CN110083851B - Method and device for determining bottom hole pressure of gas well and storage medium - Google Patents
Method and device for determining bottom hole pressure of gas well and storage medium Download PDFInfo
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- CN110083851B CN110083851B CN201810082032.9A CN201810082032A CN110083851B CN 110083851 B CN110083851 B CN 110083851B CN 201810082032 A CN201810082032 A CN 201810082032A CN 110083851 B CN110083851 B CN 110083851B
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Abstract
The invention discloses a method and a device for determining bottom hole pressure of a gas well and a storage medium, and belongs to the technical field of gas reservoir exploitation. The method comprises the following steps: determining a seepage area at the bottom of a gas well and a plurality of unit grids included in the seepage area, and determining a seepage linear differential equation and a linear constraint condition of the seepage area. Then, a discrete numerical model of each of the plurality of unit grids is determined, and a bottom hole pressure of the gas well is determined based on the discrete numerical model of each unit grid, and a seepage linear differential equation and a linear constraint condition of the seepage area. The invention is implemented by discretizing the percolation region into a plurality of unit cells and determining a discrete numerical model for each cell taking into account the wellbore reservoir effect and the skin effect. And then, determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid, the seepage linear differential equation of the seepage area and the linear constraint condition, so that the accuracy of the bottom hole pressure is improved.
Description
Technical Field
The invention relates to the technical field of gas reservoir exploitation, in particular to a method and a device for determining bottom hole pressure of a gas well and a storage medium.
Background
In the process of exploiting a gas reservoir through a gas well, the actual production conditions of the gas well are different, so that the exploitation efficiency of the gas reservoir through the gas well is different. Therefore, in order to improve the gas reservoir exploitation efficiency of the gas well, the actual production condition of the gas well can be determined in advance, so that an operator can take corresponding measures according to different actual production conditions, and the gas reservoir exploitation efficiency of the gas well is improved. The actual production condition of the gas well mainly depends on the flowing rule of the gas in the seepage area at the bottom of the gas well, and the flowing rule of the gas in the seepage area at the bottom of the gas well is mainly determined by the bottom hole pressure in the seepage area at the bottom of the gas well. Therefore, the bottom hole pressure in the seepage area at the bottom of the gas well can be determined before the actual production condition of the gas well is determined, and the flowing rule of the gas is further determined through the bottom hole pressure in the seepage area at the bottom of the gas well.
In the related art, when determining the bottom hole pressure in the seepage area at the bottom of the gas well, the seepage area at the bottom of the gas well can be discretized into a plurality of unit grids by a finite element method, and then an interpolation shape function of each unit grid in the plurality of unit grids is determined. And then, solving the seepage differential equation and the interpolation shape function of each unit grid to obtain the bottom hole pressure of each unit grid in the seepage area at the bottom of the gas well.
However, during the production of the gas well, deviations in the bottom hole pressure determined by the finite element method are caused by the compressibility of the gas in the gas well wellbore, thereby making it difficult to analyze the actual production of the gas well.
Disclosure of Invention
In order to solve the problem that the bottom hole pressure accuracy of a gas well is low in the related technology, and therefore deviation exists in analysis of the actual production condition of the gas well, the embodiment of the invention provides a method and a device for determining the bottom hole pressure of the gas well and a storage medium. The technical scheme is as follows:
in a first aspect, a method for determining a bottom hole pressure of a gas well is provided, the method comprising:
determining a seepage area at the bottom of a gas well and a plurality of unit grids included in the seepage area;
determining a seepage linear differential equation and a linear constraint condition of the seepage area;
determining a discrete numerical model for each of the plurality of unit grids, the discrete numerical model determined while accounting for wellbore reservoir effects and skin effects;
and determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid, the seepage linear differential equation of the seepage area and the linear constraint condition.
Optionally, the determining a seepage area at the bottom of the gas well and the plurality of unit grids included in the seepage area comprises:
acquiring a central point and a plurality of boundary points of the bottom of the gas well;
determining the seepage zone based on a plurality of boundary points at the bottom of the gas well;
and carrying out finite element dispersion on the seepage area based on the central point to obtain the plurality of unit grids.
Optionally, the determining a seepage linear differential equation and a linear constraint condition of the seepage region includes:
acquiring a seepage differential equation and a nonlinear constraint condition of the seepage area;
acquiring a simulated pressure function and a simulated time function of the seepage area;
determining a percolation linear differential equation and a linear constraint condition for the percolation region based on the percolation differential equation, the non-linear constraint condition, the pseudo-pressure function, and the pseudo-time function.
Optionally, the determining a discrete numerical model of each of the plurality of unit grids includes:
obtaining a boundary flow model of the seepage region, the boundary flow model being determined while considering the wellbore reservoir effect and the skin effect;
and determining a discrete numerical model of each unit grid based on the boundary flow model and the quasi-pressure function.
Optionally, the determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid and the seepage linear differential equation and the linear constraint condition of the seepage area comprises:
determining a seepage linear differential equation and a linear constraint condition of each unit grid based on the seepage linear differential equation and the linear constraint condition of the seepage area;
determining a finite element solution model of each unit grid based on the seepage linear differential equation and the discrete numerical model of each unit grid;
the bottom hole pressure for each element mesh is determined based on the finite element solution model and the linear constraints for each element mesh.
In a second aspect, there is provided an apparatus for determining the bottom hole pressure of a gas well, the apparatus comprising:
the system comprises a first determination module, a second determination module and a control module, wherein the first determination module is used for determining a seepage area at the bottom of a gas well and a plurality of unit grids included in the seepage area;
the second determination module is used for determining a seepage linear differential equation and a linear constraint condition of the seepage area;
a third determination module for determining a discrete numerical model for each of the plurality of unit grids, the discrete numerical model being determined while accounting for wellbore reservoir effects and skin effects;
and the fourth determination module is used for determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid, the seepage linear differential equation of the seepage area and the linear constraint condition.
Optionally, the first determining module includes:
the first acquisition unit is used for acquiring a central point and a plurality of boundary points of the bottom of the gas well;
a first determination unit for determining the seepage area based on a plurality of boundary points at the bottom of the gas well;
and the discrete unit is used for carrying out finite element dispersion on the seepage area based on the central point to obtain the plurality of unit grids.
Optionally, the second determining module includes:
the second acquisition unit is used for acquiring a seepage differential equation and a nonlinear constraint condition of the seepage area;
the third acquisition unit is used for acquiring a pseudo-pressure function and a pseudo-time function of the seepage area;
a second determination unit for determining a percolation linear differential equation and a linear constraint condition of the percolation region based on the percolation differential equation, the non-linear constraint condition, the pseudo-pressure function, and the pseudo-time function.
Optionally, the third determining module includes:
a fourth obtaining unit, configured to obtain a boundary flow model of the seepage area, where the boundary flow model is determined by considering the wellbore reservoir effect and the skin effect;
and the third determining unit is used for determining a discrete numerical model of each unit grid based on the boundary flow model and the quasi-pressure function.
Optionally, the fourth determining module is mainly configured to:
determining a seepage linear differential equation and a linear constraint condition of each unit grid based on the seepage linear differential equation and the linear constraint condition of the seepage area;
determining a finite element solution model of each unit grid based on the seepage linear differential equation and the discrete numerical model of each unit grid;
the bottom hole pressure for each element mesh is determined based on the finite element solution model and the linear constraints for each element mesh.
In a third aspect, a storage medium is provided, in which a computer program is stored, which, when executed by a processor, implements any of the methods provided in the first aspect.
The technical scheme provided by the embodiment of the invention has the following beneficial effects: in the embodiment of the invention, when the bottom hole pressure of the seepage area at the bottom of the gas well is determined, in order to facilitate calculation and improve the operation efficiency and reduce the operation amount, the seepage area can be dispersed into a plurality of unit grids after the seepage area at the bottom of the gas well is determined, the seepage linear differential equation and the linear constraint condition of the seepage area are determined, and the discrete numerical model of each unit grid is determined under the condition of considering the well bore reservoir effect and the skin effect. And then, determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid under the condition of considering the well bore storage effect and the skin effect, and the seepage linear differential equation and the linear constraint condition of the seepage area, so that the influence of neglecting the well bore storage effect and the skin effect generated by gas at the bottom of the gas well on the bottom hole pressure of the gas well is avoided, the accuracy of the bottom hole pressure is improved, and more accurate support is provided for determining the actual production condition of the gas well.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method of determining the bottom hole pressure of a gas well provided by an embodiment of the present invention;
FIG. 2A is a flow chart of another method of determining the bottom hole pressure of a gas well provided by an embodiment of the present invention;
FIG. 2B is a graph comparing a pseudo-pressure determined based on a finite element solution model and a pseudo-pressure determined using commercial software, according to an embodiment of the present invention;
FIG. 3A is a schematic structural diagram of a first gas well bottom pressure determination apparatus provided by an embodiment of the present invention;
FIG. 3B is a schematic diagram of a second gas well bottom pressure determination apparatus provided by an embodiment of the present invention;
FIG. 3C is a schematic diagram of a third gas well bottom pressure determination apparatus provided in accordance with an embodiment of the present invention;
FIG. 3D is a schematic diagram of a fourth gas well bottom pressure determination apparatus provided in accordance with an embodiment of the present invention;
fig. 4 is a block diagram of a terminal according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
FIG. 1 is a flow chart of a method for determining the bottom hole pressure of a gas well according to an embodiment of the invention. Referring to fig. 1, the method includes the following steps.
Step 101: determining a seepage area at the bottom of the gas well, and a plurality of unit grids included in the seepage area.
Step 102: determining a seepage linear differential equation and a linear constraint condition of the seepage area.
Step 103: a discrete numerical model is determined for each of the plurality of unit grids, the discrete numerical model being determined while accounting for wellbore reservoir effects and skin effects.
Step 104: and determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid, the seepage linear differential equation of the seepage area and the linear constraint condition.
In the embodiment of the invention, when the bottom hole pressure of the seepage area at the bottom of the gas well is determined, in order to facilitate calculation and improve the operation efficiency and reduce the operation amount, the seepage area can be dispersed into a plurality of unit grids after the seepage area at the bottom of the gas well is determined, the seepage linear differential equation and the linear constraint condition of the seepage area are determined, and the discrete numerical model of each unit grid is determined under the condition of considering the well bore reservoir effect and the skin effect. And then, determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid under the condition of considering the well bore storage effect and the skin effect, and the seepage linear differential equation and the linear constraint condition of the seepage area, so that the influence of neglecting the well bore storage effect and the skin effect generated by gas at the bottom of the gas well on the bottom hole pressure of the gas well is avoided, the accuracy of the bottom hole pressure is improved, and more accurate support is provided for determining the actual production condition of the gas well.
Optionally, determining a seepage zone at the bottom of the gas well, and a plurality of unit grids included in the seepage zone, comprises:
acquiring a central point and a plurality of boundary points of the bottom of the gas well;
determining the seepage zone based on a plurality of boundary points at the bottom of the gas well;
and carrying out finite element dispersion on the seepage area based on the central point to obtain the plurality of unit grids.
Optionally, determining a percolation linear differential equation and linear constraints for the percolation region comprises:
acquiring a seepage differential equation and a nonlinear constraint condition of the seepage area;
acquiring a quasi-pressure function and a quasi-time function of the seepage area;
and determining the seepage linear differential equation and the linear constraint condition of the seepage area based on the seepage differential equation, the nonlinear constraint condition, the quasi-pressure function and the quasi-time function.
Optionally, determining a discrete numerical model for each of the plurality of unit meshes comprises:
acquiring a boundary flow model of the seepage area, wherein the boundary flow model is determined and obtained when the shaft reservoir effect and the skin effect are considered;
and determining a discrete numerical model of each unit grid based on the boundary flow model and the simulated pressure function.
Optionally, determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid, and the seepage linear differential equation and the linear constraint condition of the seepage area, comprises:
determining a seepage linear differential equation and a linear constraint condition of each unit grid based on the seepage linear differential equation and the linear constraint condition of the seepage area;
determining a finite element solution model of each unit grid based on the seepage linear differential equation and the discrete numerical model of each unit grid;
the bottom hole pressure for each element mesh is determined based on the finite element solution model and the linear constraints for each element mesh.
All the above optional technical solutions can be combined arbitrarily to form an optional embodiment of the present invention, which is not described in detail herein.
Fig. 2A is a flow chart of a method for determining a bottom-hole pressure of a gas well according to an embodiment of the present invention. Referring to fig. 2A, the method includes the following steps.
Step 201: determining a seepage area at the bottom of the gas well, and a plurality of unit grids included in the seepage area.
In the process of exploiting the gas reservoir through the gas well, in order to improve the exploitation efficiency of the gas well on the gas reservoir, the actual production condition of the gas well can be analyzed, so that an operator can conveniently take corresponding production measures. The actual production condition of the gas well mainly depends on the flowing rule of the gas in the seepage area at the bottom of the gas well, so that the seepage area at the bottom of the gas well can be determined, and the flowing rule of the gas in the seepage area is further determined. In addition, since the seepage area may be a continuous area, that is, an infinite number of points may be included in the seepage area. Therefore, after the seepage area at the bottom of the gas well is determined, in order to simplify the calculation amount and improve the calculation efficiency, a plurality of unit grids included in the seepage area can be determined.
Specifically, a central point and a plurality of boundary points of the bottom of the gas well may be obtained, the seepage area is determined based on the plurality of boundary points of the bottom of the gas well, and the plurality of unit grids are obtained by performing finite element discretization on the seepage area based on the central point.
The seepage area at the bottom of the gas well can be a two-dimensional continuous area or a three-dimensional continuous area, and the two-dimensional continuous area or the three-dimensional continuous area is a continuous area taking the center of the shaft of the gas well as a central point. When the seepage area is a two-dimensional continuous area, the seepage area can be a continuous area such as a circle, a rectangle or a triangle, and when the seepage area is a three-dimensional continuous area, the seepage area can be a continuous area such as an ellipsoid. Therefore, when determining the seepage area of the gas well, the coordinate point of the center point of the bottom of the gas well, that is, the coordinate point of the center of the wellbore of the gas well at the bottom of the gas well, and the coordinate point of each boundary point of the plurality of boundary points of the seepage area of the bottom of the gas well may be obtained in advance. And drawing a continuous area of the bottom of the gas well based on the coordinates of the boundary points, and determining the continuous area as a seepage area of the bottom of the gas well. Of course, when the seepage area of the gas well bottom is a circular area, the coordinate point where the central point of the gas well bottom is located and the radius of the circular area may be obtained in advance, and then the circular area of the gas well bottom is drawn based on the coordinate point where the central point of the gas well bottom is located and the radius of the circular area, and is determined as the seepage area of the gas well bottom.
After the seepage area of the bottom of the gas well is determined, the seepage area can be dispersed into a plurality of unit grids based on the central point of the bottom of the gas well through a radial logarithmic encryption method, of course, the wellbore radius of the gas well can also be obtained, and then the seepage area can be dispersed into a plurality of unit grids based on the wellbore radius of the gas well through the radial logarithmic encryption method. Wherein each unit cell may be in the shape of an acute triangle. When the seepage region is discretized, the seepage region may be discretized into a plurality of unit meshes by other methods, for example, the seepage region may be discretized into a plurality of unit meshes by a delaunay triangulation method or a frontal propulsion method, which is not limited in the embodiment of the present invention.
For example, the wellbore radius of the gas well is 0.1 meter, the seepage area controlled by the gas well is a circular area, and the radius of the circular area is 300 meters, when the circular area is discretized by a radial logarithmic encryption method, a plurality of concentric circles can be made in the circular area by a radial logarithmic discretization method with the center of the wellbore as the center of the circle and the wellbore radius of the gas well as the reference, and the circumference of each concentric circle is equally divided to obtain a plurality of equally divided nodes included in the plurality of concentric circles. Connecting any three nodes in the plurality of equally-divided nodes into a triangle, ensuring that no other equally-divided nodes exist in a circumscribed circle of the triangle, thereby obtaining a plurality of triangles included in the circular area, and determining the triangles as a plurality of unit meshes of the seepage area. Wherein each triangle can be a regular triangle.
Step 202: determining a seepage linear differential equation and a linear constraint condition of the seepage area.
Specifically, a seepage differential equation and a nonlinear constraint condition of the seepage area are obtained, a pseudo-pressure function and a pseudo-time function of the seepage area are obtained, and a seepage linear differential equation and a linear constraint condition of the seepage area are determined based on the seepage differential equation, the nonlinear constraint condition, the pseudo-pressure function and the pseudo-time function.
The gas in the seepage area satisfies the seepage differential equation of the gas in the flowing process, that is, the flowing rule of the gas in the seepage area satisfies the seepage differential equation of the gas, and meanwhile, the gas in the seepage area satisfies the nonlinear constraint condition in the flowing process. Therefore, the seepage differential equation in the seepage region and the nonlinear constraint condition of the seepage region can be obtained in advance. The non-linear constraints may include initial boundary conditions, closed boundary conditions, and constant pressure boundary conditions. Because the factors influencing the gas flow in the seepage area are more and the factors influencing the gas flow mutually influence each other, namely, the parameters of the seepage differential equation of the gas are more and mutually influence. Therefore, in order to solve the gas seepage differential equation, the gas seepage differential equation can be converted into a seepage linear differential equation based on the obtained quasi-pressure function and the obtained quasi-time function, and the nonlinear constraint condition can be converted into a linear constraint condition, so that the influence of the parameter is reduced, and the solution efficiency of the seepage differential equation is improved.
For example, when the seepage zone is a two-dimensional continuous zone, the obtained seepage differential equation of the gas may be described by the following formula (1) based on the actual bottom hole pressure, the bottom hole rock porosity, the bottom hole rock permeability, the gas viscosity, the gas compressibility, the gas deviation factor, and the time factor in the seepage zone, the obtained nonlinear constraint condition may be described by the following formula (2), formula (3), and formula (4), the obtained pseudo-pressure function may be described by the following formula (5) based on the actual bottom hole pressure, the gas viscosity, the gas deviation factor, and the pseudo-pressure, and the obtained pseudo-time function may be described by the following formula (6) based on the time factor, the gas viscosity, and the gas compressibility. Thereafter, the seepage linear differential equation determined based on the above-described formula (1), formula (2), formula (3), formula (4), formula (5), and formula (6) may be described by the following formula (7), and the determined linear constraint condition may be described by the following formula (8), formula (9), and formula (10).
p(x,y,t)＝pi (2)
p|Γ＝p0 (4)
m(x,y,ta)＝mi (8)
m|Γ＝m0 (10)
Wherein, in the above formula (1), p is the actual bottom hole pressure at time t of any point in the seepage zone, k is the rock permeability, μ is the gas viscosity, Z is the gas deviation factor, φ is the rock porosity, cgFor gas compressibility, t refers to the time factor of the percolation region. The above formula (2) refers to the initial condition of the percolation region, in the above formula (2), x refers to the abscissa of any point in the percolation region, y refers to the ordinate of any point in the percolation region, piThe bottom hole pressure at any point in the seepage area at the initial moment is referred to, and the physical meaning of the rest parameters can be the physical meaning of the corresponding parameters in the formula (1) as above. The above formula (3) indicates a closed boundary condition of the seepage region, that is, a change rate of the bottom hole pressure of the seepage region along a boundary normal direction is 0. The above formula (4) is a constant pressure boundary condition of the seepage region, and in the above formula (4), p is0Refers to the bottom hole pressure of the seepage zone at the boundary. In the above formula (5), m is the pseudo pressure at any point in the seepage region, and the physical meanings of the remaining parameters can be the physical meanings of the corresponding parameters in the above formula (1). In the above formula (6), taIs an intended time, t0Refers to the initial time (μ c)g)iWhich is the product between the viscosity of the gas and the compressibility of the gas at the initial moment, the physical significance of the remaining parameters may be the same as the physical significance of the corresponding parameters in equation (1) above. In the above formula (7), the physical meanings of the parameters can be as described aboveThe physical meaning of the corresponding parameter in equation (1) or equation (5). In the above formula (8), m is a pseudo pressure at any point in the seepage region, and m isiRefers to the pseudo-pressure at any point in the seepage area at the initial moment, and the physical meaning of the remaining parameters can be the same as the physical meaning of the corresponding parameters in the above formula (2) or formula (6). The above equation (9) indicates a closed boundary condition of the percolation region, that is, a change rate of a pseudo pressure of the percolation region along a boundary normal direction is 0. The above formula (10) is a constant pressure boundary condition of the seepage region, and in the above formula (10), m is0Refers to the pseudo-pressure of the percolation region at the boundary.
After converting the seepage differential equation and the nonlinear constraint condition of the seepage region into a seepage linear differential equation and a linear constraint condition based on the pseudo-pressure function and the pseudo-time function, a discrete numerical model of each unit grid in the seepage region can be determined while considering the wellbore reservoir effect and the skin effect. Specifically, it can be determined by steps 203 to 204 as follows.
Step 203: and acquiring a boundary flow model of the seepage area, wherein the boundary flow model is determined by considering the reservoir effect and the skin effect of the shaft.
In the production process of the gas well, due to compressibility of gas, the gas in the gas well has a wellbore storage effect and a skin effect at the boundary of a wellbore, so in order to improve accuracy of the boundary flow model, influences caused by the wellbore storage effect and the skin effect on the boundary flow model at the boundary of the wellbore can be considered. The flow model of the seepage region obtained when the wellbore reservoir effect and the skin effect are considered may be described by the following formula (11) based on the surface actual production of the gas well, the surface temperature, the thickness of the reservoir corresponding to the gas well, the wellbore reservoir coefficient, the bottom hole pressure at the wellbore boundary, the equivalent hole diameter when the skin effect is considered, and the skin factor.
Wherein, in the above formula (11) In (q)scThe method is characterized in that the method refers to the ground actual yield of the gas well, h refers to the thickness of a reservoir corresponding to the gas well, T refers to the ground temperature, r refers to the distance between any point in the seepage area of the gas well and the center of a shaft, and r refers to the distance between any point in the seepage area of the gas well and the center of the shaftwThe radius of the gas well shaft is referred to, V is a shaft storage coefficient, S is a skin factor, pi is a constant, e is a constant, and the physical meanings of the rest parameters can be the physical meanings of the corresponding parameters in the formula (1).
Step 204: and determining a discrete numerical model of each unit grid based on the boundary flow model and the simulated pressure function.
The boundary flow model of the seepage area is only applicable to the boundary of the gas well shaft, that is, the boundary flow model of the seepage area is only applicable to at least one unit grid of which any side of the plurality of unit grids is located on the boundary of the gas well shaft. Therefore, the discrete numerical model of each of the plurality of unit meshes may be determined based on the boundary flow rate model and the pseudo-pressure function obtained in step 202, so that the discrete numerical model determined based on the boundary flow rate model may be applied to each of the plurality of unit meshes.
Specifically, the quasi-pressure function may be multiplied by two equal-sign sides of the formula (11) based on the quasi-pressure function, so as to convert the boundary flow model into a flow model under the quasi-pressure condition, and the flow model under the quasi-pressure condition may be described according to the following formula (12) based on the ground actual yield of the gas well, the ground temperature, the thickness of the reservoir corresponding to the gas well, the wellbore storage coefficient, the quasi-pressure at the bottom of the gas well, the equivalent well diameter in consideration of the skin effect, and the skin factor. Then, an interpolation function is introduced, the difference function is multiplied by the equal-sign sides of the formula (12), and the equal-sign sides are integrated by the wellbore boundary to obtain a discrete numerical model of each unit grid, and the obtained discrete numerical model of each unit grid can be described according to the following formula (13). For the obtained discrete numerical model of each unit grid, when at least one unit grid including no boundary of the shaft is used, the result of integration based on the shaft boundary is 0, that is, when at least one unit grid including no boundary of the shaft is used, the boundary flow rate does not exist. The result of integration based on the wellbore boundary is not 0 at the at least one cell including the boundary of the wellbore, that is, there is a boundary flow rate at the at least one cell including the boundary of the wellbore.
In the above formula (12), the physical meaning of each parameter may be the physical meaning of the corresponding parameter in the above formula (1) or formula (11). In the above formula (13), NwIs referred to as an interpolated shape function, ΓeReferring to the wellbore boundary, and l refers to a small length of the wellbore boundary, the physical significance of the remaining parameters may be as described above for the corresponding parameters in equation (12).
Continuing with the above example, when the percolation region is a two-dimensional continuous region, the shape function N is interpolatedwMay be a three-dimensional row matrix and may be described by the coordinates of any point within the percolation region according to equation (14) below. Further, after the integral solution of the above equation (13), the discrete numerical model of each unit grid can be described by the following equation (15).
Wherein, in the above formula (14), NwRefers to an interpolation shape function, a refers to the area of each unit grid, i, j, k refers to three vertexes on each unit grid respectively,ai＝xjyk-xkyj，aj＝xkyi-xiyk，ak＝xiyj-xjyi，bi＝yj-yk，bj＝yk-yi，bk＝yi-yj，ci＝xk-xj，cj＝xi-xk，ck＝xj-xi. In the above formula (15), sijThe length of the edge of each cell grid located on the wellbore boundary, and the remaining parameters may be defined as the corresponding parameters of equation (13) above.
After the discrete numerical model for each cell grid is determined, the bottom hole pressure of the gas well may be determined based on the discrete numerical model for each cell grid, as well as the seepage linear differential equation and the linear constraints for the seepage zone. Specifically, the bottom hole pressure of the gas well may be determined as follows from step 205-step 207.
Step 205: and determining the seepage linear differential equation and the linear constraint condition of each unit grid based on the seepage linear differential equation and the linear constraint condition of the seepage area.
Because the gas at any point in the seepage area meets the seepage differential equation and the nonlinear constraint condition of the gas in the flowing process, the seepage differential equation and the nonlinear constraint condition of the seepage area are converted into the seepage linear differential equation and the linear constraint condition on the basis of the quasi-pressure function and the quasi-time function, and the whole seepage area is converted. Therefore, the gas at any point in the seepage area satisfies the seepage linear differential equation and the linear constraint condition of the seepage area in the flowing process, that is, the seepage linear differential equation and the linear constraint condition of the seepage area can be determined as the seepage linear differential equation and the linear constraint condition of each unit grid.
Step 206: and determining a finite element solution model of each unit grid based on the seepage linear differential equation and the discrete numerical model of each unit grid.
After the seepage linear differential equation of each unit grid is determined, the finite element form of the seepage linear differential equation of each unit grid is determined based on the seepage linear differential equation of each unit grid, and then the finite element solving model of each unit grid is determined based on the finite element form and the discrete numerical model of the seepage linear differential equation of each unit grid.
Specifically, an equivalent integral form of the problem of the predetermined solution of the seepage linear differential equation of each cell grid is established for the seepage linear differential equation of each cell grid determined in the above step 205, that is, the seepage linear differential equation described in the above equation (7) determined in the above step 202. And then, according to a step-by-step integration method and the deformation of the Green Gaussian formula, the finite element form of the seepage linear differential equation of each unit grid can be determined. And determining a finite element solution model of each unit grid based on the finite element form of the seepage linear differential equation of each unit grid and the discrete numerical model of each unit grid.
Continuing with the above example, when the percolation region is a two-dimensional continuous region, each unit cell is a regular triangle, the equivalent integral form of the problem of the predetermined solution of the determined percolation linear differential equation for each regular triangle can be described according to the following equation (16) based on the interpolated shape function, the pseudo pressure at any point in each regular triangle, the coordinates, the porosity of the downhole rock, the permeability of the downhole rock, the gas viscosity, the gas compressibility, and the pseudo time, the finite element form of the determined percolation linear differential equation for each regular triangle can be described according to the following equation (17), and the finite element solution model of each unit cell determined based on the above equations (15) and (17) can be described according to the following equation (18).
In the above formula (16), epsilon refers to the seepage area where each regular triangle is located, omega refers to any small area in each regular triangle, and the physical meaning of the remaining parameters can be the meaning of the corresponding parameters in the above formula (7) or formula (8). In the above formula (17), the physical meaning of each parameter may be the physical meaning of the corresponding parameter in the above formula (15) or formula (16). In the above-mentioned formula (18),
Kij＝Kji＝(bibj+cicj)/4A，Kik＝Kki＝(bibk+cick)/4A，Kjk＝Kkj＝(bjbk+cjck)/4A，
mi，mj，mkthe pressure values are pseudo pressures of three vertexes of the regular triangle, Δ t is a preset time length, and the physical meanings of the remaining parameters can be the physical meanings of the corresponding parameters in the above formula (15), wherein Δ t can be preset, for example, Δ t can be 1 hour, 5 hours or 10 hours, ai，aj，ak，bi，bj，bk，ci，cj，ckAs described above in step 204, embodiments of the present invention are not described in detail.
Step 207: the bottom hole pressure for each element mesh is determined based on the finite element solution model and the linear constraints for each element mesh.
After the finite element solution model of each element mesh is determined, for any element mesh in the plurality of element meshes, the finite element solution model of each element mesh can be solved by adopting a computer programming method under the constraint of the linear constraint condition of each element mesh, so that the difference between the pseudo-pressure of any vertex on each element mesh at the current moment and the pseudo-pressure at the initial moment is determined. And further determining the pseudo-pressure at the current moment based on the pseudo-pressure of any vertex on each unit grid at the initial moment, thereby determining the bottom hole pressure of any vertex on each unit grid at the current moment.
Continuing with the above example, when the seepage area is a two-dimensional continuous area, for the finite element solution model of the regular triangle, since the coordinates of any point and any vertex in the regular triangle are known, the area or volume of the regular triangle can be determined based on the vertex coordinates of the unit mesh, and the porosity of the downhole rock, the permeability of the downhole rock, the gas viscosity at the initial time, the gas compressibility at the initial time, the actual surface yield of the gas well, the thickness of the reservoir corresponding to the gas well, the surface temperature, the radius of the wellbore of the gas well, the wellbore storage coefficient, and the skin factor are known. Therefore, after taking in the time difference between the current time and the initial time, the finite element solution model described in the above equation (18) can be solved under the constraint of the linear constraint condition of the triangle, and the difference between the pseudo pressure of any vertex on the regular triangle at the current time and the pseudo pressure at the initial time is determined. And further determining the pseudo-pressure at the current moment based on the pseudo-pressure of any vertex on the regular triangle at the initial moment, thereby determining the bottom hole pressure of any vertex on each unit mesh at the current moment.
Further, in order to verify the utility of the finite element solution model of each unit mesh, referring to fig. 2B, the variation curve of the difference value between the pseudo pressure at any time and the pseudo pressure at the initial time at any point in the two-dimensional continuous region, and the variation trend curve of the difference value between the pseudo pressure at any time and the pseudo pressure at the initial time at any point in the two-dimensional continuous region determined by the commercial software are all shown in fig. 2BAnd the change curve of the difference value between the simulated pressure at one moment and the simulated pressure at the initial moment is the same as the change trend curve of the difference value between the simulated pressure at any moment and the simulated pressure at the initial moment of any point in the two-dimensional continuous area, so that the practicability of the finite element solution model of each unit grid is verified. In FIG. 2B, Δ m is the difference between the pseudo-pressure at any one time and the pseudo-pressure at the initial time for any one vertex, Δ m' taThe variation trend of the difference value between the pseudo pressure of any vertex at any moment and the pseudo pressure at the initial moment is referred to.
In the embodiment of the invention, the technical scheme provided by the embodiment of the invention has the following beneficial effects: in the embodiment of the invention, when the bottom hole pressure of the seepage area at the bottom of the gas well is determined, the seepage area at the bottom of the gas well can be determined based on the obtained center of the shaft of the gas well and a plurality of boundary points of the seepage area at the bottom of the gas well, and the seepage differential equation and the nonlinear constraint condition of the seepage area are determined. In order to facilitate the calculation simplification and improve the operation efficiency, the seepage linear differential equation and the linear constraint condition of the seepage area can be determined based on the seepage differential equation and the nonlinear constraint condition of the seepage area. Then, in order to facilitate calculation and improve the calculation efficiency and reduce the calculation amount, the seepage area can be dispersed into a plurality of unit grids through a radial logarithm encryption method, and a discrete numerical model of each unit grid is determined based on a boundary flow model at the well shaft boundary of the gas well when the well shaft reservoir effect and the skin effect are considered. And finally, determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid, the seepage linear differential equation of the seepage area and the linear constraint condition, avoiding the influence on the bottom hole pressure of the gas well caused by neglecting the shaft reservoir effect and the skin effect generated by the gas at the bottom of the gas well, improving the accuracy of the bottom hole pressure, and thus providing more accurate support for determining the actual production condition of the gas well.
Fig. 3A is a schematic structural diagram of a device for determining the bottom-hole pressure of a gas well according to an embodiment of the present invention. Referring to fig. 3A, the apparatus includes:
the first determination module 301 is used for determining a seepage area at the bottom of a gas well and a plurality of unit grids included in the seepage area;
a second determining module 302, configured to determine a seepage linear differential equation and a linear constraint condition of the seepage area;
a third determining module 303, configured to determine a discrete numerical model of each of the plurality of unit grids, the discrete numerical model being determined while considering a wellbore reservoir effect and a skin effect;
a fourth determination module 304 for determining a bottom hole pressure of the gas well based on the discrete numerical model for each unit cell, and the seepage linear differential equation and the linear constraint condition for the seepage zone.
Optionally, referring to fig. 3B, the first determining module 301 includes:
the first obtaining unit 3011 is configured to obtain a central point and a plurality of boundary points at the bottom of the gas well;
a first determination unit 3012 for determining the seepage zone based on a plurality of boundary points at the bottom of the gas well;
and the discrete unit 3013 is configured to perform finite element discrete on the seepage area based on the central point to obtain the multiple unit grids.
Optionally, referring to fig. 3C, the second determining module 302 includes:
a second obtaining unit 3021, configured to obtain a seepage differential equation and a nonlinear constraint condition of the seepage area;
a third acquiring unit 3022, configured to acquire a pseudo-pressure function and a pseudo-time function of the seepage area;
a second determining unit 3023, configured to determine a seepage linear differential equation and a linear constraint condition for the seepage region based on the seepage differential equation, the nonlinear constraint condition, the pseudo-pressure function, and the pseudo-time function.
Optionally, referring to fig. 3D, the third determining module 303 includes:
a fourth obtaining unit 3031, configured to obtain a boundary flow model of the seepage area, where the boundary flow model is determined when a wellbore reservoir effect and a skin effect are considered;
a third determining unit 3032, configured to determine a discrete numerical model for each unit grid based on the boundary flow model and the pseudo-pressure function.
Optionally, the fourth determining module 304 is mainly configured to:
determining a seepage linear differential equation and a linear constraint condition of each unit grid based on the seepage linear differential equation and the linear constraint condition of the seepage area;
determining a finite element solution model of each unit grid based on the seepage linear differential equation and the discrete numerical model of each unit grid;
the bottom hole pressure for each element mesh is determined based on the finite element solution model and the linear constraints for each element mesh.
The technical scheme provided by the embodiment of the invention has the following beneficial effects: in the embodiment of the invention, when the bottom hole pressure of the seepage area at the bottom of the gas well is determined, in order to facilitate calculation and improve the operation efficiency and reduce the operation amount, the seepage area can be dispersed into a plurality of unit grids after the seepage area at the bottom of the gas well is determined, the seepage linear differential equation and the linear constraint condition of the seepage area are determined, and the discrete numerical model of each unit grid is determined under the condition of considering the well bore reservoir effect and the skin effect. And then, determining the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid under the condition of considering the well bore storage effect and the skin effect, and the seepage linear differential equation and the linear constraint condition of the seepage area, so that the influence of neglecting the well bore storage effect and the skin effect generated by gas at the bottom of the gas well on the bottom hole pressure of the gas well is avoided, the accuracy of the bottom hole pressure is improved, and more accurate support is provided for determining the actual production condition of the gas well.
It should be noted that: in the determining device for the bottom-hole pressure of the gas well provided by the embodiment, when the bottom-hole pressure of the gas well is determined, only the division of the functional modules is taken as an example, and in practical application, the function distribution can be completed by different functional modules according to needs, that is, the internal structure of the equipment is divided into different functional modules so as to complete all or part of the functions described above. In addition, the determining device of the bottom-hole pressure of the gas well provided by the embodiment and the determining method of the bottom-hole pressure of the gas well belong to the same concept, and the specific implementation process is detailed in the method embodiment and is not described again.
Fig. 4 shows a block diagram of a terminal 400 according to an exemplary embodiment of the present invention. The terminal 400 may be: a smartphone, a tablet, a laptop, or a desktop computer. The terminal 400 may also be referred to by other names such as user equipment, portable terminal, laptop terminal, desktop terminal, etc. Referring to fig. 4, the terminal 400 may include a processor 401 and a memory 402.
In some embodiments, the terminal 400 may further optionally include: a peripheral interface 403 and at least one peripheral. The processor 401, memory 402 and peripheral interface 403 may be connected by bus or signal lines. Each peripheral may be connected to the peripheral interface 403 via a bus, signal line, or circuit board. Specifically, the peripheral device includes: at least one of radio frequency circuitry 404, a display screen 405, a positioning component 406, and a power supply 407.
The peripheral interface 403 may be used to connect at least one peripheral related to I/O (Input/Output) to the processor 401 and the memory 402. In some embodiments, processor 401, memory 402, and peripheral interface 403 are integrated on the same chip or circuit board; in some other embodiments, any one or two of the processor 401, the memory 402 and the peripheral interface 403 may be implemented on a separate chip or circuit board, which is not limited by this embodiment.
The Radio Frequency circuit 404 is used for receiving and transmitting RF (Radio Frequency) signals, also called electromagnetic signals. The radio frequency circuitry 404 communicates with communication networks and other communication devices via electromagnetic signals. The rf circuit 404 converts an electrical signal into an electromagnetic signal to transmit, or converts a received electromagnetic signal into an electrical signal. Optionally, the radio frequency circuit 404 includes: an antenna system, an RF transceiver, one or more amplifiers, a tuner, an oscillator, a digital signal processor, a codec chipset, a subscriber identity module card, and so forth. The radio frequency circuitry 404 may communicate with other terminals via at least one wireless communication protocol. The wireless communication protocols include, but are not limited to: the world wide web, metropolitan area networks, intranets, generations of mobile communication networks (2G, 3G, 4G, and 5G), Wireless local area networks, and/or WiFi (Wireless Fidelity) networks. In some embodiments, the rf circuit 404 may further include NFC (Near Field Communication) related circuits, which are not limited in this application.
The display screen 405 is used to display a UI (User Interface). The UI may include graphics, text, icons, video, and any combination thereof. When the display screen 405 is a display screen, the display screen 405 also has the ability to capture touch signals on or over the surface of the display screen 405. The touch signal may be input to the processor 401 as a control signal for processing. At this point, the display screen 405 may also be used to provide virtual buttons and/or a virtual keyboard, also referred to as soft buttons and/or a soft keyboard. In some embodiments, the display screen 405 may be one, providing the front panel of the terminal 400; in other embodiments, the display screen 405 may be at least two, respectively disposed on different surfaces of the terminal 400 or in a folded design; in still other embodiments, the display 405 may be a flexible display disposed on a curved surface or a folded surface of the terminal 400. Even further, the display screen 405 may be arranged in a non-rectangular irregular pattern, i.e. a shaped screen. The Display screen 405 may be made of LCD (Liquid Crystal Display), OLED (Organic Light-Emitting Diode), and other materials.
The positioning component 406 is used to locate the current geographic Location of the terminal 400 for navigation or LBS (Location Based Service). The Positioning component 406 may be a Positioning component based on the Global Positioning System (GPS) in the united states, the beidou System in china, or the galileo System in russia.
The power supply 407 is used to supply power to the various components in the terminal 400. The power source 407 may be alternating current, direct current, disposable or rechargeable. When the power source 407 includes a rechargeable battery, the rechargeable battery may be a wired rechargeable battery or a wireless rechargeable battery. The wired rechargeable battery is a battery charged through a wired line, and the wireless rechargeable battery is a battery charged through a wireless coil. The rechargeable battery may also be used to support fast charge technology.
Those skilled in the art will appreciate that the configuration shown in fig. 4 is not intended to be limiting of terminal 400 and may include more or fewer components than those shown, or some components may be combined, or a different arrangement of components may be used.
In the above embodiments, there is also provided a non-transitory computer-readable storage medium comprising instructions for storing at least one instruction for execution by a processor to implement the method provided by the above-described embodiment shown in fig. 1 or fig. 2A.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program instructing relevant hardware, where the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (9)
1. A method of determining a bottom hole pressure of a gas well, the method comprising:
determining a seepage area at the bottom of a gas well and a plurality of unit grids included in the seepage area;
determining a seepage linear differential equation and a linear constraint condition of the seepage area, wherein the seepage linear differential equation is as follows:
the linear constraints include: m (x, y, t)a)＝mi，
m|Γ＝m0；
Wherein k is the rock permeability, phi is the rock porosity, taIs the pseudo-time, m is the pseudo-pressure at any point in the vadose zone, (μ c)g)iIs the product between the viscosity of the gas and the compressibility of the gas at the initial moment, m0Refers to seepage flowMagnitude of pseudo-pressure of region at boundary, miRefers to the pseudo-pressure of any point in the seepage area at the initial moment, x refers to the abscissa of any point in the seepage area, y refers to the ordinate of any point in the seepage area,
the change rate of the pseudo pressure of the seepage area along the normal direction of the boundary; m < u >ΓPseudo-pressure at the boundary for the percolation region;
determining a discrete numerical model for each of the plurality of unit grids, the discrete numerical model being:
wherein N islIs referred to as an interpolated shape function, ΓeIs the wellbore boundary, l is a small length at the wellbore boundary, qscThe method is characterized in that the method refers to the ground actual yield of a gas well, h refers to the thickness of a reservoir corresponding to the gas well, T refers to the ground temperature, r refers to the distance between any point in the seepage area of the gas well and the center of a shaft, and r refers to the distance between any point in the seepage area of the gas well and the center of the shaftwThe radius of a gas well shaft, V, a shaft reservoir coefficient, S, a skin factor, pi, e, k, rock permeability, m, a pseudo pressure of any point in a seepage area, mu, a gas viscosity and t, wherein the S is a constant;
determining a seepage linear differential equation and a linear constraint condition of each unit grid based on the seepage linear differential equation and the linear constraint condition of the seepage area;
determining a finite element solution model of each unit grid based on the seepage linear differential equation and the discrete numerical model of each unit grid, wherein the finite element solution model is as follows:
wherein m isi，mj，mkRespectively refers to the pseudo pressure of three vertexes of the regular triangle, delta t refers to a preset time length, sijThe length of the edge of each unit grid on the boundary of the shaft is indicated, A is the area of each unit grid, i, j and k are three vertexes of each unit grid respectively,
Kij＝Kji＝(bibj+cicj)/4A，Kik＝Kki＝(bibk+cick)/4A，Kjk＝Kkj＝(bjbk+cjck)/4A，
bi＝yj-yk，bj＝yk-yi，bk＝yi-yj，ci＝xk-xj，cj＝xi-xk，ck＝xj-xi；
the bottom hole pressure for each element mesh is determined based on the finite element solution model and the linear constraints for each element mesh.
2. The method of claim 1, wherein determining a seepage zone at the bottom of the gas well, and wherein the seepage zone comprises a plurality of unit cells, comprises:
acquiring a central point and a plurality of boundary points of the bottom of the gas well;
determining the seepage zone based on a plurality of boundary points at the bottom of the gas well;
and carrying out finite element dispersion on the seepage area based on the central point to obtain the plurality of unit grids.
3. The method of claim 1, wherein said determining a percolation linear differential equation and linear constraints for said percolation region comprises:
acquiring a seepage differential equation and a nonlinear constraint condition of the seepage area, wherein the seepage differential equation is as follows:
the nonlinear constraint conditions are as follows: p (x, y, t) ═ pi，
p|Γ＝p0；
Wherein p is the actual bottom hole pressure at time t of any point in the seepage zone, μ is the gas viscosity, Z is the gas deviation factor, φ is the rock porosity, cgIn order to be the compression factor of the gas,
the rate of change of bottom hole pressure of the vadose zone along the boundary normal direction; p-Γ＝p0Refers to the constant pressure boundary condition, p, of the percolation region0Refers to the bottom hole pressure, p, of the zone at the boundaryiRefers to the bottom hole pressure of any point in the seepage area at the initial moment;
obtaining a pseudo-pressure function and a pseudo-time function of the seepage area, wherein the pseudo-pressure function is as follows:
the quasi-time function is:
wherein, t0Refers to the initial time;
determining a percolation linear differential equation and a linear constraint condition for the percolation region based on the percolation differential equation, the non-linear constraint condition, the pseudo-pressure function, and the pseudo-time function.
4. The method of claim 3, wherein said determining a discrete numerical model for each of said plurality of unit cells comprises:
obtaining a boundary flow model of the seepage area, wherein the boundary flow model is determined by considering a wellbore reservoir effect and a skin effect, and the boundary flow model is as follows:
and determining a discrete numerical model of each unit grid based on the boundary flow model and the quasi-pressure function.
5. An apparatus for determining the bottom hole pressure of a gas well, the apparatus comprising:
the system comprises a first determination module, a second determination module and a control module, wherein the first determination module is used for determining a seepage area at the bottom of a gas well and a plurality of unit grids included in the seepage area;
the second determination module is used for determining a seepage linear differential equation and a linear constraint condition of the seepage area, wherein the seepage linear differential equation is as follows:
the linear constraints include: m (x, y, t)a)＝mi，
m|Γ＝m0；
Wherein k is the rock permeability, phi is the rock porosity, taIs the pseudo-time, m is the pseudo-pressure at any point in the vadose zone, (μ c)g)iMeans the gas viscosity at the initial timeProduct of the compression factor of the gas, m0Refers to the magnitude of the pseudo-pressure, m, of the percolation region at the boundaryiRefers to the pseudo-pressure of any point in the seepage area at the initial moment, x refers to the abscissa of any point in the seepage area, y refers to the ordinate of any point in the seepage area,
the change rate of the pseudo pressure of the seepage area along the normal direction of the boundary; m < u >ΓPseudo-pressure at the boundary for the percolation region;
a third determining module, configured to determine a discrete numerical model of each of the plurality of unit grids, where the discrete numerical model is:
wherein N islIs referred to as an interpolated shape function, ΓeIs the wellbore boundary, l is a small length at the wellbore boundary, qscThe method is characterized in that the method refers to the ground actual yield of a gas well, h refers to the thickness of a reservoir corresponding to the gas well, T refers to the ground temperature, r refers to the distance between any point in the seepage area of the gas well and the center of a shaft, and r refers to the distance between any point in the seepage area of the gas well and the center of the shaftwThe radius of a gas well shaft, V, a shaft reservoir coefficient, S, a skin factor, pi, e, k, rock permeability, m, a pseudo pressure of any point in a seepage area, mu, a gas viscosity and t, wherein the S is a constant;
the fourth determination module is used for determining the seepage linear differential equation and the linear constraint condition of each unit grid based on the seepage linear differential equation and the linear constraint condition of the seepage area;
determining a finite element solution model of each unit grid based on the seepage linear differential equation and the discrete numerical model of each unit grid, wherein the finite element solution model is as follows:
wherein m isi，mj，mkRespectively refers to the pseudo pressure of three vertexes of the regular triangle, delta t refers to a preset time length, sijThe length of the edge of each unit grid on the boundary of the shaft is indicated, A is the area of each unit grid, i, j and k are three vertexes of each unit grid respectively,
Kij＝Kji＝(bibj+cicj)/4A，Kik＝Kki＝(bibk+cick)/4A，Kjk＝Kkj＝(bjbk+cjck)/4A，
bi＝yj-yk，bj＝yk-yi，bk＝yi-yj，ci＝xk-xj，cj＝xi-xk，ck＝xj-xi；
the bottom hole pressure for each element mesh is determined based on the finite element solution model and the linear constraints for each element mesh.
6. The apparatus of claim 5, wherein the first determining module comprises:
the first acquisition unit is used for acquiring a central point and a plurality of boundary points of the bottom of the gas well;
a first determination unit for determining the seepage area based on a plurality of boundary points at the bottom of the gas well;
and the discrete unit is used for carrying out finite element dispersion on the seepage area based on the central point to obtain the plurality of unit grids.
7. The apparatus of claim 5, wherein the second determining module comprises:
a second obtaining unit, configured to obtain a seepage differential equation and a nonlinear constraint condition of the seepage area, where the seepage differential equation is:
the nonlinear constraint conditions are as follows: p (x, y, t) ═ pi，
p|Γ＝p0；
Wherein p is the actual bottom hole pressure at time t of any point in the seepage zone, μ is the gas viscosity, Z is the gas deviation factor, φ is the rock porosity, cgIn order to be the compression factor of the gas,
the rate of change of bottom hole pressure of the vadose zone along the boundary normal direction; p-Γ＝p0Refers to the constant pressure boundary condition, p, of the percolation region0Refers to the bottom hole pressure, p, of the zone at the boundaryiRefers to the bottom hole pressure of any point in the seepage area at the initial moment;
a third obtaining unit, configured to obtain a pseudo-pressure function and a pseudo-time function of the seepage area, where the pseudo-pressure function is:
the quasi-time function is:
wherein, t0Refers to the initial time;
a second determination unit for determining a percolation linear differential equation and a linear constraint condition of the percolation region based on the percolation differential equation, the non-linear constraint condition, the pseudo-pressure function, and the pseudo-time function.
8. The apparatus of claim 7, wherein the third determining module comprises:
a fourth obtaining unit, configured to obtain a boundary flow model of the seepage area, where the boundary flow model is determined when a wellbore reservoir effect and a skin effect are considered, where the boundary flow model is:
and the third determining unit is used for determining a discrete numerical model of each unit grid based on the boundary flow model and the quasi-pressure function.
9. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the method of any one of claims 1 to 4.
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