CN111125905A - Two-dimensional fracture network expansion model coupled with reservoir fluid flow and simulation method thereof - Google Patents
Two-dimensional fracture network expansion model coupled with 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 solves the fluid pressure, the fracture width and the flow equation of the matrix block at the natural fracture intersection point through coupling, so that the network fracture geometric dimensions at different times can be obtained.
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
Numerous studies have shown that natural fractures may alter the propagation path of hydraulic fractures, and fracturing fractured reservoirs may create complex fractures that are multi-branched, non-planar. Laboratory experimental research shows that under certain approaching angle and stress difference conditions, natural fractures change the extension path of hydraulic fractures. In recent years, a number of researchers begin to research the influence of natural fractures on hydraulic fractures by using a numerical simulation method, and micro-seismic monitoring proves that the hydraulic fractures in shale reservoirs extend into complex fracture networks. It can be seen that the hydraulic fracture propagation pattern of fractured formations is complex and is very different from the symmetric plane fractures generated by homogeneous formation fracturing.
The numerical simulation research of the shale gas yield shows that the network cracks with certain flow conductivity have an important effect on improving the shale gas yield. Therefore, the development of hydraulic fracturing technology has also transitioned from conventional double-winged symmetric plane fractures to how network fractures are created in ultra-low permeability reservoirs. The extension simulation of network fractures is an important component of hydraulic fracturing design, a plurality of scholars provide a mathematical model for simulating a fracture network, and research finds that the fracture network is simulated mainly by simulating the extension and the steering of each natural fracture and communicating with other natural fractures to generate the fracture network according to the interaction criteria of the natural fractures and the hydraulic fractures, and the simulation model is complex in calculation.
The fractured reservoir is often developed with macro fractures with large scale and a large amount of natural micro fractures, related scholars analyze seepage characteristics of the fractured reservoir, concepts of the macro fractures and the micro fractures are introduced, and a dual fracture medium model is provided, wherein the dual fracture medium model divides fractures and matrixes into two systems for independent solution, so that the problem of difficulty in calculation convergence caused by the adoption of a single medium solution system is avoided.
In the application, based on the idea of coupling flow of natural fractures and matrixes in dual media, the fractures and the matrixes are taken as two relatively independent flow systems, and the inventor provides a set of two-dimensional fracture network expansion model and fracture network simulation method for coupling oil reservoir fluid flow.
Disclosure of Invention
The invention aims to provide a two-dimensional fracture network expansion model coupled with reservoir fluid flow and a simulation method thereof.
In order to achieve the purpose, the basic scheme of the invention is as follows:
coupling a two-dimensional fracture network expansion model for reservoir fluid flow, and setting model conditions: the opening deformation of the crack is linear elastic behavior; the fluid is viscous Newtonian fluid, and fluid hysteresis at the end of the crack and stress interference effect between cracks are not considered; the whole crack extends to meet the plane strain state in a vertical plane, and the vertical section is elliptical; the natural fractures are vertical fractures, and the height of the fractures is constant and equal to the thickness of the reservoir; the method comprises an in-fracture flow equation, an extension path after intersection of a hydraulic fracture and a natural fracture, a fracture width equation and a material conservation equation, and specifically comprises the following steps:
A. flow equation in fracture
The natural fractures are vertical fractures, the height of the fractures is constant and equal to the thickness of a reservoir, the fracture section is elliptical, the fluid is viscous Newtonian fluid, and a flow equation of the Newtonian fluid in the elliptical fractures along the x direction and the y direction is established;
B. the extension path after the hydraulic fracture and the natural fracture are intersected comprises the following three paths:
(a) the hydraulic fracture opens the closed natural fracture and turns and extends along the natural fracture to meet the mechanical condition equation;
(b) the hydraulic fracture extends through the natural fracture but the natural fracture is not opened, and the mechanical condition equation is met;
(c) extending the hydraulic fracture through the natural fracture and opening the natural fracture; the net pressure at the intersection point simultaneously satisfies the 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. the material conservation 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 reservoir fluid comprises the following steps:
step a: establishing a solving area, wherein the solving area represents the hydraulic fracture network expansion by a dynamic coordinate, and represents the unactivated natural fracture by a static coordinate;
step b: building 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 the model to solve: the method comprises the following steps of (1) solving a material conservation equation and an oil reservoir fluid flow control equation of fluid flowing in a fracture network in a coupling mode, and obtaining fluid pressure and fracture width distribution at the intersection of a fracture in a solving area by taking fluid filtration loss as a coupling condition between the two control equations; in the solution process, loop iteration is performed to satisfy the global material balance equation.
The basic scheme of the invention has the working principle and the beneficial effects that:
under the influence of natural fractures, the extension of hydraulic fractures in fractured reservoirs may be a non-planar complex fracture system, which is greatly different from the double-wing symmetric plane fractures generated by homogeneous reservoir fracturing, because a conventional hydraulic fracture extension model cannot be used for simulating fracture morphology and fracture geometry of non-planar extension of hydraulic fractures in fractured formations. Therefore, in the application, based on the thought of coupled flow of natural fractures and matrixes in dual media, the fractures and the matrixes are taken as two relatively independent flow systems, the action modes of the pre-natural fractures and the hydraulic fractures are considered, a two-dimensional hydraulic fracture network expansion, fluid loss and fracture network extension mathematical model of 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 fracture width equation and an oil reservoir fluid flow equation of two-dimensional fracture network expansion are solved numerically to obtain the geometric form and the size of the network fracture.
The model can be used for researching the influence of sensitive parameters including injection volume, fracture height, elastic modulus, horizontal main stress difference, discharge capacity and fracturing fluid viscosity on the shape of the fracture network, the size of the fracture network, the average fracture width of the fracture network and the contact area of the fracture oil reservoir, and numerical calculation results show that the model can simulate the expansion of network fractures and obtain the geometric dimension of the fracture network. By the scheme, the unconventional reservoir staged volume fracturing fracture network morphology can be quantitatively analyzed, the method is an effective means for evaluating and optimizing the fracturing scheme, and the difficulty in calculating the network fracture geometric dimension in the prior art is greatly reduced.
Drawings
FIG. 1 is a schematic diagram of a two-dimensional fracture network expansion simulation according to an embodiment of the present invention, in which a denotes an activated dynamic coordinate, b denotes an inactivated static coordinate, c denotes a natural fracture, d denotes a matrix block, e denotes a perforation position, f denotes a hydraulic fracture extension, and g denotes a solving unit;
FIG. 2 shows the volume of injected fluid, the total volume of the fracture and the relative error at different construction times, wherein A denotes the fracture half-length (PKN analytic solution), B denotes the fracture half-length (model), C denotes the fracture width (PKN analytic solution), D denotes the fracture width (model), the abscissa denotes time (min), the left ordinate denotes the fracture half-length (m), and the right ordinate denotes the bottom hole fracture width (mm);
FIG. 3 is a comparison of a model numerical solution and a PKN analytic solution in an embodiment of the present application;
FIG. 4 is the final fracture network geometry and fracture width profile (mm);
FIG. 5 is a pore pressure distribution (MPa) of the matrix system;
FIGS. 6 and 7 are fracture network geometry and fracture width profiles at different fluid viscosities;
FIGS. 8 and 9 are fracture network geometry and fracture width profiles for different injected fluid volumes;
FIGS. 10 and 11 are fracture network geometry and fracture width profiles for different rock elastic moduli;
FIGS. 12 and 13 are fracture network geometry and fracture width profiles at different levels of principal stress difference;
FIGS. 14 and 15 are different displacement lower slot web geometries and slot width profiles;
fig. 16 and 17 are fracture network geometry and fracture width profiles at different fracture heights.
Detailed Description
The following is further detailed by way of specific embodiments:
example (b):
the two-dimensional fracture network expansion model coupled with reservoir fluid flow and the simulation method thereof comprise the following steps:
step a: establishing a solution region
The hydraulic fracture network expansion is represented by dynamic coordinates, the natural fractures which are not activated are represented by static coordinates, and the whole dynamic and static coordinates form a solving area shown in figure 1. During fluid injection, the natural fracture opens and propagates. When the fracture propagates to the intersection of the hydraulic fracture and the natural fracture and the fluid pressure at the 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 injection fluid acts to open the closed natural fracture and propagate the natural fracture in both directions from the intersection.
In model building, 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 fluid hysteresis at the end of the crack and stress interference effect between cracks are not considered; assuming that the whole crack extension satisfies the plane strain state in the vertical plane, the vertical section is elliptical; the natural fractures are vertical fractures, and the height of the fractures is constant and equal to the reservoir thickness.
Step b: establishing two-dimensional fracture network expansion model for coupling oil reservoir fluid flow
According to the hydraulic fracture propagation idea described in fig. 1, a mathematical model of hydraulic fracture propagation along two directions is established, and the model includes an intra-fracture flow equation, an extension path after the hydraulic fracture intersects with a natural fracture, a fracture width equation and a material conservation equation, which are as follows:
A. fluid flow equation 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 profile is elliptical, rather than a parallel plate, and the flow pressure drop in an elliptical fracture is 16/3 pi times that of a parallel plate flow under the same flow conditions, so the flow equation of a newtonian fluid in the elliptical fracture along the x and y directions is:
in the formula: q (x, t) and q (y, t) represent the volumetric flow (m) through the cross-section of the x and y point fracture, respectively3S); μ represents a fracturing fluid viscosity (mPa · s); h isfIndicates the height (m) of the crack; wfxAnd WfyThe slit widths (m) along the x and y directions are indicated, respectively. PfIndicating 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. Extended path after intersection of hydraulic fracture and natural fracture
The extension path after the hydraulic fracture intersects with the natural fracture is a key factor influencing the formation of a fracture network, and according to related theoretical and experimental researches, the hydraulic fracture has three extension paths after the hydraulic fracture intersects with the natural fracture:
(a) the hydraulic fracture opens the closed natural fracture and turns and extends along the natural fracture, and the mechanical conditions are as follows:
(b) the hydraulic fracture extends through the natural fracture but the natural fracture is not opened, and the mechanical conditions are met:
(c) the hydraulic fracture extends through and opens the natural fracture: the net pressure at the intersection is required to satisfy both the above inequality (3) and inequality (4).
Wherein Δ σ represents a horizontal principal stress difference (MPa); θ represents the natural fracture angle (°) from the horizontal maximum principal stress; t isoRepresents the tensile strength (MPa) of the rock; pnetRepresenting the hydraulic fracture net pressure (MPa) at the intersection.
C. Equation of crack width
Based on the plane strain assumption, neglecting the fluid pressure gradient in the vertical direction, the width of the fracture can be expressed according to the two-dimensional PKN model as:
wherein: wfxAnd WfyRepresenting hydraulic fracture widths (m) extending in the x and y directions, respectively; e represents the elastic modulus (MPa) of the rock; ν denotes the poisson ratio of the rock, a dimensionless quantity. SigmanxAnd σnyRespectively representing the normal stress of the natural crack surface spread along the x and y directions, and can be obtained according to the two-dimensional linear elasticity theory (MPa).
D. Equation of conservation of matter
The geometry of the fracture network is determined by the material balance equation, and at any given 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 equation for fluid flow in the x and y directions can be expressed as:
the sum of equation (7) and equation (8) yields the mass conservation equation for the propagation of the fracture along the x and y directions as:
in the formula: q. q.sL(x, t) and qL(y, t) represents the volumetric flow rate (m) of fluid lost to the formation by a fracture element of length Δ x and Δ y, respectively3/min)；QLRepresents the total fluid loss (m) of the fracture unit along the x and y directions with lengths Deltax and Deltay, respectively3Min); a (x, t) and A (y, t) represent the cross-sectional area (m) of the fracture at the point of flow x and y, respectively2) (ii) a t represents the construction time(s). The fracture cross-sectional area at the point of flow x and y can be expressed as:
substituting equations 1 and 2, and equations 10 and 11 into equation 9, then equation 9 can be expressed as:
the global material conservation equation is:
in the formula: q (t) represents the injection displacement (m)3Min); l (t) represents the length (m) of all open cracks at time t.
Step c: setting initial and boundary conditions
Initial conditions:
Wf(x,y,t)|t＝0＝Wfi(14)
outer boundary conditions:
inner boundary conditions:
in the formula: q0Indicating injection displacement (m)3/min)；WfiRepresents the initial crack width (m); gamma-shapedoAnd ΓIRespectively representing the inner and outer boundary conditions of the simulation model.
Step d: establishing reservoir fluid flow control equations
In the dual-medium seepage model, a fracture system and a matrix system are two independent and mutually-connected hydrodynamic fields. According to the dual media model, the continuity equation for the matrix system is:
the fluid loss volume is mainly controlled by the pressure difference between a fracture system and a matrix system, the fluid channeling quantity between the fracture and the matrix in a dual-medium model can be adopted for characterization, and a fluid loss model based on pressure dependence is established:
fluid loss will change the matrix system pore pressure, natural micro-fractures that are not open in the matrix system will exhibit a strong pressure sensitivity effect, and the equations describing the micro-fracture permeability and pressure sensitivity are:
Km＝Kmiexp{-Cm(Pi-Pm)} (19)
in the formula: kmiRepresents the permeability (mD) under the microcrack initiation condition; cmShows the natural fracture stress sensitivity coefficient (MPa)-1)；PiIndicating the initial pressure (MPa) of the matrix system.
Shape factor αmIn relation to the large scale fracture spacing in the reservoir, expressed by definition as:
in the formula: μ is injection fluid viscosity (mPa · s); b represents a fluid volume coefficient, a dimensionless quantity; pmThe pore pressure (MPa) of the matrix system;
α is the porosity of the matrix, dimensionless quantitymRepresents the shape factor (1/m)2)；KmPermeability (mum) of matrix2)。Lfx、LfyRepresenting the spacing (m) of the fracture system in the x and y directions in the coordinate system; Δ x, Δ y represent the dimensions (m) of the grid block in the x, y directions, respectively, in the coordinate system; vbRepresents the grid block volume (m)3)。
Step e: solving by substituting numerical parameters into model
And (3) solving a material conservation equation and an oil reservoir fluid flow control equation of the fluid flowing in the fracture network by coupling, wherein the two control equations use fluid filtration loss as a coupling condition. However, both the fracture width and the fluid pressure in the fracture network propagation material conservation equation are unknown quantities, so equation (12) needs to be coupled with equations (5) and (6) to obtain the fluid pressure and fracture width distribution at the fracture intersection points in the whole solution area. In the solution process of the model, loop iteration is needed to satisfy the global material balance equation. The whole control equation can be solved numerically by adopting an implicit finite difference method.
The following experiments were performed:
according to the established mathematical model and the numerical solving method, the seam network is subjected to simulation calculation, a numerical simulation program is programmed to simulate the form of the seam network, and table 1 is a basic parameter. In consideration of the symmetry of the shaft in the physical model, in order to improve the calculation efficiency, a quarter cell with the shaft as the center is taken as a research object.
TABLE 1
| Parameter(s) | Numerical value | Parameter(s) | Numerical value |
| Construction time (min) | 30 | Angle of approach (°) | 90 |
| Displacement (m)3/min) | 6 | Maximum horizontal principal stress (MPa) | 51 |
| Fracturing fluid viscosity (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 |
| Modulus of elasticity (GPa) | 35 | Permeability of matrix (mD) | 0.1 |
| Poisson ratio (-) | 0.2 | Porosity of matrix (-) | 0.05 |
From the above mathematical model, we can see that hydraulic fracturing will form a single planar fracture when the horizontal principal stress difference is large enough that all natural fractures along the y-direction cannot be activated by hydraulic fractures. According to the basic parameters in the table, the main stress difference is set to be 20MPa, the numerical simulation result shows that only a single plane crack is formed in the reservoir, and the calculation result of the single plane crack is compared with the analytic solution of PKN, as shown in FIG. 2. It can be seen that the numerical simulation result and the analytic result of the model are in good agreement, and the average error of the numerical simulation result and the analytic result is calculated, so that the relative errors of the half length and the width of the crack are respectively about 6.1% and 3.7%.
Similarly, if the horizontal primary stress difference is 0, it can be inferred that the crack will propagate the same length in the x and y directions. For this reason, the numerical simulation results are shown in fig. 3 and table 2 based on the basic parameters of table 1, and 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 all used to propagate 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 the fracture was 179.38m3And the total volume of injected liquid is 180m3The two are almost the same, and the rationality of the model is also proved.
TABLE 2
| Calculation results | Numerical value |
| Gap net size/(10)4m3) | 64.0 |
| Length of sewing net/(m) | 200.0 |
| Seam net width/(m) | 200.0 |
| Total volume of crack/(m)3) | 179.38 |
| Total priming volume/(m)3) | 180 |
| Oil reservoir fracture contact area/(10)4m2) | 6.4 |
| Average width of X-direction crack/(mm) | 0.892 |
| Average width of Y-direction crack/(mm) | 0.892 |
The experimental results are as follows:
fig. 4 shows a fracture network geometry and fracture width profile calculated based on the base parameters, and fig. 5 shows the pore pressure distribution of the reservoir matrix under the condition of considering pressure-dependent fluid loss, and it is obvious from the graph that the pore pressure of the reservoir matrix within the fracture network expansion range is obviously increased due to the fluid loss. Next, we will perform a parameter sensitivity study on the model, analyze the influence of the relevant construction parameters and formation parameters on the seam network, and further verify the practicability of the model.
1. Effect of fluid viscosity on gap web size
Fig. 6 and 7 show fracture network geometry and fracture width profiles for 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 found that the size of the fracture network and the fracture contact area of the reservoir increase with the decrease of the fluid viscosity, and the width of the primary and secondary fractures greatly decreases with the increase of the fluid viscosity. When the fluid viscosity is reduced from 120 mPas to 10 mPas and then to 1 mPas, the size of the seam net is from 21.7X 104m3Increased to 35.2X 104m3Then increased to 56.3X 104m3The contact area of reservoir fracture is from 3.115 multiplied by 104m2Increased to 4.88 × 104m2Then increased to 6.74X 104m2. The sizes of the seam networks are respectively increased by 62.2 percent and 59.9 percent, and the contact areas of the reservoir fractures are respectively increased by 56.6 percent and 38.1 percent. It can be seen that the low viscosity fluid has a greater effect on the size of the slotted web. In addition, a decrease in fluid viscosity may make the slotted network more prone to lengthwise growth and a decrease in slotted network width, since a decrease in fluid viscosity will reduce the net pressure within the fracture, which is detrimental to the opening and propagation of the secondary fracture.
TABLE 3
| viscosity/(mPa. s) | 1 | 10 | 120 |
| Gap net size/(10)4m3) | 56.3 | 35.2 | 21.7 |
| Oil reservoir fracture contact area/(10)4m2) | 6.74 | 4.88 | 3.115 |
| Length of sewing net/(m) | 1250 | 470 | 240 |
| Seam net width/(m) | 30 | 50 | 60 |
| Average width of X-direction crack/(mm) | 0.958 | 1.390 | 2.016 |
| Average width of Y-direction crack/(mm) | 0.207 | 0.500 | 1.169 |
2. Influence of liquid injection volume on size of slotted net
Fig. 8 and 9 show the fracture network geometry and fracture width cross-sections at different injection volumes. Table 4 shows the effect of shot 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 found 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 equivalent increase in the injection volume. While the maximum width increase of the slotted net decreases with an equal increase in the injection volume. The average width of the primary and secondary cracks increases slightly with increasing injection volume. This indicates that the injection volume is one of the most critical factors affecting the stimulated volume of the reservoir.
TABLE 4
| Injection volume/(m)3) | 60 | 120 | 180 |
| Gap net size/(10)4m3) | 12.8 | 24.2 | 35.2 |
| Oil reservoir fracture contact area/(10)4m2) | 1.75 | 3.34 | 4.88 |
| Length of sewing net/(m) | 280 | 390 | 470 |
| Seam net width/(m) | 30 | 45 | 50 |
| Average width of X-direction crack/(mm) | 1.344 | 1.366 | 1.390 |
| Average width of Y-direction crack/(mm) | 0.492 | 0.495 | 0.500 |
3. Effect of modulus of elasticity on seamed webs
Fig. 10 and 11 show fracture network geometry and fracture width profiles for different rock elastic moduli, and table 5 shows the effect of elastic modulus on fracture network size, reservoir fracture contact area, fracture network length and width, and mean primary and secondary fracture width. From the data in the table, it can be found that the size of the fracture network and the fracture contact area of the reservoir increase with increasing elastic modulus. When the elastic modulus is increased from 25GPa to 35GPa and then to 45GPa, the size of the seam net is increased from 29.6 multiplied by 104m3Increased to 35.2X 104m3Then increased to 39.2X 104m3The size of the slotted net is increased by 18.9% and 11.4%, respectively. The contact area of reservoir fracture is from 3.965 multiplied by 104m2Increased to 4.88 × 104m2Then increased to 5.53X 104m2The corresponding reservoir fracture contact area is increased by 23.1% and 13.3%, respectively. This indicates that reservoirs with high elastic modulus are favored for the creation of larger networks of seams. SeamThe width of the web and the average width of the secondary fractures increase with increasing modulus of elasticity while the length of the slotted web and the average width of the primary fractures decrease with increasing modulus of elasticity. This is due to the higher the elastic modulus of the reservoir, the higher the 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 net
Fig. 12 and 13 show the fracture network geometry and fracture width profiles for different levels of primary stress differential, and table 6 shows the effect of the level of primary stress differential 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 observed that the slotted net size increases from 42.1 × 10 when the primary stress difference increases from 0.5MPa to 1.5MPa4m3Reduced to 30.4 × 104m3And the contact area of reservoir fracture is from 6.115 multiplied by 104m2Reduced to 3.935 × 104m2. 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 greater the difference in primary stresses, the more difficult it is to open and extend the secondary fractures. Thus, an increase in the primary stress difference will also decrease the width of the secondary fractures, injecting more fluid into the primary fractures. Thus, the slit width in the x-direction increases and the slit width in the y-direction decreases.
TABLE 6
| Horizontal principal stress difference/(MPa) | 0.5 | 1 | 1.5 |
| Gap net size/(10)4m3) | 42.1 | 35.2 | 30.4 |
| Oil reservoir fracture contact area/(10)4m2) | 6.115 | 4.88 | 3.935 |
| Length of sewing net/(m) | 330 | 470 | 670 |
| Seam net width/(m) | 85 | 50 | 30 |
| Average width of X-direction crack/(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 screens
Fig. 14 and 15 show the fracture network geometry and fracture width profiles for different injection volumes, and table 7 shows the effect of injection volume on fracture network size, reservoir fracture contact area, length and width of the fracture network, and average primary and secondary fracture width. From the data in the table, it can be seen that the injection displacement is from 3m3The/min is increased to 9m3At/min, the size of the fracture network and the contact area of the oil reservoir fracture are respectively reduced by 17.5 percent and 15.1 percent. 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 the displacement increases the width of the seam in the x and y directions as well as the width of the seam web and decreases the seam web length. This indicates that increasing the displacement makes it easier for the slotted net to expand in the direction of maximum principal stress.
TABLE 7
6. Effect of crack height on slotted 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, length and width of the fracture network, and average primary and secondary fracture width. From the data in the table, it can be found that when the fracture height is reduced from 30m to 10m, the size of the fracture network is from 32.1 × 104m3Increased to 41.9 × 104m3And the contact area of reservoir fracture is from 4.18 multiplied by 104m2Increased to 6.11 × 104m2. This indicates that a reduction in fracture height will increase the fracture network size and reservoir fracture contact area. In addition, as the fracture height decreases, the length of the fracture network and the width of the main fractureAnd also decreases, while the width of the secondary fracture and the width of the seam network increase. This is because the smaller the fracture height, the higher the net pressure within the main fracture, and the easier the branch fracture opens and propagates.
TABLE 8
| Crack height/(m) | 10 | 20 | 30 |
| Gap net size/(10)4m3) | 41.9 | 35.2 | 32.1 |
| Oil reservoir fracture contact area/(10)4m2) | 6.11 | 4.88 | 4.1775 |
| Length of sewing net/(m) | 470 | 470 | 540 |
| Seam net width/(m) | 120 | 50 | 30 |
| Average width of X-direction crack/(mm) | 1.102 | 1.390 | 1.668 |
| Average width of Y-direction crack/(mm) | 0.633 | 0.500 | 0.402 |
In conclusion, based on the dual medium theory, the fluid filtration loss of pressure dependence is represented by using the flow rate, and a set of two-dimensional fracture network expansion mathematical model coupling the oil reservoir fluid flow is established. The numerical calculation result shows that the model can simulate the geometric dimension of the network fracture and can analyze the influence of relevant reservoir and construction parameters on the size of the fracture network and the 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 slotted net, which is almost linear with the injected volume. The injected fluid volume has little effect on the average width of the fracture, with the average width of the primary and secondary fractures increasing slightly as the injected fluid volume increases.
(2) Reducing the viscosity of the injected fluid can greatly increase the size of the fracture network and the contact area of the reservoir and the fracture, but the width of the primary fracture and the secondary fracture is reduced, and the injected low-viscosity fluid can form a long and narrow fracture network.
(3) Reducing the primary stress difference will expand the size of the fracture network, the contact area of the reservoir fractures, the width of the secondary fractures and the width of the fracture network. But the width of the main slit and the length of the slit network will decrease.
(4) Increasing the injection displacement may reduce the size and contact area of the slotted net. But the width of the secondary fractures and the width of the network of fractures can be increased because the increase in displacement increases the net pressure within the fractures.
(5) High elastic modulus reservoirs can form larger and wider network fractures and can enlarge the contact area of reservoir fractures. But the width of the fracture is reduced which may limit proppant migration.
(6) Reducing the fracture height produces a wider and larger network of fractures, with the fracture height having an effect on both the network morphology and the fracture width.
The foregoing is merely an example of the present invention and common general knowledge of known specific structures and features of the embodiments is not described herein in any greater detail. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several changes and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the patent.
Claims (4)
1. The two-dimensional fracture network expansion model for coupling oil reservoir fluid flow is characterized in that model conditions are set as follows: the opening deformation of the crack is linear elastic behavior; the fluid is viscous Newtonian fluid, and fluid hysteresis at the end of the crack and stress interference effect between cracks are not considered; the extension of the crack meets the plane strain state in a vertical plane, and the vertical section is elliptical; the natural fractures are vertical fractures, and the height of the fractures is constant and equal to the thickness of the reservoir; the method comprises an in-fracture flow equation, an extension path after intersection of a hydraulic fracture and a natural fracture, a fracture width equation and a material conservation equation, and specifically comprises the following steps:
A. flow equation in fracture
The natural fractures are vertical fractures, the height of the fractures is constant and equal to the thickness of a reservoir, the fracture section is elliptical, the fluid is viscous Newtonian fluid, and a flow equation of the Newtonian fluid in the elliptical fractures along the x direction and the y direction is established;
B. the extension path after the hydraulic fracture and the natural fracture are intersected comprises the following three paths:
(a) the hydraulic fracture opens the closed natural fracture and turns and extends along the natural fracture to meet the mechanical condition equation;
(b) the hydraulic fracture extends through the natural fracture but the natural fracture is not opened, and the mechanical condition equation is met;
(c) extending the hydraulic fracture through the natural fracture and opening the natural fracture; the net pressure at the intersection point simultaneously satisfies the 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. the material conservation equation: the volume of fluid injected into the fracture is equal to the sum of the fracture volume change and the fluid loss volume.
2. The method for simulating the two-dimensional fracture network propagation model for coupling reservoir fluid flow according to claim 1, comprising the steps of:
step a: establishing a solving area, wherein the solving area represents the hydraulic fracture network expansion by a dynamic coordinate, and represents the unactivated natural fracture by a static coordinate;
step b: building 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 the model to solve: the method comprises the following steps of (1) solving a material conservation equation and an oil reservoir fluid flow control equation of fluid flowing in a fracture network in a coupling mode, and obtaining fluid pressure and fracture width distribution at the intersection of a fracture in a solving area by taking fluid filtration loss as a coupling condition between the two control equations; in the solution process, loop iteration is performed to satisfy the global material balance equation.
3. The method for simulating the two-dimensional fracture network propagation model for coupling reservoir fluid flow according to claim 2, wherein: and e, carrying out numerical solution by adopting an implicit finite difference method.
4. The method for simulating the two-dimensional fracture network propagation model for coupling reservoir fluid flow according to claim 2, wherein: in the step c, in the step of the method,
the initial conditions were:
Wf(x,y,t)|t＝0＝Wfi
the outer boundary conditions are as follows:
the inner boundary conditions were:
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