CN115758851B - Method for selecting multi-scale propping agent for natural fracture-containing stratum fracture - Google Patents
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Abstract
The invention discloses a method for selecting a multi-scale propping agent for a natural fracture-containing stratum fracture, which comprises the steps of carrying out fracture expansion numerical simulation under the natural fracture condition according to the geomechanical condition of a reservoir stratum to obtain the fracture expansion condition of the natural fracture-containing stratum after fracturing; evaluating and dividing the main crack, the first-stage branch crack and the second-stage branch crack to obtain a multi-scale crack form; extracting the geometric type of the main crack according to the multi-scale crack morphology; establishing a multi-scale fracture solid-liquid two-phase flow numerical model; carrying out conveying numerical simulation by adopting propping agents with different particle sizes respectively to obtain the distribution condition of the propping agents; counting propping agent duty ratios of the main fracture, the first-stage branch fracture and the second-stage branch fracture under the condition of multi-scale fracture width according to propping agent distribution conditions; and the highest-efficiency propping agent filling particle sizes of the cracks with different dimensions are optimized according to the propping agent ratio in the main cracks, the primary branch cracks and the secondary branch cracks. The method can accurately obtain the optimal propping agent particle size of the multi-scale fracture.
Description
Technical Field
The invention relates to a method for selecting a multi-scale propping agent for a natural fracture-containing stratum fracture, and belongs to the technical field of oil and gas well yield increase transformation.
Background
The method is characterized in that the fracture conductivity is supported under different proppant combination conditions based on single fracture expansion simulation analysis, and finally parameters such as the type, the particle size and the addition amount of the propping agent capable of meeting the full-purpose requirement of the oil reservoir are obtained through simulation by using fracturing software. For example, the patent "a non-conventional reservoir fracturing propping agent optimizing method and application" of China oil and gas stock company describes that a fracture image processing method is used for extracting fracture parameters, namely, a morphological refinement algorithm is used for acquiring the central axis of a fracture image, so that the fracture width is acquired. However, the main problem in the prior art is that the diversion capability of the combined propping agent is studied only for single cracks, and the optimal proportion of the combined propping agent is difficult to reach for a natural fracture reservoir due to the limited width of the cracks, so that the capability of entering the cracks with different widths of different particle sizes is inconsistent.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a method for selecting a multi-scale propping agent for a natural fracture-containing stratum fracture.
The technical scheme provided by the invention for solving the technical problems is as follows: a method for selecting a multi-scale propping agent for a natural fracture-containing stratum fracture, comprising the following steps:
step one, carrying out fracture expansion numerical simulation under natural fracture conditions according to the geomechanical conditions of the reservoir to obtain the fracture expansion condition of the natural fracture reservoir after fracturing;
step two, evaluating and dividing the main fracture, the first-stage branch fracture and the second-stage branch fracture according to the fracture expansion condition of the fractured natural fracture reservoir to obtain a multi-scale fracture morphology;
extracting the geometric type of the main crack according to the multi-scale crack shape;
step four, establishing a multi-scale fracture solid-liquid two-phase flow numerical model according to the geometric type of the main fracture;
step five, carrying out conveying numerical simulation by adopting propping agents with different particle sizes respectively to obtain propping agent distribution conditions;
step six, counting propping agent proportion of the main fracture, the first-stage branch fracture and the second-stage branch fracture under the condition of multi-scale fracture width according to propping agent distribution conditions;
and step seven, optimizing the highest-efficiency propping agent filling particle sizes of the cracks with different dimensions according to the propping agent ratio in the main cracks, the first-stage branch cracks and the second-stage branch cracks.
The further technical scheme is that the solid-liquid two-phase flow numerical model in the fourth step comprises:
(1) Equation of fluid control
Wherein: ρ l Is of liquid phase density of kg/m 3 ；ε l Liquid phase volume fraction,%; u (u) l Is the liquid phase flow speed, m/s; t is time, s; p is flow field pressure, pa; g is gravity acceleration, m/s 2 ；M pl Momentum exchange source items for the liquid phase and the particle phase; k is the turbulence energy of the fluid phase, m 2 /s 2 The method comprises the steps of carrying out a first treatment on the surface of the ε is the turbulent dissipation ratio, m 2 /s 3 ；G k kg/mS as a generating term of turbulent energy 3 ；σ k To turbulent energy pairThe plannd number of the response, dimensionless, is taken to be sigma k ＝1.0；σ ε Taking sigma for planner number corresponding to turbulence dissipation rate ε ＝1.3；S K 、S ε For turbulent flow exchange between liquid phase and solid phase, kg/m.s 3 ；C 1ε 、C 2ε Taking C as empirical constant and dimensionless 1ε ＝1.44、C 2ε ＝1.92；
(2) Equation of particle motion control
Wherein: m is m i The mass of the particles i is kg; u (u) p,i The linear velocity of the particles i, m/s; f (F) pc,ij A contact force N generated for the contact of the particle i with other particles; f (F) lp,i Acting force of fluid on the particles i, N; i pc,ij Kg.m for the moment of inertia of the particles i 2 ；ω p,i Rad/s is the angular velocity of particle i; t (T) pc,ij The contact moment generated by the contact of the particle i and the particle j is N.m;
(3) Fluid-particle force
F v ＝C v V p ρ l (Du slip /Dt)
Wherein: f (F) F Welfare for propping agent, N; v (V) p For proppant volume, m 3 ；F d N, the drag force of the fluid on the particulate phase(s); c (C) d As drag coefficient, dimensionless; epsilon p Is the volume fraction of the proppant, dimensionless; ρ l Is fluid density, kg/m 3 ；u p Is the movement speed of the propping agent, m/s; u (u) l Is the movement speed of the liquid phase, m/s; d is the particle size of the propping agent, m; f (F) v N, the proppant virtual mass force; u (u) slip Slip velocity, m/s, of the proppant relative to the continuous phase; c (C) v Is a virtual mass force coefficient, C V ＝0.5；
(4) Particle-particle force model
F c,ij ＝F cn，ij +F ct，ij
F cn，ij ＝k n,ij δ n,ij n+γ n,ij u n,ij
F ct，ij ＝k t,ij δ t,ij t+γ t,ij u t,ij
Wherein: f (F) c,ij N is the contact resultant force of the particles i and the particles j; f (F) cn，ij N, the normal contact force of particle i and particle j; f (F) ct，ij N, the tangential contact force of particle i and particle j; k (k) n,ij Is the normal stiffness coefficient; delta n,ij M is the normal displacement between the impinging particles; n is a normal unit vector between contact particles; gamma ray n,ij Is the normal dissipation coefficient; u (u) n,ij Is the normal component of the relative velocity between the impinging particles; k (k) t,ij Is a tangential stiffness coefficient; delta t,ij M is the normal displacement between the impinging particles; t is a tangential unit vector between contact particles; gamma ray t,ij Is the tangential dissipation factor; u (u) t,ij Is the tangential component of the relative velocity between impinging particles.
According to a further technical scheme, proppants with different particle sizes in the fifth step comprise 30/50 meshes, 40/70 meshes, 70/140 meshes and 100/200 meshes.
The technical scheme is that the proppant migration and transportation rule under the actual working condition is simulated in the fifth step.
According to a further technical scheme, the actual working conditions comprise displacement and fluid viscosity.
In the seventh step, the propping agent particle size corresponding to the optimal propping agent ratio of each crack in the main crack, the first-stage branch crack and the second-stage branch crack is respectively selected to be the propping agent filling particle size of the crack;
the filling degree is low;
filling degree is moderate;
the filling degree is good;
wherein: w (W) f1 The width of the first-stage crack is mm; w (W) f2 The width of the secondary crack is mm; v (V) P-f1 Is the volume of the first-stage fracture propping agent, m 3 ；V P-f2 Is the volume of the secondary fracture propping agent, m 3 The method comprises the steps of carrying out a first treatment on the surface of the α, β are coefficients related to the angle of the fracture, and are obtained through experiments, and α=0.089 and β=0.318 are taken as an example of a 90 ° orthogonal fracture.
The invention has the following beneficial effects: the method can accurately obtain the optimal propping agent particle size of the multi-scale fracture.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of the results of a natural fracture-containing reservoir fracture propagation simulation;
FIG. 3 is a statistical plot of multi-scale slit width distribution;
fig. 4 is a graph of proppant particle flow rate.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the method for selecting the multi-scale proppants for the natural fracture-containing stratum fracture comprises the following steps:
step one, performing fracture expansion numerical simulation under a natural fracture condition according to the geomechanical condition of the reservoir to obtain the fracture expansion condition (shown in figure 2) of the natural fracture reservoir after fracturing;
step two, evaluating and dividing the main fracture, the primary branch fracture and the secondary branch fracture according to the fracture expansion condition after fracturing the natural fracture reservoir to obtain a multi-scale fracture morphology and multi-scale fracture width distribution (shown in figure 3);
extracting the geometric type of the main crack according to the multi-scale crack shape;
step four, establishing a multi-scale fracture solid-liquid two-phase flow numerical model according to the geometric type of the main fracture;
the solid-liquid two-phase flow numerical model comprises:
(1) Equation of fluid control
Wherein: ρ l Is of liquid phase density of kg/m 3 ；ε l Is the volume fraction of the liquid phase，％；u l Is the liquid phase flow speed, m/s; t is time, s; p is flow field pressure, pa; g is gravity acceleration, m/s 2 ；M pl Momentum exchange source items for the liquid phase and the particle phase; k is the turbulence energy of the fluid phase, m 2 /s 2 The method comprises the steps of carrying out a first treatment on the surface of the ε is the turbulent dissipation ratio, m 2 /s 3 ；G k kg/mS as a generating term of turbulent energy 3 ；σ k Taking sigma as planner number corresponding to turbulent energy k ＝1.0；σ ε Taking sigma for planner number corresponding to turbulence dissipation rate ε ＝1.3；S K 、S ε For turbulent flow exchange between liquid phase and solid phase, kg/m.s 3 ；C 1ε 、C 2ε Taking C as empirical constant and dimensionless 1ε ＝1.44、C 2ε ＝1.92；
(2) Equation of particle motion control
Wherein: m is m i The mass of the particles i is kg; u (u) p,i The linear velocity of the particles i, m/s; f (F) pc,ij A contact force N generated for the contact of the particle i with other particles; f (F) lp,i Acting force of fluid on the particles i, N; i pc,ij Kg.m for the moment of inertia of the particles i 2 ；ω p,i Is the angular velocity of particle i, rsd/s; t (T) pc,ij The contact moment generated by the contact of the particle i and the particle j is N.m;
(3) Fluid-particle force
F v ＝C v V p ρ l (Du slip /Dt)
Wherein: f (F) F Welfare for propping agent, N; v (V) p For proppant volume, m 3 ；F d N, the drag force of the fluid on the particulate phase(s); c (C) d As drag coefficient, dimensionless; epsilon p Is the volume fraction of the proppant, dimensionless; ρ l Is fluid density, kg/m 3 ；u p Is the movement speed of the propping agent, m/s; u (u) l Is the movement speed of the liquid phase, m/s; d is the particle size of the propping agent, m; f (F) v N, the proppant virtual mass force; u (u) slip Slip velocity, m/s, of the proppant relative to the continuous phase; c (C) v Is a virtual mass force coefficient, C V ＝0.5；
(4) Particle-particle force model
F c,ij ＝F cn，ij +F ct，ij
F cn，ij ＝k n,ij δ n,ij n+γ n,ij u n,ij
F ct，ij ＝k t,ij δ t,ij t+γ t,ij u t,ij
Wherein: f (F) c,ij N is the contact resultant force of the particles i and the particles j; f (F) cn，ij N, the normal contact force of particle i and particle j; f (F) ct，ij N, the tangential contact force of particle i and particle j; k (k) n,ij Is the normal stiffness coefficient; delta n,ij M is the normal displacement between the impinging particles; n is a normal unit vector between contact particles; gamma ray n,ij Is the normal dissipation coefficient; u (u) n,ij Is the normal component of the relative velocity between the impinging particles; k (k) t,ij Is a tangential stiffness coefficient; delta t,ij M is the normal displacement between the impinging particles; t is a tangential unit vector between contact particles; gamma ray t,ij For cuttingTo the dissipation factor; u (u) t,ij Tangential component of the relative velocity between impinging particles;
step five, propping agents with different particle sizes (30/50 meshes, 40/70 meshes, 70/140 meshes and 100/200 meshes) are adopted to simulate the migration and transportation rule of the propping agents under the condition of actual working conditions (displacement and fluid viscosity) so as to obtain the distribution condition of the propping agents;
step six, counting propping agent proportion of the main fracture, the primary branch fracture and the secondary branch fracture under the condition of multi-scale fracture width according to propping agent distribution conditions (shown in figure 4);
step seven, optimizing the highest-efficiency propping agent filling particle sizes of the cracks with different dimensions according to the propping agent occupation ratio in the main cracks, the first-stage branch cracks and the second-stage branch cracks;
in the seventh step, propping agent particle sizes corresponding to the optimal propping agent duty ratio of each crack in the main crack, the first-stage branch crack and the second-stage branch crack are respectively selected to be propping agent filling particle sizes of the crack;
the filling degree is low;
filling degree is moderate;
the filling degree is good;
wherein: w (W) f1 The width of the first-stage crack is mm; w (W) f2 The width of the secondary crack is mm; v (V) P-f1 Is the volume of the first-stage fracture propping agent, m 3 ；V P-f2 Is the volume of the secondary fracture propping agent, m 3 The method comprises the steps of carrying out a first treatment on the surface of the α, β are coefficients related to the angle of the fracture, and are obtained through experiments, taking 90 ° orthogonal fracture as an example, α=0.089, β=0.318;
and the propping agent grain size corresponding to the optimal propping agent ratio of each crack in the main crack, the first-stage branch crack and the second-stage branch crack is respectively selected to be the propping agent filling grain size of the crack.
The present invention is not limited to the above-mentioned embodiments, but is not limited to the above-mentioned embodiments, and any person skilled in the art can make some changes or modifications to the equivalent embodiments without departing from the scope of the technical solution of the present invention, but any simple modification, equivalent changes and modifications to the above-mentioned embodiments according to the technical substance of the present invention are still within the scope of the technical solution of the present invention.
Claims (4)
1. The method for selecting the multi-scale propping agent for the natural fracture-containing stratum fracture is characterized by comprising the following steps of;
step one, carrying out fracture expansion numerical simulation under natural fracture conditions according to the geomechanical conditions of the reservoir to obtain the fracture expansion condition of the natural fracture reservoir after fracturing;
step two, evaluating and dividing the main fracture, the first-stage branch fracture and the second-stage branch fracture according to the fracture expansion condition of the fractured natural fracture reservoir to obtain a multi-scale fracture morphology;
extracting the geometric type of the main crack according to the multi-scale crack shape;
step four, establishing a multi-scale fracture solid-liquid two-phase flow numerical model according to the geometric type of the main fracture;
step five, carrying out conveying numerical simulation by adopting propping agents with different particle sizes respectively to obtain propping agent distribution conditions;
the numerical model in the fifth step comprises the following steps:
(1) Equation of fluid control
Wherein: ρ l Is of liquid phase density of kg/m 3 ；ε l Liquid phase volume fraction,%; u (u) l Is the liquid phase flow speed, m/s; t is time, s; p is flow field pressure, pa; g is gravity acceleration, m/s 2 ；M pl Momentum exchange source items for the liquid phase and the particle phase; k is the turbulence energy of the fluid phase, m 2 /s 2 The method comprises the steps of carrying out a first treatment on the surface of the ε is the turbulent dissipation ratio, m 2 /s 3 ；G k kg/mS as a generating term of turbulent energy 3 ；σ k Taking sigma as planner number corresponding to turbulent energy k ＝1.0；σ ε Taking sigma for planner number corresponding to turbulence dissipation rate ε ＝1.3；S K 、S ε For turbulent flow exchange between liquid phase and solid phase, kg/m.s 3 ；C 1ε 、C 2ε Taking C as empirical constant and dimensionless 1ε ＝1.44、C 2ε ＝1.92；
(2) Equation of particle motion control
Wherein: m is m p,i The mass of the particles i is kg; u (u) p,i The linear velocity of the particles i, m/s; f (F) pc,ij A contact force N generated for the contact of the particle i with other particles; f (F) lp,i Acting force of fluid on the particles i, N; i pc,ij Kg.m for the moment of inertia of the particles i 2 ；ω p,i Rad/s is the angular velocity of particle i; t (T) pc,ij The contact moment generated by the contact of the particle i and the particle j is N.m;
(3) Fluid-particle force
F v ＝C v V p ρ l (Du slip /Dt)
Wherein: f (F) F The propping agent is subjected to buoyancy, N; v (V) p For proppant volume, m 3 ；F d N, the drag force of the fluid on the particle phase; c (C) d As drag coefficient, dimensionless; epsilon p Is the volume fraction of the proppant, dimensionless; ρ l Is fluid density, kg/m 3 ；u p Is the movement speed of the propping agent, m/s; u (u) l Is the movement speed of the liquid phase, m/s; d is the particle size of the propping agent, m; f (F) v N, the proppant virtual mass force; u (u) slip Slip velocity, m/s, of the proppant relative to the continuous phase; c (C) v Is a virtual mass force coefficient, C V ＝0.5；
(4) Particle-particle force model
F c,ij ＝F cn，ij +F ct，ij
F cn，ij ＝k n,ij δ n,ij n+γ n,ij u n,ij
F ct，ij ＝k t,ij δ t,ij t+γ t,ij u t,ij
Wherein: f (F) c,ij N is the contact resultant force of the particles i and the particles j; f (F) cn，ij N, the normal contact force of particle i and particle j; f (F) ct，ij N, the tangential contact force of particle i and particle j; k (k) n,ij Is the normal stiffness coefficient; delta n,ij M is the normal displacement between the impinging particles; n is a normal unit vector between contact particles; gamma ray n,ij Is the normal dissipation coefficient; u (u) n,ij Is the normal component of the relative velocity between the impinging particles; k (k) t,ij Is a tangential stiffness coefficient; delta t,ij M is the normal displacement between the impinging particles; t is a tangential unit vector between contact particles; gamma ray t,ij Is the tangential dissipation factor; u (u) t,ij Tangential component of the relative velocity between impinging particles;
step six, counting propping agent proportion of the main fracture, the first-stage branch fracture and the second-stage branch fracture under the condition of multi-scale fracture width according to propping agent distribution conditions;
step seven, optimizing the highest-efficiency propping agent filling particle sizes of the cracks with different dimensions according to the propping agent occupation ratio in the main cracks, the first-stage branch cracks and the second-stage branch cracks;
in the seventh step, propping agent particle sizes corresponding to the optimal propping agent duty ratio of each crack in the main crack, the first-stage branch crack and the second-stage branch crack are respectively selected to be propping agent filling particle sizes of the crack;
the filling degree is low;
filling degree is moderate;
the filling degree is good;
wherein: w (W) f1 The width of the first-stage crack is mm; w (W) f2 For the width of the secondary crack, mm；V P-f1 Is the volume of the first-stage fracture propping agent, m 3 ；V P-f2 Is the volume of the secondary fracture propping agent, m 3 The method comprises the steps of carrying out a first treatment on the surface of the α, β are coefficients related to the angle of the fracture, and are obtained through experiments, and α=0.089 and β=0.318 are taken as an example of a 90 ° orthogonal fracture.
2. The method of claim 1, wherein the proppants of different particle sizes in the fifth step comprise 30/50 mesh, 40/70 mesh, 70/140 mesh and 100/200 mesh.
3. The method for selecting the multi-scale propping agent for the natural fracture-containing stratum fracture according to claim 1, wherein the proppant migration and transportation rule under the actual working condition is simulated in the fifth step.
4. A method of selecting a multi-scale proppant for a fracture of a subterranean formation containing a natural fracture according to claim 3, wherein the actual conditions include displacement and fluid viscosity.
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