CN107545113B - Method for simulating formation process of complex fracture network of hydraulic fracturing of unconventional oil and gas reservoir - Google Patents
Method for simulating formation process of complex fracture network of hydraulic fracturing of unconventional oil and gas reservoir Download PDFInfo
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Abstract
The invention discloses a method for simulating a formation process of a complicated fracture network of a staged hydraulic fracturing of an unconventional oil and gas reservoir, which comprises the following steps: a. reconstructing natural fracture distribution, estimating the nature of natural fractures, obtaining rock mechanical information and stratum stress information of a stratum from logging data or a geological model, and obtaining a data file related to a construction process of a well factory; b. inputting the obtained parameters into a natural fractured reservoir fracturing model of the coupling shaft, the fracture and the reservoir; c. carrying out numerical solution on the model to obtain information such as fracture morphology, opening distribution, pressure distribution and the like after fracturing; d. and analyzing the fracturing effect by adopting the model calculation result, and preparing for numerical simulation in the later production process. The numerical simulation method for fractured reservoir coupled with wellbore flow, fracture deformation expansion, multi-state natural fractures and fluid flow in fractures can quantitatively analyze the form of the unconventional reservoir segmented volume fracturing network, and is an effective means for evaluating and optimizing a fracturing scheme.
Description
Technical Field
The invention relates to the technical field of oil and gas field development, in particular to a method for simulating a formation process of a hydraulic fracturing complex fracture network of an unconventional oil and gas reservoir.
Background
In unconventional reservoirs such as shale and the like, the matrix permeability is only nano Darcy, and the requirement of economic exploitation can not be met far if a horizontal well staged fracturing technology is not adopted. But the length of the horizontal well and the construction scale of hydraulic fracturing are increased, so that the construction cost of the fractured horizontal well is far higher than that of a conventional well. In the United states, the cost for drilling a new horizontal well is about 1.5-2.5 times of that of a vertical well. The fracturing effect is improved, and the method has very important significance for improving the fracturing well productivity and shale gas development economic benefit.
Researchers find that complex fracture network structures are likely to be formed by the interaction of fracturing fractures and natural fractures by observing field outcrops. With the continuous development of fracture monitoring technology, especially the progress of microseism three-dimensional monitoring technology, people can obtain more information about fracture morphology after fracturing. On-site micro-seismic data show that complex fracture networks are easily formed after fracturing of low-permeability and ultra-low-permeability unconventional reservoirs represented by shale. The reasonable prediction of the complex fracture network after fracturing is vital to the optimization of fracturing construction. The geometrical shape of the fractured crack can be obtained through simulation of the fracturing process, and the property of the crack directly determines the magnitude of the later-stage production energy and the quality of the fracturing scheme.
The industry has long used simple single double-wing straight fracture models to perform fracture analysis. The double-wing straight fracture model assumes that the fracture is a single plane after fracturing, and the phenomena of turning or intersection with a natural fracture and the like do not exist. The current mainstream fracturing commercial software adopts the method. The model is not suitable for fracturing simulation of a fractured unconventional reservoir because the model cannot depict the growth process of a fractured fracture when a natural fracture exists, and has great limitation.
Researchers have performed a great deal of work in order to improve the double-wing straight slit model. Most of the work is still limited to very small scale and very simple crack distribution, and cannot be used in space on the scale of hundreds of meters on site. At present, the following methods can be used for simulating the generation of the fracture network of the oil reservoir scale:
a. the representative software was the MShale fracture simulator of beckhause, assuming that the fractures extend outward in the form of two orthogonal sets of fractures that are perpendicular to each other. The method can lead the simulated crack to be a crack network instead of a single crack. However, the method carries out too strong constraint on the fracture form, the actual distribution of natural fractures in the stratum cannot be followed, and the stress interference among the fractures is calculated by adopting an empirical formula, so that the fracturing process is difficult to be accurately reduced.
b. Assuming that the fracture network in the formation is formed by communicating the natural fractures in the formation, it is believed that the orientation of the fractured fractures is still in the direction of the vertical minimum horizontal principal stress, and the fracture meeting the natural fractures must pass through the natural fractures. The model is based on a discrete element method, the natural fracture is considered to divide the stratum into different blocks, and the displacement and deformation of the natural fracture are simulated by simulating the slippage of the blocks. This type of description can be made of complex natural fracture networks, with capabilities not available with traditional discrete element methods, but it also has significant limitations. In this method, all the damage occurs only on the preexisting fracture faces, and it is impossible to simulate a fracture newly formed on the natural fracture wall face. Meanwhile, the method assumes that the fracturing fracture must penetrate through the natural fracture, and experimental research shows that the fracturing fracture is possibly intercepted by the natural fracture after meeting the natural fracture.
c. Schrenbach developed a fracture model UFM that simulated fractured reservoirs from 2000. The model calculates the fracture deformation by using a two-dimensional displacement discontinuity method (one of boundary element methods), and adds the correction in the height direction proposed by Olson. In order to overcome the difficulty of the two-dimensional model in describing the height to a certain extent, Weng et al adopts a three-dimensional simulated Cell-based model to calculate the length of the fracture and the distribution of the opening in the height direction, and adopts a one-dimensional simplified proppant model to describe the migration of the proppant. The UFM model has now been integrated into the schlumberger fracture simulator, Mangrove, which is one of the most comprehensive commercial simulators for simulating the growth of fracture networks in the industry at present. UFM is a great improvement over existing fracture models, but still suffers from the following problems: 1) neglecting the displacement of the fracture in the shearing direction; 2) the simulation of the natural fracture is the same as the fracturing fracture, and the processes of shearing, sliding, closing and the like of the natural fracture cannot be reflected; 3) re-initiation of a fracture at the end of a natural fracture does not follow mechanical guidelines
Although the model is a great improvement on a single straight double-wing fracture model, because the simulation difficulty of a complex fracture network is far greater than that of a single fracture, no fully-perfect model is used for describing the expansion of a fractured fracture in a natural fracture network at present. The numerical simulation method based on the finite element and the expanded finite element needs to carry out grid encryption on the periphery of the fracture, and when the natural fracture is densely distributed, the grid subdivision difficulty is high, the calculation efficiency is low, and the method is difficult to be used for the oil reservoir scale. The simulation method based on the discrete element method is limited by the simulation applicable scale and is difficult to be applied to the well factory problem of hundreds of meters. The existing numerical simulation algorithm based on the boundary element method can effectively improve the calculation efficiency, but neglects the processes of newly-generated fracturing fractures, natural fracture shearing slip and the like to different degrees, and cannot completely describe the expansion condition of the fracturing fractures when the natural fractures in the stratum exist in advance. Therefore, for reasonably predicting unconventional reservoir volume fracturing, a set of novel fracturing model which can be coupled with a shaft-fracture-reservoir, has operability on the oil reservoir scale and can be used for describing a fracture network forming process is needed.
Disclosure of Invention
In order to solve the problems, the invention provides a novel numerical simulation method for fractured reservoir. Hydraulic fracturing is the coupling of a number of physical processes, including: (1) flow of the fracturing fluid in the fracture; (2) deformation of the crack; (3) the crack is expanded; (4) loss of fracturing fluid; (5) migration of proppant, etc. In the invention, the fluid flow in the fracture is calculated by adopting a finite volume method. The invention adopts a displacement discontinuity method in an indirect boundary element method to simulate the deformation of the fracture under the action of fluid pressure and the original stress of the reservoir. The displacement discontinuity method only needs to carry out mesh subdivision on the surface of the crack, can effectively reduce the dimension of the problem and achieve the purpose of improving the calculation efficiency. Assuming that the propagation of the crack satisfies the quasi-steady state condition, the propagation direction is perpendicular to the direction of the maximum circumferential stress. The loss of fracturing fluid is simulated by a one-dimensional Carter model. The flow of proppant in the fracture is simulated using the convection equation and the distribution of proppant is described using volume fraction. Compared with a single fracture model, the fracture model has the advantages that the parts such as judgment of intersecting behavior of the fracture and the natural fracture, deformation of the natural fracture, and a special constitutive model for flowing of the natural fracture are supplemented.
The technical scheme of the invention is as follows:
a method for simulating a complex fracture network forming process of hydraulic fracturing of an unconventional oil and gas reservoir specifically simulates a fracturing process of a fractured reservoir in the following mode:
s1, input parameters: inputting relevant parameters of fracturing simulation, including the properties of the natural fractures (the cohesion, the friction angle and the initial opening degree of the natural fractures), the cohesion and the friction angle of the fractures, the Young modulus and the Poisson ratio of rocks, the directions of the in-situ maximum and minimum horizontal principal stresses, the thickness of a target layer, the pressure of pore fluid, the viscosity and the density of injection fluid, the injection rate of fracturing fluid, the positions of perforating points and construction parameters related to perforating, namely the number of the perforating holes and the diameter of the perforating holes;
s2, setting a model: the control conditions adopted by simulation are determined by inputting parameters, the control conditions comprise the length of a crack unit and an initial time step length, the following parameters are also set manually, and the default calculation mode is as follows:
a. determining the length of a fracture unit according to the length of the natural fracture; assuming that the shortest natural fracture can be split into 20 cells, the fracture cell length is set to 1/20 for the shortest natural fracture length;
b. the initial time step is determined according to the unit length and the maximum injection rate of the fracturing fluid; assuming that the unit length is L, the maximum injection rate of the fracturing fluid is V, and the initial time step is L/V;
s3, carrying out numerical simulation: carrying out numerical simulation of the fracturing process by adopting a numerical model, solving the fluid pressure, the fracture displacement, the bottom hole pressure and the flow at each perforation by adopting full-implicit Newton-Raffson iteration, keeping the variables unchanged after the integral number of the proppant and the fracturing liquid is updated, and carrying out explicit updating until the fracturing process is finished;
s4, outputting a calculation result: setting parameters to be output according to requirements, wherein the parameters comprise fracture shearing displacement distribution, fracture form distribution, images of pressure distribution and formation stress distribution in the fracture, and output files of bottom hole pressure and inflow flow of each perforation point along with time change;
s5, analyzing the fracturing effect: after the fracturing simulation is finished, analyzing the fracturing effect according to the fracturing simulation result; the fracture shape such as the total length of the fracture after fracturing is directly and briefly judged, or the calculation result of the method is transmitted to an oil deposit numerical simulator capable of simulating a fractured reservoir, so that the productivity is evaluated; and changing fracturing parameters such as the number of perforation clusters, and comparing simulation results corresponding to different fracturing schemes so as to optimize the fracturing schemes.
In the step S5, a numerical model is used to simulate a fracturing process, which includes the following steps:
s3.1, calculating the fracture deformation under the action of fluid pressure and ground stress;
s3.2, simulating a crack propagation process;
s3.3, judging the intersection behavior of the fracturing fracture and the natural fracture;
s3.4, judging the state of the natural crack;
s3.5, simulating the flow in the shaft;
s3.6, simulating flow in the crack;
and S3.7, solving coupling of multiple physical processes.
In step S3.1, the contents of the fracture deformation calculation under the action of the fluid pressure and the ground stress are:
calculating the fracture deformation under the action of fluid pressure and ground stress by a Displacement Discontinuity Method (DDM); for two-dimensional problems, the fracture is a line segment with length and curvature, and each fracture grid cell may have a different length; each unit deforms under the action of normal stress and tangential stress to generate discontinuous displacement Ds and Dn;
the stress received by any point in the space is the sum of the discontinuous induced stresses of all unit displacements, the crack is assumed to be divided into N units, and for any point (x, y) in the space, the induced stress received by the point is as follows:
in the formula AiInfluence coefficients of induced stress in different directions for different displacement discontinuity amounts; the known boundary condition is assumed to be a stress boundary condition, namely the magnitude of stress acting on the surface of each unit of the crack is known; when the induced stress sum of the discontinuous amount of the displacement of the crack on the surface of the crack unit is equal to the real stress of the surface of the crack, the obtained discontinuous amount of the displacement is the real value of the crack under the condition of the stress boundary:
in the above formula
The magnitude of the shear stress induced by the unit tangential displacement of the unit j at the position of the unit i, and the meanings of other coefficients are similar; a is called an influence coefficient;
and σn iRespectively the shear stress and the normal stress actually suffered by the surface of the unit i; introducing a height correction factor H proposed by professor Olson of Austin university, and rewriting the formula into:
wherein sigmaij,0For the magnitude of the in-situ stress acting on the fracture element i, the height correction factor expression is:
in the formula (d)ijα and β are empirical constants for the distance between the center point of the crack unit i and the center point of the unit j, and according to the numerical calculation result in the literature, α is equal to 1, and β is equal to 2.3.
The fracture propagation process simulation in the step S3.2 comprises the following steps:
the fracture propagation form in the stratum can be divided into three situations of I-type tension, II-type plane shear and III-type tearing:
the stress concentration factor SIF at the fracture tip location is as follows:
in the above formula, E is the Young's modulus of rock, uiRepresenting displacements in different directions;
when SIF in different directions reaches a critical value, the crack begins to expand; SIF is regarded as the characteristic of the material, and is irrelevant to the stress condition; the DDM method can be used for quickly and directly obtaining the tip displacement, and further quickly calculating the SIF in different directions:
in the above formula, Di is discontinuous displacement of the tip unit along different directions, and a is half length of the tip unit; the stress concentration factor calculated by the displacement discontinuity method is always greater than an analytic value; 0.806 is an empirical correction constant;
the method adopts the strain energy release rate as the criterion for judging whether the crack is expanded or not, and the rock has I-type fracture toughness (K)IC) And type II fracture toughness (K)IIC) Different, the invention adopts the F criterion to judge the crack initiation and expansion directions:
f is the direction of the maximum value, namely the crack propagation direction, and if F is more than 1, the crack propagates.
In the step S3.3, the method for judging the intersection behavior of the fracture and the natural fracture is as follows:
the interaction of natural fractures with fracturing fractures exists in a variety of forms; the fracture may be captured by and grow along the natural fracture, may propagate through the natural fracture along the original path, or may be diverted into the matrix again after growing for a distance along the natural fracture;
the method adopts I-type stress concentration factor KI and II-type stress concentration factor KII to comprehensively depict the stress field at the tip of the crack. And judging which process of the shear slippage of the natural crack and the generation of the new fracturing crack occurs first based on the stress field at the tip of the crack, wherein if the natural crack slips first, the fracturing crack cannot pass through the natural crack, otherwise, the fracturing crack passes through the natural crack and grows along the original path.
In step S3.4, the natural fracture state determination method is as follows:
normal stress sigma acting on natural fracture unitβnAnd shear stress tauβCalculating according to the displacement of all the fracture units:
there may be three states of a natural fracture during fracturing: closing, sliding and opening, wherein the type of the natural fracture unit is judged according to the following stress conditions:
a closing unit:
|τβ|＜So-λσβn
a slipping unit:
|τβ|≥So-λσβn
an opening unit:
P≥σβn
if the natural fracture is completely closed, the natural fracture unit has no displacement discontinuity and does not participate in the fracture deformation calculation; if the natural crack is completely opened, the stress boundary condition of the natural crack is the same as that of the fracturing crack; if the natural fracture is closed, but shear failure occurs due to violation of the Moore coulomb rule, the fracture unit cannot normally displace, and the tangential stress boundary condition meets the Moore coulomb law:
|τβ|＝-λσβn
the sign of the friction force should be opposite to the shear displacement change direction:
Dswhen the normal stress applied to the natural fracture is smaller than the fluid pressure in the fracture, the natural fracture unit is mechanically opened, and the control equation is the same as that of the fracturing fracture.
In S3.5, the method for simulating the flow in the shaft comprises the following steps:
using a shaft model for reference; assume total flow into the wellbore is QTWhen fracturing fluid flows through each perforation cluster, part of the flow is divided into the fractures connected with the perforation cluster, and in the figure 5, the fracture 1 is divided into wellbore flow Q1,1And Q1,2The residual flow rate is continuously transported to the next perforation position along the shaft; the flow rate in the shaft satisfies the conservation relation:
in the formula, N is the number of fracturing cracks, and i takes the values of 1 and 2 and respectively corresponds to two cracks connected with the perforation clusters;
the flow corresponding to each perforation cluster cannot be solved only through the flow conservation relation; assuming that the injection pressure of the horizontal well is P0The pressure in the crack at the position where the crack i is adjacent to the horizontal well shaft is Pf,iThe pressure inside the shaft corresponding to the crack is Pw,iAnd then each perforation cluster position satisfies the pressure relation:
Pw,f＝Pf,i+Ppf,i
the pressure intensity of the position of the shaft corresponding to each perforation cluster and the injection pressure intensity meet the relational expression:
P0＝Pw,i+Pcf,i
Pcf,ifrom the injection point to the perforation cluster i, the pressure drop is generated due to the well wall friction and the flow energy dissipation in the well bore; ppf,iThe pressure loss at the fracture i due to perforation friction is generally considered to be proportional to the square of the flow into the fracture;
the perforation friction resistance expression is as follows:
extra attention needs to be paid to the unit of each item in the friction resistance pressure difference; ppf,iIn psi, fracturing fluid density in lbs/gal, volume flow rate Q injected into fracture iiIn bpm (barrels per minute), dpIs the diameter of the perforation cluster and has the unit of in, npThe number of perforation points of the perforation cluster, KdThe method is an empirical constant, is dimensionless and has a value range of 0.56-0.89;
pressure P in the shaftw,iThe positions of different perforation clusters are different, because the pressure in the shaft can be dissipated due to shaft friction and resistance generated by fluid flow; pcf,iFor pressure loss in a horizontal wellbore, according to the descriptions of Valko and Econoids for cylindrical tubing flow, assuming the fluid is Newtonian and is in ideal advection within the wellbore, the pressure loss P at different perforation cluster locations in the wellbore iscf,iThe calculation is made by the following formula:
Qw,j＝QT(j＝1)
in the above formula, D is the diameter of the shaft;
in step S3.6, the method for simulating flow in the crack is as follows:
for fracturing fractures, it is assumed that the fluid flow in the fracture satisfies the flow rule of the pipeline with the long and narrow rectangular section:
in the above formula
The flow speed of the fluid along the fracture section is shown, k is equivalent permeability, mu is fluid viscosity, p is fluid pressure in the fracture, and w is fracture opening; since the two-dimensional fracture propagation problem is being studied herein, the fluid flow in the fracture is one-dimensional along the length of the fracture;
the flow simulation in natural fractures is slightly different, assuming that the total opening of the natural fractures is from a closed opening
And a mechanical opening degree w; when the internal pressure of the crack is far less than the external pressure stress sigmanWhen the crack is closed, the natural crack is completely closed, and because the wall surfaces of the natural crack are not smooth, and a tiny gap exists between the wall surfaces, a part of residual opening w still exists at the moment0(ii) a The gap between cracks gradually increases along with the increase of the pressure, but the wall surface is not separated yet
Further increasing the pressure of the natural crack, separating the wall surface, wherein the separation distance of the wall surface is called as the mechanical opening w, and the opening of the crack before separation is called as the closed opening
Assuming that the flow in the natural fracture meets Darcy's law, a large number of indoor experimental results show that the permeability of the fracture and the effective stress meet an exponential relation:
in the above formula knfIs the crack permeability, knf,0As initial permeability of the crack, cfIs the fracture compressibility factor, σβnχ is Biot's coefficient, P, for normal stress acting on fracture surfacefIs the fluid pressure within the natural fracture; assuming a closed opening
And the effective stress satisfies an exponential relationship, and the natural fracture permeability is calculated by adopting a formula of Mcclure:
the above equation assumes Biot's constant of 1, koIs a given constant;
further, in step S3.7, the solution method for coupling multiple physical processes is as follows:
the fracturing problem is a typical fluid-solid coupling problem, the change of the opening of the fracture influences the flowing speed of fluid, and the pressure of the fluid in the fracture influences the deformation of the fracture; the fracture model can be divided into 3 sections: a wellbore model, an in-fracture flow model and a stress-strain model;
the principal variables of the model that need to be solved for full coupling are:
xT＝[Dn,1,Dn,2,...,Dn,n,P1,P2,...,Pn,P0,Q1,Q2,...,Qm]
in the formula DiFor discontinuity of fracture normal displacement, P is the pressure in each fracture cell, QiThe flow rate of the influent for each fracture;
the fluid part equation is dispersed by adopting a finite volume method, and the dispersed equation is subjected to full implicit solution by adopting Newton-Lawson iteration:
J(xn)dxn+1＝-Rn
xn+1＝xn+dxn+1
J(xn) The Jacobian matrix when the step n is iterated, and R is a right-end term residual error;
the iteration convergence conditions employed herein are:
||R||2＜tol and ||dx||2＜tol
in the formula | · | non-conducting phosphor2A type II norm representing a vector; when the equation converges, the residual error and the variable change dx need to be smaller than the tolerance tol at the same time; through a large number of calculation examples, when the tolerance value is 1e-5And in time, the simulation of a single time step can be converged only by 3-5 times of iteration.
The invention has the beneficial effects that:
1. the method provided by the invention can be used for depicting the distribution of different natural fractures and obtaining the geometrical form of the fractured fractures, is a great improvement on the traditional single straight fracture model, and expands the traditional fracturing model which only can consider the fractured fractures into a model suitable for the fracturing problem of the natural fractured reservoir; compared with the traditional fracturing model, the method comprises the special processes of intersecting the fracturing fracture and the natural fracture, shearing and sliding the natural fracture, closing the opening change of the natural fracture and the like; through coupling solving of a plurality of physical processes, the fractured form of the fractured unconventional reservoir with natural fractured property is finally obtained, and more accurate guidance is provided for fracturing construction;
2. the method has the advantages that the storage space is saved by adopting a displacement discontinuous method (DDM method), the calculation efficiency is high, and the method can be used for fracturing problems of site construction dimensions. The method is not only beneficial to improving the knowledge of the fracturing process, but also beneficial to quickly adjusting and improving the fracturing scheme, and has a larger application prospect;
3. the method can be used for analyzing the complex fracture network state under different fracturing parameters and reasonably optimizing the fracturing construction parameters;
4. the output result of the invention can also be used for subsequent production simulation, thereby more accurately predicting the yield of the oil and gas well.
Drawings
FIG. 1 is a schematic diagram of a fracture mesh generation;
FIG. 1(a) is a schematic diagram of a fracture mesh subdivision, wherein x-0-y is a global coordinate system, and ξ -0- η is a local coordinate system of each fracture unit;
FIG. 1(b) is a schematic diagram of stress condition (cell [ i ]) and displacement discontinuity (cell [ j ]) of the crack unit;
FIG. 2 shows three cases of fracture mode I, II and III in the formation;
FIG. 3 shows a radial coordinate system definition of the fracture tip;
FIG. 4 is a representation of what may occur after a fracture intersects a natural fracture;
FIG. 5 is a schematic representation of a wellbore model;
FIG. 6 the process of natural fracture opening as a function of internal pressure;
FIG. 7 is a schematic view of a fracture model coupling mode;
FIG. 8 is a numerical simulation input output parameter case;
FIG. 9 is a natural fracture profile of an embodiment;
FIG. 10 is a schematic view of a geological model structure;
FIG. 11 is a graph of a fracture construction of the example;
FIG. 12a is a graph of the fracture opening profile of the example;
FIG. 12b is a fracture shear displacement profile of the example;
FIG. 13a is a graph of the maximum principal stress profile after fracturing of an example;
FIG. 13b is a graph of the minimum principal stress profile after fracturing of an embodiment;
FIG. 14a is a plot of flow rate versus time at each perforation during fracturing in an example;
FIG. 14b is a graph of pressure versus time at each perforation during fracturing in an example.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Firstly, inputting geomechanical parameters, natural fracture parameters, in-situ stress distribution and fracturing construction parameters, and carrying out fracturing simulation to obtain the ground stress distribution, the fracture geometric form and the bottom hole pressure variation.
The simulation input parameters in the examples are respectively as follows:
1. the distribution of the generated natural fractures is shown in FIG. 9, assuming that the natural fracture friction angle is 20 ° and the initial opening is 0.01 mm;
2. geomechanical parameters near the perforation point, such as the young modulus of the rock, the poisson ratio, the in-situ minimum horizontal principal stress, the maximum horizontal principal stress, the thickness of a fracturing layer and the like, are extracted from the geological model shown in fig. 10, and selected values are shown in table 1. The geological model is obtained by a geological modeling mode according to the logging data of different wells;
table 1 example calculation parameters
3. Fracturing construction parameters are as follows: inputting the properties of injection rate (shown in figure 11), fracturing fluid viscosity, density (table 1) and the like into the model;
4. before the simulation begins, parameters such as an initial time step length, a crack unit length, an iterative convergence condition and the like are set according to actual problem parameters, in the embodiment, the initial time step length is selected to be 0.4s, the crack unit length is 0.8m, and the convergence tolerance is 1e-5；
5. And inputting the input parameters and the model setting parameters into a fractured reservoir fracturing model of the coupled shaft, the fracture and the reservoir, and simulating the fracturing process, wherein the fluid injection time is 37.5 min.
6. Obtaining a file and graphical output of the fracture simulation results, comprising:
(A) displacement of cracks: crack opening profile, as shown in fig. 12 a; fracture shear displacement profile, as shown in fig. 12 b; as can be seen from the calculation results, the opening degree of the inner cracks is smaller due to the extrusion of the outer cracks, and the outer cracks grow predominantly. Meanwhile, due to the existence of natural cracks, the cracks are no longer single straight cracks, and the shape is more complex;
(B) the maximum principal stress distribution of the formation after fracturing, as shown in FIG. 13 a; the minimum principal stress distribution of the formation after fracturing is shown in fig. 13 b. The tensile stress is taken as positive in the figure, and the fracture acts on the stratum by squeezing, so that the pressure stress in the stratum after fracturing is increased compared with the initial stress, and the stratum is strengthened by compression. The tensile stress is increased at the tip of the crack due to the stress concentration effect;
(C) the injection flow rates at different perforation positions change with time in the fracturing process, as shown in fig. 14a, the inflow capacity of fluid is weakened due to the fact that the inner side cracks are squeezed, so that the flow rate obtained by the inner side cracks is smaller than that of the outer side cracks, even no flow rate is injected in a part of time periods, and uneven distribution of the flow rate further aggravates the imbalance of the growth of the inner side cracks and the outer side cracks; the pressure at different perforation positions changes with time in the fracturing process, as shown in fig. 14b, and as the inner side cracks are squeezed by the two outer side cracks, the cracks need to resist higher pressure for expansion, so that the pressure is higher; it can be seen that the present invention can take into account both the dynamic allocation of flow in the wellbore and the dynamic propagation process of the fracture.
Compared with the existing fracturing model, on one hand, the method considers the influence of natural fractures and is more in line with the understanding of site engineering practice on fracturing; on the other hand, the three parts of a shaft, a crack and a reservoir stratum are simultaneously considered, so that the simulation result is closer to the actual condition, and an effective tool for optimizing the fracturing effect by optimizing the shaft construction condition is provided.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A method for simulating a complex fracture network forming process of hydraulic fracturing of an unconventional oil and gas reservoir is characterized in that the specific mode for simulating the fracturing process of a fractured reservoir is as follows:
s1, input parameters: inputting fracturing simulation related parameters, including the properties of the natural fractures, namely cohesion, friction angle and initial opening degree of the natural fractures, cohesion and friction angle of the fractures, Young modulus and Poisson ratio of rocks, in-situ maximum and minimum horizontal principal stress directions, target layer thickness, pore fluid pressure intensity and injection fluid viscosity and density, fracturing fluid injection rate, perforation point positions and construction parameters related to perforation, namely perforation number and perforation diameter;
s2, setting a model: the control conditions adopted by simulation are determined by inputting parameters, the control conditions comprise the length of a crack unit and an initial time step length, the following parameters are also set manually, and the default calculation mode is as follows:
a. determining the length of a fracture unit according to the length of the natural fracture; assuming that the shortest natural fracture can be split into 20 cells, the fracture cell length is set to 1/20 for the shortest natural fracture length;
b. the initial time step is determined according to the unit length and the maximum injection rate of the fracturing fluid; assuming that the unit length is L, the maximum injection rate of the fracturing fluid is V, and the initial time step is L/V;
s3, carrying out numerical simulation: carrying out numerical simulation of the fracturing process by adopting a numerical model, solving the fluid pressure, the fracture displacement, the bottom hole pressure and the flow at each perforation by adopting full-implicit Newton-Raffson iteration, keeping the variables unchanged after the integral number of the proppant and the fracturing liquid is updated, and carrying out explicit updating until the fracturing process is finished;
s4, outputting a calculation result: setting parameters to be output according to requirements, wherein the parameters comprise fracture shearing displacement distribution, fracture form distribution, images of pressure distribution and formation stress distribution in the fracture, and output files of bottom hole pressure and inflow flow of each perforation point along with time change;
s5, analyzing the fracturing effect: after the fracturing simulation is finished, analyzing the fracturing effect according to the fracturing simulation result; the fracture shape such as the total length of the fracture after fracturing is directly and briefly judged, or the calculation result of the method is transmitted to an oil deposit numerical simulator capable of simulating a fractured reservoir, so that the productivity is evaluated; and changing fracturing parameters, and comparing simulation results corresponding to different fracturing schemes so as to optimize the fracturing schemes.
2. The method for simulating the complex fracture network formation process of hydraulic fracturing of unconventional oil and gas reservoirs according to claim 1, wherein the simulation of the fracturing process in the step S5 is performed by using a numerical model, and comprises the following steps:
s3.1, calculating the fracture deformation under the action of fluid pressure and ground stress;
s3.2, simulating a crack propagation process;
s3.3, judging the intersection behavior of the fracturing fracture and the natural fracture;
s3.4, judging the state of the natural crack;
s3.5, simulating the flow in the shaft;
s3.6, simulating flow in the crack;
and S3.7, solving coupling of multiple physical processes.
3. The method for simulating the complex fracture network formation process of hydraulic fracturing of unconventional oil and gas reservoirs according to claim 2, wherein the content of the fracture deformation calculation under the action of fluid pressure and ground stress in the step S3.1 is as follows:
calculating the fracture deformation under the action of fluid pressure and ground stress by a displacement discontinuity Method, namely DDM (distributed differential Method for short); for two-dimensional problems, the fracture is a line segment with length and curvature, and each fracture grid cell may have a different length; each unit deforms under the action of normal stress and tangential stress to generate a discontinuous displacement DsAnd Dn；
The stress received by any point in the space is the sum of the discontinuous induced stresses of all unit displacements, the crack is assumed to be divided into N units, and for any point (x, y) in the space, the induced stress received by the point is as follows:
in the formula AiInfluence coefficients of induced stress in different directions for different displacement discontinuity amounts; the known boundary condition is assumed to be a stress boundary condition, namely the magnitude of stress acting on the surface of each unit of the crack is known; when the induced stress sum of the discontinuous amount of the displacement of the crack on the surface of the crack unit is equal to the real stress of the surface of the crack, the obtained discontinuous amount of the displacement is the real value of the crack under the condition of the stress boundary:
in the above formula
The magnitude of shear stress induced at the location of cell i for a unit tangential displacement of cell j; a is called an influence coefficient;
and σn iRespectively the shear stress and the normal stress actually suffered by the surface of the unit i;
introducing a height correction factor H, and rewriting the formula as follows:
wherein sigmaij,0For the magnitude of the in-situ stress acting on the fracture element i, the height correction factor expression is:
in the formula (d)ijThe distance between the crack unit i and the center point of the unit j is represented by α and β, which are empirical constants, and according to the numerical calculation result, α is equal to 1, and β is equal to 2.3.
4. A method for simulation of complex fracture network formation process for hydraulic fracturing of unconventional hydrocarbon reservoirs according to claim 3, wherein the fracture propagation process simulation in step S3.2 is performed by:
the fracture propagation form in the stratum can be divided into three situations of I-type tension, II-type plane shear and III-type tearing:
the stress concentration factor SIF at the fracture tip location is as follows:
in the above formula, E is the Young's modulus of rock, uiRepresenting displacements in different directions;
when SIF in different directions reaches a critical value, the crack begins to expand; SIF is regarded as the characteristic of the material, and is irrelevant to the stress condition; the DDM method can be used for quickly and directly obtaining the tip displacement, and further quickly calculating the SIF in different directions:
in the above formula, Di is discontinuous displacement of the tip unit along different directions, and a is half length of the tip unit; the stress concentration factor calculated by the displacement discontinuity method is always greater than an analytic value; 0.806 is an empirical correction constant;
the strain energy release rate is used as the criterion for judging whether the crack is expanded or not, and the rock I-type fracture toughness KICWith type II fracture toughness KIICAnd (3) judging the crack initiation and propagation directions by adopting an F criterion:
f is the direction of the maximum value, namely the crack propagation direction, and if F is more than 1, the crack propagates.
5. The method for simulating the complex fracture network formation process of hydraulic fracturing of unconventional oil and gas reservoirs according to claim 4, wherein in the step S3.3, the intersecting behavior of the fractured fractures and the natural fractures is judged by the following method:
the interaction of natural fractures with fracturing fractures exists in a variety of forms; the fracturing fracture is captured by the natural fracture and grows along the natural fracture, passes through the natural fracture and expands along the original path, or turns to enter the matrix again after growing for a certain distance along the natural fracture;
the method comprises the steps of comprehensively depicting a crack tip stress field by adopting an I-type stress concentration factor KI and an II-type stress concentration factor KII, judging which process of shearing and sliding of a natural crack and generation of a new fracture occurs firstly based on the crack tip stress field, and if the natural crack slides firstly, enabling the fracture crack to not pass through the natural crack, otherwise, enabling the fracture crack to pass through the natural crack and grow along the original path.
6. The method for simulating the complex fracture network formation process of hydraulic fracturing of unconventional oil and gas reservoirs according to claim 3, wherein in the step S3.4, the natural fracture state judgment method is as follows:
normal stress sigma acting on natural fracture unitβnAnd shear stress tauβCalculating according to the displacement of all the fracture units:
there are three states of natural fractures during fracturing: closing, sliding and opening, wherein the type of the natural fracture unit is judged according to the following stress conditions:
a closing unit:
|τβ|＜So-λσβn
a slipping unit:
|τβ|≥So-λσβn
an opening unit:
P≥σβn
if the natural fracture is completely closed, the natural fracture unit has no displacement discontinuity and does not participate in the fracture deformation calculation; if the natural crack is completely opened, the stress boundary condition of the natural crack is the same as that of the fracturing crack; if the natural fracture is closed, but shear failure occurs due to violation of the Moore coulomb rule, the fracture unit cannot normally displace, and the tangential stress boundary condition meets the Moore coulomb law:
|τβ|＝-λσβn
the sign of the friction force should be opposite to the shear displacement change direction:
Dswhen the normal stress applied to the natural fracture is smaller than the fluid pressure in the fracture, the natural fracture unit is mechanically opened, and the control equation is the same as that of the fracturing fracture.
7. The method for simulation of complex fracture network formation process for hydraulic fracturing of unconventional oil and gas reservoirs according to claim 2, wherein in S3.5, the method for simulation of flow in a wellbore is as follows:
using a shaft model for reference; assume total flow into the wellbore is QTWhen fracturing fluid flows through each perforation cluster, part of the flow is shunted to the cracks connected with the perforation cluster, and the residual flow is continuously transported to the next perforation position along a shaft; the flow rate in the shaft satisfies the conservation relation:
in the formula, N is the number of fracturing cracks, and i takes the values of 1 and 2 and respectively corresponds to two cracks connected with the perforation clusters;
the flow corresponding to each perforation cluster cannot be solved only through the flow conservation relation; assuming that the injection pressure of the horizontal well is P0The pressure in the crack at the position where the crack i is adjacent to the horizontal well shaft is Pf,iThe pressure inside the shaft corresponding to the crack is Pw,iAnd then each perforation cluster position satisfies the pressure relation:
Pw,i＝Pf,i+Ppf,i
the pressure intensity of the position of the shaft corresponding to each perforation cluster and the injection pressure intensity meet the relational expression:
P0＝Pw,i+Pcf,i
Pcf,ifrom the injection point to the perforation cluster i, the pressure drop is generated due to the well wall friction and the flow energy dissipation in the well bore; ppf,iThe pressure loss at the fracture i due to perforation friction is generally considered to be proportional to the square of the flow into the fracture;
the perforation friction resistance expression is as follows:
extra attention needs to be paid to the unit of each item in the friction resistance pressure difference; ppf,iIn psi, fracturing fluid density in lbs/gal, volume flow rate Q injected into fracture iiIn barrels per minute, d is the perforation cluster diameter, in, npThe number of perforation points of the perforation cluster, KdThe method is an empirical constant, is dimensionless and has a value range of 0.56-0.89;
pressure P in the shaftw,iThe positions of different perforation clusters are different, because the pressure in the shaft can be dissipated due to shaft friction and resistance generated by fluid flow; pcf,iFor pressure loss in a horizontal wellbore, according to the descriptions of Valko and Econoids for cylindrical tubing flow, assuming the fluid is Newtonian and is in ideal advection within the wellbore, the pressure loss P at different perforation cluster locations in the wellbore iscf,iThe calculation is made by the following formula:
Qw,j＝QT，j＝1
in the above formula, D is the diameter of the shaft.
8. The method for simulating the complex fracture network formation process of hydraulic fracturing of unconventional oil and gas reservoirs according to claim 2, wherein the method for simulating the flow in the fracture in the step S3.6 is as follows:
for fracturing fractures, it is assumed that the fluid flow in the fracture satisfies the flow rule of the pipeline with the long and narrow rectangular section:
in the above formula
The flow speed of the fluid along the fracture section is shown, k is equivalent permeability, mu is fluid viscosity, p is fluid pressure in the fracture, and w is fracture opening; the fluid flow in the fracture is one-dimensional flow along the length direction of the fracture;
the flow simulation in natural fractures is slightly different, assuming that the total opening of the natural fractures is from a closed openingAnd a mechanical opening degree w; when the internal pressure of the crack is far less than the external pressure stress sigmanWhen the crack is closed, the natural crack is completely closed, and because the wall surfaces of the natural crack are not smooth, and a tiny gap exists between the wall surfaces, a part of residual opening w still exists at the moment0(ii) a The gap between cracks gradually increases along with the increase of the pressure, but the wall surface is not separated yet
Further increasing the pressure of the natural crack, separating the wall surface, wherein the separation distance of the wall surface is called as the mechanical opening w, and the opening of the crack before separation is called as the closed opening
Assuming that the flow in the natural fracture meets Darcy's law, the permeability of the fracture and the effective stress meet an exponential relation:
in the above formula knfIs the crack permeability, knf,0As initial permeability of the crack, cfCan be pressed for cracksCoefficient of contraction, σβnχ is Biot's coefficient, P, for normal stress acting on fracture surfacefIs the fluid pressure within the natural fracture; assuming a closed opening
And the effective stress satisfies an exponential relationship, and the natural fracture permeability is calculated by adopting a formula of Mcclure:
the above equation assumes Biot's constant of 1, koIs a given constant;
further, in step S3.7, the solution method for coupling multiple physical processes is as follows:
the fracturing problem is a typical fluid-solid coupling problem, the change of the opening of the fracture influences the flowing speed of fluid, and the pressure of the fluid in the fracture influences the deformation of the fracture; the fracture model can be divided into 3 sections: the main variables needing fully-coupled solution in the shaft model, the flow model in the crack and the stress-strain model are as follows:
xT＝[Dn,1,Dn,2,...,Dn,n,P1,P2,...,Pn,P0,Q1,Q2,...,Qm]
in the formula DiFor discontinuity of fracture normal displacement, P is the pressure in each fracture cell, QiThe flow rate of the influent for each fracture;
the fluid part equation is dispersed by adopting a finite volume method, and the dispersed equation is subjected to full implicit solution by adopting Newton-Lawson iteration:
J(xn)dxn+1＝-Rn
xn+1＝xn+dxn+1
J(xn) The Jacobian matrix when the step n is iterated, and R is a right-end term residual error;
the adopted iteration convergence condition is as follows:
||R||2＜tol and ||dx||2＜tol
in the formula | · | non-conducting phosphor2A type II norm representing a vector; when the equation converges, the residual error and the variable change dx need to be smaller than the tolerance tol at the same time; through a large number of calculation examples, when the tolerance value is 1e-5And in time, the simulation of a single time step can be converged only by 3-5 times of iteration.
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