Construction method of reservoir simulation agent model based on graph neural network

Abstract

The present invention discloses a method for constructing a proxy model for reservoir simulation based on a graph neural network. By using a graph neural network to extract spatial information, the present invention can conveniently process various unstructured grids in addition to regular structured grids. For more complex reservoir models, proxy models are constructed without special processing, directly treating all unstructured grids as nodes. These nodes form a graph structure, and then using a graph neural network to extract spatial information. Long-short-term memory neural networks are then used to predict output parameters. The present invention can efficiently predict output parameters under different permeability fields, with higher forward computational efficiency. When performing tasks such as uncertainty quantification and history matching, it can significantly reduce computational costs and improve work efficiency. Furthermore, the proxy model can conveniently and effectively process different types of grids, as well as various irregularly shaped research areas, making its application scenarios more flexible.

Description

Technical Field

[0001] The present invention relates to the field of petroleum engineering, and in particular to a method for constructing an oil reservoir simulation agent model based on a graph neural network. Background Art

[0002] Currently, numerical simulations of oil reservoirs are mostly performed using commercial numerical simulation software. The model simulation calculations involve discretizing and solving partial differential equations, which is computationally intensive for large reservoirs. This is especially true for tasks such as uncertainty quantification, reservoir history matching, and production optimization design. These tasks require multiple, repeated runs of the numerical simulator, which incurs a significant computational burden. However, constructing proxy models can effectively avoid this problem. Proxy models offer faster forward computation speeds, significantly improving computational efficiency.

[0003] Existing methods for constructing proxy models include Gaussian Process Regression, Polynomial Chaos Expansion, Radial Basis Function, and Neural Networks. Among them, proxy models based on deep learning (various deep neural networks) offer stronger approximation capabilities than these other methods, can more effectively handle high-dimensional problems, and effectively avoid the "curse of dimension."

[0004] Among deep learning algorithms, a common approach is to construct proxy models based on convolutional neural networks (CNNs). This approach treats the reservoir model input parameter field as an image and uses CNNs to extract spatial information from the reservoir model. However, this convolutional architecture is typically suitable for relatively regular-shaped reservoirs, and the discretization of reservoir models is typically done using regular grids. However, for irregularly shaped reservoirs, or when using irregular grids such as triangular or perpendicular bisection (PEBI) grids, discretization is more complex, making it difficult for traditional CNNs to directly extract spatial information. Summary of the Invention

[0005] In response to the above problems existing in the prior art, the present invention proposes an oil reservoir simulation agent model based on graph neural network and long short-term memory network.

[0006] The method for constructing a reservoir simulation proxy model based on a graph neural network of the present invention comprises the following steps:

[0007] 1) Establish the original reservoir model:

[0008] An original reservoir model is established for the reservoir using a reservoir numerical simulator, including discretized grids and nodes. The original reservoir model discretizes the reservoir using a regular or irregular grid to obtain a discretized grid, with the center of the grid serving as a node, and the node coordinates are obtained.

[0009] 2) Select the parameters of interest:

[0010] Select the parameters of interest when building the proxy model, namely the input parameters and output parameters of the proxy model; the input parameters are spatial distribution data that changes with space, and the output parameters are time series data that changes with time;

[0011] 3) Generate input parameters:

[0012] Randomly generate multiple different sets of realizations for the input parameters selected in step 2), where each set of realizations represents a distribution of input parameter values;

[0013] 4) Get training data:

[0014] Inputting the multiple sets of realizations of the input parameters generated in step 3) into the original reservoir model established in step 1), respectively, running the reservoir numerical simulator, and calculating the output parameter calculation results corresponding to different input parameter realizations; a set of input parameter realizations and the corresponding output parameter calculation results constitute a data pair, and multiple sets of data pairs constitute a training data set, and the calculation result of each output parameter is a time series that changes over time, and the sequence length is the total number of simulation time steps;

[0015] 5) Build the proxy model:

[0016] (1) Building a graph neural network:

[0017] According to the discretized grid and node coordinates in step 1), each node is connected to the N nodes closest to it to form edges, where N is a natural number. The nodes and edges together form a graph structure; an adjacency matrix is ​​constructed to describe the graph structure.

[0018] The elements in the adjacency matrix represent the weights of the connections between nodes, which are calculated as follows:

[0019]

[0020] Among them, z i and z j Respectively represent the node coordinates of two different nodes in the graph structure; W ij Indicates that the node coordinates in the matrix are z i and z jThe connection weight between two nodes; σ is the normalization coefficient, which is the mean of the distances between all nodes;

[0021] Based on the obtained adjacency matrix, an existing open source deep learning library is used to build a Chebyshev network (ChebNet) for the graph structure. ChebNet is a graph neural network based on Chebyshev polynomials. ChebNet is used as the graph neural network. The graph neural network is used to extract spatial information and perform dimensionality reduction on the spatially distributed input parameters through graph convolution, and the output is a latent variable column vector.

[0022] (2) Processing latent variable column vector:

[0023] The obtained latent variable column vector is copied to the same length as the total number of simulation time steps in step 4), and the copied latent variable column vectors are spliced ​​together to form a copied and spliced ​​time series;

[0024] (3) Building a long short-term memory (LSTM) network:

[0025] Use the existing open source deep learning library to build an LSTM network, with the input being the copied and spliced ​​time series and the output being the time series of the calculated results of the output parameters;

[0026] (4) Establishing an agent model:

[0027] By combining the graph neural network and the LSTM network, a proxy model for reservoir simulation is constructed. In the constructed proxy model, the input parameters are passed through the graph neural network to obtain a latent variable column vector. The latent variable column vector is copied and concatenated before being passed to the LSTM network. Finally, the LSTM network outputs a time series of the calculated output parameter results. This is the forward computation process of the constructed proxy model.

[0028] 6) Training the agent model:

[0029] The proxy model established in step 5) is trained using the training dataset obtained in step 4). The number of training iterations is set, and an optimization algorithm is used to minimize the gap between the model's predicted output and the true value. After the pre-set number of iterations is reached, the training of the proxy model is completed, resulting in a trained proxy model.

[0030] 7) Prediction output parameters:

[0031] The new input parameters are input into the trained proxy model to obtain the calculation results of the corresponding output parameters, thus realizing direct prediction of the output parameters.

[0032] Wherein, in step 1), the irregular grid in the original reservoir model adopts: a triangular grid or a perpendicular bisector parallel PEBI grid.

[0033] In step 2), the input parameters are one or more of reservoir permeability and porosity, and the output is one or more of oil production rate, water production rate, bottom hole pressure of reservoir production wells, and water injection rate and bottom hole pressure of water injection wells.

[0034] In step 3), the number of groups of randomly generated realizations of the input parameters is no less than 100. The more the number of realizations and the more training data there are, the more accurate the constructed proxy model will be.

[0035] In (1) of step 5), N satisfies 3≤N≤30.

[0036] In step 5) (2), the open source deep learning library uses the Pytorch deep learning framework or the Tensorflow deep learning framework. The dimension of the latent variable column vector obtained after the input parameters are subjected to the graph convolution operation of the graph neural network is smaller than the total number of discretized grids.

[0037] In step 5) (3), the number of LSTM network layers is 1 to 10, the number of neurons in the hidden layer is 50 to 3000, and the values ​​of the network parameters are determined by random search optimization.

[0038] In step (4) of step 5), the graph neural network and the LSTM network are connected together through programming using the existing open source deep learning library to obtain a reservoir simulation proxy model. The input of the graph neural network is the input of the proxy model, and the output of the LSTM network is the output of the proxy model.

[0039] In step 6), the optimization algorithm adopts one of the following algorithms: Stochastic Gradient Descent (SGD), Adaptive Moment Estimation (Adam), Adaptive Gradient (AdaGrad), and Root Mean Square Propagation (RMSProp). The number of iterations is 100 to 10,000. Advantages of the present invention:

[0040] The present invention uses graph neural networks to extract spatial information. In addition to regular structured grids, various unstructured grids can be processed relatively conveniently. In this way, proxy models can be constructed for more complex reservoir models without special processing. All unstructured grids are directly regarded as nodes. These nodes constitute the entire graph structure. Then, the graph neural network is used to extract spatial information, and the long short-term memory neural network is used to predict the output parameters. The proxy model of the present invention can efficiently predict the output parameters under different permeability fields. Compared with directly running the reservoir numerical simulator, the forward operation efficiency is higher. When performing tasks such as uncertainty quantification and history matching, it can significantly reduce the computing cost and improve work efficiency. Moreover, based on the structure of the graph neural network, the construction of the proxy model is no longer limited to regular grids in regular areas. It can conveniently and effectively process different types of grids and various irregularly shaped research areas, and the application scenarios are more flexible. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Figure 1 is a schematic diagram of information extraction from irregular grid data according to an embodiment of a method for constructing a reservoir simulation proxy model based on a graph neural network of the present invention. (a) is a schematic diagram of an irregular grid discretized reservoir, (b) is a graph structure constructed for the unstructured grid, and (c) is a schematic diagram of a latent variable column vector obtained by extracting spatial information through graph convolution.

[0042] Figure 2 A schematic diagram of discretizing reservoir model blocks according to an embodiment of a method for constructing a reservoir simulation proxy model based on a graph neural network of the present invention;

[0043] Figure 3 Comparison of the production data calculation results using a reservoir numerical simulator with the prediction results of the method for constructing a reservoir simulation proxy model based on a graph neural network of the present invention;

[0044] Figure 4 This is a flow chart of the method for constructing a reservoir simulation agent model based on graph neural network of the present invention. DETAILED DESCRIPTION

[0045] The present invention will be further described below through specific embodiments in conjunction with the accompanying drawings.

[0046] The method for constructing a reservoir simulation agent model based on a graph neural network in this embodiment is as follows: Figure 4 As shown, the following steps are included:

[0047] 1) Establish the original reservoir model:

[0048] The original reservoir model is established using a reservoir numerical simulator, including discretized grids and nodes, as shown in the schematic diagram. Figure 1 (a) shows that the original reservoir model uses irregular grids to discretize the reservoir, as shown in Figure 2 As shown in the figure, the solid circles represent the locations of production wells, and the solid triangles represent the locations of water injection wells. It can be seen that the grid at the well point is locally encrypted; the reservoir development process is 1500 days, divided into 50 time steps, each time step is 30 days, and the discretized grid is obtained. The center of the grid is used as the node, and the node coordinates are obtained;

[0049] 2) Select the parameters of interest:

[0050] Select the parameters of interest when constructing the proxy model, namely the input parameters and output parameters of the proxy model, where the input parameter is the reservoir permeability, and the output is one or more of the following: the oil production rate of the production well, the water cut, the injection rate of the water injection well, and the bottom well pressure; the input parameter is spatial distribution data that varies with space, and the output parameter is time series data that varies with time;

[0051] 3) Generate input parameters:

[0052] Randomly generate 1000 different sets of realizations for the input parameters selected in step 2), where each set of realizations represents a distribution of the input parameter values.

[0053] 4) Get training data:

[0054] Input the multiple sets of input parameter realizations generated in step 3) into the original reservoir model established in step 1), run the reservoir numerical simulator, and calculate the output parameter calculation results corresponding to different input parameter realizations; a set of input parameter realizations and the corresponding output parameter calculation results constitute a data pair, and 1000 sets of data pairs constitute a training data set. The calculation result of each output parameter is a time series that changes over time, and the sequence length is the total number of simulation time steps;

[0055] 5) Build the proxy model:

[0056] (1) Building a graph neural network:

[0057] According to the discretized grid and node coordinates in step 1), each node is connected to the five nodes closest to it to form edges, that is, N=5. The nodes and edges together form a graph structure, as shown in the schematic diagram. Figure 1 (b) shows the adjacency matrix used to describe the graph structure. The elements in the adjacency matrix represent the weights of the connections between nodes. The specific calculation method is as follows:

[0058]

[0059] Among them, z i and z jRespectively represent the node coordinates of two different nodes in the graph structure; W ij Indicates that the node coordinates in the matrix are z i and z j The connection weight between two nodes; σ is the normalization coefficient, which is the mean of the distances between all nodes;

[0060] According to the obtained adjacency matrix, the existing open source deep learning library is used to establish a graph neural network based on Chebyshev polynomials for the graph structure - Chebyshev network ChebNet. ChebNet is used as the graph neural network, and the structural parameters of the graph neural network are selected, such as the dimension of the latent variable column vector. In this example, the graph neural network is used to extract spatial information and reduce the dimension of the spatially distributed input parameters through graph convolution. The dimension of the output latent variable column vector is 100, as shown in the schematic diagram. Figure 1 (c)

[0061] (2) Processing latent variable column vector:

[0062] The obtained latent variable column vector is copied to the same length as the total number of simulation time steps in step 4), and the copied latent variable column vectors are spliced ​​together to form a copied and spliced ​​time series. Since there are 50 time steps in total, the length of the copied and spliced ​​time series is 50;

[0063] (3) Building a long short-term memory (LSTM) network:

[0064] Use the existing open source deep learning library to build an LSTM network, with the input being the copied and spliced ​​time series.

[0065] The output is a time series of the calculation results of the output parameters. The values ​​of the network parameters are determined by random search optimization. In this example, the number of LSTM network layers is set to 2, and the number of hidden layer neurons is set to 1500.

[0066] (4) Establishing an agent model:

[0067] Using an existing open-source deep learning library, the graph neural network and the LSTM network are connected together through programming to obtain a reservoir simulation proxy model. The input of the graph neural network is the input of the proxy model, and the output of the LSTM network is the output of the proxy model. The input parameters are converted into latent variable column vectors through ChebNet. The latent variable column vectors are copied and spliced, and then input into the LSTM network to obtain a time series of the calculated output parameter results. There are four production wells, namely production wells 1 to 4, and one water injection well. Each production well has two variables, oil production rate and water production rate, and the water injection well has only one variable, water injection rate. Therefore, there are a total of 9 time series of calculated output parameter results. Since the latent variable dimension of the graph neural network output is 100, the input dimension of the LSTM is also 100.

[0068] 6) Training the agent model:

[0069] The proxy model established in step 5) is trained using the training dataset obtained in step 4). The Adam optimization algorithm is used to minimize the gap between the model's predicted output and the true value. The initial learning rate of the training process is 0.001, and the learning rate is decayed by 10% every ten iterations until it reaches 0.00005. The training is repeated for a total of 3000 iterations. After convergence, the training of the proxy model is completed, and a trained proxy model is obtained.

[0070] 7) Prediction output parameters:

[0071] The new input parameters are input into the trained proxy model to obtain the calculation results of the corresponding output parameters, thus realizing direct prediction of the output parameters.

[0072] Figure 3 In this example, the calculation results of production data for a randomly generated new permeability field using the reservoir numerical simulator MRST and the prediction results using the proxy model of the present invention are shown. It can be seen that the proxy model of the present invention can accurately predict the corresponding production data, which is basically consistent with the results of the reservoir numerical simulator, which also illustrates the effectiveness of the reservoir simulation proxy model based on graph neural network of the present invention. In addition, from the efficiency comparison, the time required to solve a permeability field input using the reservoir numerical simulator MRST is 22.77 seconds, while the proxy model of the present invention only takes 0.4281 seconds to predict production data for 100 sets of different permeability field inputs, indicating that the proxy model of the present invention is significantly higher in forward computing efficiency than the numerical simulator.

[0073] Finally, it should be noted that the purpose of disclosing the embodiments is to facilitate a further understanding of the present invention. However, those skilled in the art will appreciate that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the contents disclosed in the embodiments; the scope of protection claimed by the present invention shall be determined by the scope defined in the claims.

Claims

1. A method for constructing a reservoir simulation agent model based on graph neural network, characterized in that: The construction method comprises the following steps: 1) Establish the original reservoir model: An original reservoir model is established for the reservoir using a reservoir numerical simulator, including discretized grids and nodes. The original reservoir model discretizes the reservoir using a regular or irregular grid to obtain a discretized grid, with the center of the grid serving as a node, and the node coordinates are obtained. 2) Select the parameters of interest: Select the parameters of interest when building the proxy model, namely the input parameters and output parameters of the proxy model; the input parameters are spatial distribution data that changes with space, and the output parameters are time series data that changes with time; 3) Generate input parameters: Randomly generate multiple different sets of realizations for the input parameters selected in step 2), where each set of realizations represents a distribution of input parameter values; 4) Get training data: Inputting the multiple sets of realizations of the input parameters generated in step 3) into the original reservoir model established in step 1), respectively, running the reservoir numerical simulator, and calculating the output parameter calculation results corresponding to different input parameter realizations; a set of input parameter realizations and the corresponding output parameter calculation results constitute a data pair, and multiple sets of data pairs constitute a training data set, and the calculation result of each output parameter is a time series that changes over time, and the sequence length is the total number of simulation time steps; 5) Build the proxy model: (1) Building a graph neural network: Based on the discretized grid and node coordinates in step 1), each node is connected to the N nearest nodes to form edges, where N is a natural number. Nodes and edges together form a graph structure. An adjacency matrix is ​​constructed to describe the graph structure. The elements in the adjacency matrix represent the weights of the connections between nodes. The specific calculation method is as follows: Among them, z i and z j Respectively represent the node coordinates of two different nodes in the graph structure; W ij Indicates that the node coordinates in the matrix are z i and z j The connection weight between two nodes; σ is the normalization coefficient, which is the mean of the distances between all nodes; Based on the obtained adjacency matrix, an existing open source deep learning library is used to build a Chebyshev network (ChebNet) for the graph structure. ChebNet is a graph neural network based on Chebyshev polynomials. ChebNet is used as the graph neural network. The graph neural network is used to extract spatial information and perform dimensionality reduction on the spatially distributed input parameters through graph convolution, and the output is a latent variable column vector. (2) Processing latent variable column vector: The obtained latent variable column vector is copied to the same length as the total number of simulation time steps in step 4). And the copied latent variable column vectors are spliced ​​together to form the copied and spliced ​​time series; (3) Build a long short-term memory LSTM network: Use the existing open source deep learning library to build an LSTM network, with the input being the copied and spliced ​​time series and the output being the time series of the calculated results of the output parameters; (4) Establishing an agent model: By combining the graph neural network and the LSTM network, a proxy model for reservoir simulation is constructed. In the constructed proxy model, the input parameters are passed through the graph neural network to obtain a latent variable column vector. The latent variable column vector is copied and concatenated before being passed to the LSTM network. Finally, the LSTM network outputs a time series of the calculated output parameter results. This is the forward computation process of the constructed proxy model. 6) Training the agent model: The proxy model established in step 5) is trained using the training dataset obtained in step 4). The number of training iterations is set, and an optimization algorithm is used to minimize the gap between the model's predicted output and the true value. After the pre-set number of iterations is reached, the training of the proxy model is completed, resulting in a trained proxy model. 7) Prediction output parameters: The new input parameters are input into the trained proxy model to obtain the calculation results of the corresponding output parameters, thus realizing direct prediction of the output parameters.

2. The construction method according to claim 1, wherein In step 1), the irregular grid in the original reservoir model adopts: a triangular grid or a perpendicular bisector parallel PEBI grid.

3. The construction method according to claim 1, wherein In step 2), the input parameters are reservoir permeability and / or porosity, and the output is one or more of the oil production rate, water production rate, bottom hole pressure of the reservoir production well, and the water injection rate and bottom hole pressure of the water injection well.

4. The construction method according to claim 1, wherein In step 3), the number of groups of realizations generated by input parameters is no less than 100.

5. The construction method according to claim 1, wherein: In step 6), the optimization algorithm adopts one of stochastic gradient descent, adaptive moment estimation, adaptive gradient and root mean square transfer algorithm.

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