Acid fracturing parameter optimization method based on full-fracture acid etching fracture conductivity simulation
By using a multi-field coupled acid etching model in the acid pressure model, the diversion capacity of acid etching cracks is calculated, which solves the problem that it is difficult to accurately optimize the acid pressure parameters in the existing technology, and achieves more accurate diversion capacity calculation and effective development of oil and gas wells.
Patent Information
- Application Number
- CN202510163489.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-14
- Publication Date
- 2025-05-06
- Estimated Expiration
- 2045-02-14
AI Technical Summary
The existing acid pressure model is difficult to accurately reflect the influence of complex geological bodies on the flow diversion capacity of acid etching cracks, resulting in poor optimization of acid pressure parameters.
A multi-field coupled acid etching model based on the flow diversion capability of full-slit acid etching cracks was used. By obtaining dynamic environmental parameters at different locations in the cracks, local acid etching simulation was performed, and the distribution characteristics of the flow diversion capability of the whole-domain acid etching cracks were calculated.
A more accurate calculation of the flow diversion capacity of acid etching cracks is achieved, and the acid pressure parameters can be optimized according to the target reservoir requirements and improve the development efficiency of oil and gas wells.
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Figure CN119933645A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of petroleum engineering, and in particular relates to an acid fracturing parameter optimization method based on full-fracture acid-etched fracture conductivity simulation. Background Art
[0002] my country's carbonate exploration area has reached 600,000 square kilometers, with large oil and gas reserves and wide distribution, especially in the three major basins of Tarim, Sichuan and Ordos, where the proven rate of oil and gas resources does not exceed 15%, and the resource potential is huge. my country's ultra-deep carbonate formations are ancient and have been affected by multiple phases of reservoir formation and transformation. Multiple types of reservoirs are vertically superimposed and highly heterogeneous. They are characterized by ultra-high temperature (160-220°C), ultra-high closure stress (80-120MPa), low permeability and density (porosity between 2-5%, permeability between 0.01-10mD), etc. Due to the poor physical properties of carbonate reservoir matrix and the discontinuous development of oil and gas-rich reservoirs, more than 80% of oil and gas wells need acid fracturing process transformation to achieve effective oil and gas development.
[0003] Numerical simulation is an important means to optimize the parameters of the acid fracturing process. The research on numerical simulation of acid fracturing is the development of multi-directional global multi-field coupling models, aiming to achieve the complete reproduction of the expansion-etching process of acid fracturing fractures under mining conditions. At present, there are many large-scale acid fracturing models for mines, but there are relatively few studies on local acid fracturing models that focus on the local etching characteristics of the fracture surface. In fact, during the acid fracturing process, the flow velocity, temperature, fracture width, acid concentration and other parameters at various positions inside the fracture are in a dynamic change process, resulting in huge differences in the etching morphology at various locations inside the fracture and the conductivity of the acid-etched fracture.
[0004] When calculating the conductivity of acid-etched fractures, the heterogeneity and anisotropy of complex geological bodies such as natural fractures and caves make the calculation results with and without complex media different. The commonly used acid fracturing model can only calculate the average dissolution amount in a single grid, and uses empirical models such as the NK model to calculate the conductivity of acid-etched fractures. Although the distribution characteristics of the conductivity of acid-etched fractures in 100m-level fractures at the oil field scale can be obtained, it is difficult to reflect the influence of rough morphology and environmental parameter changes on etching morphology and conductivity in the conductivity calculation process, and the influence of complex geological bodies on the conductivity of acid-etched fractures is ignored, so the acid fracturing parameters cannot be optimized more accurately. Summary of the invention
[0005] The technical solution adopted by the present invention is as follows:
[0006] A method for optimizing acid fracturing parameters based on full-seam acid-etched fracture conductivity simulation, characterized in that it comprises the following steps:
[0007] Step S1: Obtain basic parameters and establish a single well geological characteristic model of the target area;
[0008] Step S2: combining the construction parameters with the single well geological characteristic model, performing acid fracturing simulation calculation to obtain fracture dynamic environment parameters;
[0009] Step S3: calibrating reference positions in the acid fracturing fracture to obtain dynamic changes of environmental parameters at different positions;
[0010] Step S4: using a multi-field coupled acid etching model to carry out local acid etching simulation at different locations;
[0011] Step S5: Based on the simulation results in step S4, the conductivity calculation model of the acid-etched fractures is used to obtain the distribution characteristics of the conductivity of the whole-domain acid-etched fractures;
[0012] Step S6: Based on the conductivity of the acid-etched fractures in step S5, it is determined whether the acid-etched fracture parameter requirements are met according to the target reservoir requirements.
[0013] Furthermore, when performing the acid fracturing simulation calculation in step S2, the following steps are also included:
[0014] Based on the scale-multi-field coupled acid fracturing model, the fluid mass conservation equation, flow equation, convection-diffusion heat conduction, concentration field calculation equation and dissolution width calculation equation in the fracture domain are established.
[0015] Furthermore, the crack dynamic environment parameters include:
[0016] Slit width, flow field, temperature field, and concentration field parameters.
[0017] Furthermore, step S3 also includes:
[0018] The central axis in the fracture length direction is selected as the reference line for calculating the conductivity. The first reference point sequence is taken at a certain interval on the central axis, and then the second reference point sequence is taken at intervals in the fracture height direction parallel to the central axis of the fracture length. The first reference point sequence and the second reference point sequence can cover the fracture surface. For complex geological body areas, the entire area is covered with smaller spacing and more reference point sequences, so that the conductivity of acid-etched fractures in complex geological bodies can be calculated more precisely.
[0019] Furthermore, step S4 also includes:
[0020] The environmental parameters of the first reference point sequence and the second reference point sequence in step S3 are used as boundary conditions of the acid etching model. The etching models of the first reference point sequence and the second reference point sequence are solved, and the fracture surface is coarsened using an interpolation algorithm, so as to reproduce the dynamic etching process of the acid in the fracture.
[0021] Furthermore, step S4 also includes:
[0022] According to the simulation situation in step S3, a curve of the change of acid concentration over time is obtained;
[0023] When the acid concentration increases to 10% of the maximum acid concentration, the corresponding time is judged as the start time of acid etching at the reference point;
[0024] When the acid concentration drops to 10% of the maximum acid concentration, the corresponding time is judged as the end time of acid etching at the reference point;
[0025] Determine the acid etching time for the calculated point.
[0026] Furthermore, step S5 also includes:
[0027] The rough point cloud data obtained by acid etching the surface of the rock plate is used to establish a three-dimensional coordinate system;
[0028] The acid-etched rock slab is cut and sectioned to obtain the length of the zigzag line of the top edge of the rock slab contour on the section surface, the transverse tortuosity ratio of the rock sample surface, and the longitudinal tortuosity ratio of the rock sample surface, so as to calculate the conductivity of the acid-etched fracture.
[0029] Furthermore, step S6 also includes:
[0030] The conductivity of acid-etched cracks under different construction parameters is calculated to optimize the construction parameters.
[0031] The setting of construction parameters such as acid volume and displacement is the key parameter for optimizing the construction effect. The acid volume distribution is dynamically adjusted according to real-time monitoring data (such as pressure and temperature). The acid volume is reduced in high permeability areas and increased in low permeability areas. The dimensionless capacity index under different displacements and acid volumes is calculated, and a relationship curve between the dimensionless capacity index and the acid injection volume is drawn to determine the optimal processing volume.
[0032] In summary, the technical solution provided by the present invention can carry out acid etching simulation calculations at different positions in the fracture domain, thereby obtaining the distribution characteristics of the conductivity of the entire acid-etched fracture, and its calculation results are more accurate than the simulation methods in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] In order to more clearly illustrate the technical solutions in the examples of the present application, the following is a brief introduction to the drawings required for use in the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.
[0034] Figure 1 It is a schematic diagram of the method flow of the present invention;
[0035] Figure 2 This is a schematic diagram of the surface structure of the acid-etched rock plate in an embodiment of the present invention;
[0036] Figure 3 A schematic diagram of reference points in an embodiment of the present invention;
[0037] Figure 4 A graph showing the relationship between the acid concentration at a certain reference point and time in an embodiment of the present invention;
[0038] Figure 5 is a flow conductivity distribution diagram in an embodiment of the present invention;
[0039] Figure 6 Schematic diagram of the prediction results of acid-etched crack conductivity under different construction parameters in an embodiment of the present invention. DETAILED DESCRIPTION
[0040] The present invention will be described in detail below in conjunction with the accompanying drawings.
[0041] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.
[0042] In general, the present invention provides an acid fracturing parameter optimization method based on full-fracture acid-etched fracture conductivity simulation. By obtaining environmental parameters such as temperature, concentration, fracture width, flow rate, etc. of the calibrated reference point in the fracture during the acid fracturing process and their changes over time, the environmental parameters are used as boundary conditions for the calculation of the established acid etching and conductivity numerical model, and the full-domain acid-etched fracture conductivity of the fracture is calculated through numerical simulation.
[0043] like Figure 1 As shown, the present invention provides an acid fracturing parameter optimization method based on full-seam acid-etched fracture conductivity simulation, comprising the following steps:
[0044] Step S1: Obtain basic parameters and establish a single well geological characteristic model of the target area;
[0045] Specifically, when establishing a single well geological characteristic model of the target area, basic mechanical parameters and stress profiles can be obtained through logging parameter calculations, and the stress profile can be gridded and the ground stress can be calculated.
[0046] In one embodiment, different processing methods can be selected for fractures of different scales. For example, for small-scale (opening ≤ 50 μm, density ≥ 5 fractures / m) natural fractures, permeability tensor representation can be used, and for large-scale natural fractures, DFM and EDFM display representation can be used, and modeling can be based on the EDFM method. For complex reservoirs far from the well, a heterogeneous characteristic model of the formation can be constructed based on remote acoustic waves.
[0047] Step S2: combining the construction parameters with the single well geological characteristic model, performing acid fracturing simulation calculation to obtain fracture dynamic environment parameters;
[0048] Specifically, the acid volume and displacement can be set according to the previous experience of the block construction parameters, and the average construction parameters of the block can be selected to carry out acid fracturing simulation. When performing acid fracturing simulation calculations, the multi-field simulation model in the existing technology can be used for calculation.
[0049] In one embodiment, the multi-scale multi-field coupled acid fracturing model described in the specification of the present invention is used, and the model can realize three-dimensional dynamic calculation of fracture width, flow field, temperature and concentration field.
[0050] Among them, the mass conservation equation of the fluid in the fracture domain is:
[0051]
[0052] The flow momentum equation in the fracture domain is:
[0053]
[0054] The three-dimensional convection-diffusion equation is used to describe the convection-diffusion heat conduction of the acid fluid in the fracture domain:
[0055]
[0056] The concentration field equation inside the crack is:
[0057]
[0058] Calculation of crack wall dissolution width:
[0059] In one embodiment of the present invention, it is assumed that the acid that is lost from the hydraulic fracture wall and enters the matrix rock mass is all involved in the dissolution of the rock and the formation of acid-etched wormholes, but does not participate in the dissolution of the hydraulic fracture wall. Therefore, the calculation equation for the dissolution width of the hydraulic wall is:
[0060]
[0061] In the formula, u x 、u y 、u z are the fluid flow velocities in the length, width and height directions of the fracture domain, m / s; ψ is the flow velocity component in the length, width and height directions of the fracture domain, m / s; p hf is the fluid pressure, Pa; ρ l is the fluid density, kg / m 3 ; i is the coordinate in the x, y, and z directions, dimensionless; μ is the fluid viscosity, Pa·s; c1 is the fluid specific heat capacity, J / (kg·K); T hfis the fluid temperature in the hydraulic fracture, K; λ1 is the fluid thermal conductivity, J / (m·K·s); C hf is the acid concentration in the hydraulic fracture, mol / m3; D e is the effective mass transfer coefficient of acid solution, m 2 / s;;w hf is the width of the hydraulic fracture, m; β is the solubility of the acid on rock minerals, kg / kg; M is the molar mass of the rock, kg / mol; φ is the porosity of the rock mass, dimensionless; ρ s is the rock skeleton density, kg / m 3 ;k c is the acid-rock reaction rate, m / s.
[0062] Step S3: calibrating reference positions in the acid fracturing fracture to obtain dynamic changes of environmental parameters at different positions;
[0063] In step S3, by calibrating the reference position in the acid fracturing fracture, the dynamic changes of its environmental parameters are obtained to provide conditions for the acid etching model. The present invention adopts a multi-field coupled acid etching model to carry out acid etching simulation at different positions in the fracture domain, and predicts the conductivity of the acid etched fracture based on the acid fracturing simulation results, thereby obtaining the distribution characteristics of the conductivity of the acid etched fracture in the entire fracture domain. Figure 2 As shown in the figure, taking the acid fracturing fracture with a length of 100m and a width of 28m as an example, the central axis (y=0) in the fracture length direction is selected as the reference line for calculating the conductivity, and reference points are taken at intervals of 10m on the central axis (the specific interval can be selected according to actual needs), and then reference points are taken at an equal distance of 10m in the fracture height direction parallel to the central axis of the fracture length, so that the reference points can cover the fracture surface. Due to the strong filtration effect of the complex medium, the length of the hydraulic fracture after encountering the natural fracture is shortened, thereby affecting the expansion of the acid-etched fracture. For this reason, it is necessary to set reference points with an interval of 1m at the natural fracture in the acid fracturing fracture to more finely characterize the influence of the natural fracture on the acid etching, and calculate the conductivity of the acid-etched fracture at each reference point. Through S2, the environmental parameters such as the fracture width, temperature, flow rate, acid concentration, etc. at any point in the hydraulic fracture during the full acid fracturing process and their changes over time can be obtained.
[0064] Step S4: using a multi-field coupled acid etching model to carry out local acid etching simulation at different locations;
[0065] In this step, the solid-fluid-temperature-reaction multi-field coupled acid non-uniform etching mechanism local acid-etched fracture conductivity model can be adopted. By establishing a flow coupling algorithm between different physical and chemical fields, the numerical discretization and solution of the model can be realized based on the finite volume method.
[0066] Specifically, the environmental parameters of each reference point in S3 are used as the boundary conditions of the acid etching model. By solving the etching model of each reference point, the Kriging interpolation algorithm is used to perform the required fracture surface coarsening, thereby reproducing the dynamic acid etching process in the rough fracture under in situ conditions.
[0067] Since it takes a certain amount of time for the acid to expand in the crack, the acid loaded first at the crack mouth will react with the rock first, resulting in different acid etching times at different locations. Therefore, it is necessary to calibrate the acid etching time at different locations. During the acid fracturing process, as the acid begins to react with the rock, the acid-rock reaction consumes hydrogen ions, resulting in a decrease in the acid concentration value. The obvious change in the acid concentration value indicates that the acid begins to react chemically with the rock. The established multi-field coupled acid fracturing model is solved by numerical calculation methods, and the numerical algorithm is implemented by computer programming. The rock and acid parameters, boundary conditions and initial conditions are input, and the curve of the acid concentration changing with time can be calculated. By real-time monitoring of the acid concentration value changing with time, when the acid concentration begins to drop significantly, it can be considered that the acid begins to react with the rock. The corresponding time is the time when the acid begins to react in the crack.
[0068] like Figure 3 As shown, the steps are as follows: as the acid is injected and the reaction proceeds, record the acid concentration value every 1 minute until a period of time after the acid injection is completed to ensure that the reaction is basically completed. Based on the recorded acid concentration and time data, draw a curve of the change of acid concentration value and time;
[0069] By observing the change curve of acid concentration and time at each reference point, when the acid concentration increases to 10% of the highest acid concentration, the corresponding time is judged as the start time of acid etching at the reference point. When the acid concentration decreases to 10% of the highest concentration, the corresponding time is judged as the end time of acid etching at the reference point. Since it takes a certain time to reach the calibrated reference point after the acid injection starts, the acid begins to react when it contacts the crack wall after reaching the reference point. At this time, the acid injection is still continuing, so in general, the acid concentration in the crack increases. After the acid injection stops, the acid rock continues to react, the acid changes from active acid to residual acid, and the acid concentration decreases. When the acid concentration begins to decrease to 10% of the highest concentration, the acid concentration-time curve tends to be flat, and the time recorded at this time is the end time of the acid reaction. In this way, the acid etching time of each reference point can be calculated.
[0070] Step S5: Based on the simulation results in step S4, the conductivity calculation model of the acid-etched fractures is used to obtain the distribution characteristics of the conductivity of the whole-domain acid-etched fractures;
[0071] In order to accurately calculate the conductivity taking into account the geometric morphology of the crack surface, the surface geometric morphology of acid-etched cracks and the conductivity of cracks were studied. By obtaining the surface characterization parameters of acid-fracturing cracks, the calculation method of the contact area ratio of rough cracks under closure pressure was obtained based on experimental means and theoretical deduction. The contact ratio was used to study the variation law of the crack width of rough cracks with closure pressure. Combined with the classic cubic law of cracks, the conductivity calculation model of acid-fracturing cracks was obtained, thereby obtaining the global conductivity.
[0072] Specifically, a laser 3D scanner is used to scan the surface of the acid-etched rock plate to obtain rough point cloud data, such as Figure 4 Establish XYZ three-dimensional coordinate system. j ) cut, the top edge of the rock plate's profile on the cut surface is a zigzag line, and the length of the zigzag line is defined as L cc Similarly, any plane of the rock plate along the Y direction (x = x j ) After cutting, define the length of the top edge of the zigzag line of the rock plate on the cutting surface as L cl , take the step length L x is 0.3mm, defined is the lateral tortuosity ratio of the rock sample surface, is the longitudinal tortuosity ratio of the rock sample surface. Then the following relevant calculation formula can be obtained:
[0073]
[0074]
[0075]
[0076]
[0077] In the formula, the X and Y columns are the plane coordinates of each point on the surface of the rock plate, the Z column is the height of each point, and N x is the number of scanning steps in the X direction, N y is the number of scan steps in the Y direction.
[0078] Calculation model of conductivity of acid fracturing fractures:
[0079]
[0080]
[0081] In the formula, k f w is the crack pressure P c The flow conductivity under the action of f w) i is the initial conductivity of the fracture; is the lateral tortuosity ratio of the crack surface; is the longitudinal tortuosity ratio of the crack surface; m and n are the parameters obtained from experimental fitting; β is the fitting coefficient.
[0082] Through the above steps, the distribution of conductivity of the whole acid-etched cracks can be obtained. Figure 5 FIG. 4 is a diagram showing the distribution of flow conductivity on a fracture surface in an embodiment.
[0083] Step S6: Based on the conductivity of the acid-etched fractures in step S5, it is determined whether the acid-etched fracture parameter requirements are met according to the target reservoir requirements.
[0084] In combination with the above steps S1-S6, the construction parameters are optimized by calculating the conductivity of the acid-etched cracks under different construction parameters.
[0085] In one embodiment, given the acid fracturing requirements of the target block, the lower limit of the conductivity of the acid-etched fracture is 0.3Dc·cm. Considering that the conductivity of the acid-etched fractures between the reference points changes linearly, the requirement can be achieved by increasing the amount of acid. Therefore, it is necessary to simulate the effective acid-etched fracture length and the conductivity of the acid-etched fracture under different acid amounts, so as to determine the optimal acid amount. Figure 6 As shown in the figure, all reference points in the longitudinal direction when x=0 are selected as the research objects, and the conductivity of the farthest reference point is the lower limit of the conductivity of the acid-etched fracture. It can be seen from the simulation results under different acid conditions that when the acid dosage is 400-500m 3 When the acid consumption is 600m 3 When the conductivity is 0.38Dc·cm, the lower limit of conductivity is 0.38Dc·cm, which can meet the acid fracturing requirements.
[0086] Similarly, other optimal construction parameters can be obtained through similar multiple sets of simulation experiments.
[0087] It can be seen that when the method provided by the present invention is applied on site, the lower limit of the conductivity can be determined according to the target reservoir requirements, the average conductivity of the acid-etched fractures can be calculated by the method provided in the present invention, and whether the acid-etched fracture parameter requirements are met according to the production capacity optimization requirements is determined. If not, the parameters such as the acid injection displacement and the acid injection amount are changed, and the global conductivity distribution of the fracture is recalculated. If it is satisfied, the optimization ends, and the preset parameters are the optimal construction parameters. Compared with the prior art, the present invention can combine the heterogeneity of the formation to more realistically simulate the acid etching morphology of the fracture, and by calibrating the specified reference points, it can achieve a more accurate calculation of the conductivity of the acid-etched fracture under global conditions.
[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
Claims
1. A method for optimizing acid fracturing parameters based on simulation of conductivity of full-seam acid-etched fractures, characterized in that: The following steps are involved: Step S1: Obtain basic parameters and establish a single well geological characteristic model of the target area; Step S2: combining the construction parameters with the single well geological characteristic model, performing acid fracturing simulation calculation to obtain fracture dynamic environment parameters; Step S3: calibrating reference positions in the acid fracturing fracture to obtain dynamic changes of environmental parameters at different positions; Step S4: using a multi-field coupled acid etching model to carry out local acid etching simulation at different locations; Step S5: Based on the simulation results in step S4, the conductivity calculation model of the acid-etched fractures is used to obtain the distribution characteristics of the conductivity of the whole-domain acid-etched fractures; Step S6: Based on the conductivity of the acid-etched fractures in step S5, it is determined whether the acid-etched fracture parameter requirements are met according to the target reservoir requirements.
2. The method for optimizing acid fracturing parameters based on full-seam acid-etched fracture conductivity simulation according to claim 1, wherein step S2 further comprises: Based on the scale-multi-field coupled acid fracturing model, the fluid mass conservation equation, flow equation, convection-diffusion heat conduction, concentration field calculation equation and dissolution width calculation equation in the fracture domain are established.
3. The acid fracturing parameter optimization method based on full-seam acid-etched fracture conductivity simulation according to claim 1, wherein the fracture dynamic environment parameters include: Slit width, flow field, temperature field, and concentration field parameters.
4. The method for optimizing acid fracturing parameters based on full-seam acid-etched fracture conductivity simulation according to claim 1, wherein step S3 further comprises: The central axis in the fracture length direction is selected as the reference line for calculating the conductivity. The first reference point sequence is taken at a certain interval on the central axis, and then the second reference point sequence is taken at intervals in the fracture height direction parallel to the central axis of the fracture length. The first reference point sequence and the second reference point sequence can cover the fracture surface.
5. The method for optimizing acid fracturing parameters based on full-seam acid-etched fracture conductivity simulation according to claim 1, wherein step S4 further comprises: The environmental parameters of the first reference point sequence and the second reference point sequence in step S3 are used as boundary conditions of the acid etching model. The etching models of the first reference point sequence and the second reference point sequence are solved, and the fracture surface is coarsened using an interpolation algorithm, so as to reproduce the dynamic etching process of the acid in the fracture.
6. The method for optimizing acid fracturing parameters based on full-seam acid-etched fracture conductivity simulation according to claim 1, wherein step S4 further comprises: According to the simulation situation in step S3, a curve of the change of acid concentration over time is obtained; When the acid concentration increases to 10% of the maximum acid concentration, the corresponding time is judged as the start time of acid etching at the reference point; When the acid concentration drops to 10% of the maximum acid concentration, the corresponding time is judged as the end time of acid etching at the reference point; Determine the acid etching time for the calculated point.
7. The method for optimizing acid fracturing parameters based on full-seam acid-etched fracture conductivity simulation according to claim 1, wherein step S4 further comprises: The rough point cloud data obtained by acid etching the surface of the rock plate is used to establish a three-dimensional coordinate system; The acid-etched rock slab is cut and sectioned to obtain the length of the zigzag line of the top edge of the rock slab contour on the section surface, the transverse tortuosity ratio of the rock sample surface, and the longitudinal tortuosity ratio of the rock sample surface, and the conductivity of the acid-etched fracture is calculated.
8. The method for optimizing acid fracturing parameters based on full-seam acid-etched fracture conductivity simulation according to claim 1, wherein step S6 further comprises: Based on the influence of multivariate combination of construction parameters on the conductivity of acid-etched fractures, the acid fracturing parameters are optimized through dimensionless capacity index analysis.
Citation Information
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