A method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity

Abstract

The present invention discloses a method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return flow rate. The method first obtains geological characteristic parameters through deep coal-rock gas geological research and determines the initial and boundary conditions. Then, based on these parameters, combined with the Darcy filtration model, the continuity equation and the material balance equation, a deep coal-rock gas seepage model is established to solve the distribution of formation parameters during fracturing. Next, according to the pore pressure distribution, the stress field in the reservoir after fracturing is calculated using the stress balance equation, and the porosity and permeability are updated. On this basis, the critical starting velocity model of coal powder in the matrix pores and in the hydraulic fractures is derived respectively. Finally, combined with the simulated fluid flow velocity and the critical velocity of coal powder, the return flow rate is optimized with the goal of discharging coal powder in the fractures and controlling the non-flow of coal powder in the matrix pores. The present invention can predict the critical starting velocity of coal powder in the return flow process and optimize the construction parameters, providing guidance for the development of deep coal-rock gas.

Description

Technical Field

[0001] The invention relates to a method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity, belonging to the technical field of oil and gas field development. Background Art

[0002] Under the action of high pressure and temperature, the adsorption capacity of coal rock in my country's deep coal-rock gas reservoir reaches its limit, forming a supersaturated deep coal-bed methane reservoir with "high gas content, high saturation, and free gas". Affected by its reservoir characteristics, hydraulic fracturing technology has been widely used in the development of coal-rock gas. After the coal seam fracturing construction, it must be returned in time to reduce the residence time of the fracturing fluid in the reservoir and reduce the damage of the fracturing fluid to the coal seam. And due to the fragility of the coal seam itself, coal powder is easily generated in the coal-rock reservoir and mining process, which destroys the original flow channel of the coal seam and blocks the holes, reduces the permeability of the fracture, and greatly affects the production capacity of coal-rock gas. Therefore, it is considered that in the process of coal-rock gas pressure return, the flow rate of the return fluid is controlled to prevent the coal powder in the reservoir matrix from flowing, and at the same time, the coal powder in the fracture is discharged, reducing the probability of coal powder blocking the fracture and improving the fracture conductivity. This is the key to the efficient exploitation of deep coal-rock gas. However, there is currently no method that can accurately predict the critical flow rate of coal powder in the matrix and in the fractures after fracturing, as well as a method to optimize the return flow rate. Therefore, this calculation method was innovatively invented to solve this problem.

[0003] Although deep coal-rock gas is buried deeper than medium and shallow coal-bed methane, due to the development of natural fractures and cleats, the fracture walls and matrix are easily damaged by the interaction between fluid pressure and ground stress during the fracturing process, and coal powder particles are produced during the damage process. At present, domestic and foreign studies have been conducted on the causes of coal powder generation. It was found that there is a critical flow rate for coal powder generation during drainage, and when the radius of coal powder particles and the radius of fractures are reduced, coal powder particles are easier to migrate, and the coal powder production of coalbed methane wells will increase (Johnson RL, Sedaghat M. The Implementation of Subterranean Barriers to Reduce Shallow Gas Migration and Coal Mine Methane Emissions from Open-Cut Metallurgical-Coal Mines[R]. SPE-217310-MS, 2023) (Zhang Gongshe, Tian Wentao, Tao Shan, et al. Experimental study on the migration law of coal powder in coalbed methane reservoirs[J]. Journal of Oil and Gas, 2011, 33(9):105-108) (Liu Shenggui, He Xiaohei, Li Huifang. Mechanism and control measures of coal powder generation in coalbed methane horizontal wells[J]. Journal of Liaoning Technical University (Natural Science Edition), 2011, 30(4):508-512). Most studies believe that there are three main reasons for induced coal powder production: first, the nature of the coal seam, which is mainly related to the clay content and structural characteristics of the coal rock; second, the friction between the drill bit and the coal rock during construction and the grinding effect between the proppant and the coal seam during fracturing; third, the stress conditions of the coal seam change, the stress balance is destroyed, and coal powder is produced in the matrix (Chen Zhenhong, Wang Yibing, Sun Ping. The influence of coal powder production on the production capacity of high-rank coalbed methane wells and its control [J]. Journal of China Coal Society, 2009, 34(2): 229-232).

[0004] Although it is recognized that coal powder will be produced in the matrix and fractures due to hydraulic fracturing, few scholars have studied the critical starting velocity in the matrix and fractures of coal powder. Some scholars have studied the lifting of coarse particles in solid-liquid two-phase flow. Based on the continuity equation and motion equation of coarse particles and fine particles (particle size is 0.03~0.08mm) two-phase flow, the critical conditions for the lifting of coarse particles in solid-liquid two-phase flow are obtained (Li Heng, Li Pengcheng, Han Wenliang. Numerical simulation of unstable flow of coarse particles hydraulic lifting in vertical pipes [J]. Nonferrous Metals, 2003, 55(3): 109-111). Other scholars have obtained through analysis that the maximum velocity of the fluid in the pipe is twice the average velocity. At the same time, the velocity near the pipe wall is lower. The solid phase particles always move downward near the pipe wall. The velocity distribution must be considered when determining the critical carrying velocity. It is generally believed that when the fluid velocity reaches the sedimentation velocity of solid particles, the solid particles are in a suspended state and can be carried out (Yue Lei, Li Xueguang, Li Xiuying, et al. Determination of reasonable production of sand-producing oil wells [J]. Oil and Gas Field Surface Engineering, 2004, 23 (1): 55-56.). However, these studies are not aimed at the critical flow velocity of coal powder, but at the flow of solid particles, without considering the influence of porous media and fracture closure.

[0005] So far, there has been no research on the calculation of the critical velocity of coal powder after fracturing and the optimization of the return flow rate of deep coal-rock gas. With the vigorous development of deep coal-rock gas and the application of large-scale hydraulic fracturing production-increasing measures, controlling the migration of coal powder after fracturing has become the key to subsequent production increases. Therefore, it is an imperative trend to calculate the critical starting velocity of coal powder in the matrix and fractures after fracturing, optimize the return flow rate after fracturing, and formulate a corresponding reasonable and scientific production system. In order to accurately predict and analyze the changing law of the critical starting velocity of coal powder after fracturing and control the scientific return flow rate, it is necessary to find a mathematical simulation method that adapts to the geological conditions and fills the gap in oilfield development technology research in this aspect. Summary of the invention

[0006] The present invention mainly overcomes the shortcomings of the prior art and proposes a method for calculating the critical velocity of coal powder after deep coal-rock gas fracturing and optimizing the return flow rate. The method takes into account the fluid flow, formation stress changes and the properties of the particles themselves, the interaction between coal powder particles, and the force of the fluid on the coal powder particles during the fracturing process. Based on elastic mechanics, seepage mechanics, numerical simulation principles, and fluid-solid coupling theory, a critical starting velocity model for coal powder in the matrix and fractures after deep coal-rock gas fracturing is established. Using this model, the flow law and velocity of coal powder in the matrix and fractures can be predicted according to construction and geological parameters, and a scientific and reasonable return flow rate can be found. The proposal of this method fills the gap in existing research theories and technologies.

[0007] The technical solution provided by the present invention to solve the above technical problems is: a method for calculating the critical flow rate of coal powder after deep coal-rock gas pressure and optimizing the return flow rate, comprising the following steps:

[0008] (1) Based on deep coal-rock gas geological research, obtain the existing geological characteristic parameters of the target coal-rock gas reservoir, including formation pressure, porosity, permeability, natural fracture parameters, etc., and determine the initial conditions and boundary conditions;

[0009] (2) Based on the above-mentioned deep coal-rock gas geological characteristic parameters, a deep coal-rock gas seepage model was established by considering the comprehensive Darcy filtration model, continuity equation, material balance equation and initial conditions, and the distribution of water and gas saturation and pressure in the formation during the fracturing process was obtained;

[0010] (3) Based on the pore pressure distribution obtained from the seepage model, the stress field in the deep coal-rock gas reservoir after fracturing is calculated in combination with the stress balance equation, and the magnitude and direction distribution of stress in the matrix and near the fractures are obtained. Then, the flow law of deep coal-rock gas under the effect of fluid-solid coupling is calculated by using porosity and permeability as coupling terms;

[0011] (4) Based on the stress conditions of coal powder in the matrix pores, the critical starting velocity model of coal powder in the matrix pores is derived and established by considering the properties of coal powder particles themselves, the interaction forces between coal powder particles, the forces between coal powder and rock skeleton, and the forces of fluid on coal powder particles;

[0012] (5) Based on the stress conditions of coal powder in hydraulic fractures, the critical starting velocity model of coal powder in hydraulic fractures is derived and established by considering the properties of coal powder particles, the interaction forces between coal powder particles, and the force of fluid on coal powder particles;

[0013] (6) The fluid flow velocities in the matrix and fractures after fracturing are simulated according to step (3), and the critical starting flow rates of the coal powder in the matrix and fractures are calculated according to steps (5) and (6). The optimal flowback flow rate in the flowback process after fracturing is obtained by taking the discharge of coal powder particles in the fractures and the control of the non-flow of coal powder in the matrix pores as the optimization goal.

[0014] A further technical solution is that in step (1), based on the deep coal-rock gas geological research, the existing geological characteristic parameters of the target coal-rock gas reservoir are obtained to determine the initial conditions and boundary conditions. The specific parameters include formation pressure, porosity, permeability, natural fracture parameters, construction displacement, total liquid volume, liquid viscosity, number of fracture clusters, etc.

[0015] A further technical solution is that the specific process of step (2) is as follows: based on the deep coal-rock gas geological characteristic parameters obtained in step (1), a deep coal-rock gas comprehensive Darcy filtration model, a continuity equation, a material balance equation and initial conditions are combined to establish a deep coal-rock gas seepage model, and the water content in the formation during the fracturing process is obtained ( S fw , S mw )、Gas saturation( S fg , S mg ) and pressure ( p fg , p fw ) distribution:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] (4)

[0020] In the formula, ▽ is the symbol of the gradient operator, dimensionless; is the symbol for partial differential, dimensionless; t is time, s; f f is the fracture porosity, dimensionless; k f is the fracture permeability, 10 -3 μm 2 ; p fg , p fw are the gas phase and water phase pressures in the fracture system, MPa, respectively; m fg , m fw are the viscosities of gas and water in the fracture system, mPa·s; k rgf , k rwf are the relative permeabilities of gas and water in the fracture system, dimensionless; r fg , r fw are the densities of gas and water in the fracture system, kg / m 3 ; g is the acceleration due to gravity, g=9.8m 2 / s; H is the formation depth, m; Bfg , B fw are the volume coefficients of gas and water phases in the fracture system, respectively, dimensionless; S fg , S fw are the gas and water phase saturations in the fracture system, respectively, dimensionless; q vg , q vw are the gas and water production per unit volume of coal reservoir, m 3 / (m 3 s); q * gmf , q * wmf are the gas and water exchange amounts between the fracture and matrix pore systems, m 3 / (m 3 s); f m is the matrix porosity, dimensionless; S mg , S mw are the gas and water phase saturations in the matrix pore system, respectively, dimensionless; B mg , B mw are the volume coefficients of gas and water in the matrix pores, respectively, dimensionless; q vm is the flow rate of desorbed gas from the matrix pore surface to the matrix pore, m 3 / (m 3 ·s).

[0021] A further technical solution is that the specific process of step (3) is as follows: based on the pore pressure distribution obtained by the seepage model, the stress field in the deep coal-rock gas reservoir after fracturing is calculated in combination with the stress balance equation to obtain the magnitude and direction distribution of stress near the matrix and the fracture. Then, the flow law of deep coal-rock gas under the action of fluid-solid coupling is calculated by taking porosity and permeability as coupling terms:

[0022] (5)

[0023] Where: G is the shear modulus of rock, MPa; ▽ is the gradient operator symbol, dimensionless; u is the displacement of the rock skeleton along the x-axis, m; v is the displacement of the rock skeleton along the y-axis, m; l is the Lamé constant; is the deformation of the rock skeleton, dimensionless; is the symbol for partial differential, dimensionless; is the average formation pressure, MPa; x is the coordinate along the x-axis; y is the coordinate along the y-axis.

[0024] Among them, the fluid-solid coupling porosity and permeability models are:

[0025] (6)

[0026] (7)

[0027] Where: is the current reservoir porosity, in percentage; is the initial reservoir porosity, percentage; is the deformation of the rock skeleton, dimensionless; T is the current reservoir temperature, °C; T 0 is the initial reservoir temperature, °C; c is the coefficient of thermal expansion, 1 / °C; k is the current reservoir permeability, mD; k 0 is the initial reservoir permeability, mD; △ represents the increment of change, dimensionless.

[0028] A further technical solution is that the specific process of step (4) is as follows: considering that the resistance encountered by the skeleton coal powder particles when peeling off under the action of fluid includes the cohesive force generated by the bonding between the skeleton coal powder particles, the friction between the skeleton coal powder particles and the surrounding particles due to the peeling movement, the tensile strength between the skeleton coal powder particles and the coal particles in the peeling movement direction, and the drag force generated by the formation fluid flow on the skeleton coal powder particles when the skeleton coal powder particles peel off, the critical starting velocity model of the coal powder in the matrix is ​​derived:

[0029] (8)

[0030] Where: V sc is the critical velocity of pulverized coal particles peeling off, m / s; is the porosity of weakly cemented coal rock, in percentage; is the particle size of the skeleton coal powder particles, μm; or f is the dynamic viscosity of the fluid, mPa·s; S 0 is the cohesive force between the skeleton coal powder particles, MPa; m is the friction coefficient between the skeleton coal powder particles, dimensionless; , is the effective radial stress and axial stress on the pore wall, MPa; is the tensile strength between skeleton coal powder particles, MPa.

[0031] A further technical solution is that the specific process of step (5) is as follows: based on the stress conditions of the coal powder in the hydraulic fracture, the properties of the coal powder particles themselves, the interaction forces between the coal powder particles, and the force of the fluid on the coal powder particles are considered to derive and establish a critical starting flow velocity model of the coal powder in the hydraulic fracture:

[0032] (9)

[0033] Where: r s is the density of pulverized coal, kg / m 3 ; r is the density of the return fluid, kg / m 3 ; g is the acceleration due to gravity, g=9.81 m / s 2 ; d m is the diameter of coal powder passing through the pore throat of the proppant, m; d is the film water thickness, d =2.31×10 -7 m, which is approximately the thickness of 770 water molecules; h is the height of the liquid column acting on the coal powder; r 0 is the dry coal powder bulk density on the crack surface, kg / m 3 ; r * is the stable dry bulk density of coal powder particles, kg / m 3 ; is the bonding force parameter between coal powder particles in water, ; is the reference particle size, with a value of 10 -2 m; is the equivalent coal powder diameter, m; v f is the critical starting velocity of coal powder in the fracture, m / s.

[0034] A further technical solution is that the specific process of step (6) is as follows: according to the fluid flow velocity in the matrix and the fracture after fracturing obtained by simulation in step (3), and the critical starting flow velocity of the coal powder in the matrix and the fracture calculated in steps (5) and (6), the optimal flowback flow velocity in the flowback process after fracturing is obtained by discharging the coal powder particles in the fracture and controlling the coal powder in the matrix pores to not flow, and the following is obtained:

[0035] (10)

[0036] in, v otp is the optimal flowback velocity, m / s.

[0037] The beneficial effects of the invention are as follows: the method is used to predict the critical starting flow rate of coal powder in the matrix and hydraulic fractures during the backflow process of deep coal-rock gas reservoirs after fracturing. By determining a reasonable backflow rate, by considering the fluid flow, formation stress changes and the properties of the particles themselves, the interaction force between coal powder particles, and the force of the fluid on the coal powder particles during the fracturing process, a critical starting flow rate model for coal powder in the matrix and fractures after deep coal-rock gas fracturing is established based on elastic mechanics, seepage mechanics, numerical simulation principles, and fluid-solid coupling theory. The optimization goal is to discharge the coal powder particles in the fractures and control the non-flow of coal powder in the matrix pores. The flow law and speed of coal powder in the matrix and fractures can be predicted according to construction and geological parameters, and a scientific and reasonable backflow rate can be found. The proposal of this method fills the theoretical and technical gaps in the existing research on backflow control after deep coal-rock gas fracturing, and provides a reliable analysis and research method for backflow after coal-rock gas reservoir fracturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the force analysis diagram of coal powder being dragged by fluid;

[0039] Figure 2 It is a block diagram of the model calculation and optimization method;

[0040] Figure 3 This is the formation pressure distribution diagram during the post-pressure flowback process;

[0041] Figure 4 It is a curve diagram showing the relationship between the critical starting velocity of coal powder in the crack and the radius of coal powder;

[0042] Figure 5 This is a curve diagram showing the relationship between the critical starting flow rate of matrix coal powder and liquid viscosity. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further illustrated below with reference to the accompanying drawings and embodiments.

[0044] A method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity comprises the following steps:

[0045] (1) Based on deep coal-rock gas geological research, obtain the existing geological characteristic parameters of the target coal-rock gas reservoir, including formation pressure, porosity, permeability, natural fracture parameters, etc., and determine the initial conditions and boundary conditions;

[0046] (2) Based on the above-mentioned deep coal-rock gas geological characteristic parameters, a deep coal-rock gas seepage model was established by considering the comprehensive Darcy filtration model, continuity equation, material balance equation and initial conditions, and the distribution of water and gas saturation and pressure in the formation during the fracturing process was obtained;

[0047] (3) Based on the pore pressure distribution obtained from the seepage model, the stress field in the deep coal-rock gas reservoir after fracturing is calculated in combination with the stress balance equation, and the magnitude and direction distribution of stress in the matrix and near the fractures are obtained. Then, the flow law of deep coal-rock gas under the effect of fluid-solid coupling is calculated by using porosity and permeability as coupling terms;

[0048] (4) Based on the stress conditions of coal powder in the matrix pores, the critical starting velocity model of coal powder in the matrix pores is derived and established by considering the properties of coal powder particles themselves, the interaction forces between coal powder particles, the forces between coal powder and rock skeleton, and the forces of fluid on coal powder particles;

[0049] (5) Based on the stress conditions of coal powder in hydraulic fractures, the critical starting velocity model of coal powder in hydraulic fractures is derived and established by considering the properties of coal powder particles, the interaction forces between coal powder particles, and the force of fluid on coal powder particles;

[0050] (6) The fluid flow velocities in the matrix and fractures after fracturing are simulated according to step (3), and the critical starting flow rates of the coal powder in the matrix and fractures are calculated according to steps (5) and (6). The optimal flowback flow rate in the flowback process after fracturing is obtained by taking the discharge of coal powder particles in the fractures and the control of the non-flow of coal powder in the matrix pores as the optimization goal.

[0051] In the present invention, in step (1), based on deep coal-rock gas geological research, the existing geological characteristic parameters of the target coal-rock gas reservoir are obtained, and the initial conditions and boundary conditions are determined. The specific parameters include formation pressure, porosity, permeability, natural fracture parameters, construction displacement, total liquid volume, liquid viscosity, number of fracture clusters, etc.

[0052] In the present invention, the specific process of step (2) is as follows: based on the deep coal-rock gas geological characteristic parameters obtained in step (1), a deep coal-rock gas comprehensive Darcy filtration model, a continuity equation, a material balance equation and initial conditions are combined to establish a deep coal-rock gas seepage model, and the water content in the formation during the fracturing process is obtained ( S fw , S mw )、Gas saturation( S fg , S mg ) and pressure ( p fg , pfw ) distribution:

[0053] (1)

[0054] (2)

[0055] (3)

[0056] (4)

[0057] In the formula, ▽ is the symbol of the gradient operator, dimensionless; is the symbol for partial differential, dimensionless; t is time, s; f f is the fracture porosity, dimensionless; k f is the fracture permeability, 10 -3 μm 2 ; p fg , p fw are the gas phase and water phase pressures in the fracture system, MPa, respectively; m fg , m fw are the viscosities of gas and water in the fracture system, mPa·s; k rgf , k rwf are the relative permeabilities of gas and water in the fracture system, dimensionless; r fg , r fw are the densities of gas and water in the fracture system, kg / m 3 ; g is the acceleration due to gravity, g=9.8m 2 / s; H is the formation depth, m; B fg , B fw are the volume coefficients of gas and water phases in the fracture system, respectively, dimensionless; S fg , S fw are the gas and water phase saturations in the fracture system, respectively, dimensionless; q vg , q vw are the gas and water production per unit volume of coal reservoir, m 3 / (m 3 s); q *gmf , q * wmf are the gas and water exchange amounts between the fracture and matrix pore systems, m 3 / (m 3 s); f m is the matrix porosity, dimensionless; S mg , S mw are the gas and water phase saturations in the matrix pore system, respectively, dimensionless; B mg , B mw are the volume coefficients of gas and water in the matrix pores, respectively, dimensionless; q vm is the flow rate of desorbed gas from the matrix pore surface to the matrix pore, m 3 / (m 3 ·s).

[0058] In the present invention, the step (3) needs to calculate the stress field in the deep coal-rock gas reservoir after fracturing based on the pore pressure distribution obtained by the seepage model in step (2) in combination with the stress balance equation to obtain the magnitude and direction distribution of stress near the matrix and the fracture. Then, the flow law of deep coal-rock gas under the action of fluid-solid coupling is calculated by taking porosity and permeability as coupling terms:

[0059] (5)

[0060] Where: G is the shear modulus of rock, MPa; ▽ is the gradient operator symbol, dimensionless; u is the displacement of the rock skeleton along the x-axis, m; v is the displacement of the rock skeleton along the y-axis, m; l is the Lamé constant; is the deformation of the rock skeleton, dimensionless; is the symbol for partial differential, dimensionless; is the average formation pressure, MPa; x is the coordinate along the x-axis; y is the coordinate along the y-axis.

[0061] Among them, the fluid-solid coupling porosity and permeability models are:

[0062] (6)

[0063] (7)

[0064] Where: is the current reservoir porosity, in percentage; is the initial reservoir porosity, percentage; is the deformation of the rock skeleton, dimensionless; T is the current reservoir temperature, °C; T 0 is the initial reservoir temperature, °C; c is the coefficient of thermal expansion, 1 / °C; k is the current reservoir permeability, mD; k 0 is the initial reservoir permeability, mD; △ represents the increment of change, dimensionless.

[0065] In the present invention, the step (4) takes into account the resistance encountered by the skeleton coal powder particles when peeling off under the action of fluid, including the cohesive force generated by the bonding between the skeleton coal powder particles, the friction between the skeleton coal powder particles and the surrounding particles due to the peeling movement, the tensile strength between the skeleton coal powder particles and the coal particles in the peeling direction, and the drag force generated by the formation fluid flow on the skeleton coal powder particles as the driving force for the peeling of the skeleton coal powder particles ( Figure 1 : G is the gravity of coal powder particles, F is the force between coal powder particles), and the critical starting velocity model of coal powder in the matrix is ​​derived:

[0066] (8)

[0067] Where: V sc is the critical velocity of pulverized coal particles peeling off, m / s; is the porosity of weakly cemented coal rock, in percentage; is the particle size of the skeleton coal powder particles, μm; or f is the dynamic viscosity of the fluid, mPa·s; S 0 is the cohesive force between the skeleton coal powder particles, MPa; m is the friction coefficient between the skeleton coal powder particles, dimensionless; , is the effective radial stress and axial stress on the pore wall, MPa; is the tensile strength between skeleton coal powder particles, MPa.

[0068] In the present invention, in step (5), according to the stress conditions of the coal powder in the hydraulic fracture, the properties of the coal powder particles themselves, the interaction forces between the coal powder particles, and the force of the fluid on the coal powder particles are considered to derive and establish a critical starting flow velocity model of the coal powder in the hydraulic fracture:

[0069] (9)

[0070] Where: r s is the density of pulverized coal, kg / m 3 ; r is the density of the return fluid, kg / m 3 ; g is the acceleration due to gravity, m / s 2 , take g=9.81; d m is the diameter of coal powder passing through the pore throat of the proppant, m; d is the film water thickness, d =2.31×10 -7 m, which is approximately the thickness of 770 water molecules; h is the height of the liquid column acting on the coal powder; r 0 is the dry coal powder bulk density on the crack surface, kg / m 3 ; r * is the stable dry bulk density of coal powder particles, kg / m 3 ; is the bonding force parameter between coal powder particles in water, ; is the reference particle size, 10 -2 m; is the equivalent coal powder diameter, m; v f is the critical starting velocity of coal powder in the fracture, m / s.

[0071] In the present invention, in step (6), the fluid flow velocity in the matrix and the fracture after fracturing is first obtained by simulation according to step (3), and the critical starting flow velocity of the matrix and the coal powder in the fracture calculated in steps (5) and (6), and the optimal return flow velocity ( ) in the return flow process after fracturing is obtained by taking the discharge of the coal powder particles in the fracture and controlling the non-flow of the coal powder in the matrix pores as the optimization goal. ):

[0072] (10)

[0073] in, v otp is the optimal flowback velocity, m / s.

[0074] According to step (6), when the optimal backflow velocity is less than the critical starting velocity of the coal powder in the matrix and greater than the critical starting velocity of the coal powder in the cracks, the coal powder in the matrix pores can be prevented from flowing and the coal powder particles in the cracks can be discharged, thereby increasing the conductivity of the cracks and preventing them from being blocked by coal powder particles.

[0075] Example 1: Through field logging, geological data of a deep coal-rock gas reservoir in the Ordos Basin were obtained. The post-fracturing flowback process parameters of this well have long relied on experience and lack scientific and reasonable technical guidance. This well is representative of deep coal-rock gas reservoirs, that is, the burial depth exceeds 2500m, natural fractures and cleats are well developed, the free gas content is high, and the formation pressure is high. This well has good demonstration as a research case of this method.

[0076] Simulate the route calculation Figure 2 The specific simulation steps are as follows:

[0077] 1. The geological parameters of the reservoir were obtained through on-site logging: rock Poisson's ratio 0.1, vertical depth of the well 1600m, reservoir thickness 20m, initial formation permeability 0.05mD, initial porosity 5%, original formation pressure 29MPa, elastic modulus 50000MPa, horizontal minimum ground stress 42MPa, coal rock gas compression coefficient 8.9×10 -4 MPa -1 , rock compression coefficient 5.4×10 -4 MPa -1 , formation water compressibility coefficient 4.0×10 -4 MPa -1 , injection rate is 15m³ / min, total injection volume is 2300m³, number of fracture clusters is 3, and cluster spacing is 15m.

[0078] 2. Use the finite difference method to perform discrete differences on equations (1), (2), (3), and (4), then substitute the above geological parameters and construction parameters into equations (1), (2), (3), and (4), and iterate the four equations together until the accuracy requirements are met. Stop the calculation and the fluid pressure distribution in the fracture and matrix at any time can be obtained.

[0079] 3. Use the finite difference method to substitute the pore pressure calculated by equations (1), (2), (3), and (4) into equation (5). Combined with the initial conditions and boundary conditions, two five-diagonal matrices are obtained through numerical discretization. The matrix calculation method provided by Matlab is used to solve the distribution of formation stress during the injection and discharge of fracturing fluid ( Figure 3 ).

[0080] 4. Then, the coupling terms of stress and fluid flow are constructed through equations (6) and (7), and substituted into equations (1), (2), (3), and (4) for calculation. At the same time, the simultaneous equations (1) to (7) can obtain the true flow velocity at any position in the matrix and fracture of the deep coal-rock gas reservoir at any time.

[0081] 5. Based on the input parameters, equations (8) and (9) can be used to calculate the critical start-up flow rate of the coal powder in the current matrix and fracture, as well as the relationship between the critical start-up flow rate and the coal powder particle size and fracturing fluid viscosity ( Figure 4 , 5 ), and then the optimal return flow rate of deep coal gas can be optimized through equation (10). Finally, the actual flow rate is compared with the critical flow rate calculated by equations (8) and (9), and the return flow process can be adjusted according to this range.

[0082] According to the simulation steps of the present invention, parameters such as formation pressure, water saturation, formation flow rate and critical starting flow rate of coal powder in the process of deep coal-rock gas fracturing backflow can be obtained for optimizing the backflow process parameters.

[0083] The above description is not intended to impose any form of limitation on the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity, characterized in that: The following steps are involved: (1) Based on deep coal-rock gas geological research, obtain the existing geological characteristic parameters of the target coal-rock gas reservoir, including formation pressure, porosity, permeability, and natural fracture parameters, and determine the initial conditions and boundary conditions; (2) Based on the above-mentioned deep coal-rock gas geological characteristic parameters, a deep coal-rock gas seepage model was established by considering the comprehensive Darcy filtration model, continuity equation, material balance equation and initial conditions, and the distribution of water and gas saturation and pressure in the formation during the fracturing process was obtained; (3) Based on the pore pressure distribution obtained from the seepage model, the stress field in the deep coal-rock gas reservoir after fracturing is calculated in combination with the stress balance equation, and the magnitude and direction distribution of stress in the matrix and near the fractures are obtained; then, the flow law of deep coal-rock gas under the effect of fluid-solid coupling is calculated by using porosity and permeability as coupling terms; (4) Based on the stress conditions of coal powder in the matrix pores, the critical starting velocity model of coal powder in the matrix pores is derived and established by considering the properties of coal powder particles themselves, the interaction forces between coal powder particles, the forces between coal powder and rock skeleton, and the forces of fluid on coal powder particles; (5) Based on the stress conditions of coal powder in hydraulic fractures, the critical starting velocity model of coal powder in hydraulic fractures is derived and established by considering the properties of coal powder particles, the interaction forces between coal powder particles, and the force of fluid on coal powder particles; (6) The fluid flow velocities in the matrix and fractures after fracturing are simulated according to step (3), and the critical starting flow rates of the coal powder in the matrix and fractures are calculated according to steps (5) and (6). The optimal flowback flow rate in the flowback process after fracturing is obtained by taking the discharge of coal powder particles in the fractures and the control of the non-flow of coal powder in the matrix pores as the optimization goal.

2. The method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity according to claim 1 is characterized in that: The specific process of step (1) is as follows: based on the deep coal-rock gas geological research, obtain the existing geological characteristic parameters of the target coal-rock gas reservoir, determine the initial conditions and boundary conditions, and the specific parameters include formation pressure, porosity, permeability, natural fracture parameters, construction displacement, total liquid volume, liquid viscosity, and the number of fracture clusters.

3. The method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity according to claim 1 is characterized in that: The specific process of step (2) is as follows: based on the deep coal-rock gas geological characteristic parameters obtained in step (1), a deep coal-rock gas comprehensive Darcy filtration model, continuity equation, material balance equation and initial conditions are combined to establish a deep coal-rock gas seepage model, and the water content in the formation during the fracturing process is obtained ( S fw , S mw )、Gas saturation( S fg , S mg ) and pressure ( p fg , p fw ) distribution: （1） （2） （3） （4） In the formula, ▽ is the symbol of the gradient operator, dimensionless; is the symbol for partial differential, dimensionless; t is time, s; φ f is the fracture porosity, percentage; k f is the fracture permeability, 10 -3 μm 2 ; p fg , p fw are the gas phase and water phase pressures in the fracture system, MPa, respectively; μ fg , μ fw are the viscosities of gas and water in the fracture system, mPa·s; k rgf , k rwf are the relative permeabilities of gas and water in the fracture system, dimensionless; ρ fg , ρ fw are the densities of gas and water in the fracture system, kg / m 3 ; g is the acceleration due to gravity, g=9.8m 2 / s; H is the formation depth, m; B fg , B fw are the volume coefficients of gas and water phases in the fracture system, respectively, dimensionless; S fg , S fw are the gas and water phase saturations in the fracture system, respectively, dimensionless; q vg , q vw are the gas and water production per unit volume of coal reservoir, m 3 / (m 3 s); q * gmf , q * wmf are the gas and water exchange amounts between the fracture and matrix pore systems, m 3 / (m 3 s); φ m is the matrix porosity, percentage; S mg , S mw are the gas and water phase saturations in the matrix pore system, respectively, dimensionless; B mg , B mw are the volume coefficients of gas and water in the matrix pores, respectively, dimensionless; q vm is the flow rate of desorbed gas from the matrix pore surface to the matrix pore, m 3 / (m 3 ·s).

4. The method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity according to claim 1 is characterized in that: The specific process of step (3) is as follows: based on the pore pressure distribution obtained by the seepage model, the stress field in the deep coal-rock gas reservoir after fracturing is calculated in combination with the stress balance equation to obtain the magnitude and direction distribution of stress in the matrix and near the fractures; then, the flow law of the deep coal-rock gas under the action of fluid-solid coupling is calculated by taking porosity and permeability as coupling terms: （5） Where: G is the shear modulus of rock, MPa; ▽ is the symbol of the gradient operator, dimensionless; u is the displacement of the rock skeleton along the x-axis, m; v is the displacement of the rock skeleton along the y-axis, m; λ is the Lamé constant; is the deformation of the rock skeleton, dimensionless; is the symbol for partial differential, dimensionless; is the average formation pressure, MPa; x is the coordinate along the x-axis; y is the coordinate along the y-axis; Among them, the fluid-solid coupling porosity and permeability models are: （6） （7） Where: is the current reservoir porosity, in percentage; is the initial reservoir porosity, percentage; is the deformation of the rock skeleton, dimensionless; T is the current reservoir temperature, °C; T 0 is the initial reservoir temperature, °C; γ is the coefficient of thermal expansion, 1 / °C; k is the current reservoir permeability, mD; k 0 is the initial reservoir permeability, mD; △ represents the increment of change, dimensionless.

5. The method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity according to claim 1 is characterized in that: The specific process of step (4) is as follows: considering that the resistance encountered by the skeleton coal powder particles when peeling off under the action of fluid includes the cohesive force generated by the bonding between the skeleton coal powder particles, the friction between the skeleton coal powder particles and the surrounding particles due to the peeling movement, the tensile strength between the skeleton coal powder particles and the coal particles in the peeling direction, and the drag force generated by the formation fluid flow on the skeleton coal powder particles when the skeleton coal powder particles peel off, the critical starting velocity model of the coal powder in the matrix is ​​derived: （8） Where: V sc is the critical velocity of pulverized coal particles peeling off, m / s; is the porosity of weakly cemented coal rock, in percentage; is the particle size of the skeleton coal powder particles, μm; η f is the dynamic viscosity of the fluid, mPa·s; S 0 is the cohesive force between the skeleton coal powder particles, MPa; μ is the friction coefficient between the skeleton coal powder particles, dimensionless; , is the effective radial stress and axial stress on the pore wall, MPa; is the tensile strength between skeleton coal powder particles, MPa.

6. The method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity according to claim 1 is characterized in that: The specific process of step (5) is as follows: based on the stress of coal powder in the hydraulic fracture, the properties of the coal powder particles themselves, the interaction force between the coal powder particles, and the force of the fluid on the coal powder particles are considered to derive and establish a critical starting flow velocity model of coal powder in the hydraulic fracture: （9） Where: ρ s is the density of pulverized coal, kg / m 3 ; ρ is the density of the return fluid, kg / m 3 ; g is the acceleration due to gravity, g=9.81 m / s 2 ; d m is the diameter of coal powder passing through the pore throat of the proppant, m; δ is the film water thickness, δ =2.31×10 -7 m, is the thickness of 770 water molecules; h is the height of the liquid column acting on the coal powder; r 0 is the dry coal powder bulk density on the crack surface, kg / m 3 ; r * is the stable dry bulk density of coal powder particles, kg / m 3 ; is the bonding force parameter between coal powder particles in water, ; is the reference particle size, 10 -2 m; is the equivalent coal powder diameter, m; v f is the critical starting velocity of coal powder in the fracture, m / s.

7. The method for calculating the critical velocity of coal powder after deep coal-rock gas pressure and optimizing the return velocity according to claim 1 is characterized in that: The specific process of step (6) is as follows: according to the fluid flow velocity in the matrix and the fracture after fracturing obtained by simulation in step (3), and the critical starting flow velocity of the coal powder in the matrix and the fracture calculated in steps (5) and (6), the optimal flowback flow velocity in the flowback process after fracturing is obtained by taking the coal powder particles in the fractures and controlling the coal powder in the matrix pores to not flow as the optimization goal. ,in, v otp is the optimal flowback velocity, m / s.

Images