Multi-well pressure monitoring mathematical model modeling method, device and equipment and storage medium

Abstract

The present disclosure provides a multi-well pressure monitoring mathematical modeling method, device, equipment and storage medium, comprising: obtaining underground gas storage data and actual pressure data of the underground gas storage; based on the underground gas storage data and the multi-well pressure monitoring mathematical model, the pressure solution of the multi-well pressure monitoring mathematical model is obtained by superimposing the pressure of adjacent wells and the target well; based on the curve fitting result drawn by the pressure solution and the actual pressure data, the reservoir parameters in the multi-well pressure monitoring mathematical model are inversely calculated to obtain an updated multi-well pressure monitoring mathematical model. On the basis of the existing pressure monitoring model, the influence of adjacent wells is included in the calculation range by using the pressure superposition principle, thereby reducing the error existing in pressure calculation, improving the accuracy of the multi-well pressure monitoring mathematical model, and simulating the real situation of the underground gas storage.

Description

Technical Field

[0001] This disclosure relates to the field of gas storage technology, and in particular to a method, apparatus, equipment and storage medium for modeling mathematical models of multi-well pressure monitoring. Background Technology

[0002] With the rapid development of the national economy, natural gas accounts for an increasingly larger proportion of energy consumption. Due to the imbalance between the distribution range of natural gas and the supply and demand relationship, underground gas storage facilities are an important means to solve seasonal peak shaving and emergency gas supply. Furthermore, constructing pressure monitoring mathematical models for underground gas storage facilities can help technicians predict the production capacity of the storage facilities.

[0003] While significant progress has been made in pressure monitoring models for underground gas storage facilities, many challenges remain. For instance, after a gas storage facility is officially put into operation, the alternating cycles of intense natural gas injection and extraction, coupled with the short well shut-in pressure recovery time, exacerbate interference from multiple wells. Existing pressure monitoring models typically only consider individual wells, neglecting the influence of adjacent wells. This results in a poor fit between field pressure monitoring data and the calculations from existing models, making it difficult for technicians to accurately determine the working status and production capacity of the gas storage facility using current monitoring models. Summary of the Invention

[0004] According to one aspect of this disclosure, a mathematical modeling method for multi-well pressure monitoring is provided, including:

[0005] The data of the underground gas storage facility and the actual pressure data of the underground gas storage facility are obtained. The underground gas storage facility data includes: geological parameters and fluid properties of the gas storage facility, injection and production history of the target well and adjacent wells. The adjacent wells and the target well belong to the same underground gas storage facility and are connected by a porous medium. The actual pressure data is obtained by sensors that are pre-installed in the underground gas storage facility.

[0006] Based on the underground gas storage data and the multi-well pressure monitoring mathematical model, the pressure solution of the multi-well pressure monitoring mathematical model is obtained by superimposing the pressure of the adjacent wells and the target well.

[0007] Based on the curve fitting results plotted using the pressure solution and the actual pressure data, the reservoir parameters in the multi-well pressure monitoring mathematical model are inverted and calculated to obtain the updated multi-well pressure monitoring mathematical model.

[0008] According to another aspect of this disclosure, a modeling apparatus for a multi-well pressure monitoring mathematical model is provided, comprising:

[0009] The data acquisition module is used to acquire underground gas storage data and actual pressure data of the underground gas storage. The underground gas storage data includes: geological parameters and fluid properties of the gas storage, injection and production history of the target well and adjacent wells. The adjacent wells and the target well belong to the same underground gas storage and are connected by a porous medium. The actual pressure data is obtained through sensors pre-installed in the underground gas storage.

[0010] The pressure solution acquisition module is used to obtain the pressure solution of the multi-well pressure monitoring mathematical model by superimposing the pressure of the adjacent wells and the target well based on the underground gas storage data and the multi-well pressure monitoring mathematical model.

[0011] The model update module is used to invert and calculate the reservoir parameters in the multi-well pressure monitoring mathematical model based on the curve fitting results drawn from the pressure solution and the actual pressure data, so as to obtain the updated multi-well pressure monitoring mathematical model.

[0012] According to another aspect of this disclosure, an electronic device is provided, comprising:

[0013] Processor; and,

[0014] Memory for stored programs;

[0015] The program includes instructions that, when executed by the processor, cause the processor to perform the method according to an exemplary embodiment of the present disclosure.

[0016] According to another aspect of this disclosure, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the method according to exemplary embodiments of this disclosure.

[0017] One or more technical solutions provided in this disclosure involve acquiring underground gas storage data and actual pressure data of the underground gas storage, and then, based on the underground gas storage data and a multi-well pressure monitoring mathematical model, obtaining the pressure solution of the multi-well pressure monitoring mathematical model by superimposing the pressures of adjacent wells and the target well. Based on the curve fitting results plotted using the pressure solution and actual pressure data, the reservoir parameters in the multi-well pressure monitoring mathematical model are inverted and calculated to obtain an updated multi-well pressure monitoring mathematical model. Specifically, to calculate the reservoir parameters of the multi-well pressure monitoring mathematical model and improve its fit with the underground gas storage, the pressure solution is fitted with the actual pressure data, a fitting curve is plotted, and then inversion calculations are performed based on the fitting points of the fitting curve to obtain accurate reservoir parameters. Finally, the multi-well pressure monitoring mathematical model is updated based on these reservoir parameters.

[0018] Because underground gas storage facilities employ a production mode involving simultaneous injection and production from multiple horizontal wells, significant multi-well interference occurs. In solving the multi-well pressure monitoring mathematical model, the principle of multi-well pressure superposition can be applied to account for the influence of adjacent wells, offsetting the multi-well interference caused by simultaneous injection and production from multiple horizontal wells, thus obtaining the pressure solution for the underground gas storage facility. Then, based on the fitted curve, reservoir parameters are calculated backwards to update the multi-well pressure monitoring mathematical model, resulting in a higher degree of fit between the multi-well pressure monitoring mathematical model and the underground gas storage facility. Therefore, the method of this exemplary embodiment can solve the technical problem of large errors in reservoir pressure calculation and monitoring caused by existing single-well pressure monitoring models that do not consider the influence of multi-well interference. The multi-well pressure monitoring mathematical model of this exemplary embodiment can realistically simulate the actual situation of underground gas storage facilities. Technical personnel can also accurately determine the working status of the gas storage facility and obtain the reservoir physical properties and the gas injection and production capacity of the gas storage wells through this exemplary embodiment. Attached Figure Description

[0019] Further details, features, and advantages of this disclosure are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which:

[0020] Figure 1 A flowchart illustrating a mathematical modeling method for multi-well pressure monitoring in an underground gas storage facility, as shown in an exemplary embodiment of this disclosure, is provided.

[0021] Figure 2 The fluid properties of the block where the gas storage facility is located, as shown in an exemplary embodiment of this disclosure, are illustrated.

[0022] Figure 3 The injection and production history of a target well in a gas storage facility is shown in an exemplary embodiment of this disclosure;

[0023] Figure 4 The injection and production history of adjacent wells in a gas storage facility is shown in an exemplary embodiment of this disclosure;

[0024] Figure 5 A physical model of multi-well pressure monitoring, illustrating an exemplary embodiment of this disclosure, is shown;

[0025] Figure 6 A fitting curve diagram of a multi-well pressure monitoring mathematical model of an exemplary embodiment of this disclosure is shown;

[0026] Figure 7 A flowchart illustrating the mathematical modeling method for multi-well pressure monitoring in an underground gas storage facility, as shown in an exemplary embodiment of this disclosure, is provided.

[0027] Figure 8 A schematic block diagram of the functional modules of a mathematical modeling apparatus for multi-well pressure monitoring of an underground gas storage facility according to an exemplary embodiment of the present disclosure is shown.

[0028] Figure 9 A schematic block diagram of a chip according to an exemplary embodiment of the present disclosure is shown;

[0029] Figure 10 A structural block diagram of an exemplary electronic device that can be used to implement embodiments of the present disclosure is shown. Detailed Implementation

[0030] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0031] It should be understood that the steps described in the method embodiments of this disclosure may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of this disclosure is not limited in this respect.

[0032] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below. It should be noted that the concepts of "first", "second", etc., used in this disclosure are only used to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0033] It should be noted that the terms "a" and "a plurality of" used in this disclosure are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0034] After multiple cycles of alternating strong natural gas injection and extraction, underground gas storage facilities will experience significant multi-well interference. Since the pressure monitoring models in related technologies usually only consider a single well and ignore the influence of adjacent wells, the fit between the field pressure monitoring data and the calculation results of the existing monitoring models is not high. As a result, technicians cannot accurately determine the working status and production capacity of the gas storage facility through the existing monitoring models.

[0035] Therefore, in order to construct a mathematical model for multi-well pressure monitoring of underground gas storage facilities that considers interference from multiple wells, and to facilitate technicians in accurately judging the working status of the gas storage facility and obtaining the reservoir physical properties and well injection and production capacity, this disclosure first provides a modeling method for a mathematical model of multi-well pressure monitoring of underground gas storage facilities. Figure 1 A flowchart illustrating a mathematical modeling method for multi-well pressure monitoring in an underground gas storage facility, as described in an exemplary embodiment of this disclosure, is shown. Figure 1 As shown, the method may include the following steps:

[0036] Step S110: Obtain underground gas storage data and actual pressure data of the underground gas storage. The underground gas storage data here may include, but is not limited to, the geological parameters of the gas storage, the fluid properties of the gas storage, the injection and production history of the target well, and the injection and production history of adjacent wells. The above-mentioned underground gas storage data can be obtained by consulting well logging, geological data, and drilling data. The adjacent wells and the target well belong to the same underground gas storage, and are connected to each other by a porous medium. The above-mentioned actual pressure data is obtained through sensors pre-installed in the underground gas storage.

[0037] For example, relevant data of an underground gas storage facility to be pressure monitored are obtained: the total area of ​​the gas storage facility is approximately 28.6 km². 2 The reservoir has a top depth of 3500m and a thickness of approximately 355m. It was converted from a depleted gas reservoir and can be considered to have single-phase flow within the gas storage facility. The reservoir is mainly composed of siltstone, fine-grained sandstone, unequal sandstone, pebble unequal sandstone, and pebble argillaceous sandstone. The target well was drilled in 2018. Adjacent wells belong to the same drilling platform as the target well. Unstable well testing was conducted on the target well at the end of the fifth injection-production cycle of the gas storage facility. The testing period was from November 18th to 23rd, with a total testing time of 113 hours. During this period, both the target well and adjacent wells were in the gas injection phase.

[0038] Geological parameters, fluid properties, injection and production history of the target well, and injection and production history of adjacent wells in the block where the gas reservoir is located were obtained by reviewing well logging, geological data, and drilling data. The geological parameters are shown in Table 1 below:

[0039] Table 1 Geological parameters of the block where the gas storage facility is located

[0040]

[0041] Figure 2 The fluid properties of the block containing the gas storage facility, as shown in the exemplary embodiments of this disclosure, include gas volume factor, gas compressibility factor, gas viscosity, and gas density.

[0042] Figure 3The illustration shows the injection and production history of a target well in a gas storage facility, with time on the horizontal axis and the injection and production rate of the target well on the vertical axis.

[0043] Figure 4 The illustration shows the injection and production history of adjacent wells in a gas storage facility according to an exemplary embodiment of this disclosure, with time as the horizontal axis and the injection and production rate of adjacent wells as the vertical axis to display the injection and production status of adjacent wells.

[0044] Step S120: Construct a multi-well pressure monitoring physical model. The multi-well pressure monitoring physical model is based at least on geological parameters, fluid properties, and the location of each horizontal well in the gas storage facility. In practical applications, the multi-well pressure monitoring physical model is constructed based on parameters such as geological parameters, fluid properties, and the location of each horizontal well in the gas storage facility.

[0045] Figure 5 A physical model for multi-well pressure monitoring, representing an exemplary embodiment of this disclosure, is shown. (As follows) Figure 5 As shown, a rectangular coordinate system is established for each horizontal well in the porous medium to describe the position of each horizontal well in the underground gas storage, thereby constructing a physical model for multi-well pressure monitoring.

[0046] Step S130: Based on the physical model and target assumptions of the multi-well pressure monitoring system, obtain the mathematical model for multi-well pressure monitoring. The method for constructing the mathematical model for multi-well pressure monitoring includes the following steps:

[0047] Step S131: Define the target assumptions. These assumptions include at least one of the following: ① The fluid in the underground gas storage tank is assumed to be a single-phase compressible gas; ② The effects of gravity and capillary forces are not considered during gas flow; ③ Before the unstable well test, the initial pressure of the underground gas storage tank is assumed to be uniformly distributed; ④ The porous medium is anisotropic and satisfies the homogeneity and uniform thickness of the water; ⑤ Gas flow follows Darcy's law, and the gas's equation of state conforms to Boyle's law; ⑥ The pseudo-pressure method is used to eliminate nonlinearity.

[0048] For example, the equation of state for the gas in the gas storage tank, obtained based on the target assumption ⑤, can be expressed by the following formulas (1) and (2):

[0049] pV = ZnRT (1)

[0050]

[0051] In the formula: p is the pressure, and its unit is MPa; V is the volume, and its unit is m³. 3 Z is the gas compressibility coefficient; n is the amount of substance, in mol; R is the universal gas constant, in Pa·m. 3 / (mol·K); T is temperature, its unit is K; B gThis is the volume factor, and its unit is m. 3 / stm 3 ;sc represents the standard condition.

[0052] For example, based on the target assumption ⑥, a pseudo-pressure equation is introduced to eliminate nonlinearity, which can be expressed by the following formula (3):

[0053]

[0054] In the formula: m is the pseudo-pressure, and its unit is MPa. 2 / mPa·s;p i The reference pressure is arbitrarily selected, and its unit is MPa; p is the pressure, and its unit is MPa; μ is the gas viscosity, and its unit is mPa·s; Z is the gas compressibility coefficient.

[0055] Because pressure changes in underground gas storage facilities are a highly nonlinear process, traditional linear regression models cannot adequately describe this change. The pseudo-pressure method, however, employs a nonlinear optimization algorithm that can more accurately fit this nonlinear process, thereby improving the model's accuracy and reliability. Therefore, using the pseudo-pressure method can eliminate nonlinearity, improve the accuracy and reliability of multi-well pressure monitoring models for underground gas storage facilities, and thus better support the management and operation of gas storage facilities.

[0056] Step S132: Define dimensionless variables and discretize the multi-horizontal wells in the multi-well pressure monitoring mathematical model into multiple points, and establish the governing equations for each point. The dimensionless variables here include dimensionless production time, dimensionless distance, dimensionless coordinate origin position, dimensionless reservoir thickness, and dimensionless wellbore storage coefficient, etc.

[0057] For example, dimensionless production time can be expressed by the following formula (4):

[0058]

[0059] In the formula: k is the permeability, and its unit is mD; t is the time, and its unit is h; μ is the gas viscosity, and its unit is mPa·s; Porosity; C t The overall compressibility factor is expressed in MPa. -1 L is the reference length, and its unit is meters.

[0060] For example, dimensionless distance can be expressed by the following formula (5):

[0061]

[0062] In the formula: x, y, z are the distances in the rectangular coordinate system, and their units are m; r is the radial distance, and its unit is m; L is the reference length, and its unit is m.

[0063] For example, the position of the origin of the dimensionless coordinate system can be represented by the following formula (6):

[0064]

[0065] In the formula: x w ,y w ,z w L represents the position of the origin of the rectangular coordinate system, with units of meters (m); L represents the reference length, with units of meters (m).

[0066] For example, the dimensionless reservoir thickness can be expressed by the following formula (7):

[0067]

[0068] In the formula: h is the reservoir thickness, and its unit is m; L is the reference length, and its unit is m.

[0069] For example, the dimensionless wellbore storage factor can be expressed by the following formula (8):

[0070]

[0071] In the formula: C is the wellbore storage coefficient, and its unit is m. 3 / MPa; Porosity; C t The overall compressibility factor is expressed in MPa. -1 h represents the reservoir thickness, in meters (m); L represents the reference length, in meters (m).

[0072] For example, the multi-level wells in the multi-well pressure monitoring mathematical model can be discretized into multiple points, and the control equations at each point can be established, which can be expressed by the following formula (9):

[0073]

[0074] In the formula: m is the pseudo-pressure, and its unit is MPa. 2 / mPa·s;r D t is the dimensionless radial distance; D This refers to dimensionless production time.

[0075] Step S133: Define the initial conditions, inner boundary conditions, and outer boundary conditions of the gas storage facility.

[0076] For example, the initial conditions of a gas storage facility can be represented by the following formula (10):

[0077]

[0078] In the formula: t D The dimensionless production time is represented by m, which is the pseudo-pressure in MPa. 2 / mPa·s.

[0079] For example, the internal boundary conditions of a gas storage facility can be expressed by the following formula (11):

[0080]

[0081] In the formula: L is the reference length, in meters; k is the permeability, in cubic meters (mD); r D m is the dimensionless radial distance; m is the pseudo-pressure, and its unit is MPa. 2 / mPa·s; It is a point source in three-dimensional space, and its unit is m. 3 / d; T is temperature, and its unit is K.

[0082] Wherein, δ(t) D This is related to time and can be expressed by the following formula (12):

[0083]

[0084] For example, the outer boundary conditions of a gas storage facility can be represented by the following formula (13):

[0085]

[0086] In the formula: r D m is the dimensionless radial distance; m is the pseudo-pressure, and its unit is MPa. 2 / mPa·s.

[0087] Step S140: Based on the underground gas storage data and the multi-well pressure monitoring mathematical model, obtain the pressure solution of the multi-well pressure monitoring mathematical model.

[0088] like Figure 1 As shown, the total simulation duration, simulation time t, and time step Δt are set, where the total simulation duration, simulation time t, and time step Δt can all be randomly defined according to experimental requirements.

[0089] Step S141: Obtain the point source solution of the multi-well pressure monitoring mathematical model of the underground gas storage in the Laplace domain. This can be achieved by applying a Laplace transform to the governing equations, initial conditions, and internal and external boundary conditions.

[0090] For example, the point source in the internal boundary condition equation of the gas storage in step S133 As a unit intensity, the Laplace transformation can be expressed by the following formula (14):

[0091]

[0092] In the formula: L is the reference length, and its unit is m; r D The radial distance is dimensionless. Porosity; C t The overall compressibility factor is expressed in MPa. -1 .

[0093] Where Δm=mm i Substituting these equations into the governing equations and performing a Laplace transformation on the governing equations, initial conditions, and external boundary conditions, we obtain the following set of equations, which can be expressed by the following formula (15):

[0094]

[0095] In the formula: r D is the dimensionless radial distance; u is the Laplace variable; L is the reference length, in meters. Porosity; C t The overall compressibility factor is expressed in MPa. -1 .

[0096] In the above system of equations, the first equation is the governing equation, the second equation is the inner boundary condition, and the third equation is the outer boundary condition.

[0097] Solving the Laplace transformed governing equations, inner boundary conditions, and outer boundary conditions yields the point source solution of the multi-well pressure monitoring mathematical model in the Laplace domain, which can be expressed by the following formula (16):

[0098]

[0099] In the formula: T is the temperature, and its unit is K; It is a point source in three-dimensional space, and its unit is m. 3 / d; u is the Laplace variable; r D is the dimensionless radial distance; k is the permeability, in mD; L is the reference length, in meters. To consider the point source solution of any unbounded horizontal well in the Lagrange domain.

[0100] Step S142: Using the mirror reflection method and the line source function integration method, the basic pressure solution of any horizontal well in the Lagrange domain in the multi-well pressure monitoring mathematical model is obtained from the point source solution.

[0101] For example, the point source solution of the multi-well pressure monitoring mathematical model in the Lagrange domain is first subjected to the mirror reflection method, and the infinite series is eliminated.

[0102] In practical applications, considering that underground gas storage facilities have impermeable top and bottom boundaries, the point source solution of the multi-well pressure monitoring mathematical model in step S141 in the Lagrange domain can be represented by the following formula (17) using the mirror reflection method:

[0103]

[0104] In the formula: T is the temperature, and its unit is K; It is a point source in three-dimensional space, and its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D ,z D The distance in a dimensionless rectangular coordinate system; x wD ,y wD ,z wD The position of the origin of the dimensionless rectangular coordinate system; This is the point source solution of any horizontal well in the Lagrange domain in a multi-well pressure monitoring mathematical model that considers the boundary.

[0105] In practical applications, the new point source solution of the multi-well pressure monitoring mathematical model obtained by the mirror reflection method contains an infinite series. In order to facilitate calculation, the infinite series is eliminated by using the Poisson summation formula to obtain the following formula (18):

[0106]

[0107] In the formula: T is the temperature, and its unit is K; It is a point source in three-dimensional space, and its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D The distance in a dimensionless rectangular coordinate system; x wD ,y wD K0 represents the position of the origin of a dimensionless rectangular coordinate system; K0 is a zeroth-order Bessel function of the first kind. This is the point source solution in the Lagrange domain for any horizontal well in the multi-well pressure monitoring mathematical model after eliminating the infinite series.

[0108] For example, the point source solution after eliminating infinite series in the multi-well pressure monitoring mathematical model is obtained by integrating the line source function to obtain the basic pressure solution of any horizontal well in the Lagrange domain in the multi-well pressure monitoring mathematical model.

[0109] In practical applications, the bottom hole pressure of a horizontal well in the multi-well pressure monitoring mathematical model can be regarded as the integral of a point source on the horizontal wellbore. By integrating the point source solution after eliminating infinite series along the gas flow direction in the horizontal well using the method of line source function integration, the basic solution of the bottom hole pressure of any horizontal well in the multi-well pressure monitoring mathematical model can be obtained, which can be expressed by the following formula (19):

[0110]

[0111] In the formula: T is the temperature, and its unit is K; It is a point source in three-dimensional space, and its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D The distance in a dimensionless rectangular coordinate system; x wD ,y wD K0 represents the position of the origin of a dimensionless rectangular coordinate system; K0 is a zeroth-order Bessel function of the first kind. This represents the fundamental pressure solution for any horizontal well in the Lagrange domain within the multi-well pressure monitoring mathematical model.

[0112] Step S143: Superimpose the basic pressure solutions of adjacent wells and the target well to obtain the superimposed pressure solution of the multi-well pressure monitoring mathematical model in the Lagrange domain.

[0113] In practical applications, considering the impact of adjacent wells on the target well, pressure superposition is used to offset the multi-well interference problem caused by injection and production.

[0114] For example, a new dimensionless distance r is introduced. D,i It can be expressed by the following formula (20):

[0115]

[0116] Based on the principle of pressure superposition, the summation formula for the pressure of multiple horizontal wells in the multi-well pressure monitoring mathematical model is obtained, and the pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain is obtained, which can be expressed by the following formula (21):

[0117]

[0118] In the formula: N is the number of wells; The pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain; The fundamental pressure solution for well 1; The fundamental pressure solution for well 2; Let T be the fundamental pressure solution for well N; T is the temperature, and its unit is K. It is a point source in three-dimensional space, and its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D ,z D The distance in a dimensionless rectangular coordinate system; x wD ,y wD ,z wD K0 represents the position of the origin of a dimensionless rectangular coordinate system; K0 is a zero-order Bessel function of the first kind.

[0119] In practical applications, considering that the target well can be injected and produced, it is necessary to define a flow constraint equation, which can be expressed by the following formula (22):

[0120]

[0121] In the formula: + represents extraction; - represents injection; u is the Laplace variable.

[0122] In one alternative approach, since it is not necessary to distinguish between the fundamental pressure solutions of the target well and adjacent wells during the actual solution process, equation (19) is both the fundamental pressure solution equation for the target well and the fundamental pressure solution equation for adjacent wells. Therefore, equation (19) and equation (22) can be combined into a matrix equation, and the Gaussian elimination method can be used to solve it, thereby obtaining the production rate q, pseudo-pressure m, and bottom hole pseudo-pressure m of each horizontal well. w .

[0123] Step S144: Apply Gaussian elimination to the pressure superposition solution to obtain the bottom hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the Lagrange domain.

[0124] In practical applications, horizontal wells undergoing intensive injection and production operations can cause reservoir contamination in the near-wellbore zone, leading to changes in the wellbore storage coefficient and skin coefficient. This significantly impacts the analysis of the bottom hole pseudo-pressure and, consequently, the production capacity of underground gas storage facilities. Furthermore, since the bottom hole pseudo-pressure solution in the time domain is difficult to obtain, it is necessary to first determine the bottom hole pseudo-pressure in the Lagrange domain.

[0125] For example, by introducing the wellbore storage coefficient and the skin coefficient, the bottom hole pseudo-pressure of the multi-well pressure monitoring mathematical model considering the influence of the wellbore storage coefficient and the skin coefficient in the Lagrange domain can be expressed by the following formula (23):

[0126]

[0127] In the formula: S is the epidermal coefficient; C D is the wellbore storage coefficient; u is the Laplace variable; m w To simulate the pressure at the bottom of the well.

[0128] Step S145: The bottom hole pressure in the Lagrange domain is obtained by using the Stehfest numerical inversion method to obtain the bottom hole pressure in the time domain of the multi-well pressure monitoring mathematical model.

[0129] For example, the bottom hole pressure of the multi-well pressure monitoring mathematical model in the Laplace domain is first subjected to an inverse Laplace transformation, which can be expressed by the following formula (24):

[0130]

[0131] In the formula: N is an empirical constant, typically taken as 8, 10, or 12; m w To simulate the pressure at the bottom of the well.

[0132] Furthermore, V i Defined as follows (25):

[0133]

[0134] In the formula: N is an empirical constant, usually taken as 8, 10, or 12; i is the loop variable; k is the loop variable.

[0135] Define u as follows (26):

[0136]

[0137] In the formula: i is the loop variable; t is the simulation time.

[0138] Given a value of i and a value of t, calculate V. i The value of V is calculated by measuring V within each time step. i The value of is obtained to obtain the bottom hole pressure of the multi-well pressure monitoring mathematical model in the time domain.

[0139] Step S146: Check if t is equal to the total simulation time. If t is not equal to the total simulation time, execute t = t + Δt and restart the solution of the pressure of the multi-well pressure monitoring mathematical model. If t is equal to the total simulation time, execute step S147.

[0140] Step S147: Use the pseudo-pressure at the bottom of the well in the time domain as the pressure solution of the multi-well pressure monitoring mathematical model.

[0141] Step S150: Plot the fitting curves. Based on the pressure solution of the multi-well pressure monitoring mathematical model, plot the pressure and pressure derivative curves. Fit the pressure solution of the multi-well pressure monitoring mathematical model and the data output from the single-well model to the actual pressure data. Here, the single-well model is a mathematical model that only considers a single well and ignores interference from multiple wells.

[0142] For example, based on the pressure solution of the multi-well pressure monitoring mathematical model, pressure and pressure derivative curves are plotted on a double logarithmic coordinate system with dimensionless time as the horizontal axis and dimensionless pressure as the vertical axis. The pressure solution of the multi-well pressure monitoring mathematical model and the data output by the single-well model are respectively fitted with the actual pressure data. Figure 6 A fitting curve diagram of a multi-well pressure monitoring mathematical model, representing an exemplary embodiment of this disclosure, is shown. (See diagram below.) Figure 6 As shown, the pressure data from the multi-well pressure monitoring mathematical model fits the actual pressure data well, and has higher accuracy than the single-well model.

[0143] Step S160: Determine the fitting point based on the fitted curve, and inversely calculate the reservoir parameters of the multi-well pressure monitoring mathematical model. These reservoir parameters include: wellbore storage coefficient, skin coefficient, permeability, well spacing, and initial pressure.

[0144] In one alternative approach, the least-squares fit point on the fitted curve is selected as the fit point, which is the point where the actual pressure data and the predicted value on the fitted curve are closest.

[0145] In one alternative approach, the curve fitting method can employ a goodness-of-fit method, based on the least squares principle, to determine reservoir parameters by minimizing the objective function. Based on the reservoir parameters obtained from the inversion calculation, the underground gas storage facility is evaluated and analyzed, and the degree of agreement between the inversion results and measured data is compared to assess the accuracy and reliability of the inversion.

[0146] For example, based on Figure 6 The fitted curve shown indicates the fitting point. Inversion calculations are used to obtain the reservoir parameters of the multi-well pressure monitoring mathematical model, specifically including a wellbore storage coefficient of 6.5m. 3 / MPa, skin factor is -0.003, permeability is 0.68mD, well spacing is 502m, and initial pressure is 27.28MPa.

[0147] Step S170: Update the multi-well pressure monitoring mathematical model based on the inverted reservoir parameters. Since the fitting points are determined by the fitting curve plotted between actual pressure data and the pressure solution of the multi-well pressure monitoring mathematical model, the reservoir parameters of the inverted multi-well pressure monitoring mathematical model can be equivalent to the reservoir parameters of the underground gas storage facility. Updating the multi-well pressure monitoring mathematical model based on the inverted reservoir parameters improves the fit between the model and the underground gas storage facility. Therefore, the multi-well pressure monitoring mathematical model considering multi-well interference can accurately reflect the working status and production capacity of the underground gas storage facility.

[0148] For example, in order to verify the accuracy of the multi-well pressure monitoring mathematical model, the reservoir parameters obtained in step S160 can be substituted into the production capacity index to calculate the production capacity of the existing single-well model and the multi-well pressure monitoring mathematical model respectively.

[0149] The capacity index PI is defined by the following formula (27):

[0150]

[0151] In the formula: PI is the production capacity indicator; Q is the injection-production rate, and its unit is m. 3 / d;m i The pressure at the outlet is measured in MPa; m w This represents the bottom hole pressure, and its unit is MPa.

[0152] Substituting the reservoir parameters obtained in step S160 into the productivity index formula, we can calculate that the maximum recovery rate of the single-well model under unit pressure difference is 1.1 × 10⁻⁶. 6 m 3 / d / MPa, the maximum recovery rate of the multi-well pressure monitoring mathematical model under unit pressure difference is 9.46×10 5 m 3 The potential gas extraction capacity of the target well increased by 16.2% at / d / MPa, which is significantly different from the actual injection and production capacity of the underground gas storage facility. This shows that ignoring the influence of multiple well interference will lead to an overestimation of the potential injection and production capacity of the target well, causing technicians to misjudge the working status and production capacity of the gas storage facility.

[0153] Based on the above embodiments, in another embodiment provided in this disclosure, a mathematical modeling method for multi-well pressure monitoring of underground gas storage is also provided. Figure 7 A flowchart illustrating the mathematical modeling method for multi-well pressure monitoring in underground gas storage facilities, as shown in the exemplary embodiment of this disclosure, is provided. Figure 7 As shown, the method includes the following steps:

[0154] Step 710: Obtain underground gas storage data and actual pressure data of the underground gas storage.

[0155] In the exemplary embodiments disclosed herein, the underground gas storage data includes, but is not limited to: the geological parameters and fluid properties of the gas storage, the injection and production history of the target well, and the injection and production history of adjacent wells. Adjacent wells and the target well belong to the same underground gas storage, and are connected by a porous medium. The actual pressure data of the underground gas storage can be obtained through monitoring by sensors pre-installed within the underground gas storage.

[0156] Step 720: Based on the underground gas storage data and the multi-well pressure monitoring mathematical model, the pressure solution of the multi-well pressure monitoring mathematical model is obtained by superimposing the pressure of adjacent wells and the target well.

[0157] In an exemplary embodiment of this disclosure, underground gas storage data is input into a multi-well pressure monitoring mathematical model, and the pressure solution of the multi-well pressure monitoring mathematical model is obtained by superimposing the pressures of adjacent wells and the target well.

[0158] Step 730: Based on the curve fitting results plotted from the pressure solution and actual pressure data, inversely calculate the reservoir parameters in the multi-well pressure monitoring mathematical model to obtain the updated multi-well pressure monitoring mathematical model.

[0159] In an exemplary embodiment of this disclosure, pressure and pressure derivative curves are plotted based on the pressure solution of the multi-well pressure monitoring mathematical model. The pressure solution of the multi-well pressure monitoring mathematical model and the data output from the single-well model are respectively fitted with actual pressure data. Here, the single-well model is a mathematical model that only considers a single well and ignores interference from multiple wells. Then, based on the fitted curves, the fitting points are determined, and the reservoir parameters of the multi-well pressure monitoring mathematical model are calculated by inversion. These reservoir parameters include: wellbore storage coefficient, skin coefficient, permeability, well spacing, and initial pressure. Finally, the multi-well pressure monitoring mathematical model is updated based on the inverted reservoir parameters.

[0160] One or more technical solutions provided in this disclosure involve acquiring underground gas storage data and actual pressure data of the underground gas storage, and then, based on the underground gas storage data and a multi-well pressure monitoring mathematical model, obtaining the pressure solution of the multi-well pressure monitoring mathematical model by superimposing the pressures of adjacent wells and the target well. Based on the curve fitting results plotted using the pressure solution and actual pressure data, the reservoir parameters in the multi-well pressure monitoring mathematical model are inverted and calculated to obtain an updated multi-well pressure monitoring mathematical model. Specifically, to calculate the reservoir parameters of the multi-well pressure monitoring mathematical model and improve its fit with the underground gas storage, the pressure solution is fitted with the actual pressure data, a fitting curve is plotted, and then inversion calculations are performed based on the fitting points of the fitting curve to obtain accurate reservoir parameters. Finally, the multi-well pressure monitoring mathematical model is updated based on these reservoir parameters.

[0161] Experiments have demonstrated that the multi-well pressure monitoring mathematical model of this exemplary embodiment can realistically simulate the actual conditions of underground gas storage facilities. The pressure solution of the multi-well pressure monitoring mathematical model shows a good fit with the actual pressure data and has higher accuracy than existing single-well pressure monitoring models. Compared with existing single-well pressure monitoring models, the multi-well pressure monitoring mathematical model of this exemplary embodiment can solve the problem of large errors in reservoir pressure calculation and monitoring caused by the lack of consideration for the interference of multiple wells in existing single-well pressure monitoring models. This improves the fit between actual pressure data and the output results of the multi-well pressure monitoring mathematical model, accurately determines the working status of underground gas storage facilities, obtains reservoir physical parameters, and assesses the gas injection and production capacity of gas storage wells.

[0162] The foregoing primarily describes the solutions provided by the embodiments of this disclosure from a methodological perspective. It is understood that, in order to achieve the above-mentioned functions, the apparatus corresponding to the methods of the exemplary embodiments of this disclosure includes hardware structures and / or software modules corresponding to the execution of each function. Those skilled in the art should readily recognize that, based on the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein, this disclosure can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this disclosure.

[0163] This disclosure embodiment can divide the server into functional units according to the above method example. For example, it can divide each function into a separate functional module, or it can integrate two or more functions into one processing module. The integrated module can be implemented in hardware or as a software functional module. It should be noted that the module division in this disclosure embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0164] By dividing each function into corresponding functional modules, an exemplary embodiment of this disclosure provides a mathematical modeling device for multi-well pressure monitoring of an underground gas storage facility. This mathematical modeling device for multi-well pressure monitoring of an underground gas storage facility can be a server or a chip applied to a server. Figure 8 A schematic block diagram of the functional modules of a multi-well pressure monitoring mathematical modeling apparatus 800 for underground gas storage facilities according to an exemplary embodiment of this disclosure is shown. Figure 8 As shown, the mathematical modeling device for multi-well pressure monitoring in this underground gas storage facility includes:

[0165] The data acquisition module 801 is used to acquire underground gas storage data and actual pressure data of the underground gas storage. The underground gas storage data includes: geological parameters and fluid properties of the gas storage, injection and production history of the target well and adjacent wells. The adjacent wells and the target well belong to the same underground gas storage and are connected by a porous medium. The actual pressure data is obtained by sensors pre-installed in the underground gas storage.

[0166] The multi-well pressure monitoring physical model acquisition module 802 is used to construct a multi-well pressure monitoring physical model, which is obtained at least based on the geological parameters, the fluid property parameters, and the location of each horizontal well in the gas storage.

[0167] The multi-well pressure monitoring mathematical model acquisition module 803 is used to obtain the multi-well pressure monitoring mathematical model based on the multi-well pressure monitoring physical model and the target assumptions.

[0168] The multi-well pressure monitoring mathematical model acquisition module 803 specifically includes at least one of the following target assumptions: the fluid in the underground gas storage is a single-phase compressible gas; the effects of gravity and capillary force are not considered during gas flow; the initial pressure of the underground gas storage is uniformly distributed before the unstable well test; the porous medium is anisotropic, homogeneous, and of uniform thickness; the gas flow follows Darcy's law; and the gas's equation of state conforms to Boyle's law.

[0169] The pressure solution acquisition module 804 is used to obtain the pressure solution of the multi-well pressure monitoring mathematical model by superimposing the pressure of the adjacent wells and the target well based on the underground gas storage data and the multi-well pressure monitoring mathematical model.

[0170] The model update module 805 is used to invert and calculate the reservoir parameters in the multi-well pressure monitoring mathematical model based on the curve fitting results drawn from the pressure solution and the actual pressure data, so as to obtain the updated multi-well pressure monitoring mathematical model.

[0171] The pressure solution acquisition module 804 is specifically used to obtain the point source solution of the multi-well pressure monitoring mathematical model of the underground gas storage in the Lagrange domain; to obtain the basic pressure solution of any horizontal well in the multi-well pressure monitoring mathematical model in the Lagrange domain by applying the mirror reflection method and the line source function integration method to the point source solution; to superimpose the basic pressure solutions of the adjacent wells and the target well to obtain the pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain; to obtain the bottom hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the Lagrange domain by applying the Gaussian elimination method to the pressure superposition solution; to obtain the bottom hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the time domain by applying the Stehfest numerical inversion method to the bottom hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the Lagrange domain, and to use the bottom hole pseudo-pressure in the time domain as the pressure solution of the multi-well pressure monitoring mathematical model.

[0172] The pressure solution acquisition module 804 is specifically used to define the governing equations, initial conditions, and internal and external boundary conditions; and to solve the governing equations, initial conditions, and internal and external boundary conditions using Laplace transform to obtain the point source solution of the multi-well pressure monitoring mathematical model in the Laplace domain. The point source solution is:

[0173]

[0174] In the formula: T is the temperature, and its unit is K; A point source in three-dimensional space, its unit is m. 3 / d; u is the Laplace variable; r D is the dimensionless radial distance; k is the permeability, in mD; L is the reference length, in m. To consider the point source solution of any unbounded horizontal well in the Lagrange domain.

[0175] The pressure solution acquisition module 804 is specifically used to obtain the point source solution using the mirror reflection method:

[0176]

[0177] In the formula: T is the temperature, and its unit is K; A point source in three-dimensional space, its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D ,z D The distance in a dimensionless rectangular coordinate system; x wD ,y wD ,z wD The position of the origin of the dimensionless rectangular coordinate system; For the point source solution of any horizontal well in the Lagrange domain in the multi-well pressure monitoring mathematical model considering the boundary;

[0178] After obtaining the new point source solution of the multi-well pressure monitoring mathematical model using the mirror reflection method, the infinite series is eliminated using the Poisson summation formula to obtain:

[0179]

[0180] In the formula: T is the temperature, and its unit is K; A point source in three-dimensional space, its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D The distance in a dimensionless rectangular coordinate system; x wD ,y wD K0 represents the position of the origin of a dimensionless rectangular coordinate system; K0 is a zeroth-order Bessel function of the first kind. For any horizontal well in the multi-well pressure monitoring mathematical model, the point source solution in the Lagrange domain after eliminating the infinite series is obtained;

[0181] The point source solution of the multi-well pressure monitoring mathematical model after eliminating infinite series is used to obtain the fundamental pressure solution of any horizontal well in the Lagrange domain by integrating the line source function.

[0182]

[0183] In the formula: T is the temperature, and its unit is K; A point source in three-dimensional space, its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D The distance in a dimensionless rectangular coordinate system; x wD ,y wD K0 represents the position of the origin of a dimensionless rectangular coordinate system; K0 is a zeroth-order Bessel function of the first kind. This represents the fundamental pressure solution for any horizontal well in the Lagrange domain within the multi-well pressure monitoring mathematical model.

[0184] The pressure solution acquisition module 804 is specifically used to sum the pressures of multiple horizontal wells in the multi-well pressure monitoring mathematical model, and to obtain the pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain.

[0185]

[0186] In the formula: N is the number of wells; The pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain; The fundamental pressure solution for well 1; The fundamental pressure solution for well 2; Let T be the fundamental pressure solution for well N; T is the temperature, and its unit is K. A point source in three-dimensional space, its unit is m. 3 / d; u is the Laplace variable; n is the summation number; h D denoted as dimensionless reservoir thickness; k is permeability in mD; L is reference length in m; x D ,y D ,z D The distance in a dimensionless rectangular coordinate system; x wD ,y wD ,z wD K0 represents the position of the origin of a dimensionless rectangular coordinate system; K0 is a zero-order Bessel function of the first kind.

[0187] Figure 9 A schematic block diagram of a chip according to an exemplary embodiment of the present disclosure is shown. Figure 9 As shown, the chip 900 includes one or more processors 901 and a communication interface 902. The communication interface 902 can support the server in performing the data transmission and reception steps in the above-mentioned multi-well pressure monitoring mathematical modeling method, and the processor 901 can support the server in performing the data processing steps in the above-mentioned multi-well pressure monitoring method.

[0188] Optional, such as Figure 9 As shown, the chip 900 also includes a memory 903, which may include read-only memory and random access memory, and provides operation instructions and data to the processor. A portion of the memory may also include non-volatile random access memory (NVRAM).

[0189] In some implementations, such as Figure 9As shown, processor 901 executes corresponding operations by calling operation instructions stored in memory (which may be stored in the operating system). Processor 901 controls the processing operations of any terminal device; processor can also be called a central processing unit (CPU). Memory 903 may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory 903 may also include NVRAM. For example, in applications, memory, communication interfaces, and other components are coupled together via a bus system, which may include, in addition to a data bus, a power bus, a control bus, and a status signal bus, etc. However, for clarity, in... Figure 9 The general designated all buses as Bus System 904.

[0190] The methods disclosed in the embodiments of this disclosure can be applied to a processor or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an ASIC, a field-programmable gate array (FPA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this disclosure. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this disclosure can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0191] Exemplary embodiments of this disclosure also provide an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor. The memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to cause the electronic device to perform a method according to an embodiment of this disclosure.

[0192] Exemplary embodiments of this disclosure also provide a non-transitory computer-readable storage medium storing a computer program, wherein the computer program, when executed by a computer's processor, is used to cause the computer to perform a method according to embodiments of this disclosure.

[0193] Exemplary embodiments of this disclosure also provide a computer program product, including a computer program, wherein, when executed by a processor of a computer, the computer program is used to cause the computer to perform a method according to an embodiment of this disclosure.

[0194] refer to Figure 10 The present invention describes a structural block diagram of an electronic device 1000 that can serve as a server or client of the present disclosure, which is an example of a hardware device that can be applied to various aspects of the present disclosure. The electronic device is intended to represent various forms of digital electronic computer devices, 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, 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 present disclosure described and / or claimed herein.

[0195] like Figure 10 As shown, the electronic device 1000 includes a computing unit 1001, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 1002 or a computer program loaded from a storage unit 1008 into a random access memory (RAM) 1003. The RAM 1003 may also store various programs and data required for the operation of the device 1000. The computing unit 1001, ROM 1002, and RAM 1003 are interconnected via a bus 1004. An input / output (I / O) interface 1005 is also connected to the bus 1004.

[0196] Multiple components in electronic device 1000 are connected to I / O interface 1005, including: input unit 1006, output unit 1007, storage unit 1008, and communication unit 1009. Input unit 1006 can be any type of device capable of inputting information to electronic device 1000. Input unit 1006 can receive input digital or character information and generate key signal inputs related to user settings and / or function control of electronic device. Output unit 1007 can be any type of device capable of presenting information and may include, but is not limited to, a display, speaker, video / audio output terminal, vibrator, and / or printer. Storage unit 1008 may include, but is not limited to, disk and optical disk. Communication unit 1009 allows electronic device 1000 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks, and may include, but is not limited to, modems, network cards, infrared communication devices, wireless communication transceivers, and / or chipsets, such as Bluetooth™ devices, WiFi devices, WiMax devices, cellular communication devices, and / or the like.

[0197] The computing unit 1001 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 1001 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (PU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 1001 performs the various methods and processes described above. The various methods described above can all be implemented as computer software programs, which are tangibly contained in a machine-readable medium, such as storage unit 1008. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 1000 via ROM 1002 and / or communication unit 1009.

[0198] The program code used to implement the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0199] In the context of this disclosure, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. 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 fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0200] As used in this disclosure, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0201] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. 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).

[0202] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments 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., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0203] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other.

[0204] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instructions are loaded and executed on a computer, the processes or functions described in the embodiments of this disclosure are performed entirely or partially. The computer can be a general-purpose computer, a special-purpose computer, a computer network, a terminal, a user equipment, or other programmable device. The computer program or instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; it can also be an optical medium, such as a digital video disc (DVD); or it can be a semiconductor medium, such as a solid-state drive (SSD).

[0205] Although this disclosure has been described in conjunction with specific features and embodiments, it will be apparent that various modifications and combinations can be made therein without departing from the spirit and scope of this disclosure. Accordingly, this specification and drawings are merely exemplary illustrations of the disclosure as defined by the appended claims and are to be considered as covering any and all modifications, variations, combinations, or equivalents within the scope of this disclosure. It is obvious that those skilled in the art can make various alterations and modifications to this disclosure without departing from its spirit and scope. Thus, this disclosure is also intended to include any such modifications and modifications that fall within the scope of the claims of this disclosure and their equivalents.

Claims

1. A mathematical modeling method for multi-well pressure monitoring, characterized in that, include: Obtain data on underground gas storage facilities and their actual pressure data. The underground gas storage data includes: geological parameters and fluid properties of the gas storage, injection and production history of the target well and adjacent wells, wherein the adjacent wells and the target well belong to the same underground gas storage, and the adjacent wells and the target well are connected by a porous medium, and the actual pressure data is obtained through sensors pre-installed in the underground gas storage. Based on the underground gas storage data and the multi-well pressure monitoring mathematical model, the pressure solution of the multi-well pressure monitoring mathematical model is obtained by superimposing the pressure of the adjacent wells and the target well. Based on the curve fitting results plotted using the pressure solution and the actual pressure data, the reservoir parameters in the multi-well pressure monitoring mathematical model are inverted and calculated to obtain the updated multi-well pressure monitoring mathematical model. Wherein, obtaining the pressure solution of the multi-well pressure monitoring mathematical model includes: Obtain the point source solution of the multi-well pressure monitoring mathematical model of the underground gas storage in the Laplace domain; The point source solution is subjected to the mirror reflection method and the line source function integration method to obtain the basic pressure solution of any horizontal well in the Lagrange domain in the multi-well pressure monitoring mathematical model; The pressure fundamental solutions of the adjacent wells and the target well are superimposed to obtain the pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain. The pressure superposition solution is subjected to Gaussian elimination to obtain the bottom hole pressure of the multi-well pressure monitoring mathematical model in the Laplace domain; The bottom hole pseudo-pressure in the Lagrange domain is obtained by using the Stehfest numerical inversion method to obtain the bottom hole pseudo-pressure in the time domain of the multi-well pressure monitoring mathematical model, and the bottom hole pseudo-pressure in the time domain is used as the pressure solution of the multi-well pressure monitoring mathematical model.

2. The method according to claim 1, characterized in that, The construction method of the multi-well pressure monitoring mathematical model includes: A multi-well pressure monitoring physical model is constructed, which is obtained at least based on the geological parameters, the fluid property parameters, and the location of each horizontal well in the gas storage. Based on the physical model and target assumptions of the multi-well pressure monitoring, the mathematical model of the multi-well pressure monitoring is obtained.

3. The method according to claim 2, characterized in that, The target assumptions include at least one of the following: the fluid in the underground gas storage is a single-phase compressible gas; the effects of gravity and capillary force are not considered during gas flow; the initial pressure of the underground gas storage is uniformly distributed before the unstable well test; the porous medium is anisotropic, homogeneous, and of uniform thickness; the gas flow follows Darcy's law; and the gas's equation of state conforms to Boyle's law.

4. The method according to claim 1, characterized in that, The point source solution is processed using the mirror reflection method and the line source function integration method to obtain the fundamental pressure solution of any horizontal well in the Lagrange domain in the multi-well pressure monitoring mathematical model, including: Define the governing equations, initial conditions, and internal and external boundary conditions; The Laplace transform is applied to the governing equations, the initial conditions, and the internal and external boundary conditions to obtain the point source solution of the multi-well pressure monitoring mathematical model in the Laplace domain. The point source solution is: In the formula: For temperature; A point source in three-dimensional space; u For Laplace variables; The radial distance is dimensionless. For penetration rate; For reference length; To consider the point source solution of any unbounded horizontal well in the Lagrange domain.

5. The method according to claim 1, characterized in that, The point source solution is processed using the mirror reflection method and the line source function integration method to obtain the fundamental pressure solution of any horizontal well in the Lagrange domain in the multi-well pressure monitoring mathematical model, including: For the point source solution, the mirror reflection method is used: In the formula: For temperature; A point source in three-dimensional space; u For Laplace variables; n To find the sum; The thickness is dimensionless reservoir thickness; For penetration rate; For reference length; Distance in a dimensionless rectangular coordinate system; The position of the origin of the dimensionless rectangular coordinate system; For the point source solution of any horizontal well in the Lagrange domain in the multi-well pressure monitoring mathematical model considering the boundary; After obtaining the new point source solution of the multi-well pressure monitoring mathematical model using the mirror reflection method, the infinite series is eliminated using the Poisson summation formula to obtain: In the formula: For temperature; A point source in three-dimensional space; u For Laplace variables; n To find the sum; The thickness is dimensionless reservoir thickness; For penetration rate; For reference length; Distance in a dimensionless rectangular coordinate system; The position of the origin of the dimensionless rectangular coordinate system; It is a zero-order Bessel function of the first kind; For any horizontal well in the multi-well pressure monitoring mathematical model, the point source solution in the Lagrange domain after eliminating the infinite series is obtained; The point source solution of the multi-well pressure monitoring mathematical model after eliminating infinite series is used to obtain the fundamental pressure solution of any horizontal well in the Lagrange domain by integrating the line source function. In the formula: For temperature; A point source in three-dimensional space; u For Laplace variables; n To find the sum; The thickness is dimensionless reservoir thickness; For penetration rate; For reference length; Distance in a dimensionless rectangular coordinate system; The position of the origin of the dimensionless rectangular coordinate system; It is a zero-order Bessel function of the first kind; This represents the fundamental pressure solution for any horizontal well in the Lagrange domain within the multi-well pressure monitoring mathematical model.

6. The method according to claim 1, characterized in that, The step of superimposing the fundamental pressure solutions of the adjacent wells and the target well to obtain the pressure superposition solution of the multi-well pressure monitoring mathematical model in the Laplace domain includes: By summing the pressures of multiple horizontal wells in the multi-well pressure monitoring mathematical model, the pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain is obtained, where: In the formula: Number of wells; The pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lagrange domain; The fundamental pressure solution for well 1; The fundamental pressure solution for well 2; The fundamental solution for the pressure of well N; For temperature; A point source in three-dimensional space; u For Laplace variables; n To find the sum; The thickness is dimensionless reservoir thickness; For penetration rate; For reference length; Distance in a dimensionless rectangular coordinate system; The position of the origin of the dimensionless rectangular coordinate system; It is a zero-order Bessel function of the first kind.

7. A modeling device for a multi-well pressure monitoring mathematical model, characterized in that, include: The data acquisition module is used to acquire data from underground gas storage facilities and their actual pressure data. The underground gas storage data includes: geological parameters and fluid properties of the gas storage, injection and production history of the target well and adjacent wells, wherein the adjacent wells and the target well belong to the same underground gas storage, and the adjacent wells and the target well are connected by a porous medium, and the actual pressure data is obtained through sensors pre-installed in the underground gas storage. The pressure solution acquisition module is used to obtain the pressure solution of the multi-well pressure monitoring mathematical model based on the underground gas storage data and the multi-well pressure monitoring mathematical model by superimposing the pressures of adjacent wells and the target well. The process of obtaining the pressure solution of the multi-well pressure monitoring mathematical model includes: obtaining the point source solution of the multi-well pressure monitoring mathematical model of the underground gas storage in the Lagrange domain; applying the mirror reflection method and the line source function integration method to the point source solution to obtain the basic pressure solution of any horizontal well in the multi-well pressure monitoring mathematical model in the Lagrange domain; superimposing the basic pressure solutions of the adjacent wells and the target well to obtain the superimposed pressure solution of the multi-well pressure monitoring mathematical model in the Lagrange domain; applying the Gaussian elimination method to the superimposed pressure solution to obtain the bottom-hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the Lagrange domain; and applying the Stehfest numerical inversion method to the bottom-hole pseudo-pressure in the Lagrange domain to obtain the bottom-hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the time domain, and using the bottom-hole pseudo-pressure in the time domain as the pressure solution of the multi-well pressure monitoring mathematical model. The model update module is used to invert and calculate the reservoir parameters in the multi-well pressure monitoring mathematical model based on the curve fitting results drawn from the pressure solution and the actual pressure data, so as to obtain the updated multi-well pressure monitoring mathematical model.

8. An electronic device, characterized in that, include: processor; as well as, Memory for stored programs; The program includes instructions that, when executed by the processor, cause the processor to perform the method according to any one of claims 1-6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the method according to any one of claims 1-6.

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