CN111222271A - Numerical reservoir fracture simulation method and system based on matrix-fracture unsteady state channeling - Google Patents
Numerical reservoir fracture simulation method and system based on matrix-fracture unsteady state channeling Download PDFInfo
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Abstract
The invention belongs to the technical field of complex fracture network numerical simulation, and discloses a compact reservoir numerical simulation method and system based on matrix-fracture unsteady state channeling, wherein the hydraulic fracture conductivity in a reservoir is the largest, the natural fracture conductivity is the second, the matrix conductivity is the lowest, a model uses discrete fractures to treat hydraulic fractures, and dual media are used to treat matrixes and natural fractures; in the mesh generation process, generating denser meshes at the hydraulic fractures, namely, explicitly processing the hydraulic fractures, wherein the natural fractures and the matrix share one set of meshes; after obtaining the discrete equation, a closed equation system can be obtained by adding well constraint conditions, auxiliary equations and boundary conditions, and the pressure and the saturation of each time step are obtained by a Newton iteration method. The invention improves the oil reservoir simulation efficiency of the large-order-magnitude crack; the flow exchange between the matrix and the natural fracture is processed by utilizing the continuous medium hypothesis, and the simulation program can accurately represent the unsteady-state flow channeling problem between the matrix and the fracture.
Description
Technical Field
The invention belongs to the technical field of horizontal well numerical simulation, and particularly relates to a compact reservoir fracture numerical simulation method and system based on matrix-fracture unsteady-state channeling.
Background
With the continuous development of national economy in China, the demand for domestic petroleum is increased day by day, but the contradiction between supply and demand is increased continuously, the dependence degree is as high as 70.9% to the outside in 2018, and the country faces a severe petroleum safety problem. The quantity of conventional petroleum resources in China is less and less, and the quantity of substitute petroleum resources is increased year by year. The dense oil becomes a new hot spot for unconventional oil and gas exploration and development, and the industrial oil flow of the dense oil is obtained in basins such as Orthos, Bohai Bay, Qusongorian, Sichuan and Songliao in China, and the geological resource amount exceeds 200 hundred million tons. The physical property of compact reservoirs in China is poor, the stratum energy is low, the oil-water distribution is complex, so that the single well yield is low, the economic benefit is poor, and the effective productivity can be formed only after large-scale fracturing modification. The horizontal well technology and the volume fracturing technology are used as effective ways for tight reservoir reconstruction, and the aims are to form a space fracture network and increase the volume of reservoir reconstruction, so that the drainage area of a reservoir and the whole oil drainage capability of a region are increased, and the yield and the ultimate recovery ratio of a single well are improved. The compact oil generally has flowing spaces such as artificial fracturing fracture-natural fracture-matrix and the like, and the traditional numerical simulation method cannot adapt to yield prediction of the compact oil and should be matched with a new numerical simulation means. At present, the compact oil numerical simulation method can be divided into the following three types: extended continuous medium models, discrete fracture models, and embedded discrete fracture models.
1. Extended continuous medium model
The continuous medium model is developed mainly based on a dual medium model, the model considers a matrix and a natural fracture as two independent media, and the flow channeling quantity between the matrix and the fracture is calculated by defining a flow channeling factor. The model simplifies the crack form, and cannot accurately describe the position information of the crack, so that the model is an inaccurate model. However, the numerical simulation method developed based on the model is high in calculation speed and high in applicability when natural cracks develop. Later, a dual media model was developed further, and a multi-function continuous media model was proposed, which mainly subdivides the matrix system and better simulates the flow in the matrix, but with a low computational speed due to the increased number of computational grids.
2. Discrete fracture model
The discrete fracture model mainly carries out explicit processing on the fracture, and carries out grid encryption near the fracture so as to accurately calculate the pressure and saturation values around the fracture. The discrete method of the discrete fracture model can select finite element, finite volume and other methods, and because the grids near the fracture need to be encrypted, the matrix scale formed in the calculation process is often large, and the calculation efficiency is affected.
3. Embedded discrete crack model
An embedded discrete fracture model is a method which is commonly used in the aspect of dense oil numerical simulation at present, the method utilizes a structural grid to disperse a matrix domain, and the discrete result of the fracture is determined through the matrix grid boundary. Although the dimension of the crack is reduced in the discrete process, the crack still keeps the real dimension in the calculation process. In the calculation process, three types of non-adjacent links, namely fracture links in the same matrix grid, fracture-to-fracture links in different matrix grids and matrix grid and fracture links, need to be processed. The embedded discrete fracture model is simple to operate and has an advantage in calculation speed, but when the fracture density is high, the number of discrete units is too large, and the calculation efficiency is reduced.
At present, the method is correspondingly applied to the seepage law of the horizontal well after the fracturing of the compact oil reservoir, and lays a theoretical foundation for the capacity distribution and prediction of the compact oil volume fracturing horizontal well. There are still more problems. In summary, the problems of the prior art are as follows: the numerical simulation method based on the continuous medium model cannot accurately represent fracture morphology, so that the calculation accuracy is reduced, and the simulation efficiency of the discrete fracture model is low under the condition that large-order natural fractures exist in a reservoir due to excessive grids.
The difficulty of solving the technical problems is as follows:
because the development of the compact oil reservoir usually obtains the productivity through fracturing, hydraulic fracturing fractures, natural fractures and a matrix system exist in a reservoir after fracturing, and fluid flows in different media, corresponding flow models need to be established according to the characteristics of the different media, effective coupling needs to be carried out on the different media, and a numerical simulation method with high calculation efficiency and high precision is established to accurately predict the productivity.
The significance of solving the technical problems is as follows:
at present, aiming at the defect that a hydraulic fracture-natural fracture-matrix coupling seepage numerical simulation method is still lacked, the invention provides a novel multi-scale coupling flow calculation method, which can fully consider the flow characteristics of fluids in different media, has advantages in calculation efficiency and calculation precision, can be used for analyzing the energy production characteristics of a tight oil reservoir after fracturing, and has important significance in the establishment of a tight oil reservoir development scheme.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a compact reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling.
The invention is realized in such a way that a compact reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling comprises the following steps:
a first step, in which natural fractures, matrix and hydraulic fractures are present in the reservoir; natural fractures in a reservoir develop, in the actual grid division process, dense grids are divided at the hydraulic fractures, namely the hydraulic fractures are explicitly treated, and the natural fractures and a matrix share one set of grids;
secondly, treating the flow between the natural fracture and the matrix according to a double medium; the model treats hydraulic fractures with a discrete fracture model, and treats matrix and natural fractures with a dual-media model;
and thirdly, after obtaining the discrete equation, adding well constraint conditions, auxiliary equations and boundary conditions to obtain a closed equation system, and solving the pressure of each time step.
Further, the model of the compact reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling treats hydraulic fractures by using a discrete fracture model, and treats matrixes and natural fractures by using a dual medium model.
Further comprising:
the fracture system flow satisfies darcy's law:
wherein phi is potential Pa; under steady state assumptions, the cross-flow between the matrix and the fracture satisfies:
the shape factor is determined by:
wherein L isx，Ly，LzIs the characteristic length of the matrix block, m; the numerical simulator suitable for this phenomenon is specifically as follows:
the continuity equation for the fracture system and the matrix system is:
a complete mathematical model is obtained:
discretizing the equation yields:
wherein:
after obtaining the discrete equation, obtaining a closed equation system by adding well constraint condition conditions, auxiliary equations and boundary conditions, and further solving the pressure of each time step; and solving by the solving flow.
Further, the two-phase flow simulation of the dense oil reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling expands the model to oil-water two-phase flow, and the matrix-fracture channeling model respectively considers a quasi-steady state model and an unsteady state model.
Further comprising:
for fractures and matrices, the two-phase flow equation satisfies the following equation:
wherein k isrFor relative permeability, the continuity equation describes in the fracture:
in the matrix, the oil and water phase equations satisfy:
the mathematical model of oil and water in the fracture is:
in a matrix system, the following are satisfied:
the oil-water saturation in the crack meets the following requirements:
Sof+Swf＝1；
the oil-water capillary force equation in the crack meets the following conditions:
pcowf＝pof-pwf；
the oil-water saturation in the matrix satisfies the following conditions:
Som+Swm＝1；
the oil-water capillary force equation in the matrix meets the following requirements:
pcowm＝pom-pwm；
adding corresponding boundary conditions to form a closed equation set, and solving off-line; dispersing to obtain:
wherein, PcowIs the capillary force; in contrast to unidirectional flow, λw,oAnd Tw,oThe relative permeability phase should be added, after obtaining the discrete equation, the solved equation set is obtained by adding well control conditions at each time step, and the solution is performed by using a Newton iteration method under the known initial condition.
Another object of the present invention is to provide a matrix-fracture unsteady state channeling-based tight reservoir fracture numerical simulation system for implementing the matrix-fracture unsteady state channeling-based tight reservoir fracture numerical simulation method, which includes:
the parameter acquisition processing module is used for acquiring reservoir parameters, hydraulic fracture parameters, natural fracture parameters, matrix parameters, well production parameters and the like of the tight oil reservoir, and establishing a matrix-fracture unsteady-state cross-flow physical model according to the acquired parameters;
the mathematical model parameter setting module is used for setting each relevant calculation parameter in the mathematical model according to the parameters collected by the parameter collecting and processing module and establishing a corresponding mathematical model;
the mesh generation module is used for realizing existence of natural fractures, matrixes and hydraulic fractures in the reservoir; natural fractures in a reservoir develop, in the actual grid division process, dense grids are divided at the hydraulic fractures, the hydraulic fractures are treated in an explicit mode, and the natural fractures and a matrix share one set of grids;
the calculation module is used for forming a nonlinear calculation matrix in the numerical simulation model and solving a nonlinear equation by using a Newton iteration method to obtain a converged pressure and saturation solution;
and the prediction module is used for calculating the yield of the well according to the matrix-fracture unsteady flow channeling tight reservoir fracture numerical simulation method and analyzing the production dynamics of the well.
The invention also aims to provide application of the compact reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling in horizontal well numerical simulation.
The invention also aims to provide application of the compact reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling in compact sandstone reservoir horizontal well multi-cluster fracturing simulation.
The invention also aims to provide application of the compact reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling in complex fracture numerical simulation.
The invention also aims to provide an application of the dense reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling in volume numerical simulation of special-form fracture reformation.
In summary, the advantages and positive effects of the invention are: the invention develops PEBI grid-based discrete fracture model numerical simulation research on the basis of a Matlab Reservoir Simulanitoobox (MRST) PEBI grid subdivision tool, and performs capacity analysis on a multi-stage fractured horizontal well with a fractured modified volume. The invention mainly develops a mixed numerical simulation program based on PEBI grid discrete fractures and a dual-medium model aiming at a tight oil reservoir with natural fractures, wherein hydraulic fractures are treated explicitly, matrix and natural fractures are treated based on the dual-medium model, and quasi-steady-state and unsteady-state channeling are considered in channeling between the matrix and the natural fractures; the developed program is expanded to two-phase flow, and a PEBI grid numerical simulation program of the two-phase flow multistage fracturing horizontal well is established. The invention develops a PEBI grid mixed numerical simulation method considering the combination of double media and discrete fractures, and correspondingly analyzes the productivity of the multi-stage fractured horizontal well.
The invention develops a numerical simulation method of single-phase flow and two-phase flow on the basis of a PEBI (Per enhanced bidimensional intelligence) grid, and provides a mixed type numerical simulation method. The main conclusions were obtained as follows:
(1) considering that the difference between the numerical simulation result of the unsteady flow of the compact oil and the yield result of the steady-state flow is large, the yield of the unsteady flow mode is high in the early stage, the difference between the unsteady flow mode and the steady-state flow mode is small in the later stage, but the unsteady flow mode is higher than the quasi-steady-state model in terms of the accumulated yield, and the difference between the unsteady flow mode and the quasi-steady-state flow mode is not large after the production is carried out for a. The pressure drops faster in the early pseudo-steady-state model fractures, slower in the non-steady-state model fractures, and the laws in the matrix are reversed.
(2) For an unsteady model and a steady model, the difference of Newton iteration steps of numerical simulation is large, particularly the difference of convergence of the first time step and the unsteady model is obvious, the unsteady model is not easy to converge at the early stage of simulation, and the model considering unsteady cross flow needs to set a small time step at the early stage so as to improve the efficiency of numerical simulation.
Drawings
FIG. 1 is a flow chart of a method for simulating a tight reservoir fracture numerical value based on matrix-fracture unsteady-state cross-flow according to an embodiment of the present invention.
FIG. 2 is a diagram of a PEBI grid case generated based on MRST according to an embodiment of the present invention;
in the figure: (a) complex cracks; (b) fracturing a horizontal well in multiple stages; (c) a small spatial scale PEBI grid; coordinate units in the figure: and m is selected.
FIG. 3 is a schematic diagram of a PEBI grid provided by an embodiment of the present invention.
FIG. 4 is a physical model diagram of a natural fracture tight reservoir provided by an embodiment of the invention; wherein the thick solid line is a hydraulic fracture, and the thin solid line is a natural fracture unit: and m is selected.
Fig. 5 is a schematic diagram for explaining a physical model provided by the embodiment of the invention.
FIG. 6 is a schematic diagram illustrating a geological model provided by an embodiment of the invention.
FIG. 7 is a schematic diagram of comparative model meshing (unit: m) provided by an embodiment of the present invention.
FIG. 8 is a schematic diagram of mixed model meshing (unit: m) according to an embodiment of the present invention.
FIG. 9 is a comparison diagram of the daily oil production and the cumulative oil production of different cross-flow models and comparison models provided by the embodiment of the present invention.
FIG. 10 is a plot of formation pressure for 10 days and 500 days as provided by an example of the present invention.
FIG. 11 is a reservoir model grid subdivision provided by embodiments of the present invention (in m).
FIG. 12 is a graph of daily oil production and cumulative oil production for the pseudo-steady-state model and the non-steady-state model provided by the embodiment of the invention.
FIG. 13 is a schematic diagram of the pressure distribution of the natural fracture and the matrix at different times in the pseudo-steady state model provided by the embodiment of the invention;
in the figure: (a)0.95 days; (b) and (5) for 600 days.
FIG. 14 is a schematic diagram of the non-steady state model of natural fracture and matrix pressure distribution at different times according to an embodiment of the present invention;
in the figure: (a)0.95 days; (b) and (5) for 600 days.
FIG. 15 is a schematic illustration of the effect of natural fracture permeability on productivity of a multi-stage fractured horizontal well provided by an embodiment of the present invention;
FIG. 16 is a schematic illustration of the effect of natural fracture permeability on productivity of a multi-stage fractured horizontal well provided by an embodiment of the present invention;
FIG. 17 is a schematic illustration of the effect of natural fracture permeability on productivity of a multi-stage fractured horizontal well provided by an embodiment of the present invention;
FIG. 18 is a graph of daily oil production and cumulative oil production for the pseudo-steady-state model and the non-steady-state model provided by the embodiment of the invention.
FIG. 19 is a graph of daily oil production and cumulative water production for the pseudo-steady-state model and the non-steady-state model provided by the embodiment of the invention.
FIG. 20 is a diagram illustrating the number of iterations of two models provided by an embodiment of the present invention;
in the figure: (a) a quasi-steady-state model; (b) non-steady state models.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a compact reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling, and the invention is described in detail below by combining with the accompanying drawings.
As shown in fig. 1, the method for simulating tight reservoir fracture numerical values based on matrix-fracture unsteady flow-through provided by the embodiment of the invention comprises the following steps:
s101: natural fractures, matrices, and hydraulic fractures are present in the reservoir; natural fractures in a reservoir develop, in the actual grid division process, dense grids are divided at the hydraulic fractures, namely the hydraulic fractures are explicitly treated, and the natural fractures and a matrix share one set of grids;
s102: treating the flow between the natural fracture and the matrix against the dual medium; the model treats hydraulic fractures with a discrete fracture model, and treats matrix and natural fractures with a dual-media model;
s103: after obtaining the discrete equation, a closed equation system can be obtained by adding corresponding conditions, and the pressure and the saturation of each time step are solved.
The technical solution of the present invention is further described below with reference to the accompanying drawings.
1. PEBI grid based discrete fracture numerical simulation basic process
The development of a discrete fracture numerical simulation program based on the PEBI grid is a hot problem of unconventional oil and gas numerical simulation at present, and the numerical simulation of compact oil and gas by using the PEBI grid has multiple advantages: (1) the non-structural grid is flexible to subdivide, and can adapt to the complex geological structure of an oil reservoir, such as faults, cracks and the like; (2) because the discrete is carried out based on the finite volume method, the transportability is strong, the numerical simulator based on the finite difference method can be corrected to directly carry out simulation, and only proper pretreatment is needed to obtain corresponding grid parameters and the link information between grids; (3) compared with methods such as finite element methods, the finite volume-based method has stronger stability and higher calculation efficiency, can be combined with a history fitting tool and a production optimization method on the basis of a simulation program to design a scheme of an oil and gas reservoir, and has strong applicability. The main procedures for numerical simulation using the PEBI grid are: 1. carrying out mesh division according to an oil reservoir geological model, wherein specific geological features such as faults, cracks and the like are considered in the mesh division process, and proper encryption is carried out in the regions so as to improve the precision of a simulation result; 2. dispersing an oil reservoir control equation, adding boundary conditions, and establishing a solution equation set; 3. and solving the equation to obtain corresponding solving parameters.
In the simulation calculation process by using the finite volume method based on the PEBI grids, the geological geometric model needs to be discretized at first, and at present, more unstructured grid subdivision software is used to obtain the corresponding PEBI grids. The invention mainly uses MRST PEBI meshing tool to carry out meshing. Figure 2 shows the results of the dissection of three fractures. FIG. 2(a) considers four hydraulic fractures, where the hydraulic fractures intersect; FIG. 2(b) considers three non-intersecting hydraulic fractures; fig. 2(c) shows the complex fracture dissection results for smaller scale geometrics models.
FIG. 3 is a schematic diagram of a grid generation process, in which spatial position information of the grid and link relation information between the grids need to be recorded after the grid generation process, for example, in FIG. 3, pressure points P need to be recorded by taking a two-dimensional grid ① as an example1And coordinates of 6 nodes, wherein the pressure point P1Is obtained from the Voronoi diagram triangulated mesh node that is dual to the PEBI mesh, and its linked mesh contains ②③④⑤⑥⑦ six meshes.
2. Single-phase flow simulation of dual-medium oil reservoir multistage fracturing horizontal well
The invention develops a dense oil discrete network numerical simulation program based on a PEBI grid, but in an actual dense oil reservoir, a natural fracture with a large order of magnitude may exist, as shown in FIG. 4, if the hydraulic fracture and the natural fracture are both subjected to grid subdivision, in the specific process of numerical simulation, the solving matrix scale is very large, and the calculation efficiency is greatly reduced. Therefore, it is a feasible idea to treat natural fractures by using a dual medium, but in the process of developing the compact oil, the cross flow of the natural fractures and the matrix is in an unsteady state for a long time due to the extremely low permeability of the matrix, so that the shape factor of the unsteady cross flow of the fractures and the matrix needs to be considered when the assumption of the continuous medium is used. At present, a steady-state cross flow model is considered in a mature numerical simulator, and a large error is caused in the actual simulation of the compact oil. In view of this, the invention respectively develops and considers PEBI grid simulation programs of quasi-steady-state channeling and non-steady-state channeling, compares the difference of different models in the capacity calculation after hydraulic fracturing, and mainly performs simulation and analysis aiming at single-phase flow.
2.1 model building and solving
The invention is mainly directed to reservoir development analysis of natural fractures contained in a reservoir, as shown in fig. 4, a model assumes the presence of natural fractures, matrix and hydraulic fractures in the reservoir; natural fractures in a reservoir develop, the number of grids is huge by carrying out grid division on all the fractures, in the actual grid division process, dense grids are divided at the hydraulic fractures, namely, the hydraulic fractures are treated in an explicit mode, and the natural fractures and matrixes share one set of grids, as shown in a figure 5; the assumption of dual media is followed to treat the flow between the natural fracture and the matrix. The model uses a discrete fracture model to treat hydraulic fractures, and uses a dual-medium model to treat matrixes and natural fractures, and is a mixed numerical simulation method.
Then, the analysis was performed according to the single-phase flow simulation model.
2.2 model validation
A case is used below to verify the correctness of the model. The basic parameter settings are shown in table 1, fig. 6 is a schematic diagram of a model, an oil reservoir area is 100 x 100m, 10 matrix blocks are arranged in each direction, the matrix blocks are cut by natural fractures, the length of a hydraulic fracture is 50m according to a red line, a green point represents a perforation well position and is positioned in the center of the oil reservoir. FIG. 7 is a grid split plot of a comparative model, with a total grid number of 19600, encrypted during natural fracture treatment, and natural fracture opening bf0.0002m, hydraulic fracture opening bF0.001m, here by Poiseulle equation[148]Determining the permeability of natural fracture and hydraulic fracture as kf＝bf 2/12＝3333um2，kF 2＝bF 2/12＝83333um2。
In the solution using the dual medium hybrid model, the grid of fig. 8 is used for calculation, here, a rectangular grid is used for simulation, and after the grid information and the inter-grid link information are obtained through preprocessing, the simulation can be directly performed through a simulation program. Wherein, the horizontal direction is encrypted at the hydraulic fracture, the minimum size of the grid is 0.001m, and the total number of the grids is 380. This example utilizes a rectangular grid forward running model, setting the bottom hole pressure to be maintained at 8MPa during the calculation. In the process of solving by using the dual-medium mixed model, the equivalent permeability, equivalent porosity and equivalent rock compression coefficient of the natural fracture and the matrix need to be obtained. Because the volume of the natural fracture is smaller than that of the matrix block, the related parameters of the matrix block still adopt the parameters of the comparison model, and for the natural fracture, the equivalent porosity is 2bf/Lx＝0.00004，Equivalent permeability of 2bfkf/Lx＝0.1333um2And the natural fracture equivalent rock compressibility is equal to the natural fracture rock compressibility multiplied by the equivalent porosity of the natural fracture. In the simulation process, both hydraulic fractures and natural fractures penetrate a reservoir, namely the model is a 2.5D model, and unsteady state channeling and quasi-steady state channeling models are considered for simulation respectively.
Fig. 9 is a curve of daily oil production and cumulative oil production of the dual medium mixed model and the comparison model, and it can be seen that the difference between the result obtained by using the quasi-steady-state model and the comparison model is large, but the non-steady-state model can be well matched with the comparison model. In the early stage, the yield of the quasi-steady-state model is lower, the degressive rule thereof is more different from the other two models, and in the later stage, the yield is higher than the other two models. In the whole production process, the cumulative yield of the quasi-steady-state model is lower than that of the other two models, and the cumulative yield of the three models is the same after 500 days of production. As shown in fig. 10, the pressure difference between the matrix and the fracture is large at 10 days of production, and the difference between the matrix and the fracture is already small at 500 days, at which time the oil produced by the reservoir by the fluid and the elasticity of the rock is close to the maximum value. Meanwhile, in the simulation process, the calculation scale of each iteration step matrix of the comparison model is 19600 multiplied by 19600, and the calculation scale of the matrix of the hybrid model is (380 multiplied by 2) multiplied by (380 multiplied by 2), so that the hybrid model can greatly reduce the calculation time while ensuring the calculation accuracy.
TABLE 1 verification of model base parameters
2.3 case analysis
The productivity of the multi-stage fractured horizontal well will be analyzed by the dual medium mixing model. As shown in fig. 11, a multi-stage fractured horizontal well was placed in the reservoir to contain 6 hydraulic fractures, the fractures were densified near the grid, the well was located in the center of the reservoir, and the well, reservoir and fluid parameters were set as shown in table 2. Controlling the bottom hole pressure to be 8MPa in the simulation process, setting the minimum time step to be 0.1 day and the maximum time step to be 30 days, and for the nth time step,setting the step size to 0.1 × 1.05nThe maximum number of iteration steps is set to 20. The simulation time was set to 720 days.
TABLE 2 Multi-stage fractured horizontal well case basic parameters
Fig. 12 is a graph comparing the daily oil production and the cumulative oil production of the pseudo-steady-state model and the non-steady-state model, and it can be seen that the pseudo-steady-state model has a low yield but a slow decrement rate at the initial stage of production, while the non-steady-state model has a large yield but a fast decrement rate at the initial stage of production. From the cumulative oil production graph, the cumulative yield of the unsteady model in the whole production process is higher than that of the steady state, and the cumulative yield of the unsteady model are close to each other by the time of terminating the simulation. FIGS. 13 and 14 show the profiles of reservoir pressure at the initial and final stages of production, and it can be seen that at the initial stage, the pseudo-steady state model natural fracture has a faster pressure drop and a slower pressure drop in the matrix; and the pressure of the natural fracture in the early stage of the unstable state model is slowly reduced, the pressure of the matrix is quickly reduced, and the contribution value of the matrix to the well yield is higher than that of the stable state model in the early stage.
FIG. 15 shows the effect of natural fractures on productivity, setting natural fracture permeability at three levels of 0.05, 0.5, 5 mD. It can be seen that the presence of natural fractures can effectively increase the production capacity of the well, with the greater the permeability of the natural fracture, the higher the initial production, but the faster the later production will decline, e.g. at 5mD of the natural fracture. The incoming yield drops rapidly around 100 days. Comparing the quasi-steady state model and the unsteady state model under the three conditions, the yield of the quasi-steady state model is lower than that of the unsteady state model at the initial stage, the yield difference of the quasi-steady state model and the unsteady state model is not large at the later stage, and the yield of the quasi-steady state model is slightly higher.
Fig. 16 is a yield curve of matrix block sizes 1, 10m, and 30m, and it can be seen that the matrix block size has a large influence on well yield, the smaller the matrix block size is, the larger the early yield is, when the matrix block size is 1m, the yield difference between the quasi-steady state channeling and the non-steady state channeling is not large, and the yield difference only within 1 day is obvious, mainly because the matrix block size is small, the early stage channeling coefficient between the matrix and the fracture is large, the quasi-steady state can be achieved by the flow between the two media in a short time, and when the matrix size is 30m, the yield difference between the quasi-steady state channeling model and the non-steady state channeling model is obvious at the early stage, and in the whole simulation time period, the yield difference between the two is obvious, that when the matrix grid block is large, a large error can be caused when the productivity is evaluated by the quasi-steady state model at the early stage.
Figure 17 is the effect of matrix permeability on well productivity, considering that the permeability of the matrix is 0.1, 0.001, 0.00001mD, it can be seen that the smaller the matrix permeability the lower the early production of the well, the earlier well production is affected by hydraulic fractures, natural fractures and the matrix together. When the matrix permeability is 0.1mD, the well yield is highest, and the yield difference between a quasi-steady-state model and an unsteady-state model is not large, mainly because the large matrix permeability increases the channeling capacity of the matrix to a natural fracture, the channeling of the matrix to the natural fracture quickly reaches the quasi-steady state, and when the matrix permeability is low, the channeling of the matrix to the natural fracture is in an unsteady-state channeling stage for a long time, so that the difference between the two models is large. When the substrate permeability is 0.00001mD, the initial production is the lowest, but the later production is higher.
3. Two-phase flow simulation
In the actual production process of compact oil, formation water or fracturing fluid is often produced along with the production, so an oil-water two-phase numerical simulation program must be developed to expand a model to oil-water two-phase flow, and a quasi-steady model and an unsteady model are respectively considered in a matrix-to-fracture channeling model.
3.1 model building and solving
The analysis was performed according to a two-phase flow simulation model.
3.2 case analysis
The invention still uses the well and reservoir model of fig. 18, with a multi-stage fractured horizontal well in the reservoir, the well in the center of the reservoir, the well, reservoir and fluid parameters set forth in table 3, and the relative permeability curves set forth in table 4, where the relative permeabilities in the matrix and fractures are considered to be the same. Controlling the bottom hole pressure to be 5.5MPa in the simulation process, setting the minimum time step to be 0.1 day,the maximum time step is 30 days, and for the nth time step, the step size is set to be 0.1 multiplied by 1.05nThe maximum number of iteration steps is set to 20. The simulation time was set to 2000 days.
Fig. 19 and 20 show the comparison of oil and water production of the two models, and it can be seen that under the elastic development condition, the oil and water production of the quasi-steady model and the unsteady model are greatly different, and the yield of the unsteady model is higher, which shows the same rule as that of the single heavy medium model. Fig. 20 shows the iteration steps of the two models, and it can be seen that the unsteady state cross-flow model considering two-phase flow needs more average iteration steps in the calculation, for example, at the first time step, the converged iteration step is 9, the quasi-steady state model is 6, the later unsteady state model has more iteration steps of 4 and 5, and the quasi-steady state model is 3, which indicates that the computation time required for the quasi-steady state is more than that of the quasi-steady state model in the calculation process. Due to the poor convergence properties of the initial unsteady state model, a small time step should be set at the initial simulation time.
TABLE 3 Multi-stage fractured horizontal well case basic parameters
TABLE 4 relative permeability curves
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. The dense reservoir fracture numerical simulation method based on the matrix-fracture unsteady flow channeling is characterized by comprising the following steps of:
a first step, in which natural fractures, matrix and hydraulic fractures are present in the reservoir; natural fractures in a reservoir develop, in the grid division process, dense grids are divided at the hydraulic fractures, namely the hydraulic fractures are explicitly treated, and the natural fractures and a matrix share one set of grids;
secondly, treating the flow between the natural fracture and the matrix according to a double medium; the model treats hydraulic fractures with a discrete fracture model, and treats matrix and natural fractures with a dual-media model;
and thirdly, after obtaining a discrete equation, adding a well constraint condition, an auxiliary equation and a boundary condition to obtain a closed equation system, and solving the pressure and the saturation of each time step.
2. The method for tight reservoir fracture numerical simulation based on matrix-fracture unsteady flow-through of claim 1, wherein the model of the tight reservoir fracture numerical simulation based on matrix-fracture unsteady flow-through treats hydraulic fractures with a discrete fracture model and treats matrix and natural fractures with a dual medium model.
3. The method for tight reservoir fracture numerical simulation based on matrix-fracture unsteady-state channeling according to claim 2, further comprising:
the fracture system flow satisfies darcy's law:
wherein phifIs the potential of the fluid in the fracture; v. offIs the fluid flow rate; k is a radical offIs the crack permeability; μ is the fluid viscosity; under steady state assumptions, the cross-flow between the matrix and the fracture satisfies:
wherein u is*The flow channeling quantity between the matrix and the fracture; k is a radical ofmAs the permeability of the matrix; p is a radical offIs a crackPressure; p is a radical ofmIs the matrix pressure; under steady state assumptions, the cross-flow between the matrix and the fracture satisfies:
the shape factor is determined by:
wherein L isx，Ly，LzIs the characteristic length of the matrix block, m;
considering unsteady-state channeling between the matrix and the fracture, the numerical simulator adapted to this phenomenon is specifically as follows:
the continuity equation for the fracture system and the matrix system is:
wherein ρ is the fluid density; rhofIs the fluid density in the fracture; rhomIs the density of the fluid in the matrix; q. q.smIs a source and sink item; phi is afIs the fracture porosity; phi is amIs the porosity of the matrix; t is time; p is a radical ofiIs the initial pressure;
the complete mathematical model obtained is:
discretizing the equation yields:
wherein:
wherein phimIs the potential of the fluid in the matrix; vbIs the grid volume; a is the contact area between grids; d is the grid spacing; n is a time step;
after obtaining the discrete equation, a closed equation system is obtained by adding well constraint condition conditions, auxiliary equations and boundary conditions, and then the pressure of each time step is obtained.
4. The tight reservoir fracture numerical simulation method based on matrix-fracture unsteady-state channeling according to claim 1, wherein the two-phase flow simulation of the tight reservoir fracture numerical simulation method based on matrix-fracture unsteady-state channeling extends the model to oil-water two-phase flow, and the matrix-to-fracture channeling model respectively considers a pseudo-steady-state model and an unsteady-state model.
5. The method of tight reservoir fracture numerical simulation based on matrix-fracture unsteady-state cross-flow as claimed in claim 4, further comprising:
for fractures and matrices, the two-phase flow equation satisfies the following equation:
wherein k isrIs relative toPermeability; subscript o is the oil phase and subscript w is the oil phase, the continuity equation describes in the fracture:
wherein S is saturation;
in the matrix, the oil and water phase equations satisfy:
the mathematical model of oil and water in the fracture is:
in a matrix system, the following are satisfied:
the oil-water saturation in the crack meets the following requirements:
Sof+Swf＝1；
the oil-water capillary force equation in the crack meets the following conditions:
pcowf＝pof-pwf；
the oil-water saturation in the matrix satisfies the following conditions:
Som+Swm＝1；
the oil-water capillary force equation in the matrix meets the following requirements:
pcowm＝pom-pwm；
adding corresponding boundary conditions to form a closed equation set, and solving off-line; dispersing to obtain:
wherein, PcowIs the capillary force; in contrast to unidirectional flow, λw,oAnd Tw,oThe relative permeability phase should be increased when obtainingAfter obtaining the discrete equation, obtaining a solved equation set by adding well control conditions at each time step, and solving by using a Newton iteration method under the known initial condition.
6. A tight reservoir fracture numerical simulation system based on matrix-fracture unsteady flow channeling for implementing the fracture numerical simulation method of any one of claims 1-5, wherein the tight reservoir fracture numerical simulation system based on matrix-fracture unsteady flow channeling comprises:
the parameter acquisition processing module is used for acquiring reservoir parameters, hydraulic fracture parameters, natural fracture parameters, matrix parameters, well production parameters and the like of the tight oil reservoir, and establishing a matrix-fracture unsteady-state cross-flow physical model according to the acquired parameters;
the mathematical model parameter setting module is used for setting each relevant calculation parameter in the mathematical model according to the parameters collected by the parameter collecting and processing module and establishing a corresponding mathematical model;
the mesh generation module is used for realizing existence of natural fractures, matrixes and hydraulic fractures in the reservoir; natural fractures in a reservoir develop, in the actual grid division process, dense grids are divided at the hydraulic fractures, the hydraulic fractures are treated in an explicit mode, and the natural fractures and a matrix share one set of grids;
the calculation module is used for forming a nonlinear calculation matrix in the numerical simulation model and solving a nonlinear equation by using a Newton iteration method to obtain a converged pressure and saturation solution;
and the prediction module is used for calculating the yield of the well according to the matrix-fracture unsteady flow channeling tight reservoir fracture numerical simulation method and analyzing the production dynamics of the well.
7. The application of the matrix-fracture unsteady state channeling-based tight reservoir fracture numerical simulation method according to any one of claims 1-5 in horizontal well numerical simulation.
8. The application of the matrix-fracture unsteady state channeling-based tight reservoir fracture numerical simulation method according to any one of claims 1-5 in tight sandstone reservoir horizontal well multi-cluster fracturing simulation.
9. The application of the dense reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling in complex fracture numerical simulation according to any one of claims 1-5.
10. The application of the dense reservoir fracture numerical simulation method based on matrix-fracture unsteady state channeling in the numerical simulation of the specific-form fracture reformation volume according to any one of claims 1 to 5.
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