A calculation method for the interlayer interference mechanism of multi-layer commingled production in different types of gas reservoirs

By constructing a single-layer dimensionless mathematical model and combining it with Laplace transform and least squares fitting, the inter-layer interference phenomenon in multi-layer commingled production was solved, the accuracy of gas production prediction and recovery rate were improved, and the development plan was optimized.

CN120159365BActive Publication Date: 2025-09-23CHINA UNIV OF GEOSCIENCES (BEIJING)
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Patent Information

Application Number
CN202510525761.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-04-25
Publication Date
2025-09-23
Estimated Expiration
2045-04-25

AI Technical Summary

Technical Problem

In the process of multi-layer co-production with existing technologies, inter-layer interference occurs frequently, resulting in reduced single-layer production capacity and decreased recovery rate. Existing methods are difficult to accurately characterize the non-Darcy flow effect during shale gas-tight gas co-production, which affects the development effect.

Method used

Single-layer dimensionless mathematical models of different types of gas reservoirs are constructed. Through Laplace transform and least squares fitting, combined with the Blasingame curve, the bottomhole pressure and gas production of commingled production wells are calculated. Considering the dynamic coupling effect between the wellbore and the reservoir, a calculation method for the interference mechanism between multiple layers of commingled production is established.

Benefits of technology

It has achieved a refined analysis of the interference between layers during multi-layer combined production, improved the accuracy of gas production prediction and recovery rate, and optimized the development plan.

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Abstract

The present invention relates to the technical field of multi-layer commingled production, and discloses a method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs, comprising: constructing a single-layer dimensionless mathematical model that respectively characterizes each reservoir of a commingled production well, and solving the bottom hole pressure solution of the corresponding model; inputting the known gas production of the commingled production well into the model to calculate the theoretical bottom hole pseudo-pressure value through the superposition principle; performing historical fitting on the actual bottom hole pseudo-pressure value of each reservoir and the theoretical bottom hole pseudo-pressure value to obtain a characterization parameter; combining the characterization parameters, calculating and obtaining the predicted gas production of the corresponding model, and summing up the gas production of the commingled production well; obtaining the abscissa material balance time, ordinate normalized production and calculation formula of the Blasingame curve, and calculating and obtaining the gas production of the commingled production well; and determining the gas production of the commingled production well in the current time step by obtaining the gas production of the commingled production well to determine the influence of inter-reservoir interference between the gas production obtained by the commingled production well during multi-layer commingled production and the gas production of the commingled production well obtained by summing up.
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Description

Technical Field

[0001] The present invention relates to the technical field of multi-layer commingled production of different types of gas reservoirs, and in particular to a method for calculating an inter-layer interference mechanism of multi-layer commingled production of different types of gas reservoirs. Background Art

[0002] As oil and gas exploration and development expand into deeper, unconventional areas, multi-layer commingled production from different types of gas reservoirs (such as conventional, tight, and shale) has become an important technical means to increase single-well productivity and reduce development costs. Multi-layer commingled production technology offers the intensive advantage of "penetrating multiple layers through a single well."

[0003] However, during the combined production process, the dynamic coupling effect between high-permeability layers and low-permeability layers, high-pressure layers and low-pressure layers, and dry gas layers and condensate gas layers is significant, resulting in frequent interlayer interference. Interlayer interference is essentially the result of the coupling of multiple systems of reservoir, fluid and wellbore. Due to the differences in physical properties of each layer, such as permeability, porosity, pressure, etc., as well as the different properties of fluids, interlayer interference is a common phenomenon. Interlayer interference will reduce the production capacity of a single layer, affect the overall recovery rate, and even cause premature water or gas channeling in some layers, resulting in unsatisfactory development results.

[0004] Current interlayer interference analysis relies primarily on two approaches. One approach simplifies multiple layers into a single homogeneous layer and uses permeability-weighted average or production-overlay models to predict production. This approach ignores dynamic interlayer flow coupling and results in significant errors. Interference assessment based on black oil models or dual-porosity and dual-permeability models, however, is limited by the coarse meshing and simplified phase equations, making it difficult to accurately characterize the non-Darcy flow effects of shale gas and tight gas mixed production.

[0005] Therefore, studying the mechanism of inter-layer interference in multi-layer commingled production and its calculation method is of great significance for optimizing development plans and improving recovery efficiency. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for calculating the interference mechanism between multiple layers of combined production in different types of gas reservoirs, so as to solve the technical problems in the prior art that restrict the refined development of combined production gas wells due to the shortcomings of the existing methods in terms of dynamics, efficiency and adaptability to multiple gas reservoirs.

[0007] In order to solve the above technical problems, the present invention specifically provides the following technical solutions:

[0008] A method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs includes the following steps:

[0009] Step 100: constructing a single-layer dimensionless mathematical model representing each reservoir of the commingled production well based on the model assumptions, performing a Laplace transform on each single-layer dimensionless mathematical model and substituting the boundary conditions and initial conditions of the corresponding model into the model, and obtaining the bottom hole pressure solution of the corresponding model after solving;

[0010] Step 200: Input the known gas production of the combined production well into each single-layer dimensionless mathematical model, and calculate the theoretical bottom hole pseudo-pressure value of the corresponding model using the superposition principle;

[0011] Step 300: historically fitting the actual bottom hole pseudo-pressure value of each reservoir with the theoretical bottom hole pseudo-pressure value of the corresponding model of each reservoir by introducing the least square method to obtain the characterization parameters of each reservoir;

[0012] Step 400: Assuming a time-dependent decrease curve of the pseudo bottom hole pressure, combined with the obtained characterization parameters of each reservoir, the predicted gas production corresponding to each single layer dimensionless mathematical model is calculated, and then the gas production of the combined production well is obtained by summing the results.

[0013] Step 500: Using the obtained gas production of the commingled production well, obtain the material balance time on the abscissa and the normalized production on the ordinate of the Blasingame curve, and the calculation formula of the material balance time on the abscissa and the normalized production on the ordinate based on the time step, thereby determining the gas production of the commingled production well at the current time step;

[0014] The gas production of the combined production well at the current time step is obtained to determine the influence of inter-reservoir interference between the gas production of the combined production well obtained during multi-layer combined production and the gas production of the combined production well obtained by summing.

[0015] As a preferred solution of the present invention, the calculation formula based on time steps is used, and a series of gas production rates from small to large are assumed in each time step:

[0016] The first bottom hole flowing pressure based on the time step is found through the corresponding relationship between the bottom hole pseudo pressure and the bottom hole flowing pressure, and the second bottom hole flowing pressure corresponding to the time step is calculated through the two-phase pipe flow pressure conversion method;

[0017] At each time step, a curve is constructed with gas production as the horizontal coordinate and the first bottom hole flowing pressure and the second bottom hole flowing pressure as the vertical coordinate. The intersection of the two curves is found to determine the gas production of the combined production well at the current time step.

[0018] As a preferred embodiment of the present invention, the assumptions based on the model assumptions include:

[0019] The reservoir is a square formation, each formation is horizontal and of unequal thickness, length and width; an artificial fracture is set in the middle of the square formation, and the artificial fracture is used for constant pressure production;

[0020] There are impermeable layers between the reservoirs of the commingled wells with different geological characteristics, and the bottom hole flowing pressures between the reservoirs are set to be equal or similar.

[0021] As a preferred solution of the present invention, constructing a single-layer dimensionless mathematical model to characterize each reservoir of the combined production well specifically includes:

[0022] A trilinear flow model is established to characterize the single-layer dimensionless mathematical model of shale gas reservoirs;

[0023] A trilinear flow warren-root model is established to characterize the single-layer dimensionless mathematical model of tight gas reservoirs.

[0024] A five-linear flow internal warren-root model is established to characterize the single-layer dimensionless mathematical model of coalbed methane reservoir;

[0025] The dimensionless mathematical model of each reservoir layer is converted into dimensionless one.

[0026] As a preferred solution of the present invention, the dimensionless mathematical model of each reservoir is Laplace transformed and the boundary conditions and initial conditions assumed in the model assumption process of the trilinear flow model, the Warren-Root model within the trilinear flow, and the Warren-Root model within the pentaxial flow are substituted into the model. After solving, the bottom hole pressure solution of the corresponding model is obtained. The specific calculation formula is:

[0027] ;

[0028] in, A a , B a represents the undetermined coefficients of the trilinear flow model, A b , B b represents the undetermined coefficients of the Warren-Root model in the trilinear flow, A c , B c represents the undetermined coefficients of the Warren-Root model in the five linear flows, s represents the Laplace variable; represents the dimensionless bottomhole pressure of the trilinear flow model; represents the dimensionless bottomhole pressure of the Warren-Root model in trilinear flow; represents the dimensionless bottomhole pressure of the Warren-Root model in the pentalinear flow; Represents the dimensionless boundary distance.

[0029] As a preferred solution of the present invention, the known gas production of the combined production well is input into each single-layer dimensionless mathematical model, and the theoretical bottom hole pseudo-pressure value of the corresponding model is calculated by the superposition principle. The specific calculation formula includes:

[0030] ;

[0031] in, ; ;

[0032] Where, Indicates the time steps; represents the difference between two adjacent time steps; t represents the total production time; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represent the governing equations of the trilinear flow model; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represents the governing equations of the Warren-Root model in trilinear flow; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represent the governing equations of the Warren-Root model within the pentalinear flow; Indicates the The change in liquid production in the time step; express Liquid production in the time step; express Liquid production in the time step; Indicates the initial pressure.

[0033] As a preferred embodiment of the present invention, the horizontal axis material balance time and the vertical axis normalized yield are based on the time step The calculation formula specifically includes:

[0034] ;

[0035] in: ;

[0036] Where, represents the material equilibrium time, represents the normalized yield, represents the pseudo bottom hole pressure difference, Indicates the Cumulative gas production in each time step; Indicates the current liquid production; Indicates the initial pressure; Indicates the current bottom hole flowing pressure.

[0037] As a preferred solution of the present invention, the first bottom hole flowing pressure based on the time step is found through the correspondence between the bottom hole pseudo pressure and the bottom hole flowing pressure, specifically:

[0038] Each time step Assume a series of gas production from small to large: ;

[0039] pass Corresponding material balance time Find the corresponding vertical coordinate in the Blasingame curve chart , using regularized yield The bottom hole pseudo pressure of the corresponding time step is calculated by the formula: m twi1 , m twi2 , m twi3 m twin .

[0040] Through the corresponding relationship between the bottomhole pseudo pressure and the bottomhole flowing pressure, the difference method is used to find the first bottomhole flowing pressure based on the time step: ;

[0041] As a preferred solution of the present invention, the second bottom hole pressure corresponding to the time step is calculated by a two-phase pipe flow pressure conversion method, specifically:

[0042] At each time step ti, a curve of wellhead pressure phi changing with time t is assumed, and at each time ti, a series of wellhead gas production rates from small to large are assumed: Qi1, Qi2, Qi3 Qin;

[0043] The second bottom hole pressure of the corresponding time step calculated by the two-phase pipe flow pressure conversion method is obtained: pi1, pi2, pi3 pin.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention establishes a corresponding dimensionless single-layer digital model for each type of reservoir in a commingled production well by means of model assumptions, and obtains the predicted gas production of each reservoir and the sum of the predicted gas production based on the theoretical bottom hole pseudo-pressure value of the dimensionless single-layer digital model of each reservoir and the characterization parameters of the reservoir, and then calculates and analyzes the gas production of the commingled production well using the abscissa material balance time, ordinate normalized production and calculation formula of the Blasingame curve, thereby realizing the analysis of the coupling state between multiple reservoirs in the commingled production well and obtaining an efficient interlayer interference mechanism calculation method that is suitable for analyzing multiple types of gas reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.

[0047] Figure 1 Schematic diagram of the flow of a method for calculating the mechanism of inter-layer interference in multi-layer commingled production of different types of gas reservoirs according to an embodiment of the present invention;

[0048] Figure 2 Schematic diagram of a three-linear flow single-layer dimensionless mathematical model based on model assumptions according to an embodiment of the present invention;

[0049] Figure 3 Schematic diagram of a Warren-Root single-layer dimensionless mathematical model based on trilinear flow according to an embodiment of the present invention;

[0050] Figure 4 Schematic diagram of a Warren-Root single-layer dimensionless mathematical model within a five-linear flow according to an embodiment of the present invention;

[0051] Figure 5 A line graph showing the calculated cumulative gas production and daily gas production according to an embodiment of the present invention;

[0052] Figure 6 This is a cross-line graph of the wellhead conversion relationship curve A and the Blasingame curve corresponding to the relationship curve B in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0054] like Figure 1 As shown, the present invention provides a method for calculating the interference mechanism between multiple layers of commingled production in different types of gas reservoirs, comprising the following steps:

[0055] Step 100: constructing a single-layer dimensionless mathematical model representing each reservoir of the commingled production well based on the model assumptions, performing a Laplace transform on each single-layer dimensionless mathematical model and substituting the boundary conditions and initial conditions of the corresponding model into the model, and obtaining the bottom hole pressure solution of the corresponding model after solving;

[0056] Step 200: Input the known gas production of the combined production well into each single-layer dimensionless mathematical model, and calculate the theoretical bottom hole pseudo-pressure value of the corresponding model using the superposition principle;

[0057] Step 300: historically fitting the actual bottom hole pseudo-pressure value of each reservoir with the theoretical bottom hole pseudo-pressure value of the corresponding model of each reservoir by introducing the least square method to obtain the characterization parameters of each reservoir;

[0058] Step 400: Assuming a time-dependent decrease curve of the pseudo bottom hole pressure, combined with the obtained characterization parameters of each reservoir, the predicted gas production corresponding to each single layer dimensionless mathematical model is calculated, and then the gas production of the combined production well is obtained by summing the results.

[0059] Step 500: Using the obtained gas production of the commingled production well, obtain the material balance time on the abscissa and the normalized production on the ordinate of the Blasingame curve, and the calculation formula of the material balance time on the abscissa and the normalized production on the ordinate based on the time step, thereby determining the gas production of the commingled production well at the current time step;

[0060] The gas production of the combined production well at the current time step is obtained to determine the influence of inter-reservoir interference between the gas production of the combined production well obtained during multi-layer combined production and the gas production of the combined production well obtained by summing.

[0061] like Figure 6 As shown, using the time-step-based calculation formula, assuming a series of gas production rates from small to large at each time step:

[0062] The first bottom hole flowing pressure based on the time step is found through the corresponding relationship between the bottom hole pseudo pressure and the bottom hole flowing pressure, and the second bottom hole flowing pressure corresponding to the time step is calculated through the two-phase pipe flow pressure conversion method;

[0063] At each time step, a curve is constructed with gas production as the horizontal coordinate and the first bottom hole flowing pressure and the second bottom hole flowing pressure as the vertical coordinate. The intersection of the two curves is found to determine the gas production of the combined production well at the current time step.

[0064] The inter-layer interference of this method is mainly reflected in the following aspects: since the wellbore diameter is fixed, the gas production of each layer will be compressed during multi-layer combined production, resulting in gas production loss. Taking into account the impact of the wellbore on the combined production effect, the gas production of the combined production gas well obtained in this step is the actual gas production of the wellbore, which will be smaller than the gas production of a single production layer.

[0065] The assumptions based on the model include:

[0066] Model assumptions: square strata, each stratum is horizontal, of unequal thickness, length, and width.

[0067] There is an impermeable layer between the upper and lower layers with different geological characteristics (such as permeability and pore structure), an artificial fracture in the middle of the square formation, and constant pressure production, considering the slip effect and adsorption analysis, without considering the physical and chemical reactions of the rock;

[0068] Single-phase gas reservoir, compressible fluid, isothermal development process, fluid follows Darcy's law and gravity effect is ignored;

[0069] Natural fractures develop in the matrix within the warren-root model of the five-linear flow;

[0070] The bottom hole flowing pressure among the reservoirs is approximately equal.

[0071] The construction of a single-layer dimensionless mathematical model to represent each reservoir of the combined production well specifically includes:

[0072] A three-linear flow model is established to characterize the dimensionless mathematical model of a single layer of shale gas reservoirs. A dimensionless mathematical model is established, and the radial coordinate partial differential equation of seepage flow in the vertical well of the jth region and the initial conditions, inner boundary conditions, and outer boundary conditions are respectively (i represents the number of matrix blocks in the vertical direction and k represents the number of matrix blocks in the horizontal direction);

[0073] like Figure 2 As shown, the trilinear flow model has matrix region 2, matrix region 1, and artificial fracture region:

[0074] ;

[0075] ;

[0076] ;

[0077] A trilinear flow warren-root model is established to characterize the single-layer dimensionless mathematical model of tight gas reservoirs.

[0078] like Figure 3 As shown, the warren-root model in trilinear flow has matrix region 2, matrix region 1, and artificial fracture region:

[0079] ;

[0080] ;

[0081] ;

[0082] A five-linear flow internal warren-root model is established to characterize the single-layer dimensionless mathematical model of coalbed methane reservoir;

[0083] like Figure 4As shown, the warren-root model in the five linear flows has matrix region 4, matrix region 3, matrix region 2, matrix region 1 and artificial fracture region:

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] .

[0089] The dimensionless mathematical model of each reservoir layer is converted into a dimensionless model. The dimensionless conversion formula is as follows:

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] In the formula, ∂ represents the partial derivative of the parameter; m mjD represents the dimensionless matrix pseudo-pressure in the j-th matrix region; m nfjD represents the dimensionless natural fracture pseudo-pressure in the jth matrix region; m fD represents the dimensionless artificial fracture pseudo-pressure; k mi represents the dimensionless matrix permeability of the jth matrix region; k nfirepresents the dimensionless natural fracture permeability of the jth matrix region; w D Indicates the dimensionless artificial crack width; y iD represents the dimensionless longitudinal distance from the ith matrix block to the flow boundary direction; x iD represents the dimensionless lateral distance from the ith matrix block to the flow boundary direction; y eiD represents the dimensionless width of the i-th matrix block in the longitudinal direction; x eiD represents the dimensionless transverse length of the i-th matrix block; t D represents dimensionless pseudo-time; h jD represents the conversion coefficient of the dimensionless j-th matrix region; a j represents the crossflow coefficient of the j-th matrix region. Z sc is the compression factor under standard conditions; T sc is the temperature under standard conditions; b is the conversion coefficient, which is 0.0853; k f is the permeability of artificial fractures; h is the reservoir thickness; p0 is the original formation pressure; p mj is the matrix pressure of the jth matrix region; m mj is the matrix pseudo-pressure of the j-th matrix region; p sc The pressure is under standard conditions; q sc It is the gas production under standard conditions; T is the formation temperature; p nfj is the natural fracture pressure of the jth matrix region; m nfj is the pseudo-pressure of natural fractures in the jth matrix region; p f is the artificial fracture pressure; m f is the artificial fracture pressure; t a is the pseudo time; f f is the porosity of artificial fractures; m g is the gas viscosity; c tf is the compression coefficient of artificial cracks; x j is the distance from the jth matrix region to the flow boundary in the lateral direction; h j is the distance from the jth matrix region to the flow boundary in the longitudinal direction; y ei represents the width of the i-th matrix block in the longitudinal direction; xei represents the length of the i-th matrix block in the transverse direction; w represents the crack width;h j represents the conversion coefficient of the j-th matrix region; h f Indicates the conversion coefficient of artificial cracks; k mj is the matrix permeability of the jth matrix region; k nfj is the natural fracture permeability of the jth matrix region.

[0102] The dimensionless mathematical model of each reservoir is transformed into a dimensionless model by Laplace transformation and substituted into the boundary conditions and initial conditions of the trilinear flow model, the Warren-Root model within the trilinear flow model, and the Warren-Root model within the pentaxial flow model. The bottom hole pressure solution of the corresponding model is obtained after the solution. The specific calculation formula is:

[0103] ;

[0104] in, A a , B a represents the undetermined coefficients of the trilinear flow model, A b , B b represents the undetermined coefficients of the Warren-Root model in the trilinear flow, A c , B c represents the undetermined coefficients of the Warren-Root model in the five linear flows, s represents the Laplace variable; represents the dimensionless bottomhole pressure of the trilinear flow model; represents the dimensionless bottomhole pressure of the Warren-Root model in trilinear flow; represents the dimensionless bottomhole pressure of the Warren-Root model in the pentalinear flow; Represents the dimensionless boundary distance.

[0105] The known gas production of the combined production well is input into each single-layer dimensionless mathematical model. The theoretical bottom hole pseudo-pressure value of the corresponding model is calculated by the superposition principle. The specific calculation formula includes:

[0106] ;

[0107] in, ; ;

[0108] Where, Indicates the time steps, represents the difference between two adjacent time steps; t represents the total production time; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represent the governing equations of the trilinear flow model; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represents the governing equations of the Warren-Root model in trilinear flow; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represent the governing equations of the Warren-Root model within the pentalinear flow; Indicates the The change in liquid production in the time step; express Liquid production in the time step; express Liquid production in the time step; Indicates the initial pressure.

[0109] In order to obtain more accurate reservoir parameters, the least square method is introduced to convert the actual bottom hole pseudo pressure m rw Compared with the theoretically calculated bottom hole pressure m pw Perform history matching to obtain parameters such as artificial fracture length, porosity, permeability, and reservoir thickness for the three single-layer models. The steps for establishing the least squares mathematical model are as follows:

[0110] Constructing the Matrix :

[0111] ;

[0112] Define the observation vector :

[0113] ;

[0114] Define the parameter vector :

[0115] ;

[0116] Calculating the error function Gradient:

[0117] ;

[0118] Update parameter vector :

[0119] ;

[0120] Repeated calculation of error function Until convergence. Represents the learning rate.

[0121] Since the diameter and roughness of the wellbore are constant, the gas production of the multi-layer commingled well is will be less than the gas production and : Therefore, the influence of inter-layer interference needs to be considered. The calculation steps are as follows:

[0122] like Figure 5 and Figure 6 As shown, the horizontal axis material balance time, the vertical axis normalized yield based on time step The calculation formula specifically includes:

[0123] ;

[0124] in: ;

[0125] Where, represents the material equilibrium time, represents the normalized yield, represents the pseudo bottom hole pressure difference, Indicates the Cumulative gas production in each time step; Indicates the current liquid production; Indicates the initial pressure; Indicates the current bottom hole flowing pressure.

[0126] Through the corresponding relationship between the bottom hole pseudo pressure and the bottom hole flowing pressure, the first bottom hole flowing pressure based on the time step is found, specifically:

[0127] Each time step Assume a series of gas production from small to large: ;

[0128] pass Corresponding material balance time Find the corresponding ordinate in the Blasingame curve , using regularized yield The bottom hole pseudo pressure of the corresponding time step is calculated by the formula: m twi1 , m twi2 , m twi3 m twin .

[0129] Through the corresponding relationship between the bottomhole pseudo pressure and the bottomhole flowing pressure, the difference method is used to find the first bottomhole flowing pressure based on the time step: .

[0130] The second bottom hole pressure of the corresponding time step is calculated by the two-phase pipe flow pressure conversion method, specifically:

[0131] Each time step Assume that a wellhead pressure Over time The changing curve at each time Assume a series of wellhead gas production from small to large: Q i1 , Q i2 , Q i3 Q in ;

[0132] The second bottom hole pressure of the corresponding time step calculated by the two-phase pipe flow pressure conversion method is obtained: i1 , p i2 , p i3 p in .

[0133] Each time step Cumulative gas production The calculations are all based on the previous time step Calculated gas production ,and , so each time step Material balance pseudo-time equal:

[0134] .

[0135] The above embodiments are merely exemplary embodiments of the present application and are not intended to limit the scope of the present application. The scope of protection of the present application is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present application within the essence and scope of protection of the present application, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present application.

Claims

1. A method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs, characterized by: The steps include: Step 100: constructing a single-layer dimensionless mathematical model for each reservoir of the combined production well based on the model assumption, specifically including: establishing a three-linear flow model to represent the single-layer dimensionless mathematical model of the shale gas reservoir; establishing a three-linear flow inner warren-root model to represent the single-layer dimensionless mathematical model of the tight gas reservoir; establishing a five-linear flow inner warren-root model to represent the single-layer dimensionless mathematical model of the coalbed methane reservoir; The dimensionless mathematical model of each reservoir layer is transformed into a dimensionless one, and the Laplace transformation is performed on each dimensionless mathematical model of each reservoir layer and the boundary conditions and initial conditions of the corresponding model are substituted into the model to obtain the bottom hole pressure solution of the corresponding model. The assumptions based on the model include: The reservoir is a square formation, each formation is horizontal and of unequal thickness, length and width; an artificial fracture is set in the middle of the square formation, and the artificial fracture is used for constant pressure production; There are impermeable layers between the reservoirs of commingled wells with different geological characteristics, and the bottom hole flowing pressures of the reservoirs are set to be equal or similar; Step 200: Input the known gas production of the combined production well into each single-layer dimensionless mathematical model, and calculate the theoretical bottom hole pseudo-pressure value of the corresponding model using the superposition principle; Step 300: historically fitting the actual bottom hole pseudo-pressure value of each reservoir with the theoretical bottom hole pseudo-pressure value of the corresponding model of each reservoir by introducing the least square method to obtain the characterization parameters of each reservoir; Step 400: Assuming a time-dependent decrease curve of the pseudo bottom hole pressure, combined with the obtained characterization parameters of each reservoir, the predicted gas production corresponding to each single layer dimensionless mathematical model is calculated, and then the gas production of the combined production well is obtained by summing the results. Step 500: Using the obtained gas production of the commingled production well, obtain the material balance time on the abscissa and the normalized production on the ordinate of the Blasingame curve, and the calculation formula of the material balance time on the abscissa and the normalized production on the ordinate based on the time step, thereby determining the gas production of the commingled production well at the current time step; The gas production of the combined production well at the current time step is obtained to determine the influence of inter-reservoir interference between the gas production of the combined production well obtained during multi-layer combined production and the gas production of the combined production well obtained by summing.

2. The method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs according to claim 1 is characterized in that: Using the time-step-based calculation formula, assuming a series of gas production rates from small to large at each time step: The first bottom hole flowing pressure based on the time step is found through the corresponding relationship between the bottom hole pseudo pressure and the bottom hole flowing pressure, and the second bottom hole flowing pressure corresponding to the time step is calculated through the two-phase pipe flow pressure conversion method; At each time step, a curve is constructed with gas production as the horizontal coordinate and the first bottom hole flowing pressure and the second bottom hole flowing pressure as the vertical coordinate. The intersection of the two curves is found to determine the gas production of the combined production well at the current time step.

3. The method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs according to claim 1 is characterized in that: The dimensionless mathematical model of each reservoir is transformed into a dimensionless model by Laplace transformation and substituted into the boundary conditions and initial conditions assumed in the model assumption process of the trilinear flow model, the Warren-Root model within the trilinear flow, and the Warren-Root model within the pentaxial flow. After solving, the bottom hole pressure solution of the corresponding model is obtained. The specific calculation formula is: ; in, A a , B a represents the undetermined coefficients of the trilinear flow model, A b , B b represents the undetermined coefficients of the Warren-Root model in the trilinear flow, A c , B c represents the undetermined coefficients of the Warren-Root model in the five linear flows, s represents the Laplace variable; represents the dimensionless bottomhole pressure of the trilinear flow model; represents the dimensionless bottomhole pressure of the Warren-Root model in trilinear flow; represents the dimensionless bottomhole pressure of the Warren-Root model in the pentalinear flow; Represents the dimensionless boundary distance.

4. The method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs according to claim 3 is characterized in that: The known gas production of the combined production well is input into each single-layer dimensionless mathematical model. The theoretical bottom hole pseudo-pressure value of the corresponding model is calculated by the superposition principle. The specific calculation formula includes: ; in, ; ; Where, Indicates the time steps; represents the difference between two adjacent time steps; t represents the total production time; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represent the governing equations of the trilinear flow model; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represents the governing equations of the Warren-Root model in trilinear flow; represents the theoretical bottom hole pseudo-pressure of the trilinear flow model; Represent the governing equations of the Warren-Root model within the pentalinear flow; Indicates the The change in liquid production in the time step; express Liquid production in the time step; express Liquid production in the time step; Indicates the initial pressure.

5. The method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs according to claim 2 is characterized in that: The horizontal axis is material balance time, and the vertical axis is normalized output based on time step. The calculation formula specifically includes: ; in: ; Where, represents the material equilibrium time, represents the normalized yield, represents the pseudo bottom hole pressure difference, Indicates the Cumulative gas production in each time step; Indicates the current liquid production; Indicates the initial pressure; Indicates the current bottom hole flowing pressure.

6. The method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs according to claim 2, characterized in that: Through the corresponding relationship between the bottom hole pseudo pressure and the bottom hole flowing pressure, the first bottom hole flowing pressure based on the time step is found, specifically: Each time step Assume a series of gas production from small to large: ; pass Corresponding material balance time Find the corresponding ordinate in the Blasingame curve , using regularized yield The bottom hole pseudo pressure at the corresponding time step is calculated using the following formula: ; Through the corresponding relationship between the bottomhole pseudo pressure and the bottomhole flowing pressure, the difference method is used to find the first bottomhole flowing pressure based on the time step: 。 7. The method for calculating the interference mechanism between layers of multi-layer commingled production in different types of gas reservoirs according to claim 6, characterized in that: The second bottom hole pressure of the corresponding time step is calculated by the two-phase pipe flow pressure conversion method, specifically: At each time step ti, a curve of wellhead pressure phi changing with time t is assumed, and at each time ti, a series of wellhead gas production rates from small to large are assumed: ; The second bottom hole pressure corresponding to the time step calculated by the two-phase pipe flow pressure conversion method is obtained: 。

Citation Information

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