Fractured medium SDVA self-diverting acid acidification numerical simulation method
The numerical simulation method of SDVA self-steering acid acid acid acid acid is constructed through embedded discrete fracture model, which solves the problem that acid solution in the reservoir is difficult to enter the low permeability area, and realizes accurate simulation and efficiency improvement of the acidification process of complex fracture reservoirs.
Patent Information
- Application Number
- CN202411416261.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-11
- Publication Date
- 2025-01-17
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
In reservoirs with huge differences in pore structure or permeability characteristics, it is difficult for the acid to enter the low permeability area that needs to be improved smoothly, resulting in poor acidification effect. The traditional TSC acidification model cannot effectively deal with complex cracks.
The numerical simulation method of SDVA self-steering acid acid acid acid acid is constructed using embedded discrete fracture model, including building a physical model, dividing matrix and fracture grid, establishing SDVA self-steering acid flow reaction model and pore seepage evolution model, and solving the problem through coupling iteration. Update the viscosity parameters to simulate the flow and reaction process of acid liquid in complex cracks.
Accurate simulation of the SDVA self-steering acid acid acid acid acid acid acid acid acid acid acid in complex fracture reservoirs, making up for the limitations of traditional models in handling material transportation between fractures and substrates, and improving the distribution efficiency of acid liquid in low permeability areas.
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Figure CN119324000A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of acidizing, and in particular to a numerical simulation method for SDVA self-steering acidizing of fractured media. Background Art
[0002] Fractured reservoirs are a common type of fractured media. Due to their developed fracture systems, the effect of oil and gas extraction is poor. Acidizing is a common means of reservoir production enhancement. Acidizing is usually used to improve or restore productivity. However, in reservoirs with huge differences in pore structure or permeability characteristics, the acid often enters the area with the highest permeability first, while the acid that enters the low permeability area that needs to be improved the most rarely leads to a continuous increase in the variation of permeability characteristics within and between layers. Therefore, for this type of reservoir, whether the acid can smoothly enter the area that needs to be improved is the key to acidizing.
[0003] Self-steering acid is a liquid used for acidizing fractured reservoirs. It uses specific surfactants (such as viscoelastic surfactants) to achieve self-guiding and distribution of the acid in the reservoir. By changing the viscosity and rheological properties of the acid, the acid is directed to low permeability areas for acidizing, thereby improving the production efficiency of the oil well. However, the rheological behavior and diversion mechanism of self-steering acid are relatively complex, so numerical simulation is needed to study the acidizing mechanism of self-steering acid in fractured reservoirs. The numerical simulation of self-steering acid acidizing in fractured reservoirs needs to consider the material exchange between the large number of natural fractures developed and the matrix. The traditional TSC acidizing model is often used for processing, but this type of model can only handle simple fractures and cannot cope with the situation where there are a large number of complex fractures. Summary of the invention
[0004] In view of the above problems, the present invention aims to provide a numerical simulation method for SDVA self-diverting acidizing of fractured media.
[0005] The technical solution of the present invention is as follows:
[0006] A numerical simulation method for SDVA self-steering acidizing of fractured media includes the following steps:
[0007] S1: Construct a physical model for numerical simulation of SDVA self-steering acidizing in fractured media;
[0008] S2: Using the embedded discrete fracture model, the matrix grid and fracture grid are divided based on the physical model, and basic grid parameters are assigned;
[0009] S3: constructing a numerical model of SDVA self-diverting acid acidizing for fractured media based on an embedded discrete fracture model, wherein the numerical model of SDVA self-diverting acid acidizing for fractured media includes a SDVA self-diverting acid flow reaction model and a porosity and permeability evolution model, and the SDVA self-diverting acid flow reaction model includes a SDVA self-diverting acid flow model and a SDVA self-diverting acid reaction model;
[0010] S4: coupling iterative solution of the SDVA self-steering acid acidizing numerical model of the fractured medium established in step S3;
[0011] S5: Determine whether the wormhole in the current time step has been broken through:
[0012] If there is no breakthrough, continue the numerical simulation of the next time step, update the self-steering acid viscosity, and repeat steps S4-S5;
[0013] If a breakthrough is achieved, the numerical simulation results of SDVA self-steering acidizing in fractured media are obtained.
[0014] Preferably, in step S3, the SDVA self-steering acid flow model includes a matrix acid flow control equation, a fracture acid flow control equation and a matrix-fracture acid cross-flow equation;
[0015] The matrix acid flow control equation and the fracture acid flow control equation are respectively as follows:
[0016]
[0017] Where: and They are the divergence operators in the overall three-dimensional rectangular coordinate system of the fractured medium and the local two-dimensional rectangular coordinate system of the fracture surface respectively; and are the gradient operators in the overall three-dimensional rectangular coordinate system of the fractured medium and the local two-dimensional rectangular coordinate system of the fracture surface, respectively; K m , K f are the matrix and fracture permeabilities, m 2 ;μ eff is the apparent viscosity of the self-diverting acid in the matrix or fracture, Pa·s; P m , P f are the pressure of matrix and crack, Pa; Q m , Q f are the matrix and the source phase of the fracture, respectively, m 3 / s;I mf and I ff are the cross-flow velocity terms between matrix and crack and between crack and crack, respectively, m 3 / s;
[0018] The matrix-fracture acid fluid crossflow equation is:
[0019]
[0020] Where: U m and U f are the seepage velocities in the matrix and fractures, m / s, respectively.
[0021] Preferably, the crossflow velocity terms between the matrix and the crack and between the cracks are calculated by the following formulas:
[0022]
[0023] I ff =L(P i -P j ) (6)
[0024] Where: Υ is the cross-flow coefficient between the matrix and the fracture, dimensionless; L is the overall cross-flow coefficient between the fracture units, dimensionless; P i , P j are the pressure of fracture unit i and the pressure of fracture unit j, Pa, respectively.
[0025] Preferably, the cross-flow coefficient Y between the matrix and the crack and the overall cross-flow coefficient L between the crack units are calculated by the following formulas:
[0026]
[0027] Where: L i,k is the length of crack unit k within matrix unit i, m; <d> i,k is the average distance between matrix unit i and crack unit k, m; α i , α j are the crossflow coefficients of fracture unit i and fracture unit j, dimensionless; FA i is the aperture of fracture unit i, m; λ t,i is the total fluidity of fracture unit i, dimensionless; dx f is the spacing between crack elements, m.
[0028] Preferably, in step S3, the SDVA self-steering acid reaction model includes H + Concentration equation, Ca in matrix and cracks 2+ concentration equations and SDVA concentration equations in the matrix and fractures;
[0029] The H in the matrix and cracks + The concentration equation is:
[0030]
[0031] Where: φ m and φ f are the porosity of matrix and fracture, respectively; C m,H+ and are the hydrogen ion concentrations in the matrix and cracks, kmol / m 3 ; t is time, s; For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of hydrogen ions in the matrix and cracks, m / s; X m and X f are the hydrogen ion consumption terms in the matrix and cracks, kmol / (m 2 s);
[0032] The Ca in the matrix and cracks 2+ The concentration equation is:
[0033]
[0034] Where: C m,Ca and C f,Ca are the calcium ion concentrations in the matrix and cracks, kmol / m 3 ; C Ca up For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of calcium ions in the matrix and cracks, respectively, m / s;
[0035] The equation for the SDVA concentration in the matrix and fractures is:
[0036]
[0037] Where: C m,SDVA and C f,SDVA are the SDVA concentrations in the matrix and fractures, kmol / m 3 ; C SDVA up For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of self-diverting acid in the matrix and fractures, respectively, m / s.
[0038] Preferably, in step S3, the porosity evolution model is:
[0039]
[0040] Where: φ is the matrix or fracture porosity; R(C s ) is the acid consumption rate in the matrix or fracture, kmol / (s·m 2 );a v is the pore specific surface area, m 2 / m 3 ; α c is the acid solubility, kg / kmol; ρ s is the rock density, kg / m 3 ; K init , K new are the initial and post-dissolution permeabilities, m 2 ; φ init ,φ new are the initial and post-dissolution porosity, dimensionless; β is an empirical parameter, dimensionless; r p,init 、r p,new are the initial and post-dissolution pore radius, m; a v,init 、a v,new are the initial and post-dissolution pore specific surface areas, m 2 / m 3 ; are the effective diffusion coefficients in the x and y directions, m / s; α os , L , T are constants related to pore structure and are dimensionless; D e is the effective diffusion coefficient in the matrix or fracture, m / s; |U| is the modulus of the seepage velocity, m / s; r p is the pore radius, m.
[0041] Preferably, in step S5, the self-steering acid viscosity is updated using the following formula:
[0042]
[0043] Where: μ eff , μ0, μ max are the apparent viscosity, initial viscosity and maximum viscosity of the self-diverting acid in the matrix or fracture, Pa·s; n is the power index; K is the matrix or fracture permeability, m 2 ; φ is the matrix or fracture porosity; C SDVA , C Ca are SDVA and the concentration of calcium ions in the matrix or cracks, kmol / m 3 ; C max,SDVA , C max,Ca are SDVA and the maximum concentration of calcium ions in the matrix or cracks, kmol / m 3 ; W1, W2, W3, b, c are all empirical coefficients; pH is the pH value of the acid system in the matrix or crack at a certain moment.
[0044] The beneficial effects of the present invention are:
[0045] The SDVA self-diverting acid acidizing model for fractured media constructed based on the embedded discrete fracture model method in the present invention can make up for the limitations in treating the material transport between fractures and matrix compared with the traditional self-diverting acid acidizing model, and takes into account the influence of complex natural fractures on SDVA self-diverting acid acidizing, so as to achieve accurate simulation of the SDVA self-diverting acid acidizing process of fractured media single-phase, and provide a numerical simulation method for SDVA self-diverting acid acidizing of fractured media, which is of great significance for the simulation of self-diverting acid acidizing with complex fractures. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.
[0047] Figure 1 It is a schematic flow chart of the numerical simulation method of SDVA self-diverting acid acidizing of fractured media of the present invention;
[0048] Figure 2 A schematic diagram of a physical model used in calculations of a specific embodiment of the present invention;
[0049] Figure 3 This is a schematic diagram of the morphology distribution of wormholes injected with conventional acid according to a specific embodiment of the present invention; wherein W represents the water phase; T inject :353.15 means the injection temperature is 353.15K;
[0050] Figure 4 This is a schematic diagram of the wormhole morphology distribution of a wormhole injected with self-diverting acid according to a specific embodiment of the present invention. DETAILED DESCRIPTION
[0051] The present invention is further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, in the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other. It should be pointed out that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as those generally understood by ordinary technicians in the technical field to which this application belongs. The words "including" or "comprising" and the like used in the disclosure of the present invention mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.
[0052] like Figure 1 As shown, the present invention provides a numerical simulation method for SDVA self-steering acidizing of fractured media, comprising the following steps:
[0053] S1: Construct a physical model for numerical simulation of SDVA self-diverting acidizing in fractured media.
[0054] S2: Using the embedded discrete fracture model, the matrix grid and fracture grid are divided based on the physical model, and basic grid parameters are assigned.
[0055] In a specific embodiment, the grid-based parameters include reservoir matrix porosity, fracture porosity, fracture permeability, and acid solubility.
[0056] S3: A numerical model of SDVA self-diverting acid acidizing of fractured media is constructed based on an embedded discrete fracture model, wherein the numerical model of SDVA self-diverting acid acidizing of fractured media includes a SDVA self-diverting acid flow reaction model and a porosity and permeability evolution model, and the SDVA self-diverting acid flow reaction model includes a SDVA self-diverting acid flow model and a SDVA self-diverting acid reaction model.
[0057] In a specific embodiment, the SDVA self-diverting acid flow model includes matrix acid flow control equations, fracture acid flow control equations, and matrix-fracture acid cross-flow equations;
[0058] The matrix acid flow control equation and the fracture acid flow control equation are respectively as follows:
[0059]
[0060] Where: and They are the divergence operators in the overall three-dimensional rectangular coordinate system of the fractured medium and the local two-dimensional rectangular coordinate system of the fracture surface respectively; and are the gradient operators in the overall three-dimensional rectangular coordinate system of the fractured medium and the local two-dimensional rectangular coordinate system of the fracture surface, respectively; K m , K f are the matrix and fracture permeabilities, m 2 ;μ eff is the apparent viscosity of the self-diverting acid in the matrix or fracture, Pa·s; P m , P f are the pressure of matrix and crack, Pa; Q m , Q f are the matrix and the source phase of the fracture, respectively, m 3 / s;I mf and I ff are the cross-flow velocity terms between matrix and crack and between crack and crack, respectively, m 3 / s;
[0061] The matrix-fracture acid fluid crossflow equation is:
[0062]
[0063] Where: U m and U f are the seepage velocities in the matrix and fractures, m / s, respectively.
[0064] It should be noted that the above matrix-fracture acid fluid crossflow equation is a calculation equation for the seepage velocity in the matrix and fractures under the Darcy seepage system.
[0065] In a specific embodiment, the crossflow velocity terms between the matrix and the crack and between the cracks are calculated by the following formulas:
[0066]
[0067] I ff =L(P i -P j ) (6)
[0068] Where: Υ is the cross-flow coefficient between the matrix and the fracture, dimensionless; L is the overall cross-flow coefficient between the fracture units, dimensionless; P i , P j are the pressure of fracture unit i and the pressure of fracture unit k, Pa respectively.
[0069] In a specific embodiment, the cross-flow coefficient Y between the matrix and the crack and the overall cross-flow coefficient L between the crack units are calculated by the following formulas:
[0070]
[0071]
[0072] Where: L i,k is the length of crack unit k within matrix unit i, m; <d> i,k is the average distance between matrix unit i and crack unit k, m; α i , α j are the crossflow coefficients of fracture unit i and fracture unit j, dimensionless; FA i is the aperture of fracture unit i, m; λ t,i is the total fluidity of fracture unit i, dimensionless; dx f is the spacing between crack elements, m.
[0073] In a specific embodiment, the SDVA self-diverting acid reaction model includes H in the matrix and fracture + Concentration equation, Ca in matrix and cracks 2+ concentration equations and SDVA concentration equations in the matrix and fractures;
[0074] The H in the matrix and cracks + The concentration equation is:
[0075]
[0076] Where: φ m and φ f are the porosity of matrix and fractures, respectively; and are the hydrogen ion concentrations in the matrix and cracks, kmol / m 3 ; t is time, s; For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of hydrogen ions in the matrix and cracks, m / s; X m and X f are the hydrogen ion consumption terms in the matrix and cracks, kmol / (m 2 s);
[0077] The Ca in the matrix and cracks 2+ The concentration equation is:
[0078]
[0079] Where: C m,Ca and C f,Ca are the calcium ion concentrations in the matrix and cracks, kmol / m 3 ; C Ca up For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of calcium ions in the matrix and cracks, respectively, m / s;
[0080] The equation for the SDVA concentration in the matrix and fractures is:
[0081]
[0082]
[0083] Where: C m,SDVA and c f,SDVA are the SDVA concentrations in the matrix and fractures, kmol / m 3 ; C SDVA up For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of self-diverting acid in the matrix and fractures, respectively, m / s.
[0084] In a specific embodiment, the porosity evolution model is:
[0085]
[0086] Where: φ is the matrix or fracture porosity; R(C s ) is the acid consumption rate in the matrix or fracture, kmol / (s·m 2 );a v is the pore specific surface area, m 2 / m 3 ; α c is the acid solubility, kg / kmol; ρ s is the rock density, kg / m 3 ; K init , K new are the initial and post-dissolution permeabilities, m 2 ; φ init ,φ new are the initial and post-dissolution porosity, dimensionless; β is an empirical parameter, dimensionless; r p,init 、r p,new are the initial and post-dissolution pore radius, m; a v,init 、a v,new are the initial and post-dissolution pore specific surface areas, m 2 / m 3 ; are the effective diffusion coefficients in the x and y directions, m / s; α os , L , T are constants related to pore structure and are dimensionless; D e is the effective diffusion coefficient in the matrix or fracture, m / s; |U| is the modulus of the seepage velocity, m / s; r p is the pore radius, m.
[0087] In the above implementation, the porosity, permeability, specific surface area and effective diffusion coefficient in the matrix or fracture can be updated through the porosity and permeability evolution model.
[0088] S4: Couple iteratively solve the SDVA self-steering acidizing numerical model of the fractured medium established in step S3.
[0089] S5: Determine whether the wormhole in the current time step has been broken through:
[0090] If there is no breakthrough, continue the numerical simulation of the next time step, update the self-steering acid viscosity, and repeat steps S4-S5;
[0091] If a breakthrough is achieved, the numerical simulation results of SDVA self-steering acidizing in fractured media are obtained.
[0092] In a specific embodiment, the self-steering acid viscosity is updated using the following formula;
[0093]
[0094] Where: μ eff , μ0, μ m3x are the apparent viscosity, initial viscosity and maximum viscosity of the self-diverting acid in the matrix or fracture, Pa·s; u is the power index; K is the matrix or fracture permeability, m 2 ; φ is the matrix or fracture porosity; C SDVA , C Ca are SDVA and the concentration of calcium ions in the matrix or cracks, kmol / m 3 ; C max,SDVA , C max,Ca are SDVA and the maximum concentration of calcium ions in the matrix or cracks, kmol / m 3 ; W1, W2, W3, b, c are all empirical coefficients; pH is the pH value of the acid system in the matrix or crack at a certain moment.
[0095] It should be noted that the method for determining whether a wormhole has been breached is a prior art, and the specific determination method will not be described in detail here.
[0096] It should be noted that, in addition to being applicable to SDVA self-steering acid, other self-steering acids in the prior art that have a similar mechanism to SDVA self-steering acid may also be applicable to the present invention.
[0097] In a specific embodiment, taking a fractured reservoir as an example, the fractured medium SDVA self-steering acid acidification numerical simulation method of the present invention is used to perform acidification numerical simulation, which specifically includes the following steps:
[0098] (1) Construct a physical model for numerical simulation of SDVA self-diverting acidizing in fractured media.
[0099] In this embodiment, the physical model used is as follows Figure 2 As shown, the core scale is 0.3m×0.1m (length×height). The rock contains natural fractures. The self-redirecting acid is injected from the left side of the rock, dissolving the rock and producing Ca 2+ Mixed with the waste acid, it forms a high viscosity area, forcing the acid to change its flow direction and achieve uniform acidification.
[0100] (2) Using the embedded discrete fracture model, the matrix grid and fracture grid are divided based on the physical model, and basic grid parameters are assigned.
[0101] In this embodiment, the matrix area of the physical model of step (1) is meshed using a structured uniform grid. Complex fractures are randomly displayed and generated, and the fractures generated in the physical model are meshed using a structured uniform grid. The natural fractures are located inside the matrix. The physical property values include the reservoir matrix porosity of 0.02, the fracture porosity of 0.99, the fracture permeability of 1e -10 m 2 and acid solubility of 50 kg / kmol.
[0102] (3) Based on the embedded discrete fracture model, a numerical model of SDVA self-steering acidizing of fractured media is constructed as shown in equations (1)-(4) and (10)-(24).
[0103] (4) The numerical model of SDVA self-steering acidizing of fractured media established in step (3) is coupled with the iterative solution.
[0104] (5) Determine whether the wormhole of the current time step has been broken through: if not, continue the numerical simulation of the next time step, update the model parameters such as the self-steering acid viscosity, and repeat steps S4-S5; if it has been broken through, obtain the numerical simulation results of SDVA self-steering acid acidizing of fractured media.
[0105] In this embodiment, the empirical coefficients W1, W2, W3, b, and c in the empirical formula for calculating the apparent viscosity of the self-diverting acid are 0.0173, 1.1, 2, 1, and 1, respectively.
[0106] In this embodiment, the breakthrough condition for determining whether the wormhole is broken is defined as the acid injection pressure being reduced to 2% of the initial acid injection pressure.
[0107] In this embodiment, Figure 3-4 The figure shows the difference between self-redirecting acid and conventional acid in single-phase acidizing. The wormhole branches of conventional acid are fewer and closer than those of self-redirecting acid. For example, the branches of self-redirecting acid can be redirected and connected to natural fractures, while the branches of conventional acid only produce many small branches due to the influence of porosity, causing acid diversion and failing to develop branches, resulting in closer branch development.
[0108] In summary, the present invention can accurately simulate the SDVA self-diverting acidizing process of fractured media. Compared with the prior art, the present invention has significant progress.
[0109] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments 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 according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.< / d> < / d>
Claims
1. A numerical simulation method for SDVA self-diverting acid acidizing of fractured media, characterized in that: The following steps are involved: S1: Construct a physical model for numerical simulation of SDVA self-steering acidizing in fractured media; S2: Using the embedded discrete fracture model, the matrix grid and fracture grid are divided based on the physical model, and basic grid parameters are assigned; S3: constructing a numerical model of SDVA self-diverting acid acidizing for fractured media based on an embedded discrete fracture model, wherein the numerical model of SDVA self-diverting acid acidizing for fractured media includes a SDVA self-diverting acid flow reaction model and a porosity and permeability evolution model, and the SDVA self-diverting acid flow reaction model includes a SDVA self-diverting acid flow model and a SDVA self-diverting acid reaction model; S4: coupling iterative solution of the SDVA self-steering acid acidizing numerical model of the fractured medium established in step S3; S5: Determine whether the wormhole in the current time step has been broken through: If there is no breakthrough, continue the numerical simulation of the next time step, update the self-steering acid viscosity, and repeat steps S4-S5; If a breakthrough is achieved, the numerical simulation results of SDVA self-steering acidizing in fractured media are obtained.
2. The numerical simulation method for SDVA self-diverting acid acidification of fractured media according to claim 1, characterized in that: In step S3, the SDVA self-diverting acid flow model includes a matrix acid flow control equation, a fracture acid flow control equation, and a matrix-fracture acid cross-flow equation; The matrix acid flow control equation and the fracture acid flow control equation are respectively as follows: Where: and They are the divergence operators in the overall three-dimensional rectangular coordinate system of the fractured medium and the local two-dimensional rectangular coordinate system of the fracture surface respectively; and are the gradient operators in the overall three-dimensional rectangular coordinate system of the fractured medium and the local two-dimensional rectangular coordinate system of the fracture surface, respectively; K m , K f are the matrix and fracture permeabilities, m 2 ;μ eff is the apparent viscosity of the self-diverting acid in the matrix or fracture, Pa·s; P m , P f are the pressure of matrix and crack, Pa; Q m , Q f are the matrix and the source phase of the fracture, respectively, m 3 / s;I mf and I ff are the cross-flow velocity terms between matrix and crack and between crack and crack, respectively, m 3 / s; The matrix-fracture acid fluid crossflow equation is: Where: U m and U f are the seepage velocities in the matrix and fractures, m / s, respectively.
3. The numerical simulation method of SDVA self-diverting acid acidification of fractured media according to claim 2, characterized in that: The cross-flow velocity terms between the matrix and the crack and between the cracks are calculated by the following formulas: I ff =L(P i -P j ) (6) Where: γ is the cross-flow coefficient between matrix and crack, dimensionless; L is the overall cross-flow coefficient between fracture units, dimensionless; P i , P j are the pressure of fracture unit i and the pressure of fracture unit j, Pa, respectively.
4. The numerical simulation method of SDVA self-diverting acid acidification of fractured media according to claim 3, characterized in that: The cross-flow coefficient γ between the matrix and the crack and the overall cross-flow coefficient L between the crack units are calculated by the following formulas: Where: L i,k is the length of crack unit k within matrix unit i, m; <d> i,k is the average distance between matrix unit i and crack unit k, m; α i , α j are the crossflow coefficients of fracture unit i and fracture unit j, dimensionless;< / d> FA i is the aperture of fracture unit i, m; λ t,i is the total fluidity of fracture unit i, dimensionless; dx f is the spacing between crack elements, m.
5. The numerical simulation method of SDVA self-diverting acid acidification of fractured media according to claim 2, characterized in that: In step S3, the SDVA self-diverting acid reaction model includes H + Concentration equation, Ca in matrix and cracks 2+ concentration equations and SDVA concentration equations in the matrix and fractures; The H in the matrix and cracks + The concentration equation is: Where: φ m and φ f are the porosity of matrix and fractures, respectively; and are the hydrogen ion concentrations in the matrix and cracks, kmol / m 3 ; t is time, s; For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of hydrogen ions in the matrix and cracks, m / s; X m and X f are the hydrogen ion consumption terms in the matrix and cracks, kmol / (m 2 s); The Ca in the matrix and cracks 2+ The concentration equation is: Where: C m,Ca and C f,Ca are the calcium ion concentrations in the matrix and cracks, kmol / m 3 ; C Ca up For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of calcium ions in the matrix and cracks, respectively, m / s; The equation for the SDVA concentration in the matrix and fractures is: Where: C m,SDVA and C f,SDVA are the SDVA concentrations in the matrix and fractures, kmol / m 3 ; C SDVA up For I mf Function, kmol / m 3 ; and are the effective diffusion coefficients of self-diverting acid in the matrix and fractures, respectively, m / s.
6. The numerical simulation method of SDVA self-diverting acid acidification of fractured media according to claim 5, characterized in that: In step S3, the porosity evolution model is: Where: φ is the matrix or fracture porosity; R(C s ) is the acid consumption rate in the matrix or fracture, kmol / (s·m 2 );a v is the pore specific surface area, m 2 / m 3 ; α c is the acid solubility, kg / kmol; ρ s is the rock density, kg / m 3 ; K init , K new are the initial and post-dissolution permeabilities, m 2 ; φ init ,φ new are the initial and post-dissolution porosity, dimensionless; β is an empirical parameter, dimensionless; r p,init 、r p,new are the initial and post-dissolution pore radius, m; a v,init 、a v,new are the initial and post-dissolution pore specific surface areas, m 2 / m 3 ; are the effective diffusion coefficients in the x and y directions, m / s; α os , L , T are constants related to pore structure and are dimensionless; D e is the effective diffusion coefficient in the matrix or fracture, m / s; |U| is the modulus of the seepage velocity, m / s; r p is the pore radius, m.
7. The numerical simulation method for SDVA self-diverting acid acidizing of fractured media according to any one of claims 1 to 6, characterized in that: In step S5, the self-steering acid viscosity is updated using the following formula: Where: μ eff ,ε0,μ max are the apparent viscosity, initial viscosity and maximum viscosity of the self-diverting acid in the matrix or fracture, Pa·s; n is the power index; K is the matrix or fracture permeability, m 2 ; φ is the matrix or fracture porosity; C SDVA , C Ca are SDVA and the concentration of calcium ions in the matrix or cracks, kmol / m 3 ; C max,SDVA , C Max,Ca are SDVA and the maximum concentration of calcium ions in the matrix or cracks, kmol / m 3 ; W1, W2, W3, b, c are all empirical coefficients; pH is the pH value of the acid system in the matrix or crack at a certain moment.
Citation Information
Patent Citations
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CN117494480A
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CN117744399A
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WO2021082130A1
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