CN111125905B - Two-dimensional fracture network expansion model for coupling oil reservoir fluid flow and simulation method thereof - Google Patents
Two-dimensional fracture network expansion model for coupling oil reservoir fluid flow and simulation method thereof Download PDFInfo
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Abstract
The invention belongs to the technical field of oilfield development, and particularly discloses a two-dimensional fracture network expansion model for coupling oil reservoir fluid flow and a simulation method thereof. By adopting the scheme of the invention, the model can obtain the network fracture geometry sizes at different times by solving the fluid pressure at the natural fracture intersection point, the fracture width and the flow equation of the matrix block through coupling.
Description
Technical Field
The invention belongs to the technical field of oilfield development, and particularly relates to a two-dimensional fracture network expansion model for coupling oil reservoir fluid flow and a simulation method thereof.
Background
Extensive research has shown that natural fractures may alter the propagation path of hydraulic fractures, and fracturing fractured reservoirs may form multi-branched, non-planar, complex fractures. Laboratory experiments and researches show that under the conditions of a certain approach angle and a certain stress difference, the natural fracture can change the extension path of the hydraulic fracture. In recent years, a few researchers begin to study the influence of natural cracks on hydraulic cracks by adopting a numerical simulation method, and microseism monitoring proves that the hydraulic cracks in shale reservoirs are extended into complex fracture networks. It can be seen that the hydraulic fracture propagation mode of a fractured formation is complex and has a large difference from the symmetry plane fracture generated by the fracturing of a homogeneous formation.
The numerical simulation research of shale gas yield shows that network cracks with certain diversion capacity play an important role in improving shale gas yield. Thus, the development of hydraulic fracturing technology has also transitioned from conventional formation of double-winged plane-of-symmetry fractures to how to create network fractures in ultra-low permeability reservoirs. The network fracture extension simulation is an important component of hydraulic fracturing design, a plurality of scholars put forward mathematical models for simulating the fracture network, and the investigation discovers that the fracture network simulation is mainly based on the interaction criteria of natural fractures and hydraulic fractures, the fracture network is generated by simulating the extension and the turning of each natural fracture and then communicating with other natural fractures, and the simulation model is complex in calculation.
The fractured reservoir often develops large-scale macroscopic cracks and a large number of natural microcracks, relevant scholars analyze seepage characteristics of the fractured reservoir, introduce concepts of the macroscopic cracks and the microcracks, and provide a dual-crack medium model which divides the cracks and the matrix into two sets of systems for independent solving, so that the problem of difficult calculation convergence caused by adopting a single medium solving system is avoided.
In the application, based on the idea of coupling flow of natural cracks and matrixes in dual media, the cracks and matrixes are regarded as two relatively independent flow systems, and the inventor provides a set of two-dimensional crack network expansion model and a crack network simulation method for coupling the flow of oil reservoir fluid.
Disclosure of Invention
The invention aims to provide a two-dimensional fracture network expansion model for coupling reservoir fluid flow and a simulation method thereof.
In order to achieve the above purpose, the basic scheme of the invention is as follows:
a two-dimensional fracture network expansion model for coupling oil reservoir fluid flow is provided, and model conditions are set: the opening deformation of the crack is linear elastic behavior; the fluid is viscous Newtonian fluid, and the hysteresis phenomenon of fluid at the end part of the crack and the stress interference effect between the cracks are not considered; the whole crack extension meets the plane strain state in a vertical plane, and the vertical section is elliptical; the natural cracks are vertical cracks, and the height of the cracks is constant and equal to the thickness of the reservoir; the method comprises a flow equation in a fracture, an extension path after the hydraulic fracture is intersected with a natural fracture, a fracture width equation and a material conservation equation, and specifically comprises the following steps:
A. equation of flow in fracture
The natural cracks are vertical cracks, the height of the cracks is constant and equal to the thickness of a reservoir, the section of the cracks is elliptical, the fluid is viscous Newtonian fluid, and a flow equation of the Newtonian fluid in the elliptical cracks along the x and y directions is established;
B. the extension path of the hydraulic fracture intersecting with the natural fracture comprises the following three types:
(a) The hydraulic fracture opens and closes the natural fracture and turns to extend along the natural fracture, and a mechanical condition equation is satisfied;
(b) The hydraulic fracture extends through the natural fracture, but the natural fracture is not opened, and a mechanical condition equation is satisfied;
(c) The hydraulic fracture extends through the natural fracture and opens the natural fracture; the net pressure at the intersection point satisfies both mechanical condition equations of (a) and (b);
C. based on a crack width equation of plane strain, the width of the crack is expressed according to a two-dimensional PKN model;
D. conservation of substance equation: the volume of fluid injected into the fracture is equal to the sum of the fracture volume change and the fluid loss volume.
Another basic scheme of the invention is as follows:
the simulation method of the two-dimensional fracture network expansion model for coupling the flow of the oil reservoir fluid comprises the following steps:
step a: establishing a solving area, wherein the solving area represents the expansion of a hydraulic fracture network by a dynamic coordinate, and represents an unactivated natural fracture by a static coordinate;
step b: establishing a model according to claim 1;
step c: setting initial and boundary conditions, wherein the boundary conditions comprise an inner boundary condition and an outer boundary condition;
step d: establishing an oil reservoir fluid flow control equation;
step e: substituting the numerical parameters into a model to solve: the material conservation equation and the oil reservoir fluid flow control equation of fluid flowing in the fracture network are coupled and solved, and fluid pressure and fracture width distribution at the fracture intersection point of a solving area are obtained by taking fluid loss as a coupling condition between the two control equations; in the solving process, loop iteration is performed to satisfy the global material balance equation.
The basic scheme of the invention has the working principle and beneficial effects that:
the hydraulic fracture propagation in a fractured reservoir may be a complex fracture system that is non-planar, which is greatly different from the two-wing symmetrical plane fracture created by a homogeneous reservoir fracture, because conventional hydraulic fracture propagation models cannot be used to simulate the fracture morphology and fracture geometry of the hydraulic fracture non-planar propagation in a fractured formation. Therefore, in the application, based on the idea of coupling flow of natural cracks and matrixes in dual media, the cracks and matrixes are regarded as two relatively independent flow systems, the action modes of the front natural cracks and the hydraulic cracks are considered, a two-dimensional fracture network extension mathematical model of hydraulic fracture network extension, fluid filtration and reservoir fluid flow is established, and a simulation method is provided.
The model adopts dynamic coordinates to represent an expanded hydraulic fracture network, static coordinates represent natural fractures which are not activated, and whether the natural fractures are activated or not is judged according to the action modes of the hydraulic fractures and the natural fractures. In the model solving process, the size of a simulation area is changed through a dynamic boundary, and a material balance equation, a crack width equation and a reservoir fluid flow equation of two-dimensional fracture network expansion are solved numerically to obtain the geometric form and the size of the network cracks.
The model can be used for researching the influence of some sensitive parameters including the injection volume, the fracture height, the elastic modulus, the horizontal main stress difference, the displacement and the fracturing fluid viscosity on the fracture network shape, the fracture network size, the average fracture width of the fracture network and the fracture oil reservoir contact area, and the numerical calculation result shows that the model can simulate the expansion of the network fracture and obtain the geometric dimension of the fracture network. By the scheme of the invention, quantitative analysis of the morphology of the fracture network of the unconventional reservoir segmented volume can be realized, and the method is an effective means for evaluating and optimizing the fracturing scheme, so that the difficulty in calculating the geometric dimension of the network fracture in the prior art is greatly reduced.
Drawings
FIG. 1 is a schematic diagram of two-dimensional fracture network expansion simulation in an embodiment of the invention, wherein a refers to an activated dynamic coordinate, b refers to an unactivated static coordinate, c refers to a natural fracture, d refers to a matrix block, e refers to a perforation position, f refers to hydraulic fracture extension, and g refers to a solving unit;
FIG. 2 shows the volume of injected fluid and total volume of the fracture and relative errors for different construction times, wherein A is the fracture half-length (PKN analytical solution), B is the fracture half-length (model), C is the fracture width (PKN analytical solution), D is the fracture width (model), abscissa is the time (min), left ordinate is the fracture half-length (m), and right ordinate is the bottom hole fracture width (mm);
FIG. 3 is a comparison of model numerical solutions and PKN resolution solutions of embodiments of the present application;
FIG. 4 is a final fracture network geometry and fracture width profile (mm);
FIG. 5 is a matrix system pore pressure distribution (MPa);
FIGS. 6 and 7 are cross-sections of slit web geometry and slit width at different fluid viscosities;
figures 8 and 9 are cross-sections of the slotted mesh geometry and slot width for different injected fluid volumes;
FIGS. 10 and 11 are cross sections of the slotted mesh geometry and slot width at different rock elastic moduli;
FIGS. 12 and 13 are cross-sections of slotted mesh geometry and slot width at different horizontal primary stress differences;
FIGS. 14 and 15 are cross-sections of slotted mesh geometry and slot width at different displacements;
fig. 16 and 17 are cross sections of slit web geometry and slit width at different slit heights.
Detailed Description
The following is a further detailed description of the embodiments:
examples:
a two-dimensional fracture network expansion model for coupling reservoir fluid flow and a simulation method thereof comprise the following steps:
step a: establishing a solution area
Dynamic coordinates are used for representing the expansion of the hydraulic fracture network, static coordinates are used for representing natural fractures which are not activated, and the whole dynamic coordinates form a solving area shown in figure 1. During fluid injection, the natural fracture opens and propagates. When the fracture propagates to the point of intersection of the hydraulic fracture and the natural fracture and the fluid pressure at the point of intersection is greater than the normal stress of the fracture face, the natural fracture will also open and form a hydraulic fracture network. Thus, the injected fluid acts to open the closed natural fracture and propagate the natural fracture in both directions from the intersection point.
In modeling, the following assumptions also need to be made: the opening deformation of the crack is linear elastic behavior; the fluid is viscous Newtonian fluid, and the hysteresis phenomenon of fluid at the end part of the crack and the stress interference effect between the cracks are not considered; assuming that the whole crack extension meets the plane strain state in a vertical plane, the vertical section is elliptical; the natural fractures are all vertical fractures, the height of the fracture is constant and equal to the reservoir thickness.
Step b: establishing a two-dimensional fracture network expansion model for coupling reservoir fluid flow
According to the hydraulic fracture expansion thought described in fig. 1, a mathematical model of hydraulic fracture expansion along two directions is established, wherein the model comprises a flow equation in the fracture, an extension path after the hydraulic fracture is intersected with a natural fracture, a fracture width equation and a material conservation equation, and the mathematical model is specifically as follows:
A. equation of fluid flow in fracture
The dynamic pressure within the fracture is not constant and depends entirely on the injection displacement q and the fluid viscosity μ. The fracture section is elliptical instead of parallel plates, and under the same flow conditions, the flow pressure drop in an elliptical fracture is 16/3 pi times that in a parallel plate, so the flow equation of Newtonian fluid in the elliptical fracture along the x and y directions is:
wherein: q (x, t) and q (y, t) represent the volumetric flow (m) through the x and y position point fracture cross-section, respectively 3 S); mu represents the fracturing fluid viscosity (mPas); h is a f Representing the height (m) of the crack; w (W) fx And W is fy The slit width (m) along the x and y directions are shown, respectively. P (P) f Indicating the fluid pressure (MPa) within the fracture. As can be seen from equations 1 and 2, the fracture width is related to the fluid pressure drop within the fracture, and there is a strong coupling between the fracture width equation and the fluid flow equation.
B. Extension path after intersection of hydraulic fracture and natural fracture
The extension path after the hydraulic fracture is intersected with the natural fracture is a key factor influencing the formation of a fracture network, and according to related theory and experimental research, three extension paths exist after the hydraulic fracture is intersected with the natural fracture:
(a) The hydraulic fracture opens and closes the natural fracture and turns to and extends along the natural fracture, and the satisfied mechanical conditions are:
(b) The hydraulic fracture extends through the natural fracture but the natural fracture is not opened, and the satisfied mechanical conditions are as follows:
(c) The hydraulic fracture extends through the natural fracture and opens the natural fracture: the net pressure at the intersection point is required to satisfy both the above inequality (3) and inequality (4).
Wherein Δσ represents the horizontal principal stress difference (MPa); θ represents the angle (°) of the natural fracture to the horizontal maximum principal stress; t (T) o Represents the tensile strength (MPa) of the rock; p (P) net The net hydraulic fracture pressure (MPa) at the intersection is indicated.
C. Equation of crack width
Based on the planar strain assumption, ignoring the fluid pressure gradient in the vertical direction, the width of the fracture can be expressed according to a two-dimensional PKN model as:
wherein: w (W) fx And W is fy The hydraulic fracture width (m) extending along the x and y directions are shown, respectively; e represents the elastic modulus (MPa) of the rock; v represents the poisson's ratio of the rock, the dimensionless quantity. Sigma (sigma) nx Sum sigma ny The positive stresses of the natural fracture surfaces spread along the x and y directions are expressed respectively, and can be obtained according to the two-dimensional linear elastic theory (MPa).
D. Conservation of substance equation
The geometry of the fracture network is determined by the mass balance equation, and at any time the volume of fluid injected into the fracture is equal to the sum of the fracture volume change and the fluid loss volume. Thus, the local material balance equations for fluid flow in the x and y directions can be expressed as:
the mass conservation equation for crack propagation along the x and y directions obtained by adding equation (7) and equation (8) is:
wherein: q L (x, t) and q L (y, t) represents the volumetric flow (m) of the fracture unit fluid loss to the formation for lengths Δx and Δy, respectively 3 /min)；Q L Represents the total fluid loss (m) of the crack units with lengths Deltax and Deltay along the x and y directions, respectively 3 /min); a (x, t) and A (y, t) represent the cross-sectional areas (m) of the crack flowing through the x and y location points, respectively 2 ) The method comprises the steps of carrying out a first treatment on the surface of the t represents the construction time(s). The flow through x and y location point fracture cross-sectional areas can be expressed as:
substituting equations 1 and 2, and equations 10 and 11 into equation 9, equation 9 can be expressed as:
the global conservation of substance equation is:
wherein: q (t) represents the injection displacement (m 3 /min); l (t) represents tLength (m) of all opening slits is carved.
Step c: setting initial and boundary conditions
Initial conditions:
W f (x,y,t)| t＝0 ＝W fi (14)
outer boundary conditions:
inner boundary conditions:
wherein: q (Q) 0 Representing injection displacement (m 3 /min)；W fi Represents an initial crack width (m); Γ -shaped structure o And Γ I Representing the internal and external boundary conditions of the simulation model, respectively.
Step d: establishing reservoir fluid flow control equations
In the dual media percolation model, the fracture system and the matrix system are two hydrodynamic fields that are independent of each other and are interrelated. According to the dual medium model, the continuity equation of the matrix system is:
the fluid loss volume is mainly controlled by the pressure difference between the fracture system and the matrix system, and can be characterized by the channeling flow between the fracture and the matrix in the dual-medium model, so as to establish a fluid loss model based on pressure dependence:
fluid loss will change the pore pressure of the matrix system, and natural microcracks that are not open in the matrix system will exhibit a strong pressure-sensitive effect, describing the microcrack permeability and pressure sensitivity as:
K m ＝K mi exp{-C m (P i -P m )} (19)
wherein: k (K) mi Represents permeability (mD) at the initial conditions of microcracks; c (C) m Representing the stress sensitivity coefficient (MPa) of natural cracks -1 )；P i Represents the initial pressure (MPa) of the matrix system.
Form factor alpha m In relation to the large scale fracture spacing in the reservoir, expressed by definition as:
wherein: μ is the injection fluid viscosity (mpa·s); b represents the fluid volume coefficient and the dimensionless quantity; p (P) m Pore pressure (MPa) for the matrix system;
is the porosity of the matrix, dimensionless quantity; alpha m Representing the form factor (1/m) 2 )；K m Is the matrix permeability (μm) 2 )。L fx 、L fy Representing the distance (m) between the crack system in the x and y directions in the coordinate system; Δx, Δy represent the dimensions (m) of the grid block in the x, y direction in the coordinate system, respectively; v (V) b Representing grid block volume (m 3 )。
Step e: substituting numerical parameters into a model for solution
And (3) coupling and solving a material conservation equation and an oil reservoir fluid flow control equation of fluid flowing in the fracture network, wherein the two control equations take fluid loss as a coupling condition. However, the fracture width and the fluid pressure in the conservation equation of the fracture network expanding substance are both unknown, and therefore, it is necessary to solve equation (12) and equations (5) and (6) in a coupled manner to obtain the fluid pressure and the fracture width distribution at the fracture intersection point of the entire solving area. In the solving process of the model, loop iteration is needed to meet the global material balance equation. The whole control equation can be solved numerically by an implicit finite difference method.
The following experiments were performed:
according to the established mathematical model and the numerical solution method, the fracture network is simulated and calculated, a numerical simulation program is compiled to simulate the form of the fracture network, and table 1 is a basic parameter. In order to improve the calculation efficiency, taking symmetry of a shaft in a physical model into consideration, a quarter unit taking the shaft as a center is taken as a study object.
TABLE 1
| Parameters (parameters) | Numerical value | Parameters (parameters) | Numerical value |
| Construction time (min) | 30 | Approximation angle (°) | 90 |
| Displacement (m) 3 /min) | 6 | Maximum horizontal principal stress (MPa) | 51 |
| Viscosity of fracturing fluid (mPa. S) | 10 | Minimum horizontal principal stress (MPa) | 50 |
| Crack height (m) | 20 | Horizontal principal stress difference (MPa) | 1 |
| Natural crack spacing (m) | 5,2.5 | Reservoir pore pressure (MPa) | 32 |
| Elastic modulus (GPa) | 35 | Matrix permeability (mD) | 0.1 |
| Poisson ratio (-) | 0.2 | Porosity of matrix (-) | 0.05 |
From the mathematical model described above, we can see that hydraulic fracturing will form a single planar fracture when the horizontal primary stress difference is large enough that all natural fractures along the y-direction cannot be activated by the hydraulic fracture. According to the basic parameters in the table above, the primary stress difference was set to 20MPa, and the numerical simulation results found that only one single plane fracture would be formed in the reservoir, and the single plane fracture calculation results were compared with the analytical solution of PKN, as shown in fig. 2. It can be seen that the numerical simulation result and the analysis result of the model are very identical, and the average error of the two results is calculated to find that the relative error of the half length of the crack and the width of the crack is about 6.1% and 3.7% respectively.
Similarly, if the horizontal principal stress difference is 0, it can be inferred that the crack will propagate the same length along the x and y directions. For this purpose, according to the table1, the numerical simulation results are shown in fig. 3 and table 2, it can be seen that the numerical results prove the correctness of our inference and model. If fluid loss is not a concern, the injected fluid is used entirely to extend the natural fracture, and therefore the injected fluid volume should be equal to the total fracture volume. According to the data in Table 2, the total volume of cracks was 179.38m 3 And the total volume of the injected liquid is 180m 3 Almost the same, the rationality of the model is also proved.
TABLE 2
| Calculation result | Numerical value |
| Stitch net size/(10) 4 m 3 ) | 64.0 |
| Stitch net length/(m) | 200.0 |
| Stitch net width/(m) | 200.0 |
| Total volume of cracks/(m) 3 ) | 179.38 |
| Total volume of liquid injected/(m) 3 ) | 180 |
| Oil reservoir fracture contact area/(10) 4 m 2 ) | 6.4 |
| Average width of crack in X direction/(mm) | 0.892 |
| Average width of Y-direction crack/(mm) | 0.892 |
Experimental results:
figure 4 shows a fracture network geometry and fracture width profile calculated based on the base parameters, and figure 5 shows the reservoir matrix pore pressure distribution under pressure-dependent fluid loss conditions, as evident from the figure, the reservoir matrix pore pressure increases significantly over the extended range of the fracture network due to fluid loss. Next, we will develop a parameter sensitivity study on the model, analyze the effect of the relevant construction parameters and formation parameters on the stitch net, and further verify the practicality of the model.
1. Influence of fluid viscosity on the size of the slit web
Figures 6 and 7 show the slotted mesh geometry and slot width profile at different injection fluid viscosities. Table 3 shows the effect of fluid viscosity on the size of the fracture network, the reservoir fracture contact area, the length and width of the fracture network, and the average width of the primary and secondary fractures. From the data in the table, it can be seen that the size of the fracture network and the reservoir fracture contact area increase with decreasing fluid viscosity, while the width of the primary and secondary fractures decrease substantially with increasing fluid viscosity. The size of the stitch net is 21.7X10 when the viscosity of the fluid is reduced from 120 mPas to 10 mPas and then to 1 mPas 4 m 3 Increasing to 35.2X10 4 m 3 And further increased to 56.3X10 4 m 3 The oil reservoir fracture contact area is 3.115 multiplied by 10 4 m 2 Increasing to 4.88×10 4 m 2 And further increases to 6.74×10 4 m 2 . The size of the fracture network was increased by 62.2% and 59.9%, respectively, while the reservoir fracture contact area was increased by 56.6% and 38.1%, respectively. It follows that the low viscosity fluid has a greater impact on the size of the stitch bonded web. In addition, the reduced fluid viscosity may cause the stitch net to tilt moreThe slot web width decreases as it grows along the length, as the fluid viscosity will decrease which reduces the net pressure within the fracture, which is detrimental to the opening and propagation of the secondary fracture.
TABLE 3 Table 3
| viscosity/(mPa.s) | 1 | 10 | 120 |
| Stitch net size/(10) 4 m 3 ) | 56.3 | 35.2 | 21.7 |
| Oil reservoir fracture contact area/(10) 4 m 2 ) | 6.74 | 4.88 | 3.115 |
| Stitch net length/(m) | 1250 | 470 | 240 |
| Stitch net width/(m) | 30 | 50 | 60 |
| Average width of crack in X direction/(mm) | 0.958 | 1.390 | 2.016 |
| Average width of Y-direction crack/(mm) | 0.207 | 0.500 | 1.169 |
2. Effect of injected fluid volume on stitch mesh size
Figures 8 and 9 show the mesh geometry and slit width profile at different injection volumes. Table 4 shows the effect of the injected fluid volume on the size of the fracture network, the reservoir fracture contact area, the length and width of the fracture network, and the average width of the primary and secondary fractures. From the data in the table, it can be seen that the size of the fracture network, the reservoir fracture contact area, and the maximum length of the fracture network increase almost linearly with an equal increase in injected volume. And the maximum width of the slit net is increased and is reduced along with the equal increase of the volume of the injected liquid. The average width of the primary and secondary cracks increases slightly with the volume of the injected fluid. This suggests that fluid injection volume is one of the most critical factors affecting reservoir stimulation volume.
TABLE 4 Table 4
| Volume of injected liquid/(m) 3 ) | 60 | 120 | 180 |
| Stitch net size/(10) 4 m 3 ) | 12.8 | 24.2 | 35.2 |
| Oil reservoir fracture contact area/(10) 4 m 2 ) | 1.75 | 3.34 | 4.88 |
| Stitch net length/(m) | 280 | 390 | 470 |
| Stitch net width/(m) | 30 | 45 | 50 |
| Average width of crack in X direction/(mm) | 1.344 | 1.366 | 1.390 |
| Average width of Y-direction crack/(mm) | 0.492 | 0.495 | 0.500 |
3. Impact of modulus of elasticity on stitch-bonded webs
Figures 10 and 11 show the slit net geometry and slit width profile at different rock elastic moduli,table 5 shows the effect of elastic modulus on the size of the fracture network, the reservoir fracture contact area, the length and width of the fracture network, and the average width of the primary and secondary fractures. From the data in the table, it can be seen that the size of the fracture network and the reservoir fracture contact area increase with increasing elastic modulus. When the elastic modulus is increased from 25GPa to 35GPa and then to 45GPa, the size of the stitch net is 29.6X10 4 m 3 Increasing to 35.2X10 4 m 3 And further increased to 39.2×10 4 m 3 The size of the slit net is increased by 18.9% and 11.4%, respectively. The oil reservoir fracture contact area is 3.965 multiplied by 10 4 m 2 Increasing to 4.88×10 4 m 2 And further increases to 5.53×10 4 m 2 The corresponding reservoir fracture contact areas are increased by 23.1% and 13.3%, respectively. This suggests that reservoirs with high elastic modulus are advantageous for creating larger stitch lines. The width of the slit web and the average width of the secondary slits increase with increasing modulus of elasticity and the length of the slit web and the average width of the primary slits decrease with increasing modulus of elasticity. This is due to the higher elastic modulus of the reservoir, the higher net pressure of the fracture, which will facilitate the opening and propagation of the secondary fracture.
TABLE 5
4. Influence of horizontal principal stress difference on slotted nets
Fig. 12 and 13 show fracture geometry and fracture width profiles for different horizontal primary stress differences, and table 6 shows the effect of horizontal primary stress differences on fracture size, reservoir fracture contact area, fracture length and width, and primary and secondary fracture average width. As can be seen from the data in the table, the stitch mesh size was from 42.1X10 when the primary stress difference was increased from 0.5MPa to 1.5MPa 4 m 3 Reduced to 30.4X10 4 m 3 While the oil reservoir fracture contact area is 6.115 ×10 4 m 2 Reduced to 3.935 multiplied by 10 4 m 2 . The fracture network size and the reservoir fracture contact area decrease with increasing horizontal primary stress difference. The width of the slotted net also decreases substantially with increasing primary stress difference and the length increases with increasing primary stress difference. This is because the larger the primary stress difference, the more difficult the secondary crack is to open and extend. Thus, an increase in the primary stress differential will also decrease the width of the secondary fracture, with more injection fluid into the primary fracture. Thus, the slit width along the x-direction increases and the slit width along the y-direction decreases.
TABLE 6
| Horizontal principal stress difference/(MPa) | 0.5 | 1 | 1.5 |
| Stitch net size/(10) 4 m 3 ) | 42.1 | 35.2 | 30.4 |
| Oil reservoir fracture contact area/(10) 4 m 2 ) | 6.115 | 4.88 | 3.935 |
| Stitch net length/(m) | 330 | 470 | 670 |
| Stitch net width/(m) | 85 | 50 | 30 |
| Average width of crack in X direction/(mm) | 1.1 | 1.390 | 1.683 |
| Average width of Y-direction crack/(mm) | 0.645 | 0.500 | 0.404 |
5. Effect of Displacement on slotted Net
Fig. 14 and 15 show fracture geometry and fracture width profiles at different injection displacements, and table 7 shows the effect of injection displacement on fracture size, reservoir fracture contact area, fracture length and width, and primary and secondary fracture average width. From the data in the table, it can be found that the injection displacement is from 3m 3 The/min is increased to 9m 3 At/min, the fracture network size and the oil reservoir fracture contact area are reduced by 17.5% and 15.1%, respectively. The fracture network size and reservoir fracture contact area decrease with increasing injection displacement. It can also be observed from the data in the table that increasing displacement increases the slit width along the x and y directions and the width of the mesh and decreases the mesh length. This suggests that increasing displacement makes the slotted web more prone to expansion in the direction of maximum principal stress.
TABLE 7
6. Influence of the slit height on the slit web
Fig. 16 and 17 show fracture network geometry and fracture width profiles at different fracture heights, and table 8 shows the effect of fracture height on fracture network size, reservoir fracture contact area, fracture network length and width, and primary and secondary fracture average width. From the data in the table, it can be seen that the mesh size was from 32.1X10 when the fracture height was reduced from 30m to 10m 4 m 3 Increasing to 41.9X10 4 m 3 While the oil reservoir fracture contact area is from 4.18×10 4 m 2 Increased to 6.11×10 4 m 2 . This suggests that a decrease in fracture height will increase the fracture network size and the reservoir fracture contact area. In addition, as the slit height decreases, the length of the slit web and the width of the primary slit also decrease, while the width of the secondary slit and the width of the slit web increase. This is because the smaller the fracture height, the higher the net pressure within the main fracture, and the branch fracture will open and propagate easily.
TABLE 8
| Crack height/(m) | 10 | 20 | 30 |
| Stitch net size/(10) 4 m 3 ) | 41.9 | 35.2 | 32.1 |
| Oil reservoir fracture contact area/(10) 4 m 2 ) | 6.11 | 4.88 | 4.1775 |
| Stitch net length/(m) | 470 | 470 | 540 |
| Stitch net width/(m) | 120 | 50 | 30 |
| Average width of crack in X direction/(mm) | 1.102 | 1.390 | 1.668 |
| Average width of Y-direction crack/(mm) | 0.633 | 0.500 | 0.402 |
In summary, in the application, based on the dual medium theory, the channeling is adopted to represent the fluid loss of pressure dependence, and a set of two-dimensional fracture network expansion mathematical model for coupling the fluid flow of the oil reservoir is established. Numerical calculations indicate that the model can simulate the geometry of a network fracture and can analyze the impact of related reservoir and construction parameters on fracture network size and fracture width. The basic conclusion is as follows:
(1) The volume of injected fluid is one of the most critical factors affecting the size of the mesh, which is almost linear with the injected volume. However, the volume of the injected fluid has little influence on the average width of the cracks, and the average width of the primary and secondary cracks slightly increases with the increase of the volume of the injected fluid.
(2) Reducing the viscosity of the injected fluid can greatly increase the size of the fracture network and the contact area of the oil reservoir and the fracture, but the width of the primary and secondary fractures can be reduced, and long and narrow fracture networks can be formed by injecting the low-viscosity fluid.
(3) Reducing the primary stress differential will expand the fracture network size, the reservoir fracture contact area, the secondary fracture width, and the fracture network width. But the width of the main slit and the length of the slit web are reduced.
(4) Increasing the injection displacement may reduce the size and contact area of the mesh. But the width of the secondary slit and the width of the slit web can be increased because the increase in displacement increases the net pressure within the slit.
(5) The high modulus of elasticity reservoir can form larger and wider network fractures and can expand the contact area of the reservoir fracture. But the width of the fracture is reduced which may limit migration of the proppant.
(6) Reducing the slit height creates a wider and larger slit web, which affects both the slit web morphology and the slit width.
The foregoing is merely exemplary embodiments of the present invention, and specific structures and features that are well known in the art are not described in detail herein. It should be noted that modifications and improvements can be made by those skilled in the art without departing from the structure of the present invention, and these should also be considered as the scope of the present invention, which does not affect the effect of the implementation of the present invention and the utility of the patent.
Claims (3)
1. The simulation method of the two-dimensional fracture network expansion model for coupling the flow of the oil reservoir fluid is characterized by comprising the following steps:
step a: establishing a solving area, wherein the solving area represents the expansion of a hydraulic fracture network by a dynamic coordinate, and represents an unactivated natural fracture by a static coordinate;
step b: establishing a two-dimensional fracture network expansion model for coupling reservoir fluid flow:
setting model conditions: the opening deformation of the crack is linear elastic behavior; the fluid is viscous Newtonian fluid, and the hysteresis phenomenon of fluid at the end part of the crack and the stress interference effect between the cracks are not considered; the crack extension meets the plane strain state in a vertical plane, and the vertical section is elliptical; the natural cracks are vertical cracks, and the height of the cracks is constant and equal to the thickness of the reservoir; the method comprises a flow equation in a fracture, an extension path after the hydraulic fracture is intersected with a natural fracture, a fracture width equation and a material conservation equation, and specifically comprises the following steps:
A. equation of flow in fracture
The natural cracks are vertical cracks, the height of the cracks is constant and equal to the thickness of a reservoir, the section of the cracks is elliptical, the fluid is viscous Newtonian fluid, and a flow equation of the Newtonian fluid in the elliptical cracks along the x and y directions is established;
B. the extension path of the hydraulic fracture intersecting with the natural fracture comprises the following three types:
(a) The hydraulic fracture opens and closes the natural fracture and turns to extend along the natural fracture, and a mechanical condition equation is satisfied;
(b) The hydraulic fracture extends through the natural fracture, but the natural fracture is not opened, and a mechanical condition equation is satisfied;
(c) The hydraulic fracture extends through the natural fracture and opens the natural fracture; the net pressure at the intersection point satisfies both mechanical condition equations of (a) and (b);
C. based on a crack width equation of plane strain, the width of the crack is expressed according to a two-dimensional PKN model;
D. conservation of substance equation: the volume of fluid injected into the fracture is equal to the sum of the volume change of the fracture and the fluid loss volume;
step c: setting initial and boundary conditions, wherein the boundary conditions comprise an inner boundary condition and an outer boundary condition;
step d: establishing a reservoir fluid flow control equation:
according to the dual medium model, the continuity equation of the matrix system is:
the fluid loss volume is characterized by adopting the fluid channeling flow between the crack and the matrix in the dual-medium model, and a fluid loss model based on pressure dependence is established:
fluid loss will change the pore pressure of the matrix system, and natural microcracks that are not open in the matrix system will exhibit a strong pressure-sensitive effect, describing the microcrack permeability and pressure sensitivity as:
K m ＝K mi exp{-C m (P i -P m )}
wherein: k (K) mi Represents the permeability mD in the initial conditions of microcracks; c (C) m Representing the stress sensitivity coefficient MPa of natural cracks -1 ；P i Represents the initial pressure MPa of the matrix system;
form factor alpha m In relation to the large scale fracture spacing in the reservoir, expressed by definition as:
wherein: mu is the viscosity of the injected fluid mPas; b represents the fluid volume coefficient and the dimensionless quantity; p (P) m Pore pressure MPa of the matrix system; phi (phi) m Is the porosity of the matrix, dimensionless quantity; alpha m Representing a form factor of 1/m 2 ；K m Permeability of matrix μm 2 ；L fx 、L fy Representing the distance m between the crack system in the x and y directions in a coordinate system; Δx, Δy represent the dimension m of the grid block in the x, y direction in the coordinate system, respectively; v (V) b Representing the grid block volume m 3 ；
Step e: substituting the numerical parameters into a model to solve: the material conservation equation and the oil reservoir fluid flow control equation of fluid flowing in the fracture network are coupled and solved, and fluid pressure and fracture width distribution at the fracture intersection point of a solving area are obtained by taking fluid loss as a coupling condition between the two control equations; in the solving process, loop iteration is performed to satisfy the global material balance equation.
2. The method of modeling a two-dimensional fracture network propagation model coupling reservoir fluid flow of claim 1, wherein: in the step e, an implicit finite difference method is adopted for carrying out numerical solution.
3. The method of modeling a two-dimensional fracture network propagation model coupling reservoir fluid flow of claim 1, wherein: in the step c of the process, a step of,
the initial conditions are:
W f (x,y,t)| t＝0 ＝W fi
the outer boundary conditions are:
the internal boundary conditions are:
wherein: q (Q) 0 Representing injection displacement m3/min; w (W) fi Representing an initial crack width m; Γ -shaped structure o And Γ I Representing the internal and external boundary conditions of the simulation model, respectively.
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