A rapid prediction method for injection-production dynamics of horizontal well groups

Abstract

The present invention discloses a method for rapid prediction of injection and production dynamics of a horizontal well group, and relates to the technical field of oil and gas exploration and development, including establishing a physical model; establishing a two-phase pseudo-pressure calculation model and solving the pseudo-pressure; regarding each horizontal injection and production well in the physical model as an equivalent vertical well, establishing a pressure drop calculation model at a certain point in the formation, and then establishing a horizontal well injection and production capacity prediction model; iteratively solving the capacity prediction model to obtain the flow distribution of each well section; substituting the obtained flow of each well section into the pressure drop calculation model, respectively, to obtain the formation pressure distribution around the injection well and the production well. The present invention effectively solves the problems of long modeling time and heavy workload of the injection and production simulation method by establishing an analytical model based on the two-phase seepage theory, and realizes rapid prediction of the injection and production dynamics of the horizontal well group.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and natural gas exploration and development, and specifically relates to a method for rapid prediction of injection and production dynamics of a horizontal well group. Background Art

[0002] Water injection is the process of injecting formation water, domestic sewage, etc. into the reservoir to increase the internal pressure of the reservoir and promote crude oil drive. It is an important way to improve recovery and achieve long-term stable production. Water injection can effectively supplement the pressure difference inside the reservoir and promote the movement of crude oil to the oil well. With the widespread application of horizontal well technology in oil production, the accuracy and reliability of its production capacity prediction are constantly increasing.

[0003] Existing injection-production well network capacity prediction models are mainly based on potential function theory, mirror reflection principle and superposition principle, such as the models established by Lang Zhaoxin, Qu Debin, Li Chunlan, Cheng Linsong and Zhao Chunsen. These models mainly focus on the joint injection-production well network of horizontal wells and vertical wells, focusing on the impact of potential difference on the total production of horizontal wells, and cannot quantitatively characterize the flow distribution along the horizontal well. Chinese patent CN106779211A introduces the concept of comprehensive displacement coefficient, and weights the results calculated by three methods: empirical formula, analytical equation and numerical simulation. The establishment of this model requires a lot of data support and has a limited scope of application. Based on the water drive front theory, Wang Quanlin and others calculated the injection and production volume by the distance between injection and production wells, but the model assumes that the oil production wells are single-phase flow and ignores the impact of oil-water two-phase flow on production.

[0004] In summary, existing methods have limitations when dealing with complex well patterns, especially for the dynamic prediction of horizontal well injection and production groups with oil-water two-phase flow. In order to meet the needs of injection and production dynamics of horizontal well groups under different modes (such as one injection and one production and one injection and two production), a fast and accurate prediction method is needed. Summary of the invention

[0005] To solve the above problems, the present invention aims to establish a method for dynamic prediction of injection and production of horizontal well groups that can take into account oil-water two-phase flow. The method quantitatively characterizes the flow distribution along the horizontal well, thereby achieving accurate prediction of injection and production volume and rapid calculation of formation pressure around the well.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0007] A method for rapid prediction of injection-production dynamics of a horizontal well group comprises the following steps:

[0008] S1: Establish a physical model; the top and bottom of the circular formation in the physical model are closed boundaries, with stable edge water, the reservoir thickness is h, the oil leakage radius is re, the flat plate type is kept closed vertically, and the edge is under constant pressure. The horizontal well in the physical model is located in the middle of the reservoir, and the influence of the pressure drop in the wellbore is not considered. The oil and water flow meets the Darcy seepage condition;

[0009] S2. Based on the physical model, considering the oil-water two-phase flow, a two-phase pseudo-pressure calculation model is established; the pseudo-pressure is solved by combining the pseudo-pressure calculation model and the phase permeability curve;

[0010] As a specific implementation of the present invention, step S2 mainly includes the following sub-steps:

[0011] S2-1: Based on the physical model and assumptions of S1, the motion equations of the oil phase and the water phase are obtained as follows:

[0012]

[0013] S2-2: Define the water-oil mass ratio as:

[0014]

[0015] Among them, m w 、m o Represent the mass of water and oil, kg; ρ w , o Represents the density of water and oil, kg / m 3 ;q w ,q o Represent the flow rate of water and oil, m 3 / d;ρ wsc , osc Respectively represent the density of water and oil under standard ground conditions, kg / m 3 ;k h is the reservoir permeability, mD; μ w , μ o are the viscosities of water and oil, mPa·s; k ro , k rw Represent the relative permeability of oil and water respectively; dp / dr represents the pressure gradient of the formation, MPa / m. S2-3: Combining equations (1), (2) and (3), separating the variables and integrating them, we can obtain:

[0016]

[0017] in, Defined as the oil-water two-phase pseudo pressure:

[0018]

[0019] p e 、p wf Respectively represent the formation and bottom hole pressure, MPa; R wo represents the water-oil mass ratio; r w Represents the radius of the wellbore; Indicates the pseudo pressure of oil and water phases corresponding to pressure p, kg / m 3 ×(mPa·s) -1 .

[0020] S2-4: The changes in the viscosity and density of water with pressure can be ignored. The change in the viscosity-density ratio of oil with pressure is given by experimental data or empirical formulas. Combined with the phase permeability curve, the functional relationship between pseudo-pressure and pressure at a certain water saturation can be obtained.

[0021] S3: Based on the concept of equivalent well diameter, each horizontal injection and production well in the physical model is regarded as an equivalent vertical well, and a pressure drop calculation model for a certain point in the formation is established: for horizontal injection and production wells, each horizontal well is divided into n sections, and the half length of each section is L i Each horizontal well can be equivalent to n wells with a radius of r wei The total number of horizontal injection wells is N, of which N is horizontal injection well. inj The equivalent vertical wells in the horizontal injection wells are ranked from 1 to N. inj n is the mark, and the equivalent vertical well of the horizontal production well is N inj If the number of wells is marked from n+1 to Nn, the pressure drop at any point M in the formation is the algebraic sum of the pressure drops produced at that point when each equivalent vertical well works alone.

[0022] As a specific implementation of the present invention, step S3 mainly includes the following sub-steps:

[0023] S3-1: For water injection wells, calculate the pressure drop caused by each equivalent vertical well to any point M in the formation as:

[0024]

[0025] S3-2: For production wells, calculate the pressure drop caused by each equivalent vertical well to any point M in the formation as:

[0026]

[0027] Among them, d i,M represents the distance from the ith equivalent vertical well to point M. If the coordinates of the ith well are (x i ,y i ,z i ), the coordinates of point M are (x 0 ,y 0 ,z 0 ),but q irepresents the flow rate of the i-th well, m 3 / d.

[0028] S3-3: Combining steps S3-1 and S3-2, comprehensively considering the influence of production wells and water injection wells, the pressure drop generated at any point M in the formation under horizontal well injection and production is obtained as:

[0029]

[0030] S4: Based on the pressure drop calculation model, the bottom hole pressure drop is given to establish a horizontal well injection and production capacity prediction model: According to the assumption that the wellbore in step S1 is infinitely conductive, that is, the bottom hole pressure of each equivalent vertical well of the water injection well is: Bottom hole pressure of each equivalent vertical well of production well: Combined with step S3-3, p M Replace it with the bottom hole pressure of each well section and establish a horizontal well injection and production capacity prediction model:

[0031]

[0032] Among them, p 1wf,inj 、p 2wf,inj , Respectively represent the marks 1, 2, and N inj n the bottom hole pressure of a horizontal water injection well; p Nnwf,pro Respectively indicated by N inj n+1、N inj n+2, bottom hole pressure of horizontal recovery well Nn; p Nwfi represents the bottom hole pressure of the ith equivalent vertical well, MPa; d i,j Represents the distance from the i-th well to the j-th well.

[0033] S5: For the non-homogeneous linear equations of the horizontal well injection and production capacity prediction model (Equation (9)), given the bottom hole pressures of the injection well and the production well, the Gauss-Seidel iteration is used to solve the flow distribution of each well section.

[0034] In particular, step S5 mainly includes the following sub-steps:

[0035] S5-1: Perform dimensional analysis and convert to commonly used units in the mine. The converted expression is as follows:

[0036]

[0037] Among them, p e 、p wf Respectively represent the formation and bottom hole pressure, MPa; k h is the reservoir permeability, mD; h is the reservoir thickness, m; r eis the distance from the supply edge to the well center, m; d i,j represents the distance from the i-th well to the j-th well, m; B is the crude oil volume coefficient; q i represents the flow rate of the i-th well, m 3 / d;μ w , μ o are the viscosities of water and oil, mPa·s, respectively.

[0038] S5-2: For ease of expression, the linear equations shown in equation (10) are converted into matrix form:

[0039] P=Aq (11)

[0040] in,

[0041]

[0042] q=[q 1 ,q 2 ,…q Nn-1 ,q Nn ] T ,

[0043]

[0044] S5-3: Initial solution of a given system of equations The initial solution vector is

[0045] S5-4: Iterate according to the Gauss-Seidel iterative formula to update the value of the unknown number:

[0046]

[0047] in, represents the flow rate solution of the i-th and j-th equivalent vertical wells after the k+1th iteration update; represents the flow solution of the jth equivalent vertical well after the kth iteration update; P i A represents the bottom hole pressure of the ith equivalent vertical well; ij , A ii They represent the i-th row and j-th column and the i-th row and i-th column of the coefficient matrix A respectively.

[0048] S5-5: Given a convergence criterion, when |q (k+1) -q (k) |When it is less than a preset threshold, the equation meets the accuracy requirement and the iteration stops; in addition, the maximum number of iterations N is set max , which can ensure that when the solution reaches an acceptable accuracy or maximum error limit after a finite number of iterations, the iterative process can be automatically terminated to avoid infinite iterations.

[0049] S6: Substitute the obtained flow rate of each well section into the pressure drop calculation model (Formula (8)) to obtain the formation pressure distribution around the injection well and the production well.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention regards the horizontal well injection and production system as several equivalent vertical wells, uses the pseudo-pressure function to characterize the oil-water two-phase flow, and characterizes the flow characteristics and pressure change mutual influence relationship between the injection and production wells based on the pressure drop superposition theory. By establishing an analytical model based on the two-phase seepage theory, the problems of long modeling time and large workload of the injection and production simulation method are effectively solved, and the rapid prediction of the injection and production dynamics of the horizontal well group is realized. At the same time, the present invention helps to optimize the injection and production parameters of the well group in the actual oil field development and management, and improve the oil production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below.

[0053] Figure 1 A flowchart of a method for rapid prediction of injection and production dynamics of a horizontal well group in the present invention;

[0054] Figure 2 A schematic diagram of a physical model of a horizontal well in a circular formation according to an embodiment of the present invention;

[0055] Figure 3 The oil-water relative permeability curve of the formation in one embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram of segment marking of a horizontal well one injection and one production well group in one embodiment of the present invention;

[0057] Figure 5 This is a schematic diagram of segment markings for a horizontal well with one injection and two production well groups in one embodiment of the present invention;

[0058] Figure 6 A flow rate distribution diagram along a horizontal section of a horizontal well-injection-production well group in one embodiment of the present invention;

[0059] Figure 7 A flow rate distribution diagram along a horizontal section of a horizontal well with one injection and two production well groups in one embodiment of the present invention;

[0060] Figure 8 A diagram showing the formation pressure distribution around a horizontal well with one injection and one production in one embodiment of the present invention;

[0061] Fig. 9 This is a diagram of formation pressure distribution around a horizontal well with one injection and two productions in one embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The described embodiments are 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 creative work are within the scope of protection of the present invention.

[0063] In order to verify the above injection-production well dynamic prediction method, actual data from an oil field is used for analysis and calculation. Figure 1 As shown, in this embodiment, the process of the horizontal well injection and production dynamic prediction method mainly includes the following steps:

[0064] S1: Establish a physical model and give the model assumptions. The top and bottom of the circular formation are closed boundaries with stable edge water, the reservoir thickness is h, the oil leakage radius is re, the vertical direction is flat and closed, and the edge is under constant pressure. The horizontal well is located in the middle of the reservoir zw. The influence of the pressure drop in the wellbore is not considered, and the oil and water flow meets the Darcy seepage condition. The required reservoir and horizontal well parameters are shown in Table 1. The schematic diagram of the physical model of the horizontal well in the circular formation is shown in Figure 2 shown.

[0065] Table 1 Basic parameters of reservoir and horizontal well

[0066]

[0067] S2: Considering the oil-water two-phase flow, calculate the two-phase pseudo-pressure. Define the oil-water two-phase pseudo-pressure as:

[0068]

[0069] The viscosity and density of water hardly change with pressure and can be regarded as constants. The relationship between the viscosity and density of oil and pressure obtained from experimental data is shown in Table 2. Figure 3 Substituting the phase permeability curve into the definition of pseudo-pressure can obtain the corresponding relationship between pseudo-pressure and pressure.

[0070] Table 2 Variation of crude oil viscosity-density ratio with pressure

[0071]

[0072]

[0073] S3: Divide each horizontal well into n = 20 segments, then the length of each segment is L i If the diameter is 50m, each section can be equivalent to the well diameter r wei vertical wells, it is equivalent to having 20 wells with a radius of r wei According to Figure 2 The physical model and coordinate axis position of the well, the coordinate of the i-th well is (x i ,y i ,z w ). Mark the segment numbers of the injection-production horizontal well. In particular, the segment numbers of one injection-one production and one injection-two production are as follows: Figure 4 and Figure 5 As shown. The injection wells are marked as 1, 2, ..., 20; the production well 1 is marked as 21, 22 ..., 40; the production well 2 is marked as 41, 42 ..., 60. N represents the number of wells in the well group. For a horizontal well with one injection and one production, N = 2; for a horizontal well with one injection and two production, N = 3. inj =1. According to the principle of pressure drop superposition, the pressure distribution at any point M in the formation is:

[0074]

[0075] Among them, d i,M represents the distance from the ith equivalent vertical well to point M. If the coordinates of point M are (x 0 ,y 0 ,z 0 ),but

[0076] S4: Based on the assumption of infinite wellbore conductivity, for water injection wells: p 1wf,inj =p 2wf,inj =…=p nwf,inj =25MPa; production well: p n+1wf,pro =p n+2wf,pro =…=p Nnwf,pro =15MPa. Combined with the pressure distribution expression at any point in the formation, p M Replace it with the bottom hole pressure of each well section and establish a horizontal well injection and production capacity prediction model:

[0077]

[0078] Among them, d i,j represents the distance from the i-th equivalent vertical well to the j-th well. The distance between the injection and production wells d is 300m.

[0079]

[0080] S5: The Gauss-Seidel iteration is used to solve the above equation, and the flow distribution of each well section of the horizontal well with one injection and one production is obtained as follows Figure 6 As shown in the figure, the flow rate distribution along the well is generally in the shape of a "U": this is because the supply range at the heel and toe is large, presenting a quasi-hemispherical flow, while the range in the middle is small, presenting a quasi-linear flow. Figure 7As shown, its oil production is symmetrically distributed along the well section, the injection volume is distributed in a "U" shape, and the total flow rate Q of the horizontal well is the sum of the flow rates of each section.

[0081] Specifically, S5 can be divided into the following sub-steps:

[0082] First, we conduct dimensional analysis and conversion. The dimensions are unified into practical units of the mine field. The unified expression is:

[0083]

[0084] Secondly, the linear equations are converted into matrix form for easy programming and solving.

[0085] P=Aq (18)

[0086] in,

[0087]

[0088] q=[q 1 ,q 2 ,…q Nn-1 ,q Nn ] T ,

[0089]

[0090] Then, assign an initial value to the solution vector The initial solution vector is

[0091] Next, the Gauss-Seidel iteration formula is used to iterate and update the value of the unknown number:

[0092]

[0093] Finally, the convergence criterion is given, when |q (k+1) -q (k) |When it is less than 0.00001, the equation meets the accuracy requirement and the iteration stops; the maximum number of iterations N is set max For 100 times.

[0094] S6: Based on the obtained flow rate distribution of each section of the horizontal well, substitute back to step S3 to obtain the formation pressure distribution around the well group of one injection and one production and one injection and two production of the horizontal well, such as Figure 8 and Fig. 9 shown.

[0095] The above description is not intended to impose any form of limitation on the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for rapid prediction of injection and production dynamics of a horizontal well group, characterized in that: The following steps are involved: S1. Establish a physical model; the top and bottom of the circular formation in the physical model are closed boundaries, with stable edge water, a flat plate-type closure is maintained vertically, and the edge has a constant pressure. The horizontal well of the physical model is located in the middle of the reservoir, and the oil and water flow meets the Darcy seepage condition; S2. Based on the physical model, considering the oil-water two-phase flow, a two-phase pseudo-pressure calculation model is established, and the pseudo-pressure is solved by combining the pseudo-pressure calculation model and the phase permeability curve; S3. Treat each horizontal injection and production well in the physical model as an equivalent vertical well, and establish a pressure drop calculation model for a certain point in the formation: for horizontal injection and production wells, divide each horizontal well into n sections, and each horizontal well is equivalent to n wells with a radius of r. wei The total number of horizontal injection wells is N, of which N is horizontal injection well. inj The equivalent vertical wells in the horizontal injection wells are ranked from 1 to N. inj n is the mark, and the equivalent vertical well of the horizontal production well is N inj n+1 to Nn are marked, then the pressure drop at any point M in the formation is the algebraic sum of the pressure drops produced at that point when each equivalent vertical well works alone; S4, calculating the bottom hole pressure drop based on the pressure drop calculation model, thereby establishing a horizontal well injection and production capacity prediction model; S5. Given the bottom hole pressures of the injection well and the production well, the non-homogeneous linear equations of the horizontal well injection and production capacity prediction model are solved iteratively to obtain the flow distribution of each well section; S6, substituting the flow rate of each well section obtained in step S5 into the pressure drop calculation model to obtain the formation pressure distribution around the injection well and the production well; The pseudo-pressure calculation model in step S2 includes: In the formula, represents the pseudo pressure of the oil-water phase corresponding to pressure p, p e 、p wf Represent the formation and bottom hole pressure respectively; R wo represents the water-oil mass ratio; ρ osc Indicates the density of oil under standard ground conditions; k h is the reservoir permeability; h is the reservoir thickness; r e Indicates the oil leakage radius; r w Represents the radius of the wellbore; k ro , k rw Represent the relative permeability of oil and water respectively; ρ w , o Represent the density of water and oil respectively; μ w , μ o are the viscosities of water and oil respectively; The horizontal well injection and production capacity prediction model in step S4 includes: In the formula, p e represents the formation flow pressure; p Nwfi represents the bottom hole pressure of the ith equivalent vertical well; R wo represents the water-oil mass ratio; ρ osc Indicates the density of oil under standard ground conditions; q i represents the flow rate of the i-th well; B is the crude oil volume coefficient; k h is the reservoir permeability; h is the reservoir thickness; r e Indicates the oil leakage radius; d i,j represents the distance from the i-th well to the j-th well; In step S5, Gauss-Seidel iteration is used to solve the problem, which includes the following steps: S51. The horizontal well injection and production capacity prediction model is converted into mine units. The converted linear equation group is: S52, converting the converted linear equations into a matrix form; P=Aq S53. Given an initial solution and a convergence criterion, the solution is iteratively updated according to the Gauss-Seidel iterative formula until the convergence criterion is met.

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