CN113919201A - Multi-scale expansion grid self-adaption method for hydraulic fracturing fracture - Google Patents

Multi-scale expansion grid self-adaption method for hydraulic fracturing fracture Download PDF

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CN113919201A
CN113919201A CN202111321032.8A CN202111321032A CN113919201A CN 113919201 A CN113919201 A CN 113919201A CN 202111321032 A CN202111321032 A CN 202111321032A CN 113919201 A CN113919201 A CN 113919201A
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王永亮
刘旭光
李晨锋
郝耐
王国诚
武建勋
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Abstract

The invention discloses a grid self-adaptive method for multi-scale expansion of hydraulic fracturing fractures, which comprises the following steps: calculating a fluid-solid coupling result, judging multi-scale fracture, estimating a stress error and grid repartitioning; the coupling method based on the finite element, the discrete element and the finite volume method overcomes the difficulty of high-precision simulation of multi-scale problems in the traditional numerical method, can effectively simulate the multi-scale expansion behavior of a hydraulic fracturing fracture network, has more accurate and effective simulation results, integrates the Darcy law into a model to consider the seepage effect and control fluid leakage, and utilizes the finite volume method to realize the complete coupling discretization of single-phase flow in a fracture porous medium, solves the problem of difficult grid division of the traditional finite element in the fracture tip region, processes the difficulties existing in the aspects of large-scale fractures of an engineering model and small-scale fractures of a laboratory model, and solves the problem of difficult and reliable and effective solving of the multi-scale expansion of the hydraulic fracturing fractures.

Description

Multi-scale expansion grid self-adaption method for hydraulic fracturing fracture
Technical Field
The invention relates to the technical field of shale oil and gas scale development, in particular to a grid self-adaption method for multi-scale expansion of hydraulic fracturing fractures.
Background
The shale oil and gas development in China has been gradually started, the scale development of the shale oil and gas mainly depends on a key technology of improving the permeability of a reservoir by hydraulic fracturing, the principle of the hydraulic fracturing is that a large amount of fracturing fluid which exceeds the liquid absorption capacity of a stratum is pumped into a well by using a ground high-pressure pump set, high pressure is generated between the well bottom and a well sealed by a packer, when the pressure exceeds the fracture pressure of rocks near the well wall, cracks are generated to form a complex fracture network, the complex cracks generated by the hydraulic fracturing show typical multi-scale characteristics, and the time span of the formation of the cracks extends from the microsecond order of dynamic cracks to the hour order of quasi-static cracks; the method is characterized in that the space span of the method extends from the micron magnitude of a microcrack to the hundred meter magnitude of a main crack, how to research the formation mechanism of the complex multi-scale crack and perform multi-scale characterization on the initiation and expansion form of the crack, and is always a crucial problem in petroleum engineering rock mechanics.
In the current research of hydraulic fracture network, the behavior of continuous expansion of fracture is difficult to obtain by on-site monitoring, the hydraulic fracture morphology and the evolution process under the condition of multi-scale are difficult to present in the indoor physical experiment due to the small size limitation of a sample, and the numerical method is adopted for simulation to be an effective research scheme, the numerical model and the simulation method for simulating the large-scale multi-scale hydraulic fracture expansion still have some difficult problems, such as the model seepage-stress-fracture coupling can not realize the real large-scale simulation, the dynamic expansion mechanism of the fracture is difficult to know due to the limitation of the fracture expansion path and the implicit algorithm, the reliable expansion of the fracture is limited due to the grid division of the fracture tip region in the traditional finite element, the numerical simulation scheme for effectively simulating the expansion of the fracture fluid driving the fracture in multiple scales such as engineering scale and laboratory scale is lacked, in recent years, establishing and developing various calculation methods for solid crack propagation at home and abroad, for example, improving a conventional finite element, a displacement interruption method of a boundary element method and re-dividing a grid during crack propagation to describe displacement interruption at a crack surface to obtain a deformation field in a rock body; based on the traditional finite element and numerical value popular element method, the method has certain advantages in processing the problems of discontinuous surfaces such as faults, joints and the like in the rock body, but has certain difficulty in flexibly and efficiently solving the three-dimensional multi-scale fracture problem; the discrete fracture network method based on the classical analytic or semi-analytic fracture model adopts a simple plane fracture model, has high efficiency in solving, but also has difficulty in processing multi-scale fracture problems by simplifying the model, so that the application of the discrete fracture network method is limited, the problem of multi-scale fracture expansion simulated by a grid-based numerical method has the difficult problem of grid division, particularly the grid size of the tip of a fracture becomes the key for simulating the expansion of the fracture on different scales, and a low-quality grid is difficult to efficiently and accurately simulate the multi-scale expansion behavior of a hydraulic fracture network, so the invention provides a grid self-adaption method for the multi-scale expansion of the hydraulic fracture to solve the problems in the prior art.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a grid self-adaption method for multi-scale expansion of hydraulic fracture, the method overcomes the difficulty of high-precision multi-scale simulation in the traditional numerical method based on a coupling method of a finite element, a discrete element and a finite volume method, can effectively simulate the multi-scale expansion behavior of the hydraulic fracture seam network, and has a more accurate and effective simulation result.
In order to achieve the purpose of the invention, the invention is realized by the following technical scheme: a grid self-adaptive method for multi-scale expansion of hydraulic fracturing fractures comprises the following steps:
the method comprises the following steps: calculating solid deformation of the fractured porous medium by using a finite element model, specifically a solid displacement field, a solid velocity field and a solid acceleration field, calculating a fluid pressure velocity field of the fractured porous medium by using a finite volume model, and coupling the calculated solid deformation and the fluid pressure velocity field to obtain stress solutions on the fractured models with different scales;
step two: judging the stress and energy on each scale unit interface obtained in the step one by using a fracture criterion, judging whether the porous elastic medium fracture is expanded into a multi-scale fracture, and realizing fracture expansion of the units by using a discrete element method;
step three: selecting a natural super-convergence point of the stress to perform splicing recovery to obtain stress recovery of unit nodes, obtaining a super-convergence solution of the global stress through node stress interpolation, and estimating an error of the stress solution by using the super-convergence solution;
step four: and (5) aiming at the units with the error exceeding limit, estimating the new size of the error exceeding limit unit, subdividing according to the new size to obtain a new grid, returning to the step one, if all the units meet the error limit, the grid is not subdivided, and the solving process is finished.
The further improvement lies in that: in the first step, the models of the solid displacement field, the solid velocity field and the solid acceleration field are as follows:
Figure BDA0003345185390000031
where u is the vector displacement, σ represents the stress tensor, f is the external load vector, including the human body force, the fluid pressure on the fracture surface, the spring force, and the force on the traction boundary, ρ is the density, c is the damping coefficient,
Figure BDA0003345185390000047
and
Figure BDA0003345185390000048
the derivatives over time t are shown, respectively the acceleration and velocity vectors, and Ω is the solution domain.
The further improvement lies in that: in the first step, assuming unidirectional flow in a fractured porous medium, a velocity field is obtained by using a simplified Darcy flow law, and the formula is as follows:
Figure BDA0003345185390000041
Figure BDA0003345185390000042
wherein v ismAnd vfFluid flow velocity fields, p, representing porous media and hydraulic fractures, respectivelymAnd pkThe pressure values, k, of the porous medium and the hydraulic fracture respectivelymAnd kfPermeability of the porous medium and hydraulic fracture, respectively, μ is viscosity, and in the absence of gravity and capillary forces, the pressure equation for single phase flow in the porous medium and hydraulic fracture is:
Figure BDA0003345185390000043
Figure BDA0003345185390000044
wherein S ism＝n/kfAnd Sf＝1/kfWater storage coefficients of the porous medium and the hydraulic fracture are respectively, n is porosity, the fracture porosity is equal to 1, q represents an external fluid source, and deltaVIs the volume strain of the rock matrix and the permeability is expressed as kf＝w2And/12, wherein w represents the pore size of the hydraulic fracture.
The further improvement lies in that: in the second step, the breaking criteria include a tensile failure criterion and a shear failure criterion, and the tensile failure criterion and the shear failure criterion are expressed as
Figure BDA0003345185390000045
Figure BDA0003345185390000046
Wherein σ is tensile stress, τ is shear stress, ε0Is the value of the tensile strain at which the tensile stress reaches a maximum, εfValue of tensile strain at which tensile fracture occurs, gamma0The value of the shear strain at which the shear stress reaches a maximum, gammafTo determine the shear strain value at which shear fracture occurs, GtfAnd GsfTensile and shear fracture energies, respectively.
The further improvement lies in that: in the third step, the natural super-convergence point of the stress is a gaussian integral point of the stress unit, and the stress recovery calculation formula is as follows:
σ*(x，y)＝P(x，y)a
wherein, P (x, y) is given function vector, a is determined by least square fitting of a recovery field in a Gaussian integral point value and an original solution, and a high-precision recovery value sigma of node stress is obtained by the recovery field*。
The further improvement lies in that: the super convergence solution obtained by calculation by adopting a super convergence solution calculation formula is used as the error estimation of the original finite element solution to form the following energy mode error estimation
Figure BDA0003345185390000054
Figure BDA0003345185390000051
In the formula: sigma*、σhRespectively represented in matrix formAnd (3) solving the force and the conventional stress, wherein D is an elastic constant matrix, and omega is a solution domain.
The further improvement lies in that: in the third step, a unit self-adaptive analysis target formula is established according to the error of the stress solution:
Figure BDA0003345185390000052
wherein h isnewFor the new cell size after error evaluation from cell k, hkFor the current grid size of cell k, the parameters in the equation are:
Figure BDA0003345185390000053
the invention has the beneficial effects that: the coupling method based on the finite element, the discrete element and the finite volume method overcomes the difficulty of high-precision simulation of multi-scale problems in the traditional numerical method, can effectively simulate the multi-scale expansion behavior of a hydraulic fracturing fracture network, has more accurate and effective simulation results, integrates the Darcy law into a model to consider the seepage effect and control fluid leakage, realizes the complete coupling discretization of single-phase flow in a fracture porous medium by using the finite volume method, solves the problem of difficult grid division of the traditional finite element in the fracture tip region, processes the difficulties existing in the aspects of large-scale (engineering scale) fractures and small-scale (laboratory scale) fractures, and solves the problem of difficult and reliable and effective solving of the multi-scale expansion of the hydraulic fracturing fractures.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method in an embodiment of the invention;
FIG. 2 is a schematic diagram of an iterative calculation of flow-solid coupling and finite element-discrete element-finite volume coupling algorithm in an embodiment of the present invention;
fig. 3 is a schematic diagram of mesh adaptive partitioning and fracture propagation in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," "third," "fourth," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Referring to fig. 1, the present embodiment provides a grid adaptive method for multi-scale expansion of hydraulic fracture, which includes the following steps:
the method comprises the following steps: calculating solid deformation of the fractured porous medium by using a finite element model, specifically a solid displacement field, a solid velocity field and a solid acceleration field, calculating a fluid pressure velocity field of the fractured porous medium by using a finite volume model, and coupling the calculated solid deformation and the fluid pressure velocity field to obtain stress solutions on the fractured models with different scales;
the models of the solid displacement field, the solid velocity field and the solid acceleration field are as follows:
Figure BDA0003345185390000071
where u is the vector displacement, σ represents the stress tensor, f is the external load vector, including the human body force, the fluid pressure on the fracture surface, the spring force, and the force on the traction boundary, ρ is the density, c is the damping coefficient,
Figure BDA0003345185390000081
and
Figure BDA0003345185390000082
the derivative to time t is shown, respectively representing the acceleration and velocity vectors, and Ω is the solution domain;
assuming unidirectional flow in a fractured porous medium, a velocity field is obtained by using simplified form Darcy's law of flow, and the formula is as follows:
Figure BDA0003345185390000083
Figure BDA0003345185390000084
wherein variables comprising subscript m represent variables in the porous medium and variables comprising subscript f represent variables in the porous medium, vmAnd vfRepresenting the fluid flow velocity fields of the porous medium and the hydraulic fracture respectively,pmand pkThe pressure values, k, of the porous medium and the hydraulic fracture respectivelymAnd kfPermeability of the porous medium and hydraulic fracture, respectively, μ is viscosity, and in the absence of gravity and capillary forces, the pressure equation for single phase flow in the porous medium and hydraulic fracture is:
Figure BDA0003345185390000085
Figure BDA0003345185390000086
wherein S ism＝n/kfAnd Sf＝1/kfWater storage coefficients of the porous medium and the hydraulic fracture are respectively, n is porosity, the fracture porosity is equal to 1, q represents an external fluid source, and deltaVIs the volume strain of the rock matrix and the permeability is expressed as kf＝w212, wherein w represents the pore size of the hydraulic fracture;
step two: the breaking criteria include tensile failure criteria and shear failure criteria, the tensile and shear failure criteria being expressed as
Figure BDA0003345185390000091
Figure BDA0003345185390000092
Wherein σ is tensile stress, τ is shear stress, ε0The value of the tensile strain at which the tensile stress reaches a maximum, deltafValue of tensile strain at which tensile fracture occurs, gamma0The value of the shear strain at which the shear stress reaches a maximum, gammafTo determine the shear strain value at which shear fracture occurs, GtfAnd GsfTensile and shear fracture energies, respectively;
as shown in fig. 2, in order to calculate the control equation of solid deformation and fluid flow in the fractured porous medium, the solid deformation adopts a finite element method, the fluid flow calculation adopts a finite volume method, the unit fracture adopts a discrete unit method, and the numerical method is used to form a finite element-discrete element-finite volume coupling method, so that the simulation of the hydraulic fracturing process considering the flow-solid coupling and the fluid loss effect is realized;
step three: the super convergence solution obtained by calculation by adopting a super convergence solution calculation formula is used as the error estimation of the original finite element solution to form the following energy mode error estimation
Figure BDA0003345185390000095
Figure BDA0003345185390000093
In the formula: sigma*、σhRespectively representing the hyper-convergence stress and the conventional stress solution in a matrix form, wherein D is an elastic constant matrix, and omega is a solution domain;
according to the error of the stress solution, a unit self-adaptive analysis target formula is established:
Figure BDA0003345185390000094
wherein h isnewFor the new cell size after error evaluation from cell k, hkIs the current grid size of cell k; the parameters in the formula are as follows:
Figure BDA0003345185390000101
step four: and (5) aiming at the units with the error exceeding limit, estimating the new size of the error exceeding limit unit, subdividing according to the new size to obtain a new grid, returning to the step one, if all the units meet the error limit, the grid is not subdivided, and the solving process is finished.
Fracture tip meshing and fracture propagation are shown in fig. 3: during the fluid-driven fracture propagation, stress concentration occurs at the fracture tip, forming a damaged zone (fig. 3 (a)); the damaged area indicates that the cell has been damaged and the crack achieves tensile, shear fracture propagation, the crack length being the linear distance in the damaged area in that direction (fig. 3 (b)); when the predicted crack length reaches the preset expansion length, the crack is expanded, the expansion length is the predicted crack length, the grid is divided again in the specified area of the crack tip, and a new damage area is calculated (fig. 3 (c)).
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (7)

1. A hydraulic fracturing fracture multi-scale expansion grid self-adaption method is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: calculating solid deformation of the fractured porous medium by using a finite element model, specifically a solid displacement field, a solid velocity field and a solid acceleration field, calculating a fluid pressure velocity field of the fractured porous medium by using a finite volume model, and coupling the calculated solid deformation and the fluid pressure velocity field to obtain stress solutions on the fractured models with different scales;
step two: judging the stress and energy on each scale unit interface obtained in the step one by using a fracture criterion, judging whether the porous elastic medium fracture is expanded into a multi-scale fracture, and realizing fracture expansion of the units by using a discrete element method;
step three: selecting a natural super-convergence point of the stress to perform splicing recovery to obtain stress recovery of unit nodes, obtaining a super-convergence solution of the global stress through node stress interpolation, and estimating an error of the stress solution by using the super-convergence solution;
step four: and (5) aiming at the units with the error exceeding limit, estimating the new size of the error exceeding limit unit, subdividing according to the new size to obtain a new grid, returning to the step one, if all the units meet the error limit, the grid is not subdivided, and the solving process is finished.
2. The grid adaptive method for multi-scale expansion of hydraulic fracturing fractures as claimed in claim 1, wherein: in the first step, the models of the solid displacement field, the solid velocity field and the solid acceleration field are as follows:
Figure FDA0003345185380000011
where u is the vector displacement, σ represents the stress tensor, f is the external load vector, including the human body force, the fluid pressure on the fracture surface, the spring force, and the force on the traction boundary, ρ is the density, c is the damping coefficient,
Figure FDA0003345185380000012
and
Figure FDA0003345185380000013
the derivatives over time t are shown, respectively the acceleration and velocity vectors, and Ω is the solution domain.
3. The grid adaptive method for multi-scale expansion of hydraulic fracturing fractures as claimed in claim 1, wherein: in the first step, assuming unidirectional flow in a fractured porous medium, a velocity field is obtained by using a simplified Darcy flow law, and the formula is as follows:
Figure FDA0003345185380000021
Figure FDA0003345185380000022
wherein v ismAnd vfFluid flow velocity fields, p, representing porous media and hydraulic fractures, respectivelymAnd pkThe pressure values, k, of the porous medium and the hydraulic fracture respectivelymAnd kfPermeability of the porous medium and hydraulic fracture, respectively, μ is viscosity, and in the absence of gravity and capillary forces, the pressure equation for single phase flow in the porous medium and hydraulic fracture is:
Figure FDA0003345185380000023
Figure FDA0003345185380000024
wherein S ism＝n/kfAnd Sf＝1/kfWater storage coefficients of the porous medium and the hydraulic fracture respectively, n is porosity, the fracture porosity is equal to 1, q represents an external fluid source, epsilonVIs the volume strain of the rock matrix and the permeability is expressed as kf＝w2And/12, wherein w represents the pore size of the hydraulic fracture.
4. The grid adaptive method for multi-scale expansion of hydraulic fracturing fractures as claimed in claim 1, wherein: in the second step, the breaking criteria include a tensile failure criterion and a shear failure criterion, and the tensile failure criterion and the shear failure criterion are expressed as
Figure FDA0003345185380000025
Figure FDA0003345185380000031
Wherein σ is tensile stress, τ is shear stress, ε0Is the value of the tensile strain at which the tensile stress reaches a maximum, εfValue of tensile strain at which tensile fracture occurs, gamma0The value of the shear strain at which the shear stress reaches a maximum, gammafTo determine the shear strain value at which shear fracture occurs, GtfAnd GsfTensile and shear fracture energies, respectively.
5. The grid adaptive method for multi-scale expansion of hydraulic fracturing fractures as claimed in claim 1, wherein: in the third step, the natural super-convergence point of the stress is a gaussian integral point of the stress unit, and the stress recovery calculation formula is as follows:
σ*(x,y)＝P(x,y)a
wherein, P (x, y) is given function vector, a is determined by least square fitting of a recovery field in a Gaussian integral point value and an original solution, and a high-precision recovery value sigma of node stress is obtained by the recovery field*。
6. The grid adaptive method for multi-scale expansion of hydraulic fracturing fractures as claimed in claim 1, wherein: the super convergence solution obtained by calculation by adopting a super convergence solution calculation formula is used as the error estimation of the original finite element solution to form the following energy mode error estimation
Figure FDA0003345185380000034
Figure FDA0003345185380000032
In the formula: sigma*、σhRespectively representing the hyper-convergence stress and the conventional stress solution in a matrix form, D is an elastic constant matrix, and omega is a solution domain.
7. The grid adaptive method for multi-scale expansion of hydraulic fracturing fractures as claimed in claim 1, wherein: in the third step, a unit self-adaptive analysis target formula is established according to the error of the stress solution:
Figure FDA0003345185380000033
wherein h isnewFor the new cell size after error evaluation from cell k, hkFor the current grid size of cell k, the parameters in the equation are:
Figure FDA0003345185380000041
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CN116956626A (en) * 2023-08-03 2023-10-27 湖南工程学院 Self-adaptive analysis method and system based on energy error estimation

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CN111553108A (en) * 2020-05-20 2020-08-18 中国石油大学(华东) Shale gas reservoir fluid-solid coupling multi-scale numerical simulation method

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115288650A (en) * 2022-08-04 2022-11-04 西安石油大学 Method for parallel computing and simulating hydraulic fracturing in pore elastic medium
CN116956626A (en) * 2023-08-03 2023-10-27 湖南工程学院 Self-adaptive analysis method and system based on energy error estimation

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