Physical information neural network numerical simulation method suitable for low-permeability water-drive reservoir

Abstract

The invention relates to the technical field of reservoir engineering, and discloses a physical information neural network numerical simulation method suitable for a low-permeability water-drive reservoir, and the method comprises the steps: employing a finite volume method for full implicit solution, and considering strong nonlinear seepage; an expert experience loss function is constructed, the pressure saturation output range is limited, and the solving efficiency is improved; a full-connection neural network is adopted as a basis, and adjacent position anchoring, a self-adaptive activation function and a jump connection gating updating structure are added; respectively solving pressure and saturation by using two independent networks; introducing a well model to process a large pressure gradient problem; and substituting the pressure and saturation calculated by the network into a loss function to carry out back propagation to optimize the network. The method has high prediction precision when processing complex problems such as large capillary pressure and non-linear seepage, the problem that an existing physical information neural network is difficult to adapt to low-permeability water drive reservoir numerical simulation is effectively solved, and the whole training process does not need to depend on any label data.

Description

Technical Field

[0001] The invention relates to the technical field of oil reservoir engineering, and in particular to a physical information neural network numerical simulation method suitable for low permeability water drive oil reservoirs. Background Art

[0002] Low permeability reservoirs have low permeability and insufficient natural energy. In order to improve the development level of low permeability reservoirs, it is usually necessary to inject water into the formation to supplement energy for water flooding development. In the specific implementation process, in order to achieve the best development effect, it is necessary to optimize the injection and production scheme in combination with numerical simulation. Therefore, constructing a numerical simulation method that can accurately simulate the water flooding process of low permeability reservoirs plays an important role in the effective implementation of water flooding development.

[0003] The essence of reservoir numerical simulation is to obtain the fluid state by solving the control equations of underground fluid flow through numerical methods. This method has the problems of long simulation time and expensive calculation. In recent years, with the rapid development of machine learning technology, it has gradually emerged in the field of reservoir engineering. Among them, the physical information neural network numerical simulation method combines the physical knowledge in reservoir engineering with machine learning technology. On the basis of ensuring fast and efficient, it improves the interpretability and reliability of neural networks and has good application prospects. However, most of the existing physical information neural network numerical simulation methods use the implicit pressure explicit saturation method to solve the two-phase flow problem. Although this method has a high calculation speed, it is difficult to effectively deal with special and complex problems in low permeability reservoirs such as large capillary pressure and nonlinear seepage. Therefore, it is necessary to establish a physical information neural network numerical simulation method suitable for low permeability water drive reservoirs. Summary of the invention

[0004] The purpose of the present invention is to provide a physical information neural network numerical simulation method suitable for low permeability water drive oil reservoirs, aiming to solve the limitations of traditional physical information-based reservoir numerical simulation methods. The core innovations of this method include using the finite volume method for fully implicit solution, considering strong nonlinear seepage; constructing an expert experience loss function, limiting the output range of pressure saturation, and improving the solution efficiency; using a fully connected neural network as the basis, adding adjacent position anchoring, adaptive activation function and jump connection gated update structure; using two independent networks to solve pressure and saturation respectively; introducing a well model to deal with large pressure gradient problems; substituting the pressure and saturation calculated by the network into the loss function for back propagation optimization of the network.

[0005] In order to achieve the above purpose, the technical solutions adopted are as follows: The present invention provides a physical information neural network numerical simulation method applicable to low permeability water drive oil reservoirs, the method comprising: Step 1: Obtain nonlinear seepage characteristics; Step 2: A numerical simulation model of a low permeability water drive reservoir is established based on the nonlinear seepage characteristics, a finite volume method is used for full implicit numerical discretization, and a physical information loss function suitable for a low permeability water drive reservoir is constructed; Step 3: construct an expert experience loss function based on the injection and production well data, and combine the physical information loss function and the expert experience loss function to obtain a total loss function; Step 4: A fully connected neural network is selected as the basis, and an adjacent position anchoring, an adaptive activation function, and a skip connection gated update structure are used for improvement to construct a network model, wherein the network model includes two independent improved fully connected neural networks, which are used to solve pressure and saturation respectively; Step 5: Introduce the well model to calculate the pressure gradient of the network model; Step 6: Input the pressure and saturation of the previous time step into the network model, forward propagate and calculate the loss value, and use the gradient descent method to reversely update the network parameters based on the well model and the total loss function to complete the pressure and saturation solution for one time step; Step 7: Use the pressure, saturation and training parameters output by the network model at each time step as the input for the next time step, repeat step 6, and obtain the pressure and saturation of the low permeability water drive reservoir at any time step.

[0006] Furthermore, the step 1 comprises: Establishing a discrete grid based on the overall reservoir data; wherein the overall reservoir data includes the reservoir size, shape and internal geological structure; Inputting initial reservoir data, rock properties, fluid data, characteristic data between phases and / or production data into the discrete grid for numerical simulation to obtain nonlinear seepage characteristics; wherein the initial reservoir data includes initial reservoir pressure and / or initial water saturation, the rock properties include permeability distribution, porosity distribution and / or pore volume compression coefficient, the fluid data includes oil phase density, oil phase viscosity, oil phase volume compression coefficient, oil phase viscosity compression coefficient, water phase density, water phase viscosity, water phase volume compression coefficient and / or water phase viscosity compression coefficient, the characteristic data between phases include oil-water phase relative permeability curve and / or oil-water phase capillary force curve, and the production data includes production well bottom hole pressure, injection well bottom hole pressure and / or production time.

[0007] Furthermore, the step 2 comprises: Assume that all phases in the reservoir satisfy the same governing equations and auxiliary equations: (1) (2) (3) in, for Density of phase; for The percolation velocity of the phase; For face The unit external normal vector of ; for Phase mass flow rate; is the rock porosity; for Saturation of phase; is the capillary force; is the non-wetting phase pressure; is the wetting phase pressure; V is the volume of the control body; A To control body surface area; The velocity equation that ignores gravity and considers strong nonlinear seepage is established as follows: (4) in, for relative permeability of phases; is the absolute permeability of rock; for Phase viscosity; for Phase pressure gradient, expressed as the pressure difference between two adjacent connected grids in the discrete grid; and denote the first coefficient and the second coefficient respectively, which are determined by the following equations: (5) (6) in, is the permeability in scalar form; After discretizing equation (1) using the finite volume method, we get: (7) in, After discrete i The volume of the grid; For the i and j The mesh contact surface is composed of i The grid points to j The unit normal vector of the mesh; For the i and j The area of ​​the mesh contact surface; t For time; For i Grid A collection of connected grids; Substituting the velocity equation (4) into equation (7) and taking the first-order backward difference of the accumulation term with respect to time, we obtain: (8) in, is the size of the time step; represents the current time step, represents the next time step; for The amount of injection / production per unit volume in the time step; For the next time step, Phase fluid mass, The grid of the current time step Phase fluid quality; for j Grid flow potential; for i Grid flow potential; e is a natural constant; for The product of phase density and fluidity; for Phase pressure gradient; for The fluidity of the phase is expressed as: (9) in, for relative permeability of phases; For the i and j The conductivity between the grids is expressed as: (10) in, For the i and j The average permeability among the grids is and For the i and j The distance from the center of each grid to the connecting surface; According to formula (8), the residual equation is constructed: (11) in, for The residual of the phase; The loss function is established based on the residual equation: (12) in, is the oil phase residual; is the water phase residual; For the i The oil phase residual of the grid; For the i The water phase residual of each grid; MES is the MSE loss function; loss int is the loss of physical equation; N is the number of grids.

[0008] Furthermore, the step 3 comprises: Taking the injection well pressure greater than the reservoir formation pressure and the production well pressure less than the reservoir formation pressure as the restriction conditions, the first expert experience loss function is established, which is expressed as: (13) in, is the bottom hole pressure of the injection well, is the bottom hole pressure of the production well, is the number of grids, loss exp,p is the pressure-related expert experience loss, max is the maximum value function, is the oil phase pressure at the next time step; Limit the training range of water phase saturation to and A second expert experience loss function is established; the second expert experience loss function is expressed as: (14) in, loss exp,S is the saturation-related saturation expert experience loss, is the water phase saturation at the next time step, Represents irreducible water saturation, which refers to the lowest saturation of water phase in the reservoir. Residual oil saturation refers to the lowest saturation of oil phase in the reservoir; Based on the physical information loss function, the first expert experience loss function and the second expert experience loss function, the total loss function is established as: (15) in, loss is the total loss, loss int is the physical equation loss, loss exp,p For stress-related expert experience loss, loss exp,S is the loss of expert experience related to saturation.

[0009] Furthermore, the step 4 comprises: For input The initial pressure matrix and the initial saturation matrix Perform dimension increase at the input layer to obtain the first pressure matrix and the first saturation matrix ; The first pressure matrix and the first saturation matrix Multiply by the first learnable parameter And add the adjacency matrix to anchor the adjacency matrix. The adjacency matrix is ​​a matrix with all 0 and 1 elements. The connected position is 1 and the unconnected position is 0. The calculation process is expressed as: (16) (17) in, , are the second pressure matrix and the second saturation matrix respectively. is the adjacency matrix; After anchoring , Normalized and input into the hidden layer and multiplied by the second learnable parameter And use the ReLU activation function: (18) (19) in , The third pressure matrix and the third saturation matrix are respectively, is the weight of the hidden layer, is the bias of the hidden layer; Will , After dimensionality reduction in the input and output layers, we get , , and multiply the data before and after training by the weights and then add them together to achieve cross-layer connection: (20) (twenty one) in is the pressure matrix after cross-layer connection processing, is the saturation matrix after cross-layer connection processing is the third learnable parameter.

[0010] Furthermore, in step 5, the well model is expressed as: (twenty two) in, for output; is the bottom hole pressure; is the pressure of the grid where the well is located; is the well index, expressed as: (twenty three) in, is the thickness of the oil layer, which is the length of the grid in the z direction where the well is located in the numerical simulation; is the wellbore radius; is the skin factor; k is the permeability; is the reservoir radius, which is expressed in numerical simulation as: (twenty four) in is the length of the grid in the x direction; is the length of the grid in the y direction; is the total flow rate, expressed as: (25) in, is the oil phase fluidity, is the water phase mobility.

[0011] Furthermore, in step 6, the pressure and saturation of the current time step are respectively input into the network model constructed in step 4 for forward propagation to obtain the pressure and saturation data of the next time step, and the pressure and saturation data of the current time step and the pressure and saturation data of the next time step are used to calculate the loss value according to the total loss function of step 3 for back propagation to update the parameters of the two networks, and this process is repeated until the loss value drops to the convergence range, and the pressure and saturation of the current next time step are solved.

[0012] Furthermore, in step 7, the training process of step 6 is repeated, and the solved pressure and saturation data of the next time step are used as the initial pressure and saturation data of the current time step, so as to solve the pressure and saturation data of the next time step again, and obtain the pressure and saturation data of any time step, and solve the pressure distribution, saturation distribution, production well production, injection well injection volume and / or water production rate of the reservoir within the solution time step based on the pressure and saturation data of any time step.

[0013] The beneficial effects of the present invention are: The present invention is applicable to low permeability reservoirs; it considers strong nonlinear seepage and adopts finite volume method for full implicit solution; it constructs expert experience loss function to limit the output range of pressure saturation and improve solution efficiency; it adopts fully connected neural network as the basis and adds adjacent position anchoring, adaptive activation function and jump connection gated update structure, and adopts two independent networks to solve pressure and saturation respectively; it introduces well model to deal with large pressure gradient problem; it substitutes the pressure and saturation calculated by the network into the loss function to perform back propagation optimization network until the loss is less than the preset value to complete the current step solution. Compared with the traditional method, this method not only improves the calculation accuracy, but also can better deal with the calculation problems under complex conditions such as low permeability reservoirs, such as large capillary force and strong nonlinearity, while ensuring the solution efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A flow chart of a physical information neural network numerical simulation method applicable to low permeability water drive oil reservoirs provided in an embodiment of the present invention.

[0015] Figure 2 A graph of reservoir capillary force and relative permeability provided in an embodiment of the present invention.

[0016] Figure 3 A reservoir permeability map provided by an embodiment of the present invention.

[0017] Figure 4 A specific calculation flow chart of the neural network model provided in an embodiment of the present invention.

[0018] Figure 5 A nonlinear permeability coefficient diagram under different fluidities provided by an embodiment of the present invention.

[0019] Figure 6 The actual pressure field map, predicted pressure field map and error diagram of the two at the last moment provided in an embodiment of the present invention, wherein (a) is the actual pressure field map, (b) is the predicted pressure field map, and (c) is the error diagram.

[0020] Figure 7 The actual saturation field map, predicted saturation field map and the error diagram between the two at the last moment provided in an embodiment of the present invention, wherein (a) is the actual saturation field map, (b) is the predicted saturation field map, and (c) is the error diagram.

[0021] Figure 8 A comparison chart of the actual value and predicted value of reservoir water production rate provided in an embodiment of the present invention.

[0022] Fig. 9 A comparison chart of the actual value and predicted value of the cumulative liquid production of the oil reservoir provided in an embodiment of the present invention.

[0023] Fig.10A production comparison diagram with and without considering nonlinear seepage flow provided in an embodiment of the present invention.

[0024] Fig.11 A comparison chart of moisture contents under different capillary forces provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0025] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0026] The specific implementation of the present invention is further described in detail below in conjunction with the drawings and examples.

[0027] The embodiment of the present invention provides a physical information neural network numerical simulation method applicable to low permeability water drive reservoirs. The method has high prediction accuracy when dealing with complex problems such as large capillary pressure and nonlinear seepage, and effectively solves the problem that existing physical information neural networks are difficult to apply to low permeability water drive reservoir numerical simulation, and the entire training process does not need to rely on any label data. Figure 1 As shown, the method includes steps 1 to 7, which are described in detail as follows.

[0028] Step 1: Obtain nonlinear seepage characteristics.

[0029] In this embodiment, the nonlinear seepage characteristics can be characterized or reflected by rock properties (permeability, porosity), fluid properties (density, viscosity), relative permeability curve, capillary force curve and seepage equation under low permeability conditions. The nonlinear seepage characteristics can be obtained by the following steps: Step 1.1: Establish a discrete grid based on the overall reservoir data; wherein the overall reservoir data includes the reservoir size, shape and internal geological structure.

[0030] Step 1.2: Input the initial reservoir data, rock properties, fluid data, phase-to-phase characteristic data and / or production data into the discrete grid for numerical simulation to obtain nonlinear seepage characteristics; wherein the initial reservoir data includes the initial reservoir pressure and / or initial water saturation, the rock properties include permeability distribution, porosity distribution and / or pore volume compression coefficient, the fluid data includes oil phase density, oil phase viscosity, oil phase volume compression coefficient, oil phase viscosity compression coefficient, water phase density, water phase viscosity, water phase volume compression coefficient and / or water phase viscosity compression coefficient, the phase-to-phase characteristic data includes oil-water phase relative permeability curve and / or oil-water phase capillary force curve, and the production data includes production well bottom hole pressure, injection well bottom hole pressure and / or production time.

[0031] Step 2: A numerical simulation model of a low permeability water drive reservoir is established based on the nonlinear seepage characteristics, a finite volume method is used for full implicit numerical discretization, and a physical information loss function suitable for a low permeability water drive reservoir is constructed.

[0032] In step 2, the internal physical information loss function is constructed through the physical equation, which can be implemented by the following steps: Step 2.1: Assume that all phases in the reservoir satisfy the same governing equations and auxiliary equations: (1) (2) (3) in for Density of phase, kg / m 3 ; for The seepage velocity of the phase, m / s; For face The unit external normal vector of ; for Phase mass flow rate, kg / s; is the rock porosity, %; for Saturation of phase; is the capillary force, Pa; is the non-wetting phase pressure, Pa; is the wetting phase pressure, Pa; V is the volume of the control body; A To control body surface area; Step 2.2: The velocity equation without considering gravity and considering strong nonlinear seepage is as follows: (4) in for The percolation velocity of the phase, m / s; for relative permeability of phases; is the absolute permeability of rock, m 2 ; for Phase viscosity; for Phase pressure gradient, expressed as the pressure difference between two adjacent connected grids in the discrete grid, Pa; and are the first coefficient and the second coefficient.

[0033] The coefficient , Determined by the following equation: (5) (6) It should be noted that in the above two formulas is a non-tensor The scalar form of the permeability.

[0034] Step 2.3: After discretizing (1) using the finite volume method, we can obtain: (7) in After discrete i The volume of the grid, m 3 ; For the i and j The mesh contact surface is composed of i The grid points to j The unit normal vector of the mesh; For the i and j The area of ​​the mesh contact surface, m 2 ; t For time; For i Grid A collection of connected grids; Step 2.4: Substitute the velocity equation (4) into (7) and take the first-order backward difference of the cumulative term with respect to time to obtain: (8) in, is the size of the time step; represents the current time step, represents the next time step; for The amount of injection / production per unit volume in the time step; For the next time step, Phase fluid mass, The current time step grid Phase fluid quality; for j Grid flow potential; for i Grid flow potential; e is a natural constant; for The product of phase density and fluidity; for Phase pressure gradient; in called The mobility of the phase is defined by the following equation: (9) in, for relative permeability of phases; in called The conductivity between the grids is defined by the following equation: (10) for The average permeability between grids, , for The distance from the center of the grid to the connection surface, m.

[0035] Step 2.5: According to (8), the residual equation can be constructed: (11) in, for The residual error of the phase, is the size of the time step, s; represents the current time step, represents the next time step, for Injection / production per unit volume per time step, m 3 / (m 3 ·s).

[0036] Since the simulated reservoir contains only oil and water phases, the MSE loss function is used based on this residual: (12) in is the oil phase residual, kg / s; is the water phase residual, kg / s; For the i Oil phase residual of each grid, kg / s; For the i Water phase residual of each grid, kg / s; MES is the MSE loss function; loss int is the loss of physical equation; N is the number of grids; in this loss function, the label value is the zero matrix, which means that the numerical simulation process of the neural network does not require any label data and only needs to satisfy the physical equations.

[0037] Step 3: Based on the injection and production well data, an expert experience loss function is constructed, and the physical information loss function and the expert experience loss function are combined to obtain a total loss function.

[0038] Step 3 is implemented by the following steps: Step 3.1: Since the injection well pressure must be greater than the reservoir formation pressure and the production well pressure must be less than the reservoir formation pressure to have actual production significance, the first expert experience loss function is constructed based on this characteristic: (13) in, is the bottom hole pressure of the injection well, is the bottom hole pressure of the production well, is the number of grids, loss exp,p is the pressure-related expert experience loss, max is the maximum value function, is the oil phase pressure at the next time step; Step 3.2: For water phase saturation, the training range should also be and between Represents irreducible water saturation, which refers to the lowest saturation of water phase in the reservoir. Represents the residual oil saturation, which refers to the lowest saturation of the oil phase in the reservoir. Based on this characteristic, the second expert experience loss function is constructed: (14) in, loss exp,S is the saturation-related saturation expert experience loss, is the water phase saturation at the next time step.

[0039] The significance of introducing the expert experience loss function is to limit the training range of pressure and saturation and improve training efficiency.

[0040] Step 3.3: The total loss function consists of three parts: the physical equation loss function and two expert experience loss functions: (15) in, lossis the total loss, loss int is the physical equation loss, loss exp,p For stress-related expert experience loss, loss exp,S is the loss of saturation-related expert experience.

[0041] The network parameters are updated by backpropagation according to the total loss function until the convergence condition is reached, that is, the physical equations and expert experience are met, and then the iteration is stopped and the training results of the current time step are output.

[0042] Step 4: A fully connected neural network is selected as the basis, and an improvement is made by using adjacent position anchoring, adaptive activation function and skip connection gated update structure to construct a network model. The network model includes two independent improved fully connected neural networks, which are used to solve pressure and saturation respectively.

[0043] In step 4, the fully connected neural network is one of the most basic and common neural networks. It consists of an input layer, a hidden layer, and an output layer. The input layer receives input data, the hidden layer performs feature extraction and nonlinear transformation, and there can be multiple hidden layers. Each hidden layer processes the input information, and the output layer outputs the final result. The characteristic of a fully connected neural network is that each neuron is connected to all neurons in the previous layer. This fully connected structure enables the network to learn the complex relationship between input and output. The fully connected neural network can have multiple hidden layers to increase the network's expressive power. By adjusting the weights of each connection in the network, the relationship between input and output can be learned. Fully connected neural networks are widely used in various machine learning and deep learning tasks, such as image classification, speech recognition, natural language processing, etc. It is the basis for building more complex neural network models.

[0044] Based on the fully connected neural network, step 4 is implemented by the following steps: Step 4.1: The network form of training pressure and saturation is consistent. First, the input dimensional data (initial pressure matrix and the initial saturation matrix ) is upgraded to Data: First Pressure Matrix and the first saturation matrix ; Then multiply the dimensionally upgraded data by the first learnable parameter And add the adjacency matrix to anchor the adjacency matrix. The physical meaning of this step is to improve the training efficiency of the neural network input grid connection information. The adjacency matrix is ​​a matrix with all 0 and 1 elements. The connected position is 1 and the unconnected position is 0: (16) (17) in, , are the second pressure matrix and the second saturation matrix respectively. is the adjacency matrix.

[0045] Step 4.2: After anchoring , Normalize and input into the hidden layer and multiply by the second learnable parameter And use the ReLU activation function, multiplying a learnable second parameter before the activation function , making the activation function adaptive: (18) (19) in , They are the third pressure matrix and the third saturation matrix respectively. is the weight of the hidden layer, is the bias of the hidden layer.

[0046] Step 4.3: , After dimensionality reduction in the input and output layers, we get , At this time, the data before and after training are multiplied by a certain weight and then added to achieve cross-layer connection. The purpose of this step is to refer to historical information to improve training efficiency: (20) (twenty one) in is the pressure after cross-layer connection processing, is the saturation after cross-layer connection processing. These two parameters are the final output data after the neural network. is the third learnable parameter.

[0047] Step 5: Introduce the well model to calculate the pressure gradient of the network model.

[0048] In step 5, due to the large pressure gradient around the well, the training is difficult to converge in this case, so the well model is introduced to deal with the problem of large pressure gradient and is closer to the actual reservoir development situation. The definition of the well model is as follows: (twenty two) in is the output, m 3 / s; is the bottom hole pressure, Pa; is the pressure of the grid where the well is located, Pa; in is the well index, defined as: (twenty three) in is the oil layer thickness, m, which is the length of the grid in the z direction where the well is located in the numerical simulation; is the wellbore radius, m; is the skin factor, k is the permeability.

[0049] in is the reservoir radius, which is: (twenty four) in is the length of the grid in the x direction, m; is the length of the grid in the y direction, m.

[0050] is the total fluidity, 1 / (Pa·s), defined as: (25) in, is the oil phase fluidity, is the water phase mobility.

[0051] The significance of introducing the well model is that if the grid pressure is calculated directly using the source and sink terms, the grid pressure gradient where the well is located will be very large, and both traditional numerical simulation and neural network will be difficult to converge. After introducing the well model, the pressure gradient is reduced and it is closer to the actual situation of the reservoir.

[0052] Step 6: Input the pressure and saturation of the previous time step into the network model, forward propagate and calculate the loss value, and use the gradient descent method to reversely update the network parameters based on the well model and the total loss function to complete the pressure and saturation solution for one time step.

[0053] In step 6, the pressure and saturation of the current time step are forward propagated in the two networks described in step 4 to obtain the pressure and saturation data of the next time step, and the pressure and saturation data of the current time step and the pressure and saturation data of the next time step are used to calculate the loss value according to the loss function described in step 2 to perform back propagation to update the parameters of the two networks. This process is repeated until the loss value drops to the convergence range, and the pressure and saturation of the current next time step are solved.

[0054] Step 7: Use the pressure, saturation and training parameters output by the network model at each time step as the input for the next time step, repeat step 6, and obtain the pressure and saturation of the low permeability water drive reservoir at any time step.

[0055] In step 7, the training process of step 6 is repeated, and the pressure and saturation data of the next time step are used as the initial pressure and saturation data of the current time step to solve the pressure and saturation data of the next time step. The pressure and saturation data of any time step can be solved by repeating step 6. With the pressure and saturation data of each time step, a series of data such as the pressure distribution, saturation distribution, production well production, injection well injection volume, water production rate, etc. of the reservoir within the solution time step can be solved.

[0056] A conceptual example will be provided below to verify the feasibility and advancement of the method proposed in the present invention.

[0057] The reservoir model uses a discretized grid of 25×25×1 and a grid size of 4m×4m×10m. The initial reservoir pressure is 25MPa, the initial saturation is 0.2, the initial porosity is 0.05, and the permeability field is Figure 3 As shown, the rock pore compression coefficient is 1×10 -9 1 / Pa. The model includes a production well and an injection well. The bottom flow pressure of the production well is 5MPa and the bottom flow pressure of the injection well is 35MPa. The volume compression coefficient of the fluid is 1×10 -8 1 / Pa, the initial density of oil is 850kg / m 3 , the initial viscosity is 2mPa·s, and the initial density of water is 1000kg / m 3 , the initial viscosity is 1mPa·s, the capillary force curve and phase permeability curve are as follows Figure 2 As shown, the seepage velocity equation is shown in formula (4): Figure 5 is the nonlinear seepage velocity equation , Coefficient The simulation time is 1000 days and the time step is 0.1 day.

[0058] Construct a fully connected neural network model, such as Figure 4 As shown, the fully connected neural network includes an input layer, an output layer and a hidden layer, and the pressure and saturation are solved respectively through the two networks.

[0059] Figure 6 To simulate the pressure distribution after 1000 days, the pressure distribution was calculated by a traditional numerical simulator and compared with the two. The maximum error between the two was only 0.16MPa. Figure 7 To simulate the saturation distribution after 1000 days, the saturation distribution calculated by the traditional numerical simulator and the comparison between the two were found. The maximum error between the two was only 0.008. The results of the numerical simulation using the neural network were very accurate.

[0060] Figure 8 Comparison of water content in production wells between neural network numerical simulation and traditional numerical simulation. Fig. 9 The cumulative liquid production is compared between the neural network numerical simulation and the traditional numerical simulation. The comparison shows that the numerical simulation using the neural network has the same accuracy as the traditional numerical simulator.

[0061] Fig.10 In order to compare the cumulative liquid production with and without considering nonlinear seepage, it can be found that considering nonlinear seepage will greatly reduce the cumulative liquid production, and strong capillary force will also greatly reduce the cumulative liquid production.

[0062] Fig.11 This is a comparison of the water cut of production wells under different capillary forces. The comparison shows that when the capillary force is large, water appears earlier but the water cut curve rises more slowly.

[0063] The above implementation modes are only used to illustrate the present invention, but not to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The patent protection scope of the present invention should be defined by the claims.

Claims

1. A physical information neural network numerical simulation method suitable for low permeability water drive oil reservoirs, characterized in that: The method comprises: Step 1: Obtain nonlinear seepage characteristics; Step 2: A numerical simulation model of a low permeability water drive reservoir is established based on the nonlinear seepage characteristics, a finite volume method is used for full implicit numerical discretization, and a physical information loss function suitable for a low permeability water drive reservoir is constructed; Step 3: construct an expert experience loss function based on the injection and production well data, and combine the physical information loss function and the expert experience loss function to obtain a total loss function; Step 4: A fully connected neural network is selected as the basis, and an adjacent position anchoring, an adaptive activation function, and a skip connection gated update structure are used for improvement to construct a network model, wherein the network model includes two independent improved fully connected neural networks, which are used to solve pressure and saturation respectively; Step 5: Introduce the well model to calculate the pressure gradient of the network model; Step 6: Input the pressure and saturation of the previous time step into the network model, forward propagate and calculate the loss value, and use the gradient descent method to reversely update the network parameters based on the well model and the total loss function to complete the pressure and saturation solution for one time step; Step 7: Use the pressure, saturation and training parameters output by the network model at each time step as the input for the next time step, repeat step 6, and obtain the pressure and saturation of the low permeability water drive reservoir at any time step.

2. The method according to claim 1, characterized in that The step 1 comprises: Establishing a discrete grid based on the overall reservoir data; wherein the overall reservoir data includes the reservoir size, shape and internal geological structure; Inputting initial reservoir data, rock properties, fluid data, characteristic data between phases and / or production data into the discrete grid for numerical simulation to obtain nonlinear seepage characteristics; wherein the initial reservoir data includes initial reservoir pressure and / or initial water saturation, the rock properties include permeability distribution, porosity distribution and / or pore volume compression coefficient, the fluid data includes oil phase density, oil phase viscosity, oil phase volume compression coefficient, oil phase viscosity compression coefficient, water phase density, water phase viscosity, water phase volume compression coefficient and / or water phase viscosity compression coefficient, the characteristic data between phases include oil-water phase relative permeability curve and / or oil-water phase capillary force curve, and the production data includes production well bottom hole pressure, injection well bottom hole pressure and / or production time.

3. The method according to claim 1, characterized in that The step 2 comprises: Assume that all phases in the reservoir satisfy the same governing equations and auxiliary equations: (1) (2) (3) in, for Density of phase; for The percolation velocity of the phase; For face The unit external normal vector of ; for Phase mass flow rate; is the rock porosity; for Saturation of phase; is the capillary force; is the non-wetting phase pressure; is the wetting phase pressure; V is the volume of the control body; A To control body surface area; The velocity equation that ignores gravity and considers strong nonlinear seepage is established as follows: (4) in, for relative permeability of phases; is the absolute permeability of rock; for Phase viscosity; for Phase pressure gradient, expressed as the pressure difference between two adjacent connected grids in the discrete grid; and denote the first coefficient and the second coefficient respectively, which are determined by the following equations: (5) (6) in, is the permeability in scalar form; After discretizing equation (1) using the finite volume method, we get: (7) in, After discrete i The volume of the grid; For the i and j The mesh contact surface is composed of i The grid points to j The unit normal vector of the mesh; For the i and j The area of ​​the mesh contact surface; t For time; For i Grid A collection of connected grids; Substituting the velocity equation (4) into equation (7) and taking the first-order backward difference of the accumulation term with respect to time, we obtain: (8) in, is the size of the time step; represents the current time step, represents the next time step; for The amount of injection / production per unit volume in the time step; For the next time step, Phase fluid mass, The current time step grid Phase fluid quality; for j Grid flow potential; for i Grid flow potential; e is a natural constant; for The product of phase density and fluidity; for Phase pressure gradient; for The fluidity of the phase is expressed as: (9) in, for relative permeability of phases; For the i and j The conductivity between the grids is expressed as: (10) in, For the i and j The average permeability among the grids is and For the i and j The distance from the center of each grid to the connecting surface; According to formula (8), the residual equation is constructed: (11) in, for The residual of the phase; The loss function is established based on the residual equation: (12) in, is the oil phase residual; is the water phase residual; For the i The oil phase residual of the grid; For the i The water phase residual of each grid; MES is the MSE loss function; loss int is the loss of physical equation; N is the number of grids.

4. The method according to claim 1, characterized in that The step 3 comprises: Taking the injection well pressure greater than the reservoir formation pressure and the production well pressure less than the reservoir formation pressure as the restriction conditions, the first expert experience loss function is established, which is expressed as: (13) in, is the bottom hole pressure of the injection well, is the bottom hole pressure of the production well, is the number of grids, loss exp,p is the pressure-related expert experience loss, max is the maximum value function, is the oil phase pressure at the next time step; Limit the training range of water phase saturation to and A second expert experience loss function is established; the second expert experience loss function is expressed as: (14) in, loss exp,S is the saturation-related saturation expert experience loss, is the water phase saturation at the next time step, Represents irreducible water saturation, which refers to the lowest saturation of water phase in the reservoir. Residual oil saturation refers to the lowest saturation of oil phase in the reservoir; Based on the physical information loss function, the first expert experience loss function and the second expert experience loss function, the total loss function is established as: (15) in, loss is the total loss, loss int is the physical equation loss, loss exp,p For stress-related expert experience loss, loss exp,S is the loss of saturation-related expert experience.

5. The method according to claim 4, characterized in that The step 4 comprises: For input The initial pressure matrix and the initial saturation matrix Perform dimension increase at the input layer to obtain the first pressure matrix and the first saturation matrix ; The first pressure matrix and the first saturation matrix Multiply by the first learnable parameter And add the adjacency matrix to anchor the adjacency matrix. The adjacency matrix is ​​a matrix with all 0 and 1 elements. The connected position is 1 and the unconnected position is 0. The calculation process is expressed as: (16) (17) in, , are the second pressure matrix and the second saturation matrix respectively. is the adjacency matrix; After anchoring , Normalize and input into the hidden layer and multiply by the second learnable parameter And use the ReLU activation function: (18) (19) in , The third pressure matrix and the third saturation matrix are respectively, is the weight of the hidden layer, is the bias of the hidden layer; Will , After dimensionality reduction in the input and output layers, we get , , and multiply the data before and after training by the weights and then add them together to achieve cross-layer connection: (20) (21) in is the pressure matrix after cross-layer connection processing, is the saturation matrix after cross-layer connection processing is the third learnable parameter.

6. The method according to claim 1, characterized in that In step 5, the well model is expressed as: (22) in, for output; is the bottom hole pressure; is the pressure of the grid where the well is located; is the well index, expressed as: (23) in, is the thickness of the oil layer, which is the length of the grid in the z direction where the well is located in the numerical simulation; is the wellbore radius; is the skin factor; k is the permeability; is the reservoir radius, which is expressed in numerical simulation as: (24) in is the length of the grid in the x direction; is the length of the grid in the y direction; is the total flow rate, expressed as: (25) in, is the oil phase fluidity, is the water phase mobility.

7. The method according to claim 1, characterized in that In step 6, the pressure and saturation of the current time step are respectively input into the network model constructed in step 4 for forward propagation to obtain the pressure and saturation data of the next time step, and the pressure and saturation data of the current time step and the pressure and saturation data of the next time step are used to calculate the loss value according to the total loss function of step 3 for back propagation to update the parameters of the two networks, and this process is repeated until the loss value drops to the convergence range, and the pressure and saturation of the current next time step are solved.

8. The method according to claim 1, characterized in that In step 7, the training process of step 6 is repeated, and the solved pressure and saturation data of the next time step are used as the initial pressure and saturation data of the current time step, so as to solve the pressure and saturation data of the next time step again, and obtain the pressure and saturation data of any time step. Based on the pressure and saturation data of any time step, the pressure distribution, saturation distribution, production of production wells, injection volume of injection wells and / or water production rate of the oil reservoir in the solution time step are solved.

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