CN116595610A - Multi-well pressure monitoring mathematical model modeling method, device, equipment and storage medium - Google Patents

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

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Publication number
CN116595610A
CN116595610A CN202310522222.9A CN202310522222A CN116595610A CN 116595610 A CN116595610 A CN 116595610A CN 202310522222 A CN202310522222 A CN 202310522222A CN 116595610 A CN116595610 A CN 116595610A
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well
mathematical model
pressure
pressure monitoring
solution
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褚洪杨
张景轩
朱维耀
岳明
孔德彬
潘斌
高玉宝
刘凯
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University of Science and Technology Beijing USTB
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University of Science and Technology Beijing USTB
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00—Survey of boreholes or wells
    • E21B47/06—Measuring temperature or pressure
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A10/00—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE at coastal zones; at river basins
    • Y02A10/40—Controlling or monitoring, e.g. of flood or hurricane; Forecasting, e.g. risk assessment or mapping

Abstract

The present disclosure provides a multi-well pressure monitoring mathematical model modeling method, apparatus, device, and storage medium, comprising: acquiring underground gas storage data and actual pressure data of the underground gas storage, and acquiring a pressure solution of the multi-well pressure monitoring mathematical model by superposing the pressures of adjacent wells and target wells based on the underground gas storage data and the multi-well pressure monitoring mathematical model; and (3) inverting and calculating reservoir parameters in the multi-well pressure monitoring mathematical model based on curve fitting results drawn by the pressure solution and the actual pressure data to obtain an updated multi-well pressure monitoring mathematical model. Based on the existing pressure monitoring model, the pressure superposition principle is adopted, and the influence of adjacent wells is included in the calculation category, so that errors in pressure calculation are reduced, the accuracy of a multi-well pressure monitoring mathematical model is improved, and the real situation of an underground gas storage is simulated.

Description

Multi-well pressure monitoring mathematical model modeling method, device, equipment and storage medium
Technical Field
The disclosure relates to the technical field of gas reservoirs, and in particular relates to a multi-well pressure monitoring mathematical model modeling method, device, equipment and storage medium.
Background
With the rapid development of national economy, the natural gas accounts for a larger and larger proportion in energy consumption. Because of the contradiction of the imbalance between the distribution range and the supply and demand relationship of the natural gas, the underground gas storage is an important means for solving seasonal peak shaving and emergency gas supply of accidents, and the construction of a pressure monitoring mathematical model for the underground gas storage can help technicians to pre-judge the production capacity of the gas storage.
The current pressure monitoring model for the underground gas storage has achieved a lot of research results with obvious effect, but a lot of difficulties still remain to be solved. For example, after the gas storage is put into operation formally, natural gas is injected strongly and is mined strongly and alternately in multiple cycles, the discontinuous operation mode and the well closing pressure recovery balance time are short, multi-well interference is aggravated, the existing gas storage pressure monitoring model usually only considers a single well, but the influence of an adjacent well is ignored, so that the degree of fitting between on-site pressure monitoring data and the calculation result of the existing monitoring model is low, and a technician cannot accurately judge the working state and the production capacity of the gas storage through the existing monitoring model.
Disclosure of Invention
According to an aspect of the present disclosure, there is provided a multi-well pressure monitoring mathematical model modeling method comprising:
Acquiring underground gas storage data and actual pressure data of the underground gas storage; the underground gas reservoir data includes: the gas storage system comprises geological parameters, fluid physical parameters, a target well injection and production history and an adjacent well injection and production history of the gas storage, wherein the adjacent well and the target well belong to the same underground gas storage, the adjacent well and the target well are communicated through porous media, and the actual pressure data are obtained through a sensor preset in the underground gas storage;
based on the underground gas storage data and a multi-well pressure monitoring mathematical model, obtaining a pressure solution of the multi-well pressure monitoring mathematical model by superposing the pressures of the adjacent wells and the target well;
and inverting and calculating reservoir parameters in the multi-well pressure monitoring mathematical model based on curve fitting results drawn by the pressure solution and the actual pressure data to obtain an updated multi-well pressure monitoring mathematical model.
According to another aspect of the present disclosure, there is provided a multi-well pressure monitoring mathematical model modeling apparatus comprising:
the data acquisition module is used for acquiring underground gas storage data and actual pressure data of the underground gas storage; the underground gas reservoir data includes: the gas storage system comprises geological parameters, fluid physical parameters, a target well injection and production history and an adjacent well injection and production history of the gas storage, wherein the adjacent well and the target well belong to the same underground gas storage, the adjacent well and the target well are communicated through porous media, and the actual pressure data are obtained through a sensor preset in the underground gas storage;
The pressure solution acquisition module is used for acquiring a pressure solution of the multi-well pressure monitoring mathematical model by superposing the pressures of the adjacent wells and the target well based on the underground gas storage data and the multi-well pressure monitoring mathematical model;
and the model updating module is used for inverting and calculating reservoir parameters in the multi-well pressure monitoring mathematical model based on the curve fitting result drawn by the pressure solution and the actual pressure data to obtain an updated multi-well pressure monitoring mathematical model.
According to another aspect of the present disclosure, there is provided an electronic device including:
a processor; the method comprises the steps of,
a memory storing a program;
wherein the program comprises instructions which, when executed by the processor, cause the processor to perform the method according to an exemplary embodiment of the present disclosure.
According to another aspect of the present disclosure, there is provided a non-transitory computer readable storage medium storing computer instructions for causing the computer to perform the method according to an exemplary embodiment of the present disclosure.
According to one or more technical schemes provided by the embodiment of the disclosure, after underground gas storage data and actual pressure data of the underground gas storage are obtained, based on the underground gas storage data and a multi-well pressure monitoring mathematical model, a pressure solution of the multi-well pressure monitoring mathematical model is obtained by superposing pressures of adjacent wells and target wells, and reservoir parameters in the multi-well pressure monitoring mathematical model are calculated in an inversion mode based on curve fitting results drawn by the pressure solution and the actual pressure data, so that an updated multi-well pressure monitoring mathematical model is obtained. In order to calculate reservoir parameters of the multi-well pressure monitoring mathematical model, the fitting degree of the multi-well pressure monitoring mathematical model and the underground gas storage is higher, a pressure solution and actual pressure data are fitted, a fitting curve is drawn, inversion calculation is carried out based on fitting points of the fitting curve, accurate reservoir parameters are obtained, and finally the multi-well pressure monitoring mathematical model is updated based on the reservoir parameters.
Because the underground gas storage adopts a production mode of simultaneous injection and production of a plurality of horizontal wells in the production process, obvious multi-well interference phenomenon can occur, and in the solving process of a multi-well pressure monitoring mathematical model, the influence of adjacent wells can be considered by using a multi-well pressure superposition principle, the multi-well interference problem generated by simultaneous injection and production of a plurality of horizontal wells is counteracted, and the pressure solution of the underground gas storage is obtained. And then, back-calculating reservoir parameters based on the fitting curve, and updating the multi-well pressure monitoring mathematical model to ensure that the fitting degree of the multi-well pressure monitoring mathematical model and the underground gas storage is higher. Therefore, the method of the disclosed exemplary embodiment can solve the technical problem that the existing single-well pressure monitoring model has larger error in reservoir pressure calculation and monitoring because the influence of multi-well interference is not considered, the multi-well pressure monitoring mathematical model of the disclosed exemplary embodiment can truly simulate the real situation of an underground reservoir, and technicians can accurately judge the working state of the reservoir through the multi-well pressure monitoring mathematical model of the disclosed exemplary embodiment to obtain reservoir physical parameters and reservoir well gas injection and production capacity.
Drawings
Further details, features and advantages of the present disclosure are disclosed in the following description of exemplary embodiments, with reference to the following drawings, wherein:
FIG. 1 illustrates a flow diagram of a method of modeling a multi-well pressure monitoring mathematical model of a subsurface gas reservoir according to an exemplary embodiment of the present disclosure;
FIG. 2 illustrates fluid physical parameters of a block in which a gas reservoir is located according to an exemplary embodiment of the present disclosure;
FIG. 3 illustrates a target well injection production history in a gas reservoir according to an exemplary embodiment of the present disclosure;
FIG. 4 illustrates adjacent well injection production history in a gas reservoir according to an exemplary embodiment of the present disclosure;
FIG. 5 illustrates a multi-well pressure monitoring physical model of an exemplary embodiment of the present disclosure;
FIG. 6 illustrates a fitted graph of a multi-well pressure monitoring mathematical model in accordance with an exemplary embodiment of the present disclosure;
FIG. 7 illustrates a flow schematic of a method of modeling a multi-well pressure monitoring mathematical model of a subsurface gas reservoir according to an exemplary embodiment of the present disclosure;
FIG. 8 shows a functional block diagram of a multi-well pressure monitoring mathematical model modeling apparatus for a subsurface gas reservoir, according to an exemplary embodiment of the present disclosure;
FIG. 9 shows a schematic block diagram of a chip according to an exemplary embodiment of the present disclosure;
fig. 10 illustrates a block diagram of an exemplary electronic device that can be used to implement embodiments of the present disclosure.
Detailed Description
Embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While certain embodiments of the present disclosure have been shown in the accompanying drawings, it is to be understood that the present disclosure may be embodied in various forms and should not be construed as limited to the embodiments set forth herein, but are provided to provide a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are for illustration purposes only and are not intended to limit the scope of the present disclosure.
It should be understood that the various steps recited in the method embodiments of the present disclosure may be performed in a different order and/or performed in parallel. Furthermore, method embodiments may include additional steps and/or omit performing the illustrated steps. The scope of the present disclosure is not limited in this respect.
The term "including" and variations thereof as used herein are intended to be open-ended, i.e., including, but not limited to. The term "based on" is based at least in part 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. Related definitions of other terms will be given in the description below. It should be noted that the terms "first," "second," and the like in this disclosure are merely used to distinguish between different devices, modules, or units and are not used to define an order or interdependence of functions performed by the devices, modules, or units.
It should be noted that references to "one", "a plurality" and "a plurality" in this disclosure are intended to be illustrative rather than limiting, and those of ordinary skill in the art will appreciate that "one or more" is intended to be understood as "one or more" unless the context clearly indicates otherwise.
After the underground gas storage is subjected to natural gas strong injection and strong mining multi-period alternating operation, obvious multi-well interference phenomenon can occur, and because the pressure monitoring model in the related technology usually only considers a single well and ignores the influence of an adjacent well, the degree of fitting between on-site pressure monitoring data and the calculation result of the existing monitoring model is low, and technicians cannot accurately judge the working state and the production capacity of the gas storage through the existing monitoring model.
Therefore, in order to construct a multi-well pressure monitoring mathematical model of an underground gas storage in consideration of multi-well interference, so that a technician can conveniently and accurately judge the working state of the gas storage, and obtain physical parameters of a reservoir layer of the gas storage and gas injection and production capacity of a well of the gas storage, the embodiment of the disclosure firstly provides a multi-well pressure monitoring mathematical model modeling method of the underground gas storage, and fig. 1 shows a flow diagram of the multi-well pressure monitoring mathematical model modeling method of the underground gas storage in an exemplary embodiment of the disclosure. As shown in fig. 1, the method may include the steps of:
Step S110: and acquiring underground gas storage data and actual pressure data of the underground gas storage. The underground gas reservoir data herein may include, but is not limited to, geologic parameters of the gas reservoir, fluid physical parameters of the gas reservoir, target well injection and production history, and adjacent well injection and production history. The underground gas reservoir data may be obtained by reference to well logging, geological data and drilling data. The adjacent well and the target well belong to the same underground gas storage, and are communicated by porous media. The actual pressure data are obtained through a preset sensor in the underground gas storage.
Illustratively, relevant data of an underground gas reservoir to be pressure monitored is obtained: the total area of the gas storage is about 28.6km 2 The depth of the top is 3500m and the thickness is about 355m, which is reconstructed from a failure gas reservoir, and can be considered to flow in a single phase inside the gas reservoir. The reservoir is mainly composed of siltstone, fine-grain sandstone, unequal sandstone, pebble unequal sandstone and pebble argillite sandstone. And (3) drilling the selected target well in 2018, wherein the adjacent well and the target well belong to the same drilling platform, and performing unstable well testing analysis on the target well when the fifth injection-production cycle of the gas storage is finished. The test date is 11 months 18-23 days, the total test time is 113 hours, and the target well and the adjacent wells are in the gas injection stage.
And obtaining geological parameters, fluid physical parameters, target well injection and production histories and adjacent well injection and production histories of the block where the gas storage is located by referring to logging, geological data and drilling data. Wherein the geological parameters are shown in table 1 below:
table 1 geological parameters of the block in which the gas reservoir is located
Fig. 2 illustrates fluid physical parameters of a block in which a gas reservoir is located according to an exemplary embodiment of the present disclosure, where the fluid physical parameters include a gas volume factor, a gas compression coefficient, a gas viscosity, and a gas density.
FIG. 3 illustrates a target well injection and production history in a gas reservoir according to an exemplary embodiment of the present disclosure, with time on the abscissa and target well injection and production rate on the ordinate, showing the injection and production conditions of a target well.
Fig. 4 illustrates injection and production histories of adjacent wells in a gas storage according to an exemplary embodiment of the present disclosure, where the injection and production rates of the adjacent wells are shown on an abscissa with time.
Step S120: and constructing a multi-well pressure monitoring physical model. The multi-well pressure monitoring physical model is obtained at least according to the geological parameters, the fluid physical parameters and the positions of all horizontal wells in the gas storage. In practical application, a multi-well pressure monitoring physical model is constructed according to parameters such as geological parameters, fluid physical parameters, positions of all horizontal wells in the gas storage and the like.
Fig. 5 illustrates a multi-well pressure monitoring physical model of an exemplary embodiment of the present disclosure. As shown in fig. 5, a rectangular coordinate system is established for each horizontal well in the porous medium, describing the position of each horizontal well in the underground gas reservoir, so as to construct a multi-well pressure monitoring physical model.
Step S130: and obtaining a multi-well pressure monitoring mathematical model based on the multi-well pressure monitoring physical model and the target hypothesis condition. The construction method of the multi-well pressure monitoring mathematical model comprises the following steps:
step S131: target hypothesis conditions are defined. Wherein the target hypothesis conditions include at least one of: (1) assuming that the fluid in the underground reservoir is a single-phase compressible gas; (2) during the gas flow process, the influence of gravity and capillary force is not considered; (3) before unstable well test, the initial pressure of the underground gas storage is considered to be uniformly distributed; (4) the anisotropism of the porous medium meets the requirement of horizontal homogenization and equal thickness; (5) the gas flow follows darcy's law, and the state equation of the gas conforms to boyle's law; (6) a pseudo-pressure method is used to eliminate nonlinearities.
Illustratively, the state equation of the gas in the gas reservoir is obtained based on the target hypothesis condition (5) and can be expressed by the following formulas (1), (2):
pV＝ZnRT (1)
Wherein: p is the pressure in MPa; v is the volume, its unit is m 3 The method comprises the steps of carrying out a first treatment on the surface of the Z is the gas compression coefficient; n is the amount of the substance in mol; r is a universal gas constant, its unit is Pa.m 3 /(mol.K); t is the temperature, and the unit is K; b (B) g Is a volume factor, its unit is m 3 /stm 3 The method comprises the steps of carrying out a first treatment on the surface of the sc is the standard condition.
Illustratively, introducing a quasi-pressure equation based on the target hypothesis condition (6) eliminates nonlinearity, which can be expressed by the following equation (3):
wherein: m is the pseudo pressure in MPa 2 /mPa·s；p i The unit of the pressure is MPa for arbitrarily selected reference pressure; p is the pressure in MPa; mu is the viscosity of the gas in mPas; z is the gas compression coefficient.
Since the pressure change in underground reservoirs is a highly nonlinear process, it is not well described using conventional linear regression models. The quasi-pressure rule adopts a nonlinear optimization algorithm, and the nonlinear process can be fitted more accurately, so that the accuracy and the reliability of the model are improved. Therefore, the non-linearity can be eliminated by adopting the quasi-pressure method, and the accuracy and the reliability of the multi-well pressure monitoring model of the underground gas storage can be improved, so that support is better provided for the management and the operation of the gas storage.
Step S132: defining dimensionless variables, dispersing a multi-horizontal well in a multi-well pressure monitoring mathematical model into a plurality of points, and establishing a control equation at each point. The dimensionless variables herein include dimensionless production time, dimensionless distance, dimensionless origin location, dimensionless reservoir thickness, dimensionless wellbore storage coefficients, and the like.
Illustratively, the dimensionless production time can be represented by the following formula (4):
wherein: k is permeability in mD; t is time, its unit is h; mu is the viscosity of the gas in mPas;is porosity; c (C) t The unit of the comprehensive compression coefficient is MPa -1 The method comprises the steps of carrying out a first treatment on the surface of the L is a reference length in m.
Illustratively, the dimensionless distance can be represented by the following equation (5):
wherein: x, y and z are rectangular coordinate system distances, and the unit is m; r is the radial distance in m; l is a reference length in m.
Illustratively, the dimensionless origin position can be expressed by the following formula (6):
wherein: x is x w ,y w ,z w The unit of the position is m; l isReference length, in m.
Illustratively, the dimensionless reservoir thickness can be represented by the following equation (7):
Wherein: h is the reservoir thickness in m; l is a reference length in m.
Illustratively, the dimensionless wellbore storage coefficients can be represented by the following equation (8):
wherein: c is the storage coefficient of the shaft, and the unit is m 3 /MPa；Is porosity; c (C) t The unit of the comprehensive compression coefficient is MPa -1 The method comprises the steps of carrying out a first treatment on the surface of the h is the reservoir thickness in m; l is a reference length in m.
Illustratively, discretizing a multi-horizontal well in a multi-well pressure monitoring mathematical model into a plurality of points and establishing a control equation at each point can be represented by the following equation (9):
wherein: m is the pseudo pressure in MPa 2 /mPa·s；r D Is a dimensionless radial distance; t is t D Is the dimensionless production time.
Step S133: initial conditions, inner boundary conditions and outer boundary conditions of the gas reservoir are defined.
Illustratively, the initial condition of the air reservoir may be expressed by the following formula (10):
wherein: t is t D Is dimensionless production time; m is the pseudo pressure in MPa 2 /mPa·s。
Illustratively, the internal boundary conditions of the gas reservoir may be represented by the following formula (11):
wherein: l is a reference length in m; k is permeability in mD; r is (r) D Is a dimensionless radial distance; m is the pseudo pressure in MPa 2 /mPa·s；Is a point source in three-dimensional space, the unit of which is m 3 /d; t is the temperature in units of K.
Wherein, delta (t) D ) Time-dependent can be represented by the following formula (12):
illustratively, the outer boundary condition of the gas reservoir may be expressed by the following formula (13):
wherein: r is (r) D Is a dimensionless radial distance; m is the pseudo pressure in MPa 2 /mPa·s。
Step S140: and obtaining a 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.
As shown in fig. 1, a simulation total duration, a simulation time t and a time step Δt are set, wherein the simulation total duration, the simulation time t and the time step Δt can be randomly defined according to experimental requirements.
Step S141: and obtaining the point source solution of the multi-well pressure monitoring mathematical model of the underground gas storage in the Laplace domain. Wherein, the point source solution of the multi-well pressure monitoring mathematical model in the Laplace domain can be obtained by adopting Laplace transformation for the control equation, the initial condition and the internal and external boundary conditions.
Exemplary, the point sources in the inner boundary condition equation of the gas storage of step S133As the unit intensity, the Laplace transform is performed, and can be expressed by the following formula (14):
Wherein: l is a reference length in m; r is (r) D Is a dimensionless radial distance;is porosity; c (C) t The unit of the comprehensive compression coefficient is MPa -1 。
Wherein Δm=m-m i Substituting into the control equation and performing Laplace transformation on the control equation, the initial condition and the outer boundary condition to obtain the following equation set, which can be represented by the following formula (15):
wherein: r is (r) D Is a dimensionless radial distance; u is a laplace variable; l is a reference length in m;is porosity; c (C) t The unit of the comprehensive compression coefficient is MPa -1 。
In the above equation set, the first equation is a control equation, the second equation is an inner boundary condition, and the third equation is an outer boundary condition.
Solving the Laplace transformed control equation, the inner boundary condition and the outer boundary condition to obtain a point source solution of the multi-well pressure monitoring mathematical model in the Laplace domain, wherein the point source solution can be represented by the following formula (16):
wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, the unit of which is m 3 /d; u is a laplace variable; r is (r) D Is a dimensionless radial distance; k is permeability in mD; l is a reference length in m; />To consider the point source solution in the Laplace domain for any horizontal well without boundaries.
Step S142: and (3) adopting a mirror image reflection method and a line source function integration method for the point source solution to obtain a pressure basic solution of any horizontal well in the Laplace domain in the multi-well pressure monitoring mathematical model.
Illustratively, a point source solution of a multi-well pressure monitoring mathematical model in a Laplace domain is firstly subjected to a mirror image reflection method, and an infinite series is eliminated.
In practical application, considering that the underground gas storage has impermeable top and bottom boundaries, the point source solution of the multi-well pressure monitoring mathematical model in the Laplace domain in step S141 is represented by the following formula (17) by adopting a mirror image method:
wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, the unit of which is m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D ,z D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD ,z wD Is the origin position of a dimensionless rectangular coordinate system; />The point source solution in the Lawster domain for any horizontal well in the mathematical model is monitored for multi-well pressure taking into account the boundary.
In practical application, a new point source solution of a multi-well pressure monitoring mathematical model obtained by adopting a mirror image reflection method comprises infinite series, and in order to facilitate calculation, the infinite series is eliminated by using a poisson summation formula to obtain the following formula (18):
Wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, the unit of which is m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 A Bessel function of zero order class; />Eliminating infinite series for any horizontal well in the multi-well pressure monitoring mathematical model and then solving a point source in the Laplace domain.
The method of linear source function integration is adopted for the point source solution of the multi-well pressure monitoring mathematical model after eliminating infinite series, and the pressure basic solution of any horizontal well in the Laplace domain in the multi-well pressure monitoring mathematical model is obtained.
In practical application, the bottom hole pressure of the horizontal well in the multi-well pressure monitoring mathematical model can be regarded as the integral of a point source on the horizontal well shaft, the basic solution of the bottom hole pressure of any horizontal well in the multi-well pressure monitoring mathematical model can be obtained by integrating the point source solution after eliminating infinite series along the gas flow direction in the horizontal well by utilizing a line source function integral method, and the basic solution can be represented by the following formula (19):
Wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, the unit of which is m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 A Bessel function of zero order class; />The pressure in the Lawster domain is basically solved for any horizontal well in the multi-well pressure monitoring mathematical model.
Step S143: and superposing the pressure basic solutions of the adjacent wells and the target well to obtain a pressure superposition solution of the multi-well pressure monitoring mathematical model in the Laplace domain.
In practical applications, pressure superposition is used to counteract multi-well interference problems caused by injection and production, taking into account the influence of adjacent wells on the target well.
Illustratively, a new dimensionless distance r is introduced D,i Can be represented by the following formula (20)The illustration is:
according to the pressure superposition principle, a summation formula of the pressure of multiple horizontal wells in the multi-well pressure monitoring mathematical model is obtained, and a pressure superposition solution of the multi-well pressure monitoring mathematical model in the Lawster domain is obtained and can be represented by the following formula (21):
wherein: n is the number of wells; Pressure superposition solutions in the Lawster domain for a multi-well pressure monitoring mathematical model; />Is a basic solution to the pressure of well 1; />Is a basic solution to the pressure of well 2; />A pressure base solution for well N; t is the temperature, and the unit is K;is a point source in three-dimensional space, the unit of which is m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D ,z D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD ,z wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 Is a zero-order Bessel function.
In practice, considering that the target well can be injected and produced, a flow constraint equation needs to be defined, and the flow constraint equation can be represented by the following equation (22):
wherein: + is produced; -for injection; u is a laplace variable.
In an alternative mode, since the pressure basic solution of the target well and the pressure basic solution of the adjacent well do not need to be distinguished in the actual solving process, the formula (19) is not only the pressure basic solution equation of the target well, but also the pressure basic solution equation of the adjacent well, so that the formula (19) and the formula (22) can form a matrix equation, and the Gaussian elimination method is adopted for solving to obtain the yield q, the pseudo-pressure m and the bottom-hole pseudo-pressure m of each horizontal well w 。
Step S144: and (3) adopting a Gaussian elimination method for the pressure superposition solution to obtain the bottom-hole pseudo pressure of the multi-well pressure monitoring mathematical model in the Laplace domain.
In practical application, the horizontal well can cause reservoir pollution in the near-wellbore zone during the strong injection and production operation, and the change of the wellbore storage coefficient and the skin coefficient is caused, so that on one hand, the analysis of the bottom-hole pseudo pressure is greatly influenced, and on the other hand, the productivity of the underground gas storage is influenced. Meanwhile, since the bottom hole pseudo pressure solution in the time domain space is not easy to obtain, the bottom hole pseudo pressure in the Laplace domain needs to be obtained first.
Illustratively, introducing a wellbore storage coefficient and a skin coefficient, resulting in a multi-well pressure monitoring mathematical model taking into account the effects of the wellbore storage coefficient and the skin coefficient, the bottom hole pseudo pressure in the Laplace domain may be represented by the following equation (23):
wherein: s is the skin coefficient; c (C) D Storing coefficients for the wellbore; u is a laplace variable; m is m w Is the bottom hole pseudo pressure.
Step S145: and (3) adopting a Stehfest numerical inversion method on the bottom-hole pseudo-pressure in the Laplace domain to obtain the bottom-hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the time domain.
Illustratively, the inverse Laplace transform of the bottom hole pseudo pressure of the multi-well pressure monitoring mathematical model in the Laplace domain can be expressed by the following equation (24):
Wherein: n is an empirical constant, typically taking 8, 10, 12; m is m w Is the bottom hole pseudo pressure.
Further, V is i Defined as the following equation (25):
wherein: n is an empirical constant, typically taking 8, 10, 12; i is a cyclic variable; k is a cyclic variable.
U is defined as the following equation (26):
wherein: i is a cyclic variable; t is the simulation time.
By giving an i value and a t value, V is calculated i By calculating V in each time step i And obtaining the bottom hole pseudo pressure of the multi-well pressure monitoring mathematical model in the time domain.
Step S146: checking whether t is equal to the total simulation time, if t is not equal to the total simulation time, executing t=t+Δt, and restarting to solve the pressure solution of the multi-well pressure monitoring mathematical model; if t is equal to the simulated total duration, step S147 is performed.
Step S147: taking the bottom hole pseudo pressure in the time domain as a pressure solution of a multi-well pressure monitoring mathematical model.
Step S150: and drawing a fitting curve. And drawing pressure and pressure derivative curves according to the pressure solution of the multi-well pressure monitoring mathematical model, and fitting the pressure solution of the multi-well pressure monitoring mathematical model and the data output by the single-well model with actual pressure data respectively. The single well model herein is a mathematical model that considers only single wells, ignoring multi-well interference.
Illustratively, according to the pressure solution of the multi-well pressure monitoring mathematical model, in the double-logarithmic coordinate, the pressure and pressure derivative graphs are drawn by taking the dimensionless time as the horizontal axis and taking the dimensionless pressure as the vertical axis, and the pressure solution of the multi-well pressure monitoring mathematical model and the data output by the single-well model are respectively fitted with actual pressure data. FIG. 6 illustrates a fitted plot of a multi-well pressure monitoring mathematical model in accordance with an exemplary embodiment of the present disclosure. As shown in fig. 6, the pressure data of the multi-well pressure monitoring mathematical model has a good fitting effect with the actual pressure data, and has higher accuracy than the single-well model.
Step S160: and determining fitting points based on the fitting curve, and inverting and calculating reservoir parameters of the multi-well pressure monitoring mathematical model. Reservoir parameters here include: wellbore storage coefficients, skin coefficients, permeability, well spacing, and initial pressure.
In an alternative way, the least squares fitting point on the fitted curve is selected as the fitting point, i.e. the point where the actual pressure data and the predicted value on the fitted curve are closest.
In an alternative approach, the curve fitting method may employ a goodness-of-fit method, employing minimization of an objective function to determine reservoir parameters based on least squares principles. And according to reservoir parameters obtained by inversion calculation, evaluating and analyzing the underground gas storage, comparing the matching degree of the inversion result and the measured data, and evaluating the inversion precision and reliability.
Illustratively, fitting points are determined based on the fitted curve shown in fig. 6, and inversion calculations obtain reservoir parameters of the multi-well pressure monitoring mathematical model, specifically including: wellbore storage factor of 6.5m 3 The skin coefficient was-0.003, the permeability was 0.68mD, the well spacing was 502m, and the initial pressure was 27.28MPa.
Step S170: and updating the multi-well pressure monitoring mathematical model based on the reservoir parameters calculated by inversion. Because the fitting point is determined based on a fitting curve drawn by the actual pressure data and the pressure solution of the multi-well pressure monitoring mathematical model, the reservoir parameters of the multi-well pressure monitoring mathematical model calculated by inversion can be identical to the reservoir parameters of the underground gas reservoir. Based on the reservoir parameters calculated by inversion, the multi-well pressure monitoring mathematical model is updated, so that the fitting degree of the multi-well pressure monitoring mathematical model and the underground gas storage is higher, and the working state and the production capacity of the underground gas storage can be accurately fed back by the multi-well pressure monitoring mathematical model considering multi-well interference.
Illustratively, to verify the accuracy of the multi-well pressure monitoring mathematical model, the reservoir parameters obtained in step S160 may be brought into a productivity index, and the productivity of the existing single-well model and multi-well pressure monitoring mathematical model may be calculated, respectively.
The productivity index PI is defined as the following formula (27):
wherein: PI is the productivity index; q is the injection and production rate, and the unit is m 3 /d；m i Is the outlet pressure in MPa; m is m w Is the bottom hole pressure in MPa.
The reservoir parameters obtained in step S160 are carried into the productivity index formula to be calculated: the maximum extraction rate of the single well model under unit pressure difference is 1.1 multiplied by 10 6 m 3 The maximum extraction rate of the multi-well pressure monitoring mathematical model under unit pressure difference is 9.46 multiplied by 10 5 m 3 The potential air extraction capacity of the target well is improved by 16.2 percent and the difference between the potential air extraction capacity of the target well and the actual injection and production capacity of the underground gas storage is larger, so that the potential injection and production capacity of the target well is higher due to the fact that the influence of multi-well interference is ignored, and technicians misjudge the working state and production capacity of the gas storage.
Based on the above embodiments, in still another embodiment provided by the present disclosure, there is further provided a multi-well pressure monitoring mathematical model modeling method of an underground gas storage, and fig. 7 shows a flow schematic diagram of the multi-well pressure monitoring mathematical model modeling method of the underground gas storage according to an exemplary embodiment of the present disclosure, as shown in fig. 7, and the method includes the following steps:
step 710: and acquiring underground gas storage data and actual pressure data of the underground gas storage.
In exemplary embodiments of the present disclosure, underground gas reservoir data includes, but is not limited to: geological parameters, fluid physical parameters of the gas storage, injection and production histories of the target well and injection and production histories of adjacent wells. The adjacent well and the target well belong to the same underground gas storage, and are communicated by porous media. The actual pressure data of the underground gas storage can be obtained through monitoring of a sensor preset in the underground gas storage.
Step 720: based on 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 superposing the pressures of the adjacent wells and the target well.
In an exemplary embodiment of the present disclosure, underground gas reservoir data is input into a multi-well pressure monitoring mathematical model, and a pressure solution of the multi-well pressure monitoring mathematical model is obtained by superimposing pressures of adjacent wells and target wells.
Step 730: and (3) inverting and calculating reservoir parameters in the multi-well pressure monitoring mathematical model based on curve fitting results drawn by the pressure solution and the actual pressure data to obtain an updated multi-well pressure monitoring mathematical model.
In an exemplary embodiment of the present disclosure, pressure and pressure derivative curves are plotted from the pressure solution of a multi-well pressure monitoring mathematical model, which is fitted to actual pressure data, respectively, and data output by a single well model. The single well model herein is a mathematical model that considers only single wells, ignoring multi-well interference. Then, determining fitting points based on the fitted curve, and inverting and calculating reservoir parameters of the multi-well pressure monitoring mathematical model, wherein the reservoir parameters comprise: wellbore storage coefficients, skin coefficients, permeability, well spacing, and initial pressure. And finally, updating the multi-well pressure monitoring mathematical model based on the reservoir parameters calculated by inversion.
According to one or more technical schemes provided by the embodiment of the disclosure, after underground gas storage data and actual pressure data of the underground gas storage are obtained, based on the underground gas storage data and a multi-well pressure monitoring mathematical model, a pressure solution of the multi-well pressure monitoring mathematical model is obtained by superposing pressures of adjacent wells and target wells, and reservoir parameters in the multi-well pressure monitoring mathematical model are calculated in an inversion mode based on curve fitting results drawn by the pressure solution and the actual pressure data, so that an updated multi-well pressure monitoring mathematical model is obtained. In order to calculate reservoir parameters of the multi-well pressure monitoring mathematical model, the fitting degree of the multi-well pressure monitoring mathematical model and the underground gas storage is higher, a pressure solution and actual pressure data are fitted, a fitting curve is drawn, inversion calculation is carried out based on fitting points of the fitting curve, accurate reservoir parameters are obtained, and finally the multi-well pressure monitoring mathematical model is updated based on the reservoir parameters.
Experiments prove that the multi-well pressure monitoring mathematical model of the embodiment of the disclosure can truly simulate the real situation of an underground gas storage, has good fitting effect on pressure solutions and actual pressure data, and has higher precision than the existing single-well pressure monitoring model. Compared with the existing single-well pressure monitoring model, the multi-well pressure monitoring mathematical model of the embodiment of the disclosure can solve the problem that the existing single-well pressure monitoring model does not consider the influence of multi-well interference, so that larger errors exist in reservoir pressure calculation and monitoring, thereby improving the fitting degree of actual pressure data and output results of the multi-well pressure monitoring mathematical model, accurately judging the working state of an underground reservoir, and obtaining reservoir physical parameters and reservoir well gas injection and production capacity.
The foregoing description of the embodiments of the present disclosure has been presented primarily in terms of methods. It will be appreciated that, in order to implement the above-mentioned functions, the apparatus corresponding to the method of the exemplary embodiment of the present disclosure includes corresponding hardware structures and/or software modules that perform the respective functions. Those of skill in the art will readily appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as hardware or combinations of hardware and computer software. Whether a function is implemented as hardware or computer software driven hardware depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
The embodiments of the present disclosure may divide functional units of a server according to the above method examples, for example, each functional module may be divided corresponding to each function, or two or more functions may be integrated into one processing module. The integrated modules may be implemented in hardware or in software functional modules. It should be noted that, in the embodiment of the present disclosure, the division of the modules is merely a logic function division, and other division manners may be implemented in actual practice.
In the case of dividing each functional module by adopting corresponding each function, the exemplary embodiments of the present disclosure provide a multi-well pressure monitoring mathematical model modeling apparatus for an underground gas storage, which may be a server or a chip applied to the server. Fig. 8 shows a functional block diagram of a multi-well pressure monitoring mathematical model modeling apparatus 800 for a subsurface gas reservoir, according to an exemplary embodiment of the present disclosure. As shown in fig. 8, the multi-well pressure monitoring mathematical model modeling apparatus for an underground gas storage includes:
the data acquisition module 801 is used for acquiring underground gas storage data and actual pressure data of the underground gas storage; the underground gas reservoir data includes: the gas storage system comprises geological parameters, fluid physical parameters, a target well injection and production history and an adjacent well injection and production history of the gas storage, wherein the adjacent well and the target well belong to the same underground gas storage, the adjacent well and the target well are communicated through porous media, and actual pressure data are obtained through a sensor preset in the underground gas storage.
A multi-well pressure monitoring physical model obtaining module 802, configured to construct a multi-well pressure monitoring physical model, where the multi-well pressure monitoring physical model is obtained at least according to the geological parameter, the fluid physical parameter, and the position of each horizontal well in the gas storage.
And a multi-well pressure monitoring mathematical model obtaining module 803, configured to obtain the multi-well pressure monitoring mathematical model based on the multi-well pressure monitoring physical model and the target hypothesis condition.
The multi-well pressure monitoring mathematical model obtaining module 803 specifically includes at least one target hypothesis condition of: the fluid in the underground gas storage is single-phase compressible gas; during the gas flow process, the influence of gravity and capillary force is not considered; before unstable well test, the initial pressure of the underground gas storage is uniformly distributed; the anisotropism of the porous medium is horizontal, homogeneous and uniform in thickness; the gas flow follows darcy's law; the equation of state of the gas conforms to boyle's law.
And the pressure solution obtaining module 804 is configured to obtain a pressure solution of the multi-well pressure monitoring mathematical model by superposing the pressures of the adjacent wells and the target well based on the underground gas storage data and the multi-well pressure monitoring mathematical model.
And the model updating module 805 is configured to invert and calculate reservoir parameters in the multi-well pressure monitoring mathematical model based on the curve fitting result drawn by the pressure solution and the actual pressure data, so as to obtain an updated multi-well pressure monitoring mathematical model.
The pressure solution obtaining module 804 is specifically configured to obtain a point source solution of the multi-well pressure monitoring mathematical model of the underground gas storage in a rawster domain; adopting a mirror image reflection method and a line source function integration method for the point source solution to obtain a pressure basic solution of any horizontal well in the Laplace domain in the multi-well pressure monitoring mathematical model; superposing the pressure basic solutions of the adjacent wells and the target well to obtain a pressure superposition solution of the multi-well pressure monitoring mathematical model in a Lawster domain; adopting a Gaussian elimination method for the pressure superposition solution to obtain the bottom hole pseudo pressure of the multi-well pressure monitoring mathematical model in the Laplace domain; and adopting a Stehfest numerical inversion method for the bottom-hole pseudo-pressure in the Laplace domain to obtain the bottom-hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the time domain, and taking the bottom-hole pseudo-pressure in the time domain as a pressure solution of the multi-well pressure monitoring mathematical model.
The pressure solution obtaining module 804 is specifically configured to define a control equation, an initial condition, and an internal boundary condition; solving the control equation, the initial condition and the internal and external boundary conditions by using Laplace transformation to obtain a point source solution of a multi-well pressure monitoring mathematical model in a Laplace domain, wherein the point source solution is as follows:
Wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, and has the unit of m 3 /d; u is a laplace variable; r is (r) D Is a dimensionless radial distance; k is permeability in mD; l is a reference length in m; />To consider the point source solution in the Laplace domain for any horizontal well without boundaries.
The pressure solution obtaining module 804 is specifically configured to apply a mirror reflection method to the point source solution:
wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, and has the unit of m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D ,z D Is dimensionless straightAngular coordinate system distance; x is x wD ,y wD ,z wD Is the origin position of a dimensionless rectangular coordinate system; />A point source solution of any horizontal well in the Lawster domain in a multi-well pressure monitoring mathematical model considering boundaries; />
After a new point source solution of a multi-well pressure monitoring mathematical model is obtained by adopting a mirror image reflection method, an infinite series is eliminated by utilizing a Poisson summation formula, so that the method is obtained:
wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, and has the unit of m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 A Bessel function of zero order class; />Eliminating infinite series for any horizontal well in the multi-well pressure monitoring mathematical model, and then solving a point source in a Laplace domain;
and (3) a point source solution after eliminating infinite series for the multi-well pressure monitoring mathematical model is subjected to a line source function integration method, so that a pressure basic solution of any horizontal well in the Lawster domain in the multi-well pressure monitoring mathematical model is obtained:
wherein: t is the temperature, and the unit is K;is a point source in three-dimensional space, and has the unit of m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 A Bessel function of zero order class; />The pressure in the Lawster domain is basically solved for any horizontal well in the multi-well pressure monitoring mathematical model.
The pressure solution obtaining module 804 is specifically configured to sum the pressures of the multiple horizontal wells in the multiple-well pressure monitoring mathematical model to obtain a pressure superposition solution of the multiple-well pressure monitoring mathematical model in the rah domain, where
Wherein: n is the number of wells;pressure superposition solutions in the Lawster domain for a multi-well pressure monitoring mathematical model; />Is a basic solution to the pressure of well 1; />Is a basic solution to the pressure of well 2; />A pressure base solution for well N; t is the temperature, and the unit is K; />Is a point source in three-dimensional space, and has the unit of m 3 /d; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability in mD; l is a reference length in m; x is x D ,y D ,z D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD ,z wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 Is a zero-order Bessel function.
Fig. 9 shows a schematic block diagram of a chip according to an exemplary embodiment of the present disclosure. As shown in fig. 9, the chip 900 includes one or more (including two) processors 901 and a communication interface 902. The communication interface 902 may support the server to perform the data transceiving steps in the multi-well pressure monitoring mathematical model modeling method described above, and the processor 901 may support the server to perform the data processing steps in the multi-well pressure monitoring method described above.
Optionally, as shown in fig. 9, the chip 900 further includes a memory 903, where the memory 903 may include a read-only memory and a random access memory, and provides operating instructions and data to the processor. A portion of the memory may also include non-volatile random access memory (non-volatile random access memory, NVRAM).
In some embodiments, as shown in fig. 9, the processor 901 performs the corresponding operation by invoking a memory-stored operating instruction (which may be stored in an operating system). The processor 901 controls the processing operations of any one of the terminal devices, and the processor may also be referred to as a central processing unit (central processin unit, CPU). Memory 903 may include read only memory and random access memory and provide instructions and data to the processor. A portion of the memory 903 may also include NVRAM. Such as a memory, a communication interface, and a memory coupled together by a bus system that may include a power bus, a control bus, a status signal bus, etc., in addition to a data bus. But for clarity of illustration, the various buses are labeled as bus system 904 in fig. 9.
The method disclosed by the embodiment of the disclosure can be applied to a processor or implemented by the processor. The processor may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in a processor or by instructions in the form of software. The processor may be a general purpose processor, a digital signal processor (diital sinal processin, DSP), an ASIC, an off-the-shelf programmable gate array (FPA) or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component. The various methods, steps and logic blocks of the disclosure in the embodiments of the disclosure may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of a method disclosed in connection with the embodiments of the present disclosure may be embodied directly in hardware, in a decoded processor, or in a combination of hardware and software modules in a decoded processor. The software modules may be located in a random access memory, flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The storage medium is located in a memory, and the processor reads the information in the memory and, in combination with its hardware, performs the steps of the above method.
The exemplary embodiments of the present disclosure also provide an electronic device including: at least one processor; and a memory communicatively coupled to the at least one processor. The memory stores a computer program executable by the at least one processor for causing the electronic device to perform a method according to embodiments of the present disclosure when executed by the at least one processor.
The present disclosure also provides a non-transitory computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor of a computer, is for causing the computer to perform a method according to an embodiment of the present disclosure.
The present disclosure also provides a computer program product comprising a computer program, wherein the computer program, when executed by a processor of a computer, is for causing the computer to perform a method according to embodiments of the disclosure.
Referring to fig. 10, a block diagram of a structure of an electronic device 1000 that may be a server or a client of the present disclosure, which is an example of a hardware device that may be applied to aspects of the present disclosure, will now be described. Electronic devices are intended to represent various forms of digital electronic computer devices, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular telephones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the disclosure described and/or claimed herein.
As shown in fig. 10, the electronic device 1000 includes a computing unit 1001 that 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. In the RAM1003, various programs and data required for the operation of the device 1000 can also be stored. The computing unit 1001, the ROM 1002, and the RAM1003 are connected to each other by a bus 1004. An input/output (I/O) interface 1005 is also connected to bus 1004.
Various components in the electronic device 1000 are connected to the I/O interface 1005, including: an input unit 1006, an output unit 1007, a storage unit 1008, and a communication unit 1009. The input unit 1006 may be any type of device capable of inputting information to the electronic device 1000, and the input unit 1006 may receive input numeric or character information and generate key signal inputs related to user settings and/or function controls of the electronic device. The output unit 1007 may be any type of device capable of presenting information and may include, but is not limited to, a display, speakers, video/audio output terminals, vibrators, and/or printers. Storage unit 1008 may include, but is not limited to, magnetic disks, optical disks. Communication unit 1009 allows electronic device 1000 to exchange information/data with other devices via a computer network, 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 (TM) devices, wiFi devices, wiMax devices, cellular communication devices, and/or the like.
The computing unit 1001 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of computing unit 1001 include, but are not limited to, a Central Processing Unit (CPU), a graphics Processing Unit (PU), various specialized 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 respective methods and processes described above. Each of the methods described above may be implemented as a computer software program tangibly embodied on a machine-readable medium, such as the storage unit 1008. In some embodiments, part or all of the computer program may be loaded and/or installed onto the electronic device 1000 via the ROM 1002 and/or the communication unit 1009.
Program code for carrying out methods of the present disclosure may be written in any combination of one or more programming languages. These 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 the program code, when executed by the processor or controller, causes the functions/operations specified in the flowchart and/or block diagram to be implemented. The program code may execute entirely on the machine, partly on the machine, as a stand-alone software package, partly on the machine and partly on a remote machine or entirely on the remote machine or server.
In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. The machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
The terms "machine-readable medium" and "computer-readable medium" as used in this disclosure refer to any computer program product, apparatus, and/or device (e.g., magnetic discs, optical disks, memory, programmable Logic Devices (PLDs)) for providing machine instructions and/or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal.
To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and pointing device (e.g., a mouse or trackball) by which a user can provide input to the computer. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic input, speech input, or tactile input.
The systems and techniques described here can be implemented in a computing system that includes a background component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such background, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), wide Area Networks (WANs), and the internet.
The computer system may include a client and a server. The client and server are typically remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
In the above embodiments, it may be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part 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 by the embodiments of the present disclosure are performed in whole or in part. The computer may be a general purpose computer, a special purpose computer, a computer network, a terminal, a user equipment, or other programmable apparatus. The computer program or instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another computer readable storage medium, for example, the computer program or instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center by wired or wireless means. The computer readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that integrates one or more available media. The usable medium may be a magnetic medium, e.g., floppy disk, hard disk, tape; optical media, such as digital video discs (diital video disc, DVD); but also semiconductor media such as solid state disks (solid state drive, SSD).
Although the present disclosure has been described in connection with specific features and embodiments thereof, it will be apparent that various modifications and combinations thereof can be made without departing from the spirit and scope of the disclosure. Accordingly, the specification and drawings are merely exemplary illustrations of the present disclosure as defined in the appended claims and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the disclosure. It will be apparent to those skilled in the art that various modifications and variations can be made to the present disclosure without departing from the spirit or scope of the disclosure. Thus, the present disclosure is intended to include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.

Claims (10)

1. A method for modeling a multi-well pressure monitoring mathematical model, comprising:
acquiring underground gas storage data and actual pressure data of the underground gas storage; the underground gas reservoir data includes: the gas storage system comprises geological parameters, fluid physical parameters, a target well injection and production history and an adjacent well injection and production history of the gas storage, wherein the adjacent well and the target well belong to the same underground gas storage, the adjacent well and the target well are communicated through porous media, and the actual pressure data are obtained through a sensor preset in the underground gas storage;
Based on the underground gas storage data and a multi-well pressure monitoring mathematical model, obtaining a pressure solution of the multi-well pressure monitoring mathematical model by superposing the pressures of the adjacent wells and the target well;
and inverting and calculating reservoir parameters in the multi-well pressure monitoring mathematical model based on curve fitting results drawn by the pressure solution and the actual pressure data to obtain an updated multi-well pressure monitoring mathematical model.
2. The method of claim 1, wherein the multi-well pressure monitoring mathematical model is constructed in a manner comprising:
constructing a multi-well pressure monitoring physical model, wherein the multi-well pressure monitoring physical model is obtained at least according to the geological parameters, the fluid physical parameters and the positions of all horizontal wells in the gas storage;
and obtaining the multi-well pressure monitoring mathematical model based on the multi-well pressure monitoring physical model and target hypothesis conditions.
3. The method of claim 2, wherein the target hypothesis conditions include at least one of: the fluid in the underground gas storage is single-phase compressible gas; during the gas flow process, the influence of gravity and capillary force is not considered; before unstable well test, the initial pressure of the underground gas storage is uniformly distributed; the anisotropism of the porous medium is horizontal, homogeneous and uniform in thickness; the gas flow follows darcy's law; the equation of state of the gas conforms to boyle's law.
4. The method of claim 1, wherein the obtaining a pressure solution of the multi-well pressure monitoring mathematical model comprises:
obtaining a point source solution of a multi-well pressure monitoring mathematical model of the underground gas storage in a Laplace domain;
adopting a mirror image reflection method and a line source function integration method for the point source solution to obtain a pressure basic solution of any horizontal well in the Laplace domain in the multi-well pressure monitoring mathematical model;
superposing the pressure basic solutions of the adjacent wells and the target well to obtain a pressure superposition solution of the multi-well pressure monitoring mathematical model in a Lawster domain;
adopting a Gaussian elimination method for the pressure superposition solution to obtain the bottom hole pseudo pressure of the multi-well pressure monitoring mathematical model in the Laplace domain;
and adopting a Stehfest numerical inversion method for the bottom-hole pseudo-pressure in the Laplace domain to obtain the bottom-hole pseudo-pressure of the multi-well pressure monitoring mathematical model in the time domain, and taking the bottom-hole pseudo-pressure in the time domain as a pressure solution of the multi-well pressure monitoring mathematical model.
5. The method of claim 4, wherein the obtaining a pressure base solution in the rah domain for any horizontal well in the multi-well pressure monitoring mathematical model using a mirror image method and a line source function integration method for the point source solution comprises:
Defining a control equation, an initial condition and an internal and external boundary condition;
solving the control equation, the initial condition and the internal and external boundary conditions by adopting Laplace transformation to obtain a point source solution of a multi-well pressure monitoring mathematical model in a Laplace domain;
the point source solution is:
wherein: t is the temperature;is a point source in three-dimensional space; u is a laplace variable; rD is the dimensionless radial distance; k is permeability; l is a reference length; />To consider the point source solution in the Laplace domain for any horizontal well without boundaries.
6. The method of claim 4, wherein the obtaining a pressure base solution in the rah domain for any horizontal well in the multi-well pressure monitoring mathematical model using a mirror image method and a line source function integration method for the point source solution comprises:
and (3) for the point source solution, adopting a mirror reflection method:
wherein: t is the temperature;is a point source in three-dimensional space; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability; l is a reference length; xD, yD, zD is the dimensionless rectangular coordinate system distance; x is x w D,y w D,z w D is the origin position of a dimensionless rectangular coordinate system; />A point source solution of any horizontal well in the Lawster domain in a multi-well pressure monitoring mathematical model considering boundaries;
After a new point source solution of a multi-well pressure monitoring mathematical model is obtained by adopting a mirror image reflection method, an infinite series is eliminated by utilizing a Poisson summation formula, so that the method is obtained:
wherein: t is the temperature;is a point source in three-dimensional space; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability; l is a reference length; x is x D ,y D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 A Bessel function of zero order class; />Eliminating infinite series for any horizontal well in the multi-well pressure monitoring mathematical model, and then solving a point source in a Laplace domain;
and (3) a point source solution after eliminating infinite series for the multi-well pressure monitoring mathematical model is subjected to a line source function integration method, so that a pressure basic solution of any horizontal well in the Lawster domain in the multi-well pressure monitoring mathematical model is obtained:
wherein: t is the temperature;is a point source in three-dimensional space; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability; l is a reference length; x is x D ,y D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 A Bessel function of zero order class; />The pressure in the Lawster domain is basically solved for any horizontal well in the multi-well pressure monitoring mathematical model.
7. The method of claim 4, wherein the superimposing the pressure base solutions of the adjacent wells and the target well to obtain a pressure superimposed solution of the multi-well pressure monitoring mathematical model in the rah domain comprises:
summing the pressures of the multiple horizontal wells in the multiple well pressure monitoring mathematical model, and solving a pressure superposition solution of the multiple well pressure monitoring mathematical model in the Lawster domain, wherein:
wherein: n is the number of wells;pressure superposition solutions in the Lawster domain for a multi-well pressure monitoring mathematical model; />Is a basic solution to the pressure of well 1; />Is a basic solution to the pressure of well 2; />A pressure base solution for well N; t is the temperature; />Is a point source in three-dimensional space; u is a laplace variable; n is the sum; h is a D Is dimensionless reservoir thickness; k is permeability; l is a reference length; x is x D ,y D ,z D Is a dimensionless rectangular coordinate system distance; x is x wD ,y wD ,z wD Is the origin position of a dimensionless rectangular coordinate system; k (K) 0 Is a zero-order Bessel function.
8. A multi-well pressure monitoring mathematical model modeling apparatus, comprising:
the data acquisition module is used for acquiring underground gas storage data and actual pressure data of the underground gas storage; the underground gas reservoir data includes: the gas storage system comprises geological parameters, fluid physical parameters, a target well injection and production history and an adjacent well injection and production history of the gas storage, wherein the adjacent well and the target well belong to the same underground gas storage, the adjacent well and the target well are communicated through porous media, and the actual pressure data are obtained through a sensor preset in the underground gas storage;
The pressure solution acquisition module is used for acquiring a pressure solution of the multi-well pressure monitoring mathematical model by superposing the pressures of the adjacent wells and the target well based on the underground gas storage data and the multi-well pressure monitoring mathematical model;
and the model updating module is used for inverting and calculating reservoir parameters in the multi-well pressure monitoring mathematical model based on the curve fitting result drawn by the pressure solution and the actual pressure data to obtain an updated multi-well pressure monitoring mathematical model.
9. An electronic device, comprising:
a processor; the method comprises the steps of,
a memory storing a program;
wherein the program comprises instructions which, when executed by the processor, cause the processor to perform the method according to any of claims 1-7.
10. A non-transitory computer readable storage medium storing computer instructions for causing a computer to perform the method of any one of claims 1-7.
CN202310522222.9A 2023-05-10 2023-05-10 Multi-well pressure monitoring mathematical model modeling method, device, equipment and storage medium Pending CN116595610A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117072154A (en) * 2023-10-16 2023-11-17 克拉玛依市红都有限责任公司 Underground pressure monitoring method, system, equipment and medium for petroleum exploitation

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117072154A (en) * 2023-10-16 2023-11-17 克拉玛依市红都有限责任公司 Underground pressure monitoring method, system, equipment and medium for petroleum exploitation

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