CN110348031B - Numerical simulation method for horizontal well fracturing near-wellbore fracture distortion form - Google Patents
Numerical simulation method for horizontal well fracturing near-wellbore fracture distortion form Download PDFInfo
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Abstract
A numerical simulation method for horizontal well fractured near-wellbore fracture distortion morphology is disclosed. The method can comprise the following steps: establishing a multilayer heterogeneous stratum model according to the stratum parameters and the construction parameters; establishing a fluid-solid coupling numerical equation according to a fluid seepage equation, a rock deformation equation, a fracture distortion criterion and a fracture surface fluid flow equation; and performing extended finite element numerical simulation in the multilayer heterogeneous stratum model according to a fluid-solid coupling numerical equation, and determining the distortion form of the horizontal well at each moment of fracturing the near-wellbore fracture. According to the method, the influence of factors such as construction parameters on the fracture distortion change is analyzed by calculating the fracture width change, the pertinence of the horizontal well fracturing optimization design is improved according to the fracture distortion change degree and change time, and a theoretical basis is provided for the site horizontal well fracturing optimization design.
Description
Technical Field
The invention relates to the field of oil and gas field development, in particular to a numerical simulation method for a horizontal well fractured near-wellbore fracture distortion form.
Background
At present, a horizontal well staged fracturing technology is mostly adopted for developing unconventional oil and gas reservoirs such as shale gas and dense gas, the horizontal well fracturing and the vertical well fracturing are different in that a near wellbore region can form fracture distortion, and the probability of the fracture distortion phenomenon is verified through theoretical calculation and physical modeling experiments. Zhang et al (2005) applied Lagrangian numerical calculation method to simulate three-dimensional fracture steering near the near wellbore and compared with experimental results, but their model does not consider the coupling relation between fluid flow in fracture and pore and rock deformation; lecampion et al (2013) analyzes the competition relationship between transverse and longitudinal fractures near a horizontal well fracturing near a shaft, the analysis result is mainly related to stratum characteristics, construction parameters, perforation parameters and a stress field, and the model has the main limitation that the fracture expansion and distortion forms cannot be displayed in real time and the fracture change process cannot be observed visually; sherman et al (2015) simulates the expansion and steering of the fracture near the wellbore of the horizontal well by using a three-dimensional finite element model, the result shows the complexity of the fracture near the wellbore, and the pressure relation consistent with the complexity is recorded, but the model is established on the basis of a single-layer homogeneous reservoir, the influence of factors such as construction parameters and stress difference on the complexity of the fracture is not considered, and the width change of the fracture from the transverse fracture to the longitudinal fracture is not quantified. Therefore, a numerical simulation method for the fracture distortion shape of the near-wellbore fracture of the horizontal well is needed to be developed.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention provides a numerical simulation method for fracture distortion form of a near-wellbore fractured fracture of a horizontal well, which can improve pertinence of horizontal well fracturing optimization design according to fracture distortion change degree and change time and provide theoretical basis for on-site horizontal well fracturing optimization design by calculating fracture width change and analyzing influence of factors such as construction parameters on fracture distortion change.
The method may include: establishing a multilayer heterogeneous stratum model according to the stratum parameters and the construction parameters; establishing a fluid-solid coupling numerical equation according to a fluid seepage equation, a rock deformation equation, a fracture distortion criterion and a fracture surface fluid flow equation; and performing extended finite element numerical simulation in the multilayer heterogeneous stratum model according to the fluid-solid coupling numerical equation, and determining the distortion form of the horizontal well at each moment of fracturing the near-wellbore fracture.
Preferably, the formation parameters include: initial ground stress field, initial seepage field, initial porosity, fracture surface filtration loss coefficient, number of bedding and thickness.
Preferably, the construction parameters include construction fluid displacement and construction fluid viscosity.
Preferably, the rock deformation equation is:
wherein σij,eIs the elastic stress of the ij plane, σij,e0Initial elastic stress in the ij plane, epsilonij,eIs the elastic strain of the ij plane, ΔijRepresenting the variation, epsilon, of the previous parameter in the ij planekk,eThe elastic strain in the direction perpendicular to the ij plane is shown, G is the elastic shear modulus, K is the elastic volume modulus, i and j represent the coordinate directions of i and j, and e represents the elasticity.
Preferably, the fluid seepage equation is:
where β and M are Biot coefficients, k is rock permeability, and γ is pore fluid specific gravity.
Preferably, the normal fluid loss rate of the top surface of the fracture and the normal fluid loss rate of the bottom surface of the fracture are obtained according to the fluid flow equation of the fracture surface, and then a fluid-solid coupling numerical equation is established.
Preferably, the fracture surface fluid flow equation is:
wherein v istNormal fluid loss rate of fracture top surface, vbThe normal fluid loss rate of the bottom surface of the crack, gfAnd q is fracture fluid flow volume per unit fracture width.
Preferably, the fracture top surface normal fluid loss rate is:
vt＝lt(pf-pt) (9)
wherein v istNormal fluid loss rate of the fracture top surface, /)tIs the fluid loss coefficient, ptPore fluid pressure at the top of the fracture, pfIs the fracture fluid pressure;
the normal fluid loss rate of the bottom surface of the crack is as follows:
vb＝lb(pf-pb) (10)
wherein v isbNormal fluid loss rate at the bottom of the crack,/bIs the fluid loss coefficient, pbPore fluid pressure of the bottom of the fracture, pfIs the fracture fluid pressure.
Preferably, the fracture-distortion criterion is a fracture propagation critical energy release rate criterion.
Preferably, the fracture propagation critical energy release rate criterion is:
wherein G isS＝Gs+Gt，GT＝Gn+GS,
The normal fracture critical strain energy release rate;
for two tangential fracture critical energy release rates, the B-K criterion holds
η is a constant related to the material properties itself; gCThe composite fracture critical fracture energy release rate is obtained.
The invention has the beneficial effects that: the method comprises the steps of analyzing the forming process of a space torsion curve surface of a crack near a horizontal well fracturing barrel, displaying crack expansion and distortion forms in different time periods in real time, quantifying crack distortion forming time, calculating crack width change, analyzing the influence of factors such as construction parameters on crack distortion change, improving pertinence of horizontal well fracturing optimization design according to crack distortion change degree and change time, and providing theoretical basis for field horizontal well fracturing optimization design.
The present invention has other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
Fig. 1 shows a flow chart of the steps of a numerical simulation method of a horizontal well fractured near-wellbore fracture tortuosity morphology according to the invention.
Fig. 2a and 2b show schematic diagrams of a horizontal wellbore and an initial longitudinal fracture, respectively, in a horizontal well fracture near-wellbore fracture tortuosity initial model, according to an embodiment of the present invention.
FIG. 3 shows a simulated view of crack distortion initiation formation according to one embodiment of the present invention.
Figure 4 shows a simulated view of a crack twist fully formed according to one embodiment of the present invention.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Fig. 1 shows a flow chart of the steps of a numerical simulation method of a horizontal well fractured near-wellbore fracture tortuosity morphology according to the invention.
In this embodiment, the method for simulating the distortion of the fracture near the wellbore of the horizontal well fracture according to the present invention may include: step 101, establishing a multilayer heterogeneous stratum model according to stratum parameters and construction parameters; 102, establishing a fluid-solid coupling numerical equation according to a fluid seepage equation, a rock deformation equation, a fracture distortion criterion and a fracture surface fluid flow equation; 103, performing extended finite element numerical simulation in the multilayer heterogeneous stratum model according to a fluid-solid coupling numerical equation, and determining the distortion form of the horizontal well at each moment of fracturing the near-wellbore fracture.
In one example, formation parameters include: initial ground stress field, initial seepage field, initial porosity, fracture surface filtration loss coefficient, number of bedding and thickness.
In one example, the construction parameters include construction fluid displacement and construction fluid viscosity.
In one example, the rock deformation equation is:
wherein σij,eIs the elastic stress of the ij plane, σij,e0Initial elastic stress in the ij plane, epsilonij,eIs the elastic strain of the ij plane, ΔijRepresenting the variation, epsilon, of the previous parameter in the ij planekk,eThe elastic strain in the direction perpendicular to the ij plane is shown, G is the elastic shear modulus, K is the elastic volume modulus, i and j represent the coordinate directions of i and j, and e represents the elasticity.
In one example, the fluid seepage equation is:
where β and M are Biot coefficients, k is rock permeability, and γ is pore fluid specific gravity.
In one example, the fracture top surface normal fluid loss rate and the fracture bottom surface normal fluid loss rate are obtained according to a fracture surface fluid flow equation, and then a fluid-solid coupling numerical equation is established.
In one example, the fracture face fluid flow equation is:
wherein v istNormal fluid loss rate of fracture top surface, vbThe normal fluid loss rate of the bottom surface of the crack, gfAnd q is fracture fluid flow volume per unit fracture width.
In one example, the fracture top surface normal fluid loss rate is:
vt＝lt(pf-pt) (9)
wherein v istNormal fluid loss rate of the fracture top surface, /)tIs the fluid loss coefficient, ptPore fluid pressure at the top of the fracture, pfIs the fracture fluid pressure;
the normal fluid loss rate of the bottom surface of the crack is as follows:
vb＝lb(pf-pb) (10)
wherein v isbNormal fluid loss rate at the bottom of the crack,/bIs the fluid loss coefficient, pbPore fluid pressure of the bottom of the fracture, pfIs the fracture fluid pressure.
In one example, the fracture twist criterion is a fracture propagation critical energy release rate criterion.
In one example, the fracture propagation critical energy release rate criteria is:
wherein G isS＝Gs+Gt，GT＝Gn+GS,
The normal fracture critical strain energy release rate;
for two tangential fracture critical energy release rates, the B-K criterion holds
η is a constant related to the material properties itself; gCThe composite fracture critical fracture energy release rate is obtained.
Specifically, a shale stratum model is established according to stratum parameters and construction parameters, wherein the stratum parameters comprise an initial ground stress field, an initial seepage field, initial porosity, fracture surface filtration loss coefficient, bedding number and bedding thickness, and the construction parameters comprise construction fluid discharge capacity and construction fluid viscosity. And constructing a pore elastic stratum geometric model embedded with a horizontal shaft, and cracking a longitudinal fracture from the horizontal shaft. After initialization, the fracture may propagate at any location in the model domain. The model is large enough to minimize boundary effects. The model is 250m long, 180m wide and 60m high, and the reservoir thickness is 25 m.
Fig. 2a and 2b show schematic diagrams of a horizontal wellbore and an initial longitudinal fracture, respectively, in a horizontal well fracture near-wellbore fracture tortuosity initial model, according to an embodiment of the present invention.
The simulated formation is combined with linearly coupled pore fluid diffusion/stress elements and enriched with a set of continuous media for the XFEM model, and fracture transformations will likely occur during the simulation process. In order to improve the modeling precision, the cells near the horizontal shaft are encrypted. The three-dimensional geometric model is shown in fig. 2. In the simulation process, the fracturing fluid is a Newtonian fluid and is a propagation medium with dominant viscosity/storage. Initial pore medium saturation stress and pore fluid pressure are assumed. The displacement is perpendicular to all boundaries and symmetric surfaces and limits movement at the inner corner virtual node. Pore fluid pressure remains consistent within the model boundary and the pore media. And injecting fracturing fluid at a constant speed, enabling the fracturing fluid to enter the existing longitudinal fractures and reach the pseudo-boundary nodes of the enriched elements, and further solving a fracturing fluid flow equation.
And establishing a fluid-solid coupling numerical equation according to a fluid seepage equation, a rock deformation equation, a fracture distortion criterion and a fracture surface fluid flow equation.
(1) Deformation of rock
Assuming that the porous rock is a homogeneous, isotropic porous elastic material, and quasi-static fracturing is performed, the initial constitutive equation under low stress conditions can be expressed as:
in the formula, σijStress of ij plane, σij,0Initial stress in the ij plane,. epsilonijIs the strain of the ij plane, epsilonkkStrain perpendicular to the ij plane, p is pore pressure, p0For initial pore pressure, β is the Biot coefficient. For a fully saturated porous media, the Terzaghi effective stress can be expressed as:
σij,e＝σij+pΔij (2)，
the effective strain may be expressed as:
wherein α is a Biot coefficient, so that the constitutive equation can be simplified to formula (4), which is a rock deformation equation.
(2) Pore fluid flow
For small volume strains, the pore fluid continuity equation can be expressed as:
wherein v iskkFor fluid seepage rates, β and M are Biot coefficients. The rate of seepage v when a fluid passes through a network of interconnected pores according to Darcy's lawkCan be expressed as:
wherein k is rock permeability, mu is pore fluid viscosity, gamma is pore fluid specific gravity, p'kIs the k-plane pore pressure tensor. The pore diffusion equation obtained from the above is the fluid seepage equation and is the formula (7).
(3) Flow of fracturing fluid
According to the Reynolds lubrication theory, the fracture surface fluid flow equation is a fracture fluid continuity equation in the fracture and can be expressed as (8), according to the fracture surface fluid flow equation, the normal fluid loss rate of the top surface of the fracture and the normal fluid loss rate of the bottom surface of the fracture are obtained and are respectively formula (9) and formula (10), and pt、pbAnd pfThe pressure differential therebetween results in fracturing fluid loss.
(4) Fracture initiation and propagation
The fracture distortion criterion is a fracture initiation and propagation criterion, namely when the maximum tensile effective stress acting on the fracture surface is larger than the tensile strength of the rock, the rock is initiated, and the propagation direction is along the current maximum principal stress direction. The composite type crack propagation B-K criterion is applied, namely the crack propagation critical energy release rate criterion is expressed as a formula (11).
The fluid-solid coupling numerical equation comprises the formula (4), the formula (7), the formula (8), the formula (9), the formula (10) and the formula (11), and according to the fluid-solid coupling numerical equation, the expanded finite element numerical simulation is carried out in the multilayer heterogeneous stratum model to determine the distortion form of the horizontal well fracturing near wellbore fracture at each moment. The fracturing process is simulated as a gradual loss of strength in the zero thickness interface according to the linear softening viscous drag separation law, the direction and extent of which are not predefined, butIs automatically calculated during the simulation. In the traction separation law, the cohesive energy E is equal to the product of the linear softening area and the cohesive strength. Before the crack opens, the cohesive energy is linear with the initial stiffness. From crack initiation to propagation, interface strength is from I0Reduced to 0, free opening of the interface, and a crack distance gf0. If unloaded before complete failure, the interfacial drag decreases linearly as the failure stiffness Mp decreases. As the hydraulic fracture is subjected to tension and shearing force simultaneously in the process of twisting, the crack extension process is researched by applying an energy-based mixed mode damage evolution law, namely a B-K crack criterion, a horizontal well fracture twisting model is established, a finite element numerical program is operated and calculated according to a set control equation, initial and boundary conditions, crack initiation and extension conditions are gradually reached along with the continuous injection of fluid, at the moment, a plurality of different positions of rock near a horizontal well are subjected to point fracture, a plurality of branch cracks are formed for initiation and crack stop, the steering radiuses and directions of the branch cracks are different, main cracks are twisted, transverse cracks are gradually formed, and the process is presented in a software calculation tool in real time according to the difference of time.
According to the method, the influence of factors such as construction parameters on the fracture distortion change is analyzed by calculating the fracture width change, the pertinence of the horizontal well fracturing optimization design is improved according to the fracture distortion change degree and change time, and a theoretical basis is provided for the site horizontal well fracturing optimization design.
Application example
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
The fracture distortion phenomenon of the XX block horizontal well near the shaft is to be evaluated, and the elastic performance parameters of the reservoir and the boundary pore in the simulation process are shown in the table 1.
TABLE 1
Initial, boundary condition parameters are shown in table 2.
TABLE 2
| Initial conditions | Reservoir bed | Boundary layer |
| Initial maximum horizontal principal stress (MPa) | 35 | 38 |
| Initial minimum horizontal principal stress (MPa) | 25 | 28 |
| Initial saturation of pore fluid | 1 | 1 |
| Pore fluid initial pressure (MPa) | 20 | 20 |
FIG. 3 shows a simulated view of crack distortion initiation formation according to one embodiment of the present invention.
Figure 4 shows a simulated view of a crack twist fully formed according to one embodiment of the present invention.
The simulation is carried out by utilizing the invention, and the simulation result shows that in the process of expanding the longitudinal crack of the horizontal well, along with the point fracture at different positions, a plurality of branch cracks are formed to initiate and stop the crack, the turning radiuses and directions of the branch cracks are different, so that the main crack is distorted, the transverse crack is gradually formed, the fracture points and the branch cracks at different positions which are continuously formed cause the fluctuation of a pressure curve, and the crack expanding pressure is increased along with the increase of the discharge capacity and the viscosity; at different positions of the seam height, the seam width is changed alternately due to twisting, the fracture twisting starting time is 60-90 s, as shown in FIG. 3, the time for converting the near-wellbore longitudinal fracture of the horizontal well into the transverse seam is about 240s, as shown in FIG. 4; in the formation process of crack distortion, the fluctuation degree of the crack width is large, the average is 0.5mm, and the construction friction resistance is increased; reducing the viscosity and displacement facilitates the formation of transverse seams, and the slug concentration and quantity can be adjusted depending on the time at which the distortion occurs.
In conclusion, the method improves the pertinence of the horizontal well fracturing optimization design by calculating the width change of the fracture, analyzing the influence of factors such as construction parameters on the fracture distortion change and the like according to the fracture distortion change degree and change time, and provides a theoretical basis for the site horizontal well fracturing optimization design.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (6)
1. A numerical simulation method for a fracture distortion form of a fractured near wellbore of a horizontal well comprises the following steps:
establishing a multilayer heterogeneous stratum model according to the stratum parameters and the construction parameters;
establishing a fluid-solid coupling numerical equation according to a fluid seepage equation, a rock deformation equation, a fracture distortion criterion and a fracture surface fluid flow equation;
performing extended finite element numerical simulation in the multilayer heterogeneous stratum model according to the fluid-solid coupling numerical equation, and determining the distortion form of the horizontal well at each moment of fracturing the near-wellbore fracture;
wherein the rock deformation equation is:
wherein σij,eIs the elastic stress of the ij plane, σij,e0Initial elastic stress in the ij plane, epsilonij,eIs the elastic strain of the ij plane, ΔijRepresenting the variation, epsilon, of the previous parameter in the ij planekk,eThe elastic strain is perpendicular to the ij plane direction, G is the elastic shear modulus, K is the elastic volume modulus, i and j represent the i and j coordinate directions, and e represents the elasticity;
wherein the fluid seepage equation is:
wherein, beta and M are Biot coefficients, k is rock permeability, gamma is pore fluid specific gravity, and p'kkIs the pore pressure tensor perpendicular to the ij plane, p 'is the pore pressure tensor, ε'kkIs the strain tensor perpendicular to the ij plane;
wherein the fluid flow equation of the fracture surface is as follows:
wherein v istNormal fluid loss rate of fracture top surface, vbThe normal fluid loss rate of the bottom surface of the crack, gfIs the crack distance, q is the unit crack width fracturing fluid flow volume;
wherein the fracture distortion criterion is a fracture propagation critical energy release rate criterion.
2. The horizontal well fractured near-wellbore fracture tortuosity morphology numerical simulation method of claim 1, wherein the formation parameters comprise: initial ground stress field, initial seepage field, initial porosity, fracture surface filtration loss coefficient, number of bedding and thickness.
3. The method of numerical simulation of a horizontal well fractured near-wellbore fracture tortuosity morphology of claim 1, wherein the construction parameters comprise construction fluid displacement and construction fluid viscosity.
4. The horizontal well fracturing near-wellbore fracture distortion morphology numerical simulation method of claim 1, wherein a fracture top surface normal filtration rate and a fracture bottom surface normal filtration rate are obtained according to the fracture surface fluid flow equation, and a fluid-solid coupling numerical equation is further established.
5. The numerical simulation method of the horizontal well fractured near-wellbore fracture tortuosity morphology, according to claim 4, wherein the fracture top surface normal fluid loss rate is as follows:
vt＝lt(pf-pt) (9)
wherein v istNormal fluid loss rate of the fracture top surface, /)tIs the fluid loss coefficient, ptPore fluid pressure at the top of the fracture, pfIs the fracture fluid pressure;
the normal fluid loss rate of the bottom surface of the crack is as follows:
vb＝lb(pf-pb) (10)
wherein v isbNormal fluid loss rate at the bottom of the crack,/bIs the fluid loss coefficient, pbFor pore flow at the bottom of the crackBody pressure, pfIs the fracture fluid pressure.
6. The numerical simulation method for the distortion morphology of the horizontal well fractured near-wellbore fracture according to claim 1, wherein the fracture propagation critical energy release rate criterion is as follows:
wherein G isS＝Gs+Gt，GT＝Gn+GS,
The normal fracture critical strain energy release rate;
for two tangential fracture critical energy release rates, the B-K criterion holds
η is a constant related to the material properties itself; gCThe composite fracture critical fracture energy release rate is obtained.
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