Multi-cluster fracture propagation and proppant migration simulation method considering eyelet erosion

Abstract

The invention discloses a multi-cluster fracture propagation and proppant migration simulation method considering eyelet erosion. The method comprises the steps that parameters are set, a hydraulic fracturing geometric model is established, and the initial pressure fracture width is set; determining a current time step length; solving an eyelet erosion equation, an eyelet pressure drop equation, an in-seam fluid flow equation and a rock elastic deformation equation when the sand-carrying fluid is started to be pumped; solving a proppant migration equation when the sand-carrying fluid starts to be pumped at the current moment; updating the front edge and the elastic matrix of the crack of each cluster when the tip of the crack of each cluster reaches the critical expansion condition; and when the current moment reaches the total pumping time, ending calculation, and outputting a time-varying diagram of the hole diameter and the hole shape coefficient, a three-dimensional expansion form of each cluster of cracks and an in-crack propping agent distribution cloud diagram. According to the scheme, the expansion form of the multi-cluster fracture and the concentration distribution of the propping agent in the horizontal well segmented multi-cluster fracturing can be evaluated more accurately, and the unconventional oil and gas well fracturing parameter design is guided.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic fracturing of unconventional oil and gas reservoirs, and in particular to a method for simulating multi-cluster fracture expansion and proppant migration taking into account pore erosion. Background Art

[0002] Hydraulic fracturing is a key technology for the efficient development of unconventional oil and gas reservoirs. This technique involves pumping a sand-carrying fluid—a mixture of high-pressure fluid and proppant particles—into the target rock formation. The fluid flows through the wellbore and perforations, entering the rock formation and creating fractures. Proppants maintain the fractures open, creating pathways for oil and gas flow and increasing reservoir permeability. Fracture propagation and proppant migration are two key issues in the hydraulic fracturing process. Post-fracture fracture morphology and proppant distribution within the fractures directly impact the reservoir's remodeled volume and conductivity.

[0003] Furthermore, as the sand-carrying fluid flows through the perforations, it erodes and polishes them, changing their diameter and shape coefficient, and thus their frictional resistance—this is known as the perforation erosion effect. During the propagation of multiple fracture clusters, due to stress interference between fractures and frictional resistance along the wellbore, the flow rate at each cluster of perforations varies, and the degree of polishing by the sand-carrying fluid varies. This affects the flow distribution within the clusters, and thus their propagation and even the distribution of proppant within each fracture cluster.

[0004] Therefore, establishing a coupled simulation method for the three-dimensional expansion of multi-cluster fractures and proppant migration considering the perforation erosion effect is of great practical significance for accurately evaluating the morphology of multi-cluster fractures and the distribution of proppant within the fractures, and guiding the design of fracturing parameters for unconventional oil and gas wells. Summary of the Invention

[0005] In response to the above technical problems, the present invention provides a method for simulating the expansion of multiple clusters of fractures and proppant migration taking into account pore erosion, thereby achieving the coupling of the expansion of multiple clusters of fractures and proppant migration during the fracturing process. By taking into account the influence of the pore erosion effect on these two physical processes, the morphology of multiple clusters of fractures and the distribution of proppant within the fractures can be more accurately evaluated.

[0006] The present invention is achieved by adopting the following technical solutions: A method for simulating multi-cluster fracture propagation and proppant migration considering perforation erosion includes the following steps: Step S1: Collect target well data and set reservoir parameters, completion parameters, and fracturing parameters; Step S2: establishing a hydraulic fracturing geometric model; Step S3: setting the initial fracture pressure and initial fracture width of each cluster of fractures; Step S4: Determine the current time step; Step S5: Determine whether the pumping of the sand-carrying fluid has started at the current moment. If it has started, solve the hole erosion equation and update the hole diameter and hole shape coefficient of each cluster; if it has not started, directly go to step S6; Step S6: Solve the perforation pressure drop equation and update the flow rate in each cluster of fractures; Step S7: using the finite volume method and the displacement discontinuity method to solve the fluid flow equation in the fracture and the rock elastic deformation equation respectively, and updating the width and the fracture pressure of each cluster of fractures in turn; Step S8: Determine whether the pumping of the sand-carrying fluid has started at the current moment. If it has started, solve the proppant migration equation to obtain the concentration distribution of the proppant in each cluster of fractures. If it has not started, directly proceed to step S9. Step S9: Determine whether the current crack tips of each cluster have reached the critical expansion condition according to the crack expansion criterion. If so, update the crack fronts and elastic matrices of each cluster. If not, directly proceed to step S10. Step S10: Determine whether the total pumping time has been reached at the current moment. If so, terminate the calculation and output the graphs of the variation of the hole diameter and hole shape coefficient over time, the three-dimensional expansion morphology of each cluster of fractures, and the cloud map of the proppant distribution within the fractures. If not, return to step S4 and execute steps S4 to S10 again.

[0007] Specifically, the reservoir parameters in step S1 include reservoir in situ stress, reservoir thickness, Young's modulus, Poisson's ratio, fracture toughness and formation fluid loss coefficient; the completion parameters include wellbore diameter, section length, number of clusters, cluster spacing, number of holes and initial hole diameter; and the fracturing parameters include fracturing fluid viscosity, fracturing fluid density and injection displacement.

[0008] Specifically, in step S2, the hydraulic fracturing geometric model determines the size of the geometric model according to the reservoir thickness and segment length parameters of the target fracturing segment, and performs fracture mesh division.

[0009] Specifically, the setting of the initial fracture pressure and initial fracture width in step S3 includes setting the initial activation unit and initial pressure of each fracture cluster, using the displacement discontinuity method to describe the relationship between the fracture pressure and width of the fracture unit, and solving to obtain the initial width of the initial activation unit, which is expressed as: ; in, is the total number of crack units at the current moment; For unit The fluid pressure in the crack is in MPa; For unit The width of the , in m; is the kernel function, representing the unit The width of the unit The stress generated is in MPa / m.

[0010] Specifically, in step S4, the current time step is determined according to the CFL condition, which is expressed as: ; in, is the current time step, in min; is the fracturing fluid viscosity, in mPa·s; is the Young's modulus of rock, in MPa; is the Poisson's ratio of rock; is the size of the crack grid in the crack length or crack height direction, in m; The maximum width of the currently activated unit, in meters.

[0011] Specifically, the solution process of step S5 includes: using a semi-empirical hole erosion equation to describe the change of hole diameter and hole shape coefficient over time, and solving to obtain the updated hole diameter and hole shape coefficient of each cluster, which is expressed as: ; in, is the hole diameter, in m; is the hole shape coefficient; is the maximum hole shape coefficient, which is 0.9; is the proppant mass concentration, in kg / m 3 ; and are empirical coefficients obtained from experiments, and their values ​​are 1.07×10 -13 m 2 s / kg and 1.08×10 -8 m 2 ·s / kg.

[0012] Specifically, step S6 solves the perforation pressure drop equation and updates the flow rate in each cluster of fractures, which is expressed as: ; in, is the total number of clusters in the fracturing section; is the inlet pressure of cluster 1, in MPa; From the end of the fracturing section to the The friction along the wellbore caused by the cluster, in MPa; For the The crack mouth pressure of the cluster crack, in MPa; is the density of the fracturing fluid, in kg / m 3 ; For the cell shape factor of the cluster; For the The diameter of the cluster's holes, in mm; For the Number of holes in the cluster; is the fracturing pump injection rate, in m 3 / min; For the The flow rate of the cluster fracture, in m 3 / min.

[0013] Specifically, the step S7 uses the finite volume method to update the width of each crack unit, which is expressed as: ; in, and Unit The width at the current time step and the previous time step, in meters; is a step function; For unit The volume flux at the interface between the adjacent unit and the adjacent unit, in m 2 / min; For unit The start time of filtration loss, in min; For unit The flow rate of the crack, in m 3 / min; The displacement discontinuity method is used to update the internal pressure of each fracture unit, which is expressed as: ; in, is the minimum horizontal principal stress, in MPa.

[0014] Specifically, step S8 solves the proppant migration equation to obtain the concentration distribution of the proppant in each cluster of fractures, which is expressed as: ; in, and are the volume flux of proppant generated by convective migration and sedimentation, respectively, in m 2 / min; is the normalized proppant concentration; is the radius of the spherical proppant particle, in m; is the ratio of the fracture width to the proppant particle radius; is the proppant density, in kg / m 3 ; 、 and is a dimensionless function.

[0015] Specifically, step S9 includes calculating the critical width of the crack tip unit according to the crack propagation criterion. If the actual width of the tip unit reaches the critical width, the crack propagates, which is expressed as: in, is the critical width of the crack unit, in m; is the fracture toughness, unit is MPa·m 1 / 2 ; is the plane strain Young's modulus, in units of ; is the tip unit expansion speed, in m / min.

[0016] The beneficial effects of the present invention are as follows: the present invention provides a coupled simulation method of three-dimensional expansion of multi-cluster fractures and proppant migration taking into account the pore erosion effect, which can more accurately evaluate the expansion morphology and proppant concentration distribution of multi-cluster fractures in staged multi-cluster fracturing of horizontal wells, and guide the design of fracturing parameters for unconventional oil and gas wells. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 the structures shown in these drawings without paying any creative work.

[0018] Figure 1 Flowchart of a method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion in an embodiment of the present invention; Figure 2 Schematic diagram of crack grid division in an embodiment of the present invention; Figure 3 Schematic diagram of the hole eroded by the sand-carrying fluid in an embodiment of the present invention; Figure 4 Schematic diagram of flow distribution between cracks in an embodiment of the present invention; Figure 5 Schematic diagram of a discrete fracture unit using the finite volume method in an embodiment of the present invention; Figure 6 is a graph showing changes in hole diameter and hole shape coefficient over time in an embodiment of the present invention; Figure 7 This is a cloud diagram of crack width in an embodiment of the present invention; Figure 8 This is a cloud diagram of proppant concentration distribution in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0020] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0021] The following is combined with Figures 1 to 8 , some embodiments of the present invention are described in detail. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.

[0022] This paper proposes a method for simulating multi-cluster fracture propagation and proppant migration considering perforation erosion. Figure 1 As shown, the specific steps include: S1. Collect target well data and set reservoir parameters, completion parameters, and fracturing parameters: In this embodiment, the reservoir parameters acquired in step S1 include the in situ stress, reservoir thickness, Young's modulus, Poisson's ratio, fracture toughness, and formation fluid loss coefficient; the completion parameters include the wellbore diameter, section length, number of clusters, cluster spacing, number of holes, and initial hole diameter; and the fracturing parameters include fracturing fluid viscosity, fracturing fluid density, and injection displacement. Specific parameter values ​​are shown in Table 1. In other embodiments, they can be determined according to actual conditions.

[0023] Table 1 Basic parameters S2. Perform hydraulic fracturing geometry modeling: In this embodiment, step S2 includes: determining the size of the geometric model according to parameters such as the reservoir thickness and segment length of the target fracturing segment, and performing fracture mesh division, such as Figure 2 shown.

[0024] S3. Set the initial fracture pressure and initial fracture width of each fracture cluster: In this embodiment, step S3 includes setting the initial activation unit and initial pressure of each cluster of fractures, using the displacement discontinuity method to describe the relationship between the pressure and width of the fracture unit, and solving to obtain the initial width of the initial activation unit. The calculation formula is: Where: is the total number of crack units at the current moment; For unit The fluid pressure in the crack, MPa; For unit Width, m; is the kernel function, representing the unit The width of the unit The stress generated is MPa / m.

[0025] S4. Determine the current time step: In this embodiment, step S4 includes: determining the current time step according to the CFL condition: Where: is the current time step, min; is the fracturing fluid viscosity, mPa·s; is the Young's modulus of rock, MPa; is the Poisson's ratio of rock; is the size of the crack grid in the crack length or crack height direction, m; is the maximum width of the currently activated unit, m.

[0026] S5, determining whether the sand-carrying fluid has been pumped at the current moment; if so, solving the hole erosion equation and updating the hole diameter and hole shape coefficient of each cluster; if not, directly proceeding to S6; In this embodiment, step S5 is as follows: Figure 3 As shown in the figure, the sand-carrying fluid flows through and polishes the holes, causing the hole diameter and shape to change. Therefore, a semi-empirical hole erosion equation is used to describe the changes in hole diameter and hole shape coefficient over time, and the updated hole diameter and hole shape coefficient of each cluster are obtained by solving the equation. The calculation formula is: Where: is the hole diameter, m; is the hole shape coefficient, dimensionless; is the maximum hole shape coefficient, dimensionless, taken as 0.9; is the proppant mass concentration, kg / m 3 ; and are empirical coefficients obtained from experiments, and are taken as 1.07×10 -13 m 2 s / kg and 1.08×10 -8 m 2 ·s / kg.

[0027] S6. Solve the perforation pressure drop equation and update the flow rate in each cluster of fractures: In this embodiment, step S6 is as follows Figure 4 As shown, it includes: solving the perforation pressure drop equation according to the conservation relationship between pressure and flow at each location in the fracturing section, and updating the flow rate of each cluster of fractures, which is expressed as: Where: is the total number of clusters in the fracturing section; is the inlet pressure of cluster 1, MPa; From the end of the fracturing section to the Frictional resistance along the wellbore caused by clusters, MPa; For the The crack mouth pressure of cluster cracks, MPa; is the density of fracturing fluid, kg / m 3 ; For the cell shape factor of the cluster; For the Diameter of the cluster's holes, mm; For the Number of holes in the cluster; is the fracturing pump injection rate, m 3 / min; For the Flow rate of cluster cracks, m 3 / min.

[0028] S7. Use the finite volume method and the displacement discontinuity method to solve the fluid flow equation and the rock elastic deformation equation in the fracture, and update the width and pressure of each cluster of fractures in turn: In this embodiment, step S7 is as follows Figure 5 As shown, including: First, the finite volume method is used to update the width of each crack element. The calculation formula is: Where: and Unit The width at the current time step and the previous time step, m; is a step function, dimensionless; For unit and the volume flux at the interface between adjacent units, m 2 / min; For unit The start time of filtration loss, min; For unit Flow rate of the crack, m 3 / min; Then, the displacement discontinuity method is used to update the internal pressure of each fracture unit. The calculation formula is: Where: is the minimum horizontal principal stress, MPa.

[0029] S8: Determine whether the sand-carrying fluid has been pumped at the current moment. If so, solve the proppant migration equation to obtain the concentration distribution of the proppant in each cluster of fractures. If not, proceed directly to S9: In this embodiment, step S8 includes: solving the proppant migration mass conservation equation and updating the proppant concentration distribution in the fracture: Where: and are the proppant volume fluxes generated by convective migration and sedimentation, m 2 / min; is the normalized proppant concentration, dimensionless; is the radius of the spherical proppant particle, m; is the ratio of the fracture width to the proppant particle radius, dimensionless; is the proppant density, kg / m 3 ; 、 and It is a dimensionless function and has no dimension.

[0030] S9: Determine whether the current crack tips of each cluster have reached the critical expansion condition according to the crack expansion criterion. If so, update the crack fronts and elastic matrices of each cluster. If not, proceed directly to S10: In this embodiment, step S9 includes: calculating the critical width of the crack tip unit according to the crack propagation criterion. If the current actual width of the tip unit reaches the critical width, the crack propagates, which is expressed as: Where: is the critical width of the crack unit, m; is the fracture toughness, MPa·m 1 / 2 ; is the plane strain Young's modulus, ; is the tip unit expansion speed, m / min.

[0031] S10, determine whether the total pumping time is reached at the current moment, if it is reached, then end the calculation, such as Figures 6 to 8 As shown, the output is the graph of the change of hole diameter and hole shape coefficient over time, the three-dimensional expansion morphology of each cluster of fractures and the cloud map of proppant distribution in the fractures; if it is not reached, return to S4 and execute S4~S10 again.

[0032] For the sake of simplicity, the aforementioned embodiments are described as a series of actions. However, those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are preferred embodiments, and the actions involved are not necessarily required by this application.

[0033] The above embodiments describe the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Without departing from the spirit and scope of the present invention, modifications and variations made by those skilled in the art without departing from the spirit and scope of the present invention should be within the scope of protection of the appended claims.

Claims

1. A method for simulating multi-cluster fracture propagation and proppant migration considering perforation erosion, characterized in that: The following steps are involved: Step S1: Collect target well data and set reservoir parameters, completion parameters, and fracturing parameters; Step S2: establishing a hydraulic fracturing geometric model; Step S3: setting the initial fracture pressure and initial fracture width of each cluster of fractures; Step S4: Determine the current time step; Step S5: Determine whether the pumping of the sand-carrying fluid has started at the current moment. If it has started, solve the hole erosion equation and update the hole diameter and hole shape coefficient of each cluster; if it has not started, directly go to step S6; Step S6: Solve the perforation pressure drop equation and update the flow rate in each cluster of fractures; Step S7: using the finite volume method and the displacement discontinuity method to solve the fluid flow equation in the fracture and the rock elastic deformation equation respectively, and updating the width and the fracture pressure of each cluster of fractures in turn; Step S8: Determine whether the pumping of the sand-carrying fluid has started at the current moment. If it has started, solve the proppant migration equation to obtain the concentration distribution of the proppant in each cluster of fractures. If it has not started, directly proceed to step S9. Step S9: Determine whether the current crack tips of each cluster have reached the critical expansion condition according to the crack expansion criterion. If so, update the crack fronts and elastic matrices of each cluster. If not, directly proceed to step S10. Step S10: Determine whether the total pumping time has been reached at the current moment. If so, terminate the calculation and output the graphs of the variation of the hole diameter and hole shape coefficient over time, the three-dimensional expansion morphology of each cluster of fractures, and the cloud map of the proppant distribution within the fractures. If not, return to step S4 and execute steps S4 to S10 again.

2. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The reservoir parameters in step S1 include reservoir in situ stress, reservoir thickness, Young's modulus, Poisson's ratio, fracture toughness and formation fluid loss coefficient; the completion parameters include wellbore diameter, section length, number of clusters, cluster spacing, number of holes and initial hole diameter; and the fracturing parameters include fracturing fluid viscosity, fracturing fluid density and injection displacement.

3. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: In step S2, the hydraulic fracturing geometric model determines the size of the geometric model according to the reservoir thickness and segment length parameters of the target fracturing segment, and performs fracture mesh division.

4. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The setting of the initial fracture pressure and initial fracture width in step S3 specifically includes: setting the initial activation unit and initial pressure of each fracture cluster, using the displacement discontinuity method to describe the relationship between the fracture pressure and width of the fracture unit, and solving to obtain the initial width of the initial activation unit, which is expressed as: ； in, is the total number of crack units at the current moment; For unit The fluid pressure in the crack is in MPa; For unit The width of the , in m; is the kernel function, representing the unit The width of the unit The stress generated is in MPa / m.

5. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The current time step in step S4 is determined according to the CFL condition and is expressed as: ； in, is the current time step, in min; is the fracturing fluid viscosity, in mPa·s; is the Young's modulus of rock, in MPa; is the Poisson's ratio of rock; is the size of the crack grid in the crack length or crack height direction, in m; The maximum width of the currently activated unit, in meters.

6. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The solution process of step S5 includes: using a semi-empirical hole erosion equation to describe the change of hole diameter and hole shape coefficient over time, and solving to obtain the updated hole diameter and hole shape coefficient of each cluster, which are expressed as: ； in, is the hole diameter, in m; is the hole shape coefficient; is the maximum hole shape coefficient, which is 0.9; is the proppant mass concentration, in kg / m 3 ; and are empirical coefficients obtained from experiments, and their values ​​are 1.07×10 -13 m 2 s / kg and 1.08×10 -8 m 2 ·s / kg.

7. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The step S6 solves the perforation pressure drop equation and updates the flow rate in each cluster of fractures, which is expressed as: ； in, is the total number of clusters in the fracturing section; is the inlet pressure of cluster 1, in MPa; From the end of the fracturing section to the The friction along the wellbore caused by the cluster, in MPa; For the The crack mouth pressure of the cluster crack, in MPa; is the density of the fracturing fluid, in kg / m 3 ; For the cell shape factor of the cluster; For the The diameter of the cluster's holes, in mm; For the Number of holes in the cluster; is the fracturing pump injection rate, in m 3 / min; For the The flow rate of the cluster fracture, in m 3 / min.

8. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The step S7 uses the finite volume method to update the width of each crack unit, which is expressed as: ； in, and Unit The width at the current time step and the previous time step, in meters; is a step function; For unit The volume flux at the interface between the adjacent unit and the adjacent unit, in m 2 / min; For unit The start time of filtration loss, in min; For unit The flow rate of the crack, in m 3 / min; The displacement discontinuity method is used to update the internal pressure of each fracture unit, which is expressed as: ； in, is the minimum horizontal principal stress, in MPa.

9. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The step S8 solves the proppant migration equation to obtain the concentration distribution of the proppant in each cluster of fractures, which is expressed as: ； in, and are the volume flux of proppant generated by convective migration and sedimentation, respectively, in m 2 / min; is the normalized proppant concentration; is the radius of the spherical proppant particle, in m; is the ratio of the fracture width to the proppant particle radius; is the proppant density, in kg / m 3 ; 、 and is a dimensionless function.

10. The method for simulating multi-cluster fracture propagation and proppant migration considering pore erosion according to claim 1, characterized in that: The step S9 specifically includes: calculating the critical width of the crack tip unit according to the crack propagation criterion. If the actual width of the tip unit reaches the critical width, the crack propagates, which is expressed as: in, is the critical width of the crack unit, in m; is the fracture toughness, unit is MPa·m 1 / 2 ; is the plane strain Young's modulus, in units of ; is the tip unit expansion speed, in m / min.

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