller, etc. Processor 411 performs the various methods and processes described above, such as methods for determining pressure in heterogeneous storage formations.

[0123] In some embodiments, the method for determining the pressure of heterogeneous sealed formations may be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 418. In some embodiments, part or all of the computer program may be loaded and / or installed on electronic device 410 via ROM 412 and / or communication unit 419. When the computer program is loaded into RAM 413 and executed by processor 411, one or more steps of the method for determining the pressure of heterogeneous sealed formations described above may be performed. Alternatively, in other embodiments, processor 411 may be configured to perform the method for determining the pressure of heterogeneous sealed formations by any other suitable means (e.g., by means of firmware).

[0124] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0125] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0126] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0127] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0128] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or computing systems that include middleware components (e.g., application servers), or computing systems that include frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0129] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0130] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0131] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for determining pressure in a heterogeneous reservoir, comprising: The method comprises: regional division is performed on a target region in the heterogeneous storage formation to obtain each sub-region; a time-domain pressure change expression of each coordinate position in each sub-region at each time is determined according to wellbores and interfaces involved in each sub-region; a complex frequency-domain pressure change expression of each coordinate position in each sub-region at each time is determined according to the time-domain pressure change expression of each coordinate position in each sub-region at each time and a pre-defined source function; a formation pressure of a target point in the heterogeneous storage formation is determined according to a pre-determined constraint condition and the complex frequency-domain pressure change expression, wherein the constraint condition comprises a multi-region coupling constraint, a pressure and flow continuity constraint, a variable production constraint and a gas flow constraint; the time-domain pressure change expression is: ； wherein, denotes a dimensionless time, denotes the position of the target point in the sub-area, denotes is the Green function, denotes a line source determined based on the wellbore, denotes a surface source determined based on the interface, denotes the fluid strength of the line source, denotes the fluid strength of the surface source, denotes the integration time, denotes the integration position; The source function is represented as: ; the complex frequency-domain pressure change expression is: ； in, Indicates dimensionless time. Indicates the location of the target point in the sub-region. express For Green's function, express or , , , Indicates line source segment The fluid intensity in the complex frequency domain, Indicates surface source segment The fluid intensity in the complex frequency domain, Represents the Laplace variable. This represents the source function obtained by spatial integration along the source of the Green's function. This represents the source function obtained by spatial integration of the Green's function along the surface source. Indicates the number of line source segments. Indicates the number of surface source segments; the multi-region coupling constraint comprises a formation pressure change constraint and a wellbore pressure change constraint; the formation pressure change constraint is: ; the wellbore pressure change constraint is: ; wherein, represents a sub-region index; represents an interface segment index, ; represents a pressure change of an interface segment ; represents a wellbore segment index, ; represents a pressure change of a wellbore segment ; represents a source function of a wellbore segment at an interface segment ; represents a source function of an interface segment at an interface segment ; represents a source function of a wellbore segment at a wellbore segment ; represents a source function of an interface segment at a wellbore segment ; represents a complex frequency domain fluid strength of a wellbore segment in a sub-region ; represents a complex frequency domain fluid strength of an interface segment in a sub-region ; represents a wellbore segment number, represents an interface segment number; the pressure and flow continuity constraint comprises: ， ； ； ； ； wherein, represents a sub-region adjacent to a region, represents a sub-region interface segment pressure change, represents a sub-region interface segment pressure change, represents a sub-region interface segment complex frequency domain fluid intensity, represents a sub-region interface segment complex frequency domain fluid intensity, , , , represents a well segment index within the same region, , , , , represents a well passing through a region index; represents a number of wells in a sub-region, represents a number of wellbore segments, represents a complex frequency domain fluid intensity of a wellbore segment in a sub-region, represents a length of a wellbore segment, represents a production time, represents a well production, represents a Laplace transform function; the variable production constraint comprises: ； wherein, denotes the wellbore segment index, denotes the unit step function, denotes the intercept of the rate change function at 0.

2. The method of claim 1, wherein, the gas flow constraint comprises: ； ； wherein, represents the natural gas viscosity, represents the natural gas compressibility factor, represents the compressibility factor, represents the reference pressure, represents the pseudo-time, represents the pseudo-pressure.

3. A heterogeneous reservoir pressure determination apparatus, characterized by, comprises: a sub-region division module configured to perform regional division on a target region in the heterogeneous storage formation to obtain each sub-region; a time-domain expression determination module configured to determine a time-domain pressure change expression of each coordinate position in each sub-region at each time according to wellbores and interfaces involved in each sub-region; a complex frequency-domain expression determination module configured to determine a complex frequency-domain pressure change expression of each coordinate position in each sub-region at each time according to the time-domain pressure change expression of each coordinate position in each sub-region at each time and a pre-defined source function; a formation pressure determination module configured to determine a formation pressure of a target point in the heterogeneous storage formation according to a pre-determined constraint condition and the complex frequency-domain pressure change expression, wherein the constraint condition comprises a multi-region coupling constraint, a pressure and flow continuity constraint, a variable production constraint and a gas flow constraint; the time-domain pressure change expression is: ； wherein, denotes a dimensionless time, denotes the position of the target point in the sub-region, denotes is the Green function, denotes a line source determined based on the wellbore, denotes a surface source determined based on the interface, denotes the fluid strength of the line source, denotes the fluid strength of the surface source, denotes the integration time, denotes the integration position; The source function is represented as: ; the complex frequency-domain pressure change expression is: ； in, Indicates dimensionless time. Indicates the location of the target point in the sub-region. express For Green's function, express or , , , Indicates line source segment The fluid intensity in the complex frequency domain, Indicates surface source segment The fluid intensity in the complex frequency domain, Represents the Laplace variable. This represents the source function obtained by spatial integration along the source of the Green's function. This represents the source function obtained by spatial integration of the Green's function along the surface source. Indicates the number of line source segments. Indicates the number of surface source segments; the multi-region coupling constraint comprises a formation pressure change constraint and a wellbore pressure change constraint; the formation pressure change constraint is: ; the wellbore pressure change constraint is: ; wherein, represents a sub-region index; represents an interface segment index, ; represents a pressure change of an interface segment ; represents a wellbore segment index, ; represents a pressure change of a wellbore segment ; represents a source function of a wellbore segment at an interface segment ; represents a source function of an interface segment at an interface segment ; represents a source function of a wellbore segment at a wellbore segment ; represents a source function of an interface segment at a wellbore segment ; represents a complex frequency domain fluid strength of a wellbore segment in a sub-region ; represents a complex frequency domain fluid strength of an interface segment in a sub-region ; represents a number of wellbore segments, represents a number of interface segments; the pressure and flow continuity constraint comprises: ， ； ； ； ； wherein, represents a sub-region adjacent to a region, represents a sub-region interface segment pressure variation, represents a sub-region interface segment pressure variation, represents a sub-region interface segment complex frequency domain fluid strength, represents a sub-region interface segment complex frequency domain fluid strength, , , , represents a well segment index within the same region, , , , , represents a well passing through a region index; represents a number of wells in a sub-region, represents a number of wellbore segments, represents a complex frequency domain fluid strength of a wellbore segment in a sub-region, represents a length of a wellbore segment , represents a production time, represents a well production, represents a Laplace transform function; the variable production constraint comprises: ； wherein, denotes the wellbore segment index, denotes the unit step function, denotes the intercept of the rate change function at 0.

4. An electronic device, comprising: the electronic device comprises: at least one processor; and a memory connected with the at least one processor in communication; wherein the memory stores a computer program that can be executed by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the heterogeneous storage formation pressure determination method in any one of claims 1-2.

5. A computer readable storage medium, characterized in that, The computer readable storage medium stores computer instructions for enabling a processor to execute the heterogeneous storage formation pressure determination method in any one of claims 1-2 when executed.

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