Low-permeability reservoir inter-well connectivity simulation method

Abstract

The invention provides a low-permeability reservoir inter-well connectivity simulation method. The low-permeability oil reservoir inter-well connectivity simulation method comprises the steps that a, a reservoir is discretized into a plurality of nodes according to well point positions in an oil reservoir block, every two nodes are connected, all initial connections are screened through a subdivision constraint condition, and parameters on grids are subjected to full implicit solution; b, establishing a historical fitting objective function, adjusting parameters such as the volume and the conductivity of a grid in the established initial pipeline model, generating an optimized pipeline network model, and enabling a simulation result of the pipeline network model to be matched with an actual production history; and c, generating a flow path tracking graph by using a depth-first search algorithm, and visually displaying the flow direction and flow of the water injected into the water injection well. The method solves the problems that the low-permeability fractured reservoir cannot be quickly modeled and the flow path of the injected water cannot be finely described in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil reservoir development, in particular to a low-permeability oil reservoir interwell connectivity simulation method. BACKGROUND

[0002] Low-permeability oil reservoirs are widely distributed and have great resource potential. With the decreasing of conventional oil and gas resources, the development of low-permeability oil reservoirs is becoming more and more important, and it is the main reservoir type for increasing reserves and production in the future. Compared with conventional oil and gas reservoirs, low-permeability reservoirs have poor physical properties, low porosity and permeability; small pore throat, large seepage resistance; developed fractures, and strong stress sensitivity. Therefore, the flow of fluid in low-permeability reservoirs is extremely complex, and the Darcy law of the conventional seepage mathematical model does not conform to the seepage characteristics of low-permeability oil reservoirs and is no longer applicable. Low-permeability oil reservoirs are often highly heterogeneous, especially low-permeability fractured reservoirs. Due to the extensive existence of fractures, the permeability is unevenly distributed in the plane and vertical direction. The commonly used mathematical models for describing low-permeability fractured reservoirs at present include equivalent continuous medium model, dual medium model, and discrete fracture model. Although the equivalent continuous medium model based on equivalent permeability has high calculation efficiency and strong theoretical basis and method experience, it does not consider the different seepage capacities of fractures and matrix and the fluid channeling between them, and cannot accurately simulate the unsteady process in the development of low-permeability fractured reservoirs. Based on the equivalent principle of fracture flow, the discrete fracture model explicitly represents the fractures, reduces the dimension of the fractures, and can accurately describe the seepage characteristics of fractured reservoirs. However, it has high requirements for computer hardware and numerical simulation technology, and cannot be applied to flow numerical simulation of oilfield scale at present. The dual medium model assumes that there are two different seepage systems in the reservoir system, i.e. the matrix system with high porosity and low permeability and the fracture system with low porosity and high permeability. It can reflect the preferential flow characteristics of the fracture system in low-permeability fractured reservoirs to some extent, and can use appropriate channeling functions to represent the channeling between matrix and fractures, which is more consistent with the actual situation and has high calculation efficiency.

[0003] A series of reservoir connectivity network model methods, INSIM family, are proposed in the prior art for conventional water drive reservoirs. The initial method is INSIM, which simplifies the characterization of the reservoir model, simplifies the flow of fluid in the reservoir into a connectivity network model composed of a series of one-dimensional connection units, the concept simplifies the complex multidimensional flow into one-dimensional flow, each connection unit is only defined by the conductivity and connected volume, which means that the one-dimensional connection unit has equal width and permeability, therefore, the reservoir geological parameters can be simplified from a large number of grid parameters (porosity, permeability, etc.) in the conventional network numerical simulation into a small number of characteristic parameters (conductivity, connected volume) of the one-dimensional connection unit, thereby improving the efficiency of history matching and easily achieving the accuracy required by reservoir scale engineering. On this basis, in order to improve the calculation accuracy of the model, INSIM-FT, INSIM-FT-3D, INSIM-FPT and the like are successively proposed.

[0004] Therefore, the currently well-developed reservoir connectivity network model method wants to be applicable to low-permeability fractured systems, and the following problems exist: (1) the INSIM method uses a linear seepage model of conventional reservoirs when considering oil-water two-phase flow, which is not applicable to low-permeability reservoirs with starting pressure gradient; (2) INSIM can only represent the fractured system by adding virtual well points, which has two problems, one is that it cannot well describe the flow of fluid in the fractured system, and the other is that for the reservoir with developed fractures, manually adding virtual well points has strong limitations; (3) although the INSIM model is fast in calculation, it is difficult to obtain accurate and stable solutions for complex seepage equation sets containing strong convection characteristics, and if the calculation accuracy is to be improved, a sufficient number of well points need to be added, thereby increasing the calculation cost, which is difficult to reflect the advantage of simple calculation of INSIM; (4) the research on fluid flow simulation in the INSIM family is mainly applied to single medium, and is not applicable to dual medium.

[0005] Therefore, there is a problem in the prior art that the existing reservoir connectivity network model method is difficult to be applicable to low-permeability fractured systems. SUMMARY

[0006] The main purpose of the present application is to provide a low-permeability reservoir interwell connectivity simulation method to solve the problem that the existing reservoir connectivity network model method in the prior art is difficult to be applicable to low-permeability fractured systems.

[0007] In order to achieve the above object, the present application provides a low permeability reservoir interwell connectivity simulation method, comprising: step a: discretizing the reservoir into a plurality of nodes according to the well point position in the reservoir block, connecting each two nodes to form a full connection network, screening the connection by using a restriction condition to form a connectivity model composed of a plurality of connection pipelines, each pipeline being characterized by two groups of characteristic parameters, and performing grid division on the pipeline, constructing a dual medium model by using non-Darcy seepage and stress sensitivity, and implicitly solving the parameters on the grid; step b: establishing a history matching objective function, adjusting the model parameters by using the difference between the observed reservoir production dynamic indicators and the production dynamic indicators calculated by the established pipeline model, realizing automatic history matching by using an optimization algorithm, and setting a constraint condition to adjust the characteristic parameters of the initial pipeline model to generate an optimized pipeline network model; and step c: using a depth-first search algorithm to dynamically track all possible flow paths between the injection wells and the production wells, generating a flow path tracking diagram, and thus quantitatively describing the flow channels in the low permeability fractured reservoir.

[0008] Further, step a comprises the following steps: step a1: discretizing the reservoir into a plurality of nodes according to the well point position and the position of the fracture development in the reservoir, and fully connecting the plurality of nodes, screening the connection by introducing a restriction condition, and generating a plurality of interwell connection pipelines, each connection representing a flow channel of fluid between the corresponding two wells; and step a2: performing grid division on each connection pipeline, constructing a dual medium model by considering the non-Darcy seepage equation and the stress sensitivity effect, and using a full implicit flow equation format in a traditional grid reservoir numerical simulator and a nonlinear solver based on Newton iteration to solve the parameters on the grid.

[0009] Further, the restriction condition is the maximum distance and the minimum angle in all connections.

[0010] Further, the seepage behavior of the fluid in the connected pipeline is mainly controlled by two parameters, namely the interwell conductivity and the connected volume, the interwell conductivity being used to measure the seepage capacity between the wells, and the connected volume representing the storage capacity of the connected unit.

[0011] Further, in the process of performing grid division on each connection pipeline, the grids on the same connection unit have equal seepage cross-sectional area and permeability.

[0012] Further, in the process of using the full implicit flow equation format in the traditional grid reservoir numerical simulator and the nonlinear solver based on Newton iteration to solve the parameters on the grid, the parameters on the grid at least include the pressure, the saturation and the control volume of the grid.

[0013] Further, the double medium model divides the connected network into two sets of flow systems, i.e. a high-porosity and low-permeability matrix system and a low-porosity and high-permeability fracture system.

[0014] Further, in the high-porosity and low-permeability matrix system and the low-porosity and high-permeability fracture system, the expression formulae of the permeability of the matrix and the permeability of the fracture are as follows:

[0015]

[0016] wherein subscript m represents the matrix system and f represents the fracture system; K ij,m and K ij,f are the equivalent permeability of the matrix and the fracture between i node and j node after considering non-Darcy seepage and stress sensitivity, with the unit of mD; k ij,m and k ij,f represent the initial permeability of the matrix and the fracture between i node and j node, with the unit of mD; μ is the viscosity of the fluid, with the unit of mPa·s; ▽p ij,m is the pressure difference of the matrix between the two nodes, with the unit of MPa; a and b are non-linear seepage coefficients, whose values are determined by experiments; c f is the compressibility coefficient, with the unit of MPa -1 ; P ij,f is the current pressure of the fracture between the two nodes, with the unit of MPa; P ij,f0 is the initial pressure of the fracture between the two nodes, with the unit of MPa.

[0017] Further, in the high-porosity and low-permeability matrix system and the low-porosity and high-permeability fracture system, the expression formulae of the channeling flow of the fracture and the matrix are as follows:

[0018]

[0019] wherein Q is the channeling flow between the fracture and the matrix, with the unit of kg·day -1 ; α is a shape factor, with the unit of m -2 ; ρ m,β is the density of a phase fluid in the matrix, with the unit of kg·m -3 ; K m is the equivalent permeability of the phase fluid in the matrix, with the unit of mD; μ β is the viscosity of the phase fluid, with the unit of mPa·s; P m and P f are the pressures of the matrix and the fracture, with the unit of MPa.

[0020] Further, in the high-porosity and low-permeability matrix system and the low-porosity and high-permeability fracture system, the mass conservation equations of the fracture and the matrix are as follows:

[0021]

[0022] wherein ρ m,β and ρ f,β are the density of the phase fluid in the matrix and fracture, respectively, in kg·m -3 ; φ m and φ f are the porosity of the matrix and fracture, respectively; S m,β and S f,β are the saturation of the phase fluid in the matrix and fracture, respectively; t represents time, in day; v m,β and v f,β are the seepage velocity of the phase fluid in the matrix and fracture, respectively, in m 3 ·day -1 ; q is the source-sink term, representing the mass added per unit volume per unit time, in kg·day -1 , q>0 is a source term, q<0 is a sink term.

[0023] Further, in step b, the initial pipe characteristic parameters include the connected volume V ij,m of the matrix and the connected volume V ij,f of the fracture in the connected unit, the conductivity T ij,m of the matrix and the conductivity T ij,f of the fracture, the nonlinear seepage coefficients a, b.

[0024] Further, the history matching objective function is:

[0025]

[0026] wherein m is the characteristic parameter of each grid which needs to be history matched, O(m) is the established minimization objective function, g(m) is the production dynamic index simulated by the pipe model, d obs is the observed production dynamic index, C D is the covariance main diagonal matrix of the observation error.

[0027] Further, the production dynamic index at least includes the daily oil production of each well; or the production dynamic index at least includes the oil production, water production, cumulative production of the oilfield.

[0028] Further, in step b, the set constraint condition is:

[0029]

[0030] wherein V tot,m represents the total volume of the matrix, V tot,f represents the total volume of the fracture, N w is the number of wells, a and b are the nonlinear seepage parameters.

[0031] Further, in the process of step c using the depth-first search algorithm, the generated pipe network graph is regarded as a weighted directed graph, the direction between two well points always points to the well point with lower pressure, the weight is the direct allocation factor, and each injection well is taken as a root node to find downstream wells in the direction of pressure drop until all connected well points without downstream wells are tracked.

[0032] Further, the flow calculation formula between any two wells is:

[0033]

[0034] wherein the pressure of well j is greater than that of well i, the superscript n represents the time step, is the flow between well j and well i at the current time, and are the conductivity values of the matrix and the fracture between well j and well i at the last time, respectively; and are the pressures of the matrix and the fracture of well j at the current time, and are the pressures of the matrix and the fracture of well j at the current time.

[0035] Further, the calculation formula of the direct allocation factor between well j and well i is:

[0036]

[0037] wherein, is the direct allocation factor between well j and well i at time n, N j represents the number of connected points with lower pressure than well j, represents the flow of well j into well k at time n.

[0038] Further, the calculation formula of the path allocation factor between well j and well i is:

[0039]

[0040] wherein, is the path allocation factor between well j and well i at time n, and the term in the right side of the equation, represents the direct allocation factor between well b1 and well b2.

[0041] Further, the calculation formula of the total allocation factor between well j and well i is as follows:

[0042]

[0043] wherein, is the total allocation factor between well j and well i at time n, and the value is the sum of all path allocation factors between well j and well i; Ns ijfor the possible flow path between well j and well i.

[0044] According to the technical scheme of the present application, the low-permeability oil reservoir interwell connectivity simulation method in the present application comprises the following steps: step a: discretize the reservoir into a plurality of nodes according to the well point positions in the oil reservoir block, connect each two nodes to form a full connection network, screen the connections by using a restriction condition, form a connectivity model composed of a plurality of connection pipelines, each pipeline is characterized by two groups of characteristic parameters, and the pipelines are divided into grids, and a dual medium model is constructed by using non-Darcy seepage and stress sensitivity, and the parameters on the grids are implicitly solved; step b: establish a history matching objective function, adjust the model parameters by using the difference between the observed history production dynamic indicators of the oil reservoir and the production dynamic indicators calculated by the pipeline model, realize automatic history matching by using an optimization algorithm, set a constraint condition, adjust the characteristic parameters of the initial pipeline model, and generate an optimized pipeline network model; step b: use a depth-first search algorithm to dynamically track all possible flow paths between the injection wells and the production wells, generate a flow path tracking diagram, and thus quantitatively depict the flow channels in the low-permeability fractured oil reservoir.

[0045] The technical scheme of the present application fully considers the flow rule of oil and water in a low-permeability oil reservoir and the interwell connectivity relationship, and establishes a low-permeability oil reservoir interwell connectivity simulation method by constructing a dual medium model. In order to improve the accuracy of the interwell connectivity model and identify high-permeability channels, an automatic history matching iterative solving method and a dynamic path tracking technology are established, so that the dominant channel in the low-permeability oil reservoir can be quickly identified. Meanwhile, the model is between the traditional numerical simulation technology and the INSIM method, compared with the traditional numerical simulation method, the number of grids is small, the equation dimension is low, and the calculation process is fast and efficient; compared with the INSIM, the number of grids is a little more, and a full implicit solving method is used, so that the calculation accuracy is greatly improved. The method has important significance for the oil and water two-phase simulation of the low-permeability fractured oil reservoir and the identification of the dominant channel. BRIEF DESCRIPTION OF DRAWINGS

[0046] The drawings accompanying the specification of the present application form a part thereof, serve to provide further understanding of the present application, and together with the description of the exemplary embodiments of the present application and the explanation thereof serve to explain the present application, and do not constitute improper limitations on the present application. In the drawings:

[0047] Figure 1 A flow chart of the low-permeability oil reservoir interwell connectivity simulation method of the present application is shown;

[0048] Figure 2 A schematic diagram of the interwell pipeline network of the present application is shown;

[0049] Figure 3 A schematic diagram of a single interwell connection pipeline of the present application is shown;

[0050] Figure 4 A permeability field map in one embodiment of the application is shown;

[0051] Figure 5 A dual media model section map in one embodiment of the application is shown;

[0052] Figure 6 An oilfield cumulative oil production fitting result map in one embodiment of the application is shown;

[0053] Figure 7 A flow path tracking map at the last moment in one embodiment of the application is shown. DETAILED DESCRIPTION

[0054] It should be noted that the embodiments and features of the embodiments in the present application can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0055] It should be noted that, unless otherwise specified, all technical and scientific terms used in the present application have the same meaning as generally understood by those skilled in the art to which the present application belongs.

[0056] In the present application, unless otherwise specified, the orientation words such as "up, down, top, bottom" are generally directed to the directions shown in the drawings, or are directed to the vertical, perpendicular or gravity directions of the components themselves; similarly, for the convenience of understanding and description, "inner, outer" refers to the inner and outer relative to the contour of each component itself, but the above orientation words are not used to limit the present application.

[0057] In order to solve the problem that the existing reservoir connectivity network model method in the prior art is difficult to apply to low permeability fractured systems, the present application provides a low permeability reservoir interwell connectivity simulation method.

[0058] As Figure 1As shown, the interwell connectivity simulation method for low permeability reservoirs in the application comprises the following steps: step a: discretize the reservoir into multiple nodes according to the well point positions in the reservoir block, connect each two nodes to form a full connection network, screen the connection by using the limiting condition to form a connectivity model composed of multiple connection pipelines, each pipeline is characterized by two groups of characteristic parameters, and the grid is divided on the pipeline, a dual medium model is constructed by using non-Darcy seepage and stress sensitivity, and the parameters on the grid are implicitly solved; step b: establish a history matching objective function, adjust the model parameters by using the difference between the observed history production dynamic indicators of the reservoir and the production dynamic indicators calculated by the current pipeline model, realize automatic history matching by using an optimization algorithm, and set a constraint condition to adjust the characteristic parameters of the initial pipeline model to generate an optimized pipeline network model; step b: use the depth first search algorithm to dynamically track all possible flow paths between the injection wells and the production wells, generate a flow path tracking diagram, and thus quantitatively depict the flow channels between the low permeability fractured reservoirs.

[0059] The technical scheme of the application fully considers the flow rule of oil-water two-phase flow in low permeability reservoirs and the interwell connectivity relationship, and establishes an interwell connectivity simulation method for low permeability reservoirs by constructing a dual medium model. In order to improve the accuracy of the interwell connectivity model and identify high permeability channels, an automatic history matching iterative solution method and a dynamic path tracking technology are established to realize rapid identification of the dominant channeling flow channels in low permeability reservoirs. At the same time, the model is between the traditional numerical simulation technology and the INSIM method. Compared with the traditional numerical simulation method, the number of grids is small, the equation dimension is low, and the calculation process is fast and efficient; compared with INSIM, the number of grids is a little more, and the fully implicit solution method is used, so the calculation accuracy is greatly improved. The method has important significance for oil-water two-phase simulation and identification of dominant channels in low permeability fractured reservoirs.

[0060] Furthermore, the interwell connectivity simulation method for low permeability reservoirs in the application utilizes the basic concept of the INSIM model, combines the nonlinear seepage characteristics of low permeability reservoirs and the stress sensitivity of fractured reservoirs, and effectively realizes accurate description and depiction of fluid flow numerical simulation in low permeability fractured reservoirs by constructing a dual medium model. At the same time, by using flow path tracking, the dominant channeling flow channels between the wells in the reservoir can be accurately identified, which has important guiding significance for formulating actual development schemes and improving recovery efficiency of oilfields.

[0061] Specifically, the step a comprises the following steps: step a1: discretizing the reservoir into a plurality of nodes or a series of nodes according to the positions of the well points and the fracture development in the oil reservoir, and performing full connection on the plurality of nodes, screening the connection by introducing a restriction condition, and generating a plurality of or a series of interwell connection pipelines meeting the condition, each connection representing a flow channel of fluid between the corresponding two wells; step a2: performing grid division on each connection pipeline, constructing a dual medium model by considering the non-Darcy seepage equation and stress sensitivity effect, and using the full implicit flow equation format commonly used in the traditional grid reservoir numerical simulator and the nonlinear solver based on Newton iteration to solve the parameters on the grid.

[0062] Specifically, the restriction condition is the maximum distance and the minimum angle in all connections. The screening is to delete the connections greater than the maximum distance restriction and less than the minimum internal angle of the triangle in the full connection.

[0063] The interwell connection pipeline meeting the condition is the generated well pattern profile that meets the actual flow situation of the oilfield block.

[0064] Specifically, the seepage behavior of the fluid in the connected pipeline is mainly controlled by two parameters, namely, the interwell conductivity and the connected volume. The interwell conductivity is used to measure the seepage capacity between the wells, and the connected volume represents the storage capacity of the connected unit.

[0065] Specifically, in the process of performing grid division on each connection pipeline, the grids on the same connection unit have equal seepage cross-sectional area and permeability.

[0066] The dual medium model is to divide the connected network into two sets of flow systems, namely, the high-porosity low-permeability bedrock system and the low-porosity high-permeability fracture system, which is equivalent to copying the grid generated in step a1 again, and each grid is characterized by its own parameters. When constructing the dual medium model, the non-Darcy seepage equation and the stress sensitivity effect are considered respectively.

[0067] Specifically, in the process of using the full implicit flow equation format commonly used in the traditional grid reservoir numerical simulator and the nonlinear solver based on Newton iteration to solve the parameters on the grid, the parameters on the grid at least include the pressure, saturation and control volume of the grid.

[0068] Specifically, the dual medium model is to divide the connected network into two sets of flow systems, namely, the high-porosity low-permeability bedrock system and the low-porosity high-permeability fracture system.

[0069] Step b specifically comprises the following steps: step b1: establishing a history matching objective function, automatically history matching the production dynamic index calculated by the pipeline model built at present with the observed reservoir history production dynamic index. Step b2: setting a constraint condition for the characteristic parameters while history matching, adjusting the characteristic parameters of the initial pipeline model built to generate the optimized pipeline network model.

[0070] The initial pipeline characteristic parameters include the connected volume V ij,m of the matrix and the fracture in the connected unit ij,f , and the conductivity T ij,m , T ij,f , the nonlinear seepage coefficient a, b.

[0071] The depth-first algorithm refers to regarding the generated pipeline network graph as a weighted directed graph, the direction between two well points always points to the well point with smaller pressure, and the weight value is the direct allocation factor, then taking each injection well as a root node, sequentially searching for downstream wells in the direction of pressure drop, and tracking until there is no downstream well for all connected well points. In the step of calculating the path tracking, we only take the grid where the well point is located as the research object, and ignore the grids divided in the pipeline.

[0072] Specifically, in the high-porosity low-permeability matrix system and the low-porosity high-permeability fracture system, the expression formula of the permeability of the matrix and the fracture is:

[0073]

[0074] Wherein, the subscript m represents the matrix and f represents the fracture; K ij,m and K ij,f are the permeability of the matrix and the fracture between i node and j node after considering the non-Darcy seepage and stress sensitivity, unit: mD; k ij,m and k ij,f represent the initial permeability of the matrix and the fracture between i node and j node, unit: mD; μ is the viscosity of the fluid, unit: mPa·s;▽p ij,m is the pressure difference of the two nodes in the matrix, unit: MPa; a, b are the nonlinear seepage coefficients, whose values are determined by experiments; c f is the compressibility coefficient, unit: MPa -1 ; P ij,f is the current pressure of the fracture between the two nodes, unit: MPa; P ij,f0 is the initial pressure of the fracture between the two nodes, unit: MPa.

[0075] Specifically, in the high-porosity low-permeability matrix system and the low-porosity high-permeability fracture system, the expression formula of the channeling flow of the fracture and the matrix is:

[0076]

[0077] wherein Q is the interporosity flow rate between the fracture and the matrix, in kg day -1 ; a is the shape factor, in m -2 ; p m,β is the density of the phase fluid in the matrix, in kg m -3 ; K m is the equivalent permeability of the phase fluid in the matrix, in mD; m β is the viscosity of the phase fluid, in mPa s; P m and P f are the pressures in the matrix and the fracture, respectively, in MPa.

[0078] In particular, in the high-porosity low-permeability matrix system and the low-porosity high-permeability fracture system, the mass conservation equations of the fracture and the matrix are:

[0079]

[0080] wherein p m,β and p f,β are the densities of the phase fluid in the matrix and the fracture, respectively, in kg m -3 ; f m and f f are the porosities of the matrix and the fracture, respectively; s m,β and s f,β are the saturations of the phase fluid in the matrix and the fracture, respectively; t represents time, in day; v m,β and v f,β are the seepage velocities of the phase fluid in the matrix and the fracture, respectively, in m 3 day -1 ; q is the source-sink term, representing the mass added per unit volume per unit time, in kg day -1 , q > 0 is a source term, and q < 0 is a sink term.

[0081] In particular, in step b, the initial pipe characteristic parameters include the connected volume V ij,m of the matrix and the connected volume V ij,f of the fracture in the connected element, the conductivity T ij,m of the matrix and the conductivity T ij,f of the fracture, the nonlinear seepage coefficients a and b.

[0082] In particular, the history matching objective function is:

[0083]

[0084] wherein m is the characteristic parameter of each grid that needs to be history matched, O(m) is the established minimization objective function, g(m) is the production performance index simulated by the pipe model built, dobs For the observed production dynamic indicators, C D is the covariance principal diagonal matrix of the observation error.

[0085] Specifically, the production dynamic indicators at least include daily oil production of each well; or the production dynamic indicators at least include oil production, water production and cumulative production of the oilfield.

[0086] Specifically, in step b, the constraint condition set is:

[0087]

[0088] Wherein, V tot,m represents the total volume of the matrix, V tot,f represents the total volume of the fracture, N w is the number of wells, and a and b are nonlinear seepage parameters.

[0089] Specifically, in the process of step c using the depth-first search algorithm, the generated pipe network graph is regarded as a weighted directed graph, the direction between two well points always points to the well point with lower pressure, the weight value is the direct allocation factor, and each injection well is taken as a root node, and downstream wells are searched in the direction of pressure drop in turn until all connected well points without downstream wells are tracked.

[0090] Specifically, the flow calculation formula between any two wells is:

[0091]

[0092] Wherein, the pressure of well j is greater than the pressure of well i, the superscript n represents the time step, is the flow between well j and well i at the current time, and are the conductivity values of the matrix and the fracture between well j and well i at the last time, respectively; and are the pressures of the matrix and the fracture of well j at the current time, and are the pressures of the matrix and the fracture of well j at the current time.

[0093] Specifically, the calculation formula of the direct allocation factor between well j and well i is:

[0094]

[0095] Wherein, is the direct allocation factor between well j and well i at time n, N j represents the number of connected points with lower pressure than well j, represents the flow of well j into well k at time n.

[0096] Specifically, the formulas for calculating the path allocation factors of well j and well i are as follows:

[0097]

[0098] in, The path assignment factor between well j and well i at time n is the term on the right side of the equation. This represents the direct allocation factor between wells b1 and b2.

[0099] Specifically, the formula for calculating the total allocation factor between well j and well i is as follows:

[0100]

[0101] in, Let Ns be the total allocation factor between well j and well i at time n, and its value is the sum of the path allocation factors between all wells j and well i; ij This represents the possible flow path between well j and well i.

[0102] In one specific embodiment of this application, the method for simulating inter-well connectivity in low-permeability reservoirs includes: firstly, establishing an initial pipeline network model based on the location of well points and fractures in the reservoir. The basic principle is to simplify a highly heterogeneous, low-permeability fractured reservoir into a series of inter-well connectivity channels characterized by conductivity and connectivity volume, such as... Figure 2 As shown. Whether there is a pipeline connection between the two wells is determined by the maximum well spacing and the minimum interior angle.

[0103] Each connecting pipe is then meshed, with meshes within the same connecting unit having equal seepage cross-sectional area and permeability. The connected network is divided into two flow systems: a high-porosity, low-permeability bedrock system and a low-porosity, high-permeability fracture system. This is equivalent to replicating the mesh generated in step a1, with each mesh characterized by its own parameters, such as... Figure 3 As shown, taking well points i and j as examples, the calculation methods for the connected volume and conductivity of their connecting pipes are as follows:

[0104]

[0105] Where i and j are well nodes; V ij,m V ij,f and T ij,m T ij,f Let i represent the connected volume of the matrix, the connected volume of the fractures, the conductivity of the matrix, and the conductivity of the fractures between wells i and j, respectively. The unit of connected volume is m. 3 The unit of conductivity is m. 3 ·(d·MPa) -1 A ij Let m be the partition area between well i and well j.2 ; is the average thickness between i and j wells, m; and are the average porosity of matrix and the average porosity of fracture between i and j wells, respectively, 1; and are the average permeability of matrix and the average permeability of fracture between i and j wells, respectively, mD; L ij is the length of connecting unit between i and j wells, m; μ o is the viscosity of oil phase, mPa·s; α' is a unit coefficient, whose value is 0.0864.

[0106] Assuming that a and b are two connected grids in the connected pipeline of i and j wells, the conductivity of a and b is calculated in a harmonic average manner, and the formula is as follows:

[0107]

[0108] wherein, T ij,ab is the conductivity between a and b, m 3 ·(d·MPa) -1 ; k ij is the permeability between i and j wells, mD; A ij is the flow area between i and j wells, m 2 ; d ij,a , d ij,b are the width of grid a and grid b, respectively, m.

[0109] The motion equation is expressed as follows:

[0110]

[0111] wherein, β = o, w, o, w represent oil phase and water phase, respectively; v is the seepage velocity, m 3 ·day -1 ; k is the permeability, mD; μ is the fluid viscosity, mPa·s; ▽P is the flow pressure difference, MPa.

[0112] wherein, after considering the non-Darcy seepage equation and stress sensitivity, the permeability becomes a function of pressure, and the permeability of matrix and fracture is expressed as follows:

[0113]

[0114] wherein, subscript m represents matrix and f represents fracture; K ij,m and K ij,f are the permeability in matrix and fracture between i node and j node after considering non-Darcy seepage and stress sensitivity, with the unit of mD; k ij,m and kij,f represents the initial permeability of the bedrock and fracture between nodes i and j, respectively, in mD; μ is the viscosity of the fluid, in mPa·s; ▽p ij,m The pressure difference between two nodes within the bedrock is expressed in MPa; a and b are nonlinear seepage coefficients, their values ​​determined experimentally; c f The compressibility factor is expressed in MPa. -1 ;P ij,f P represents the current pressure of the crack between the two nodes, in MPa. ij,f0 The initial pressure of the crack between the two nodes is expressed in MPa.

[0115] Fluid exchange also occurs within the bedrock and fractures, primarily under relatively gentle pressure changes. Therefore, this process can be assumed to be steady-state, i.e., the flow is independent of time. Thus, the volume of fluid discharged from a unit volume of bedrock into the fractures per unit time depends mainly on the fluid viscosity, the pressure difference between the bedrock and the fractures, and certain characteristics of the rock (length, area, volume, etc.). The flow rate between the fractures and bedrock can then be expressed as:

[0116]

[0117] Where Q is the flow rate between the fracture and the bedrock, in kg·day -1 α is the shape factor, in meters. -2 ;ρ m,β The density of a certain phase fluid within bedrock, in kg·m³. -3 ;K m The equivalent permeability of a certain phase fluid within bedrock, expressed in mD; μ β P represents the viscosity of a certain phase fluid, in mPa·s. m and P f These represent the pressures in the bedrock and the fractures, respectively, in MPa.

[0118] Considering the compressibility of the fluid and neglecting the effect of capillary forces, the mass conservation equations for the matrix and cracks are as follows:

[0119]

[0120] Where, ρ m,β and ρ f,β These are the densities of a certain phase fluid in bedrock and within fractures, respectively, in kg·m³. -3 ;φ m and φ f Porosity of bedrock and fractures, respectively; S m,β and S f,β These represent the saturation of the phase fluid in the bedrock and fractures, respectively; t represents time, in days; v m,β and v f,βVf and Vf represent the seepage velocity of the certain phase fluid in the matrix and fracture respectively, unit m / s 3 · day -1 ; q is the source-sink term, which represents the mass of the fluid added per unit volume per unit time, unit kg·day -1 , q>0 is the source term, q<0 is the sink term.

[0121] The above mass conservation equation is solved using the fully implicit flow equation format commonly used in traditional grid reservoir numerical simulators and the nonlinear solver based on Newton iteration, and the grid pressure, water saturation and other physical quantities can be obtained.

[0122] Then, by establishing a history matching objective function, the observed reservoir historical production dynamic indicators are automatically history matched with the calculated production dynamic indicators of the current pipeline model. At the same time of history matching, the constraint conditions are set for the characteristic parameters, so that the characteristic parameters of the initial pipeline model are adjusted to generate the optimized pipeline network model.

[0123] The history matching objective function is established to minimize the difference between the observed value and the simulated value. The history matching objective function we established is as follows:

[0124]

[0125] Where m is the characteristic parameter of each grid that needs to be history matched, O(m) is the established minimization objective function, g(m) is the production dynamic indicator simulated by the established pipeline model, d obs is the observed production dynamic indicator, C D is the covariance main diagonal matrix of the observation error.

[0126] The constraint conditions are as follows:

[0127]

[0128] Where V tot,m and V tot,f represent the total volume of the matrix and the fracture respectively, N w is the number of wells, and a and b are nonlinear seepage parameters.

[0129] When using the depth-first algorithm to calculate the inter-well distribution factor, first, the generated pipeline network graph is regarded as a weighted directed graph, the direction between two well points is always pointing to the well point with lower pressure, and the weight is the direct distribution factor introduced below, then taking each injection well as the root node, the downstream wells are found along the direction of pressure drop in turn, and the tracking is continued until there is no downstream well for all connected well points. We take well i and well j as an example, where well j has higher pressure, then the calculation of the flow between well j and well i is as follows:

[0130]

[0131] where the superscript n denotes the time step, Qj,i(n) is the flow rate between well j and well i at the current time step n, and Kj,i(n) and Kj,i(n-1) are the conductivity values of the matrix and the fracture between well j and well i at the previous time step n-1, respectively; and Pj,m(n) and Pj,f(n) are the pressure in the matrix and the fracture of well j at the current time step n, respectively. and Pj,m(n) and Pj,f(n) are the pressure in the matrix and the fracture of well j at the current time step n, respectively.

[0132] The direct allocation factor (DAF) between well j and well i is calculated as follows:

[0133]

[0134] where, DAFj,i(n) is the direct allocation factor between well j and well i at the time step n, and Ns j is the number of connections with lower pressure than well j, Qj,k(n) is the flow rate from well j to well k at the time step n.

[0135] When the injection well j is connected to a more downstream production well i through one or several production wells b1, b2,..., b n then the path allocation factor (PAF) between well j and well i needs to be calculated:

[0136]

[0137] where, ij PAFj,i(n) is the path allocation factor between well j and well i, and γ kl (s) is the DAF between well k and well l,

[0138] where, PAFj,i(n) is the path allocation factor between well j and well i at the time step n, and γ (s) is the DAF between well b1 and well b2, DAF is in fact a special case of PAF with only two well points in the path.

[0139] Further, the total allocation factor between well j and well i is calculated as follows:

[0140]

[0141] where, TAFj,i(n) is the total allocation factor between well j and well i at the time step n, and its value is the sum of all path allocation factors between well j and well i; Ns ij is the number of possible flow paths between well j and well i.

[0142] The following is an explanation through specific examples.

[0143] Firstly, this embodiment utilizes reservoir numerical simulation technology to model a low-permeability fractured reservoir block. The constructed reservoir model has a mesh size of 21×21×1; a mesh size of 10m×10m×5m; and a permeability field as shown below. Figure 4 As shown, the initial water saturation of the reservoir is 0.2, and the oil and water viscosities are 4 mPa·s and 1 mPa·s, respectively. There are a total of 9 wells in the reservoir, including 8 production wells and 1 water injection well. The reservoir was simulated for 1800 days of production using reservoir numerical simulation technology. The overall injection and production of the block were balanced, and the water cut of the block eventually reached 90%.

[0144] Simultaneously, using the method presented in this paper and the same parameters, a pipeline network model was constructed, and the resulting dual-medium partition diagram is shown below. Figure 5 As shown, the model takes 1.2 seconds to run once, compared to 25.2 seconds for a conventional reservoir numerical simulator, which is about 20 times faster. The model also performs historical fitting on the single-well oil production rate for the first 1800 days. The historical fitting method used is the ES-MDA method mentioned above, and the fitting converges after three cycles. Figure 6 The fitting results for the cumulative oil production of the block show that the fitting effect is good. Figure 7 This is the flow path tracking graph for this block on day 1800.

[0145] Obviously, the embodiments described above are merely some, not all, embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0146] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0147] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in sequences other than those illustrated or described herein.

[0148] The above merely provides the preferred embodiments of the present application, and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the principles and technical scope of the present application shall fall into the scope of the present application.

Claims

1. A method for simulating inter-well connectivity in low-permeability oil reservoirs, characterized in that, include: Step a: Discretize the reservoir into multiple nodes based on the well locations within the reservoir block. The nodes are connected in pairs. Use the partitioning constraints to filter all connections and form a connected network consisting of a series of connecting pipes. Each pipe represents the flow channel of fluid between wells. Grid the pipes and construct a dual-medium model by considering the non-Darcy flow equation and stress-sensitive effects. Solve the parameters on the grid implicitly. Step b: Establish a historical fitting objective function, adjust the model parameters by using the difference between the observed historical production dynamic indicators of the reservoir and the production dynamic indicators calculated by the current pipeline model, use the optimization algorithm to achieve automatic historical fitting, set constraints, adjust the characteristic parameters of the initial pipeline model, and generate an optimized pipeline network model. Step c: Using a depth-first search algorithm, dynamically track all possible flow paths between injection wells and production wells to generate a flow path tracking map, thereby quantitatively characterizing the flow channels in low-permeability fractured reservoirs.

2. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 1, characterized in that, Step a includes the following steps: Step a1: Discretize the reservoir into multiple nodes based on the location of well points and fracture development in the reservoir, and fully connect multiple nodes. Screen the connections by introducing constraints and generate multiple inter-well connection channels. Each connection represents the flow channel of fluid between two corresponding wells. Step a2: Mesh each connecting pipe, construct a dual-medium model by considering the non-Darcy flow equation and stress-sensitive effects, and solve the parameters on the mesh using the fully implicit flow equation format in the traditional grid reservoir numerical simulator and the nonlinear solver based on Newton iteration.

3. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 2, characterized in that, The constraints are the maximum distance and minimum angle among all connections.

4. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 2, characterized in that, The seepage behavior of fluids in a connected pipeline is mainly controlled by two parameters: inter-well conductivity and connected volume. Inter-well conductivity is used to measure the seepage capacity between wells, while connected volume characterizes the storage capacity of the connected unit.

5. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 2, characterized in that, During the process of meshing each connecting pipe, the meshes on the same connecting unit have equal seepage cross-sectional area and permeability.

6. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 2, characterized in that, In the process of solving the parameters on the grid using the fully implicit flow equation scheme and the nonlinear solver based on Newton iteration in the traditional grid reservoir numerical simulator, the parameters on the grid include at least the grid pressure, saturation, and control volume.

7. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 2, characterized in that, The dual-medium model divides the connected network into two flow systems: a high-porosity, low-permeability bedrock system and a low-porosity, high-permeability fracture system.

8. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 7, characterized in that, The formulas for expressing the permeability of bedrock and fractures in high-porosity, low-permeability bedrock systems and low-porosity, high-permeability fracture systems are as follows: Where the subscript m represents the bedrock system, f represents the fracture system; K ij,m and K ij,f The equivalent permeability of bedrock and fractures between nodes i and j, considering non-Darcy flow and stress sensitivity, is given in mD; k ij,m and k ij,f represents the initial permeability of the bedrock and fracture between nodes i and j, respectively, in mD; μ is the viscosity of the fluid, in mPa·s; The pressure difference between two nodes within the bedrock is expressed in MPa; a and b are nonlinear seepage coefficients, their values ​​determined experimentally; c f The compressibility factor is expressed in MPa. -1 ;P ij,f P represents the current pressure of the crack between the two nodes, in MPa. ij,f0 The initial pressure of the crack between the two nodes is expressed in MPa.

9. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 8, characterized in that, The formulas for expressing the channeling flow between fractures and bedrock in high-porosity, low-permeability bedrock systems and low-porosity, high-permeability fracture systems are as follows: Where Q is the flow rate between the fracture and the bedrock, in kg·day -1 α is the shape factor, in meters. -2 ; ρ m,β The density of a certain phase fluid within bedrock, in kg·m³. -3 ;K m The equivalent permeability of a certain phase fluid within bedrock, expressed in mD; μ β P represents the viscosity of a certain phase fluid, in mPa·s. m and P f These represent the pressures in the bedrock and the fractures, respectively, in MPa.

10. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 8, characterized in that, In a bedrock system with high porosity and low permeability and a fractured system with low porosity and high permeability, the mass conservation equations for fractures and bedrock are as follows: Where, ρ m,β and ρ f,β These are the densities of a certain phase fluid in bedrock and within fractures, respectively, in kg·m³. -3 ;φ m and φ f Porosity of bedrock and fractures, respectively; S m,β and S f,β These represent the saturation of the phase fluid in the bedrock and fractures, respectively; t represents time, in days; v m,β and v f,β These represent the seepage velocities of a certain phase fluid in bedrock and fractures, respectively, in meters (m). 3 ·day -1 q represents the source and sink terms, indicating the increase in mass per unit volume per unit time, expressed in kg·day. -1 When q > 0, it is a source term; when q < 0, it is a sink term.

11. The method for simulating inter-well connectivity in low-permeability reservoirs according to any one of claims 1 to 10, characterized in that, In step b, the initial pipeline characteristic parameters include the connectivity volume V of the bedrock within the connectivity unit. ij,m The connected volume V of the crack ij,f The conductivity T of bedrock ij,m and the conductivity T of the crack ij,f Nonlinear seepage coefficients a and b.

12. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 11, characterized in that, The objective function for historical fitting is: Where m represents the feature parameters for historical fitting of each grid, O(m) is the established minimization objective function, g(m) is the production dynamic index obtained from the simulation of the pipeline model, and d obs C represents the observed production dynamics indicators. D Let be the main diagonal matrix of the covariance of observation errors.

13. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 11, characterized in that, The production dynamic indicators include at least the daily oil production of each well; or The production dynamic indicators include at least the oilfield's oil production, water production, and cumulative production.

14. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 11, characterized in that, In step b, the constraint condition is set as follows: Among them, V tot,m V represents the total volume of bedrock. tot,f N represents the total volume of the crack. w denoted as the number of wells, and a and b as nonlinear seepage parameters.

15. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 11, characterized in that, In step c, when the depth-first search algorithm is used, the generated pipeline network graph is regarded as a weighted directed graph. The direction between two well points always points to the well point with lower pressure. The weight is the direct allocation factor. With each injection well as the root node, downstream wells are searched sequentially along the direction of pressure decrease until all connected well points are found and there are no downstream wells.

16. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 15, characterized in that, The formula for calculating the flow rate between any two wells is: Where the pressure in well j is greater than the pressure in well i, and the superscript n indicates the time step. Let J be the flow rate between well J and well I at the current moment. and These are the conductivity values ​​of the matrix and fractures between well j and well i at the previous time point, respectively. and Given the current pressure of the matrix and fractures in well j, and The pressure of the matrix and fractures in well j at the current moment.

17. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 16, characterized in that, The formula for calculating the direct allocation factor between well j and well i is as follows: in, Let N be the direct allocation factor between well j and well i at time n. j This indicates the number of connection points where the pressure is lower than that of well j. This represents the flow rate from well j into well k at time n.

18. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 17, characterized in that, The formulas for calculating the path assignment factors of wells j and i are as follows: in, The path assignment factor between well j and well i at time n is the term on the right side of the equation. This represents the direct allocation factor between wells b1 and b2.

19. The method for simulating inter-well connectivity in low-permeability reservoirs according to claim 18, characterized in that, The formula for calculating the total distribution factor between well j and well i is as follows: in, Let Ns be the total allocation factor between well j and well i at time n, and its value is the sum of the path allocation factors between all wells j and well i; ij This represents the possible flow path between well j and well i.

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