CN114462262A - History fitting prediction method based on dual dimensionality of time and space - Google Patents

History fitting prediction method based on dual dimensionality of time and space Download PDF

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CN114462262A
CN114462262A CN202111486219.3A CN202111486219A CN114462262A CN 114462262 A CN114462262 A CN 114462262A CN 202111486219 A CN202111486219 A CN 202111486219A CN 114462262 A CN114462262 A CN 114462262A
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姚为英
冯高城
尹彦君
任宜伟
张海勇
孟培伟
张凯
严侠
王晓雅
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China National Offshore Oil Corp CNOOC
CNOOC Energy Technology and Services Ltd
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CNOOC Energy Technology and Services Ltd
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Abstract

The invention provides a history fitting prediction method based on dual dimensionality of time and space, wherein input data of a sample are a permeability field image and a relative permeability vector, and output data are a saturation field image and a pressure field image of a plurality of time stepsAnd (3) mixing the sample library with the following ratio: 1, dividing a training set and a test set in proportion; constructing a proxy model based on a deep convolutional encoder decoder neural network, considering dual dimensionality of time and space, and capturing a complex nonlinear mapping relation between input data and output data; training the constructed neural network model in the training set; using the root mean square error RMSE and the decision coefficient R in the test sample set2Evaluating the performance of the trained agent model; and optimizing the proxy model by a method of adding constraint on the well point on a loss function of the neural network model, and further calculating the oil well yield by using the Peacheman model according to the predicted pressure value and saturation value of the well point. The method greatly shortens the oil reservoir production prediction time.

Description

History fitting prediction method based on dual dimensionality of time and space
Technical Field
The invention relates to the technical field of artificial intelligence and machine learning, in particular to a history fitting prediction method based on dual dimensionality of time and space.
Background
The reservoir history fitting is based on a preliminary geological model, and model parameters such as permeability, relative permeability and the like are adjusted by using dynamic monitoring data such as a production curve and the like, so that a numerical simulation result is matched with the reservoir production history, and the established geological model is similar to a real reservoir model. The history fitting is the basis for optimizing subsequent oil reservoir production measures and has an important role in oil field development. History fitting is a computationally expensive problem because it requires running the reservoir numerical simulator multiple times to perform forward calculations during history fitting. For complex reservoirs, the grid variation of the reservoir model is up to millions or tens of millions, hours or even days are needed for one numerical simulation, and a plurality of simulations are needed to be run in the history fitting process, so that a great deal of time is needed for the process.
In recent years, along with the rapid development of big data and artificial intelligence industries, the intelligent construction of the petroleum industry is also steadily advancing, and the accumulation of a large amount of oil field production data provides a new idea for reservoir production prediction. The neural network agent model is adopted to replace an oil reservoir numerical simulator, so that the machine learning method can effectively save prediction time and improve prediction speed, and becomes a research hotspot at home and abroad. The main function of the proxy model is to search the intrinsic functions of geological parameters such as permeability parameters and model dynamic responses such as saturation distribution change yield change and the like, extract features from input data and then establish the mapping relation between model input data and model output data.
The existing oil reservoir production agent model can only consider spatial data, such as parameters changing along with space, such as permeability fields, irregular boundaries, effective grids and the like, and the processing method is to regard the spatial data as images, specifically express numerical values as pixel values on the images, and then adopt an image-to-image regression method for processing. Fluid parameters such as relative permeability, viscosity, gravity, etc. which do not vary spatially cannot be processed by the above-described methods.
Disclosure of Invention
The invention overcomes the defects in the prior art, the existing oil reservoir production agent model only can consider spatial data, the oil reservoir production agent model cannot be adopted for parameters changing along with space, and the traditional oil reservoir numerical simulation production prediction has the defects of more grids, large calculation amount and long time consumption.
The purpose of the invention is realized by the following technical scheme.
A history fitting prediction method based on dual dimensionality of time and space is carried out according to the following steps:
step 1, constructing a sample library by using a numerical simulator: the input data of the sample are a permeability field image and a relative permeability vector, the output data are a saturation field image and a pressure field image of a plurality of time steps, and the sample library is expressed by 3: 1, dividing a training set and a test set in proportion;
step 2, constructing a proxy model based on a neural network of a decoder of the depth convolution encoder, considering dual dimensionality of time and space, and capturing a complex nonlinear mapping relation between input data and output data;
step 3, training the constructed neural network model in the training set;
step 4, using the root mean square error RMSE and the decision coefficient R in the test sample set2Evaluating the performance of the trained agent model;
and 5, optimizing the proxy model by a method of adding constraint on the well point on a loss function of the neural network model, and further calculating the oil well yield by using the Peacheman model according to the pressure value and the saturation value of the well point obtained through prediction.
The specific method of step 1: using an open source packet SGeMS to generate a permeability field image, using a power law model to generate relative permeability vectors with the same quantity, using a numerical simulator to calculate an oil-water two-phase flow equation of an oil reservoir, wherein the calculation principle is a finite element and finite volume principle, inputting data, namely the permeability field image and the corresponding relative permeability vector, calculating to obtain corresponding saturation field images and pressure field images at multiple time steps, using the calculated data as a model label, and using the input and output data pair according to the ratio of 3: a scale of 1 divides the training data set and the test data set.
The specific method of step 2:
step 2.1, establishing a mapping relation between input and output: y ═ f (x, θ)
Wherein: y represents the output data-saturation field and pressure field images at multiple time steps, x represents the input data-permeability field images and relative permeability field vectors,
Figure BDA0003396673530000021
Ncthe equations governing the oil-water flow system are solved in a regular grid, N, representing the number of channelsHAnd NWRepresenting the height and width of a spatial domain, namely the number of grids in the horizontal direction and the longitudinal direction of each sample image, and representing model parameters including convolution kernel weight, scaling translation parameters and the like by theta;
step 2.2, designing a neural network model of a deep convolutional coder decoder to capture the mapping relation: the network selects a dense connection convolutional neural network (DenseNet), which is proved to have a cascade characteristic structure so as to effectively relieve the gradient disappearance problem, and the calculation steps of the neural network model are as follows: firstly, inputting input data into a convolutional layer (Conv) of an encoder network, performing convolution operation on an image by each convolutional core in a sliding mode from left to right and from top to bottom to extract input features, further extracting the features from an extracted feature map into the encoder network consisting of a plurality of dense blocks and a down-sampling connecting layer, after the feature extraction is completed, enabling the feature map to enter a decoder network consisting of a plurality of dense blocks and an up-sampling connecting layer to gradually restore feature images, and directly outputting a reconstructed image from the last layer in the decoder network.
The specific method of step 3:
step 3.1, aiming at all samples in the training data set, carrying out forward calculation on input data by a neural network to obtain the calculation output of a neural network model;
step 3.2, using a regularization MSE function to carry out error comparison between the calculation result of the neural network model and the calculation result of the numerical simulation, wherein the MSE loss function value is as follows:
Figure BDA0003396673530000031
wherein n is the total number of training set samples, yiAnd
Figure BDA0003396673530000032
respectively the ith gridCalculating results of the medium numerical simulator and the neural network model;
and 3.3, updating the iterative weights of the network model by adopting a back propagation and gradient descent algorithm according to the MSE error calculated in the step 2 until the preset training times are reached or the error is smaller than the expected value, stopping the iterative updating of the weights, and storing the trained neural network model.
The specific method of step 4: using the test set to verify the performance of the trained neural network model, the loss value of the Root Mean Square Error (RMSE) and the decision coefficient R2Is used for evaluating the performance of the system, and the specific calculation formula is as follows:
Figure BDA0003396673530000033
wherein n is the total number of training set samples, yiAnd
Figure BDA0003396673530000034
RMSE was used to measure L between two images, the result of the numerical simulator in the ith mesh and the result of the neural network model, respectively2The closer the distance and the value are to 0, the higher the similarity between two images, and the decision coefficient is an important index for measuring the linear correlation relationship between two variables:
Figure BDA0003396673530000035
wherein n is the total number of training set samples, yiAnd
Figure BDA0003396673530000036
the calculation results of a plurality of time steps of the numerical simulator in the ith grid and the calculation results of the neural network model are respectively, and the closer the value is to 1, the better the linear correlation between the two variables is.
The specific method of step 5: and calculating the yield of the production well according to the saturation value and the pressure value of the well point obtained by calculation of the neural network model, wherein the calculation is based on a Peaceman model, and the calculation formula is as follows:
Figure BDA0003396673530000041
wherein k isiIs the absolute permeability, k, of the ith meshr,αIs the relative permeability of water or oil, S, at the ith cellw,iIs the value of water saturation at the ith grid, Δ z is the grid width, PiAnd PwellRespectively the pressure at the ith grid and the wellbore pressure,
Figure BDA0003396673530000042
Δ x and Δ y are the widths of the model mesh in both x and y directions, rwIs the borehole radius, μαIs the viscosity of water or oil.
In order to obtain more accurate yield calculation results, a correction method is proposed, namely constraints at the well are added on the basis of a neural network model loss function, and the modified loss function formula is as follows:
Figure BDA0003396673530000043
wherein n is the total number of training set samples, m is the number of wells in the model, yiAnd
Figure BDA0003396673530000044
the calculation results of a plurality of time steps of the numerical simulator in the ith grid and the calculation result of the neural network model are respectively obtained, w is the weight coefficient of the constraint phase, and the specific numerical value of the weight coefficient is obtained by a grid searching method.
The invention has the beneficial effects that: according to the invention, by constructing a proxy model of the oil-water two-phase flow physical problem, the mapping of the saturation and the pressure field from the permeability field and the relative permeability vector to a plurality of time steps can be realized, and further the production well yield can be calculated; compared with the traditional numerical reservoir simulation method based on a finite element or finite volume principle, the method can realize reservoir production prediction with similar precision and greatly improved speed, thereby saving a great deal of time for the reservoir history fitting process; compared with the existing agent model method, the method can take more geological parameters into consideration, is more consistent with the actual oil deposit, and the more the input parameters are considered, the more the parameter key constraint relation is, and the more accurate the agent model prediction result is.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a deep convolutional encoder decoder network structure;
FIG. 3 is a dense block diagram;
FIG. 4 is a diagram of a middle layer structure of a dense block;
FIG. 5 is a view of a connection layer structure;
FIG. 6 is a plot of saturation real field, prediction field, and error contrast;
FIG. 7 is a graph of pressure true field, predicted field, and error versus;
FIG. 8 is a comparison graph of true production from a production well, proxy model predicted production, and corrected proxy model production;
FIG. 9 is a graph of the effect of mean square error;
fig. 10 is a correlation coefficient effect graph.
Detailed Description
The technical solution of the present invention is further illustrated by the following specific examples.
Example (b):
referring to fig. 1, the history fitting prediction method based on the dual dimensions of time and space comprises the following steps:
step one, a sample library is constructed by using a numerical simulator. The input data of the sample are a permeability field image and a relative permeability vector, and the output data are a saturation field image and a pressure field image of a plurality of time steps. The sample library was read at 3: the scale of 1 divides the training set and the test set. The specific method comprises the following steps:
permeability field images were generated using an open source packet SGeMS, and equal numbers of relative permeability vectors were generated using a power law model. The numerical simulator is used for calculating the oil-water two-phase flow equation of the oil reservoir, and the calculation principle is a finite element and finite volume principle. And inputting data, namely the permeability field image and the corresponding relative permeability vector thereof, calculating to obtain a corresponding saturation field image and a corresponding pressure field image, and using the calculated data as a model label. And the input and output data are input and output according to the following ratio of 3: a scale of 1 divides the training data set and the test data set.
And step two, constructing a proxy model based on a neural network of a decoder of the depth convolution encoder, considering time and space dimensions, and capturing a complex nonlinear mapping relation between input data and output data. The specific method comprises the following steps:
and 2.1, establishing a mapping relation between input and output.
y＝f(x,θ)
Where y represents the output data-saturation field and pressure field images, x represents the input data-permeability field images and relative permeability field vectors,
Figure BDA0003396673530000051
Ncthe equations governing the oil-water flow system are solved in a regular grid, N, representing the number of channelsHAnd NWThe height and width of the spatial domain, i.e. the number of grids in the horizontal direction and the vertical direction of each sample image, and theta represents model parameters including convolution kernel weight, scaling translation parameters, and the like.
And 2.2, designing a neural network model of the deep convolutional coder decoder to capture the mapping relation. The network selects a dense connection convolutional neural network (DenseNet), which is shown in fig. 2, and thus it is proved that the gradient vanishing problem can be effectively alleviated due to the cascade characteristic structure. The neural network model calculation steps are as follows: input data is first input into convolutional layers (Conv) of the encoder network, each convolutional core convolving the image in a sliding manner from left to right and from top to bottom to extract input features. The extracted feature map further enters the coding network composed of a plurality of dense blocks shown in fig. 3 and 4 and the downsampled connection layer shown in fig. 5 to further extract features. After the feature extraction is finished, the feature image enters a decoder network consisting of a plurality of dense blocks and an up-sampling connection layer, and the feature image is gradually restored. The last layer in the decoding network directly outputs the reconstructed image.
And step three, training the constructed neural network model in the training set. The specific method comprises the following steps:
and 3.1, aiming at all samples in the training data set, carrying out forward calculation on input data by the neural network to obtain the calculation output of the neural network model.
Step 3.2, using a regularization MSE function to carry out error comparison between the calculation result of the neural network model and the calculation result of the numerical simulation, wherein the MSE loss function value is as follows:
Figure BDA0003396673530000061
wherein n is the total number of training set samples, yiAnd
Figure BDA0003396673530000062
respectively are the calculation result of the numerical simulator in the ith grid and the calculation result of the neural network model.
And 3.3, performing iterative weight updating of the network model by adopting a back propagation and gradient descent algorithm according to the MSE error obtained by calculation in the second step until the preset training times are reached or the error is smaller than the expected value, and stopping the iterative updating of the weight. And saving the trained neural network model.
Step four, using the root mean square error RMSE and the decision coefficient R in the test sample set2And evaluating the performance of the trained agent model. The specific method comprises the following steps:
the performance of the trained neural network model is verified using the test set. Root Mean Square Error (RMSE) loss value and decision coefficient R2Is used to evaluate its performance. The specific calculation formula is as follows:
Figure BDA0003396673530000063
wherein n is the total number of training set samples, yiAnd
Figure BDA0003396673530000064
respectively are the calculation result of the numerical simulator in the ith grid and the calculation result of the neural network model. RMSE is used to measure L between two images2The closer the distance, value, is to 0, the higher the two images are similar. The decision coefficient is an important index for measuring the linear correlation between two variables.
Figure BDA0003396673530000065
Wherein n is the total number of training set samples, yiAnd
Figure BDA0003396673530000066
respectively are the calculation result of the numerical simulator in the ith grid and the calculation result of the neural network model. The closer the value is to 1, the better the linear correlation between the two variables.
And fifthly, optimizing the proxy model by a method of adding constraint on the well point on a loss function of the neural network model, and further calculating the oil well yield by using the Peacheman model according to the predicted pressure value and saturation value of the well point. The specific method comprises the following steps:
and calculating the yield of the production well according to the saturation value and the pressure value of the well point obtained by calculation of the neural network model, wherein the calculation is based on a Peaceman model, and the calculation formula is as follows:
Figure BDA0003396673530000071
wherein k isiIs the absolute permeability, k, of the ith meshr,αIs the relative permeability of water or oil, S, at the ith cellw,iIs the value of water saturation at the ith grid, Δ z is the grid width, PiAnd PwellRespectively the pressure at the ith grid and the wellbore pressure,
Figure BDA0003396673530000072
Δ x and Δ y are the widths of the model mesh in both x and y directions, rwIs the borehole radius, μαIs the viscosity of water or oil.
In order to obtain more accurate yield calculation results, a correction method is proposed, namely constraints at the well are added on the basis of a neural network model loss function, and the modified loss function formula is as follows:
Figure BDA0003396673530000073
wherein n is the total number of training set samples, m is the number of wells in the model, yiAnd
Figure BDA0003396673530000074
the calculation results of the numerical simulator in the ith grid and the calculation results of the neural network model are respectively obtained, w is the weight coefficient of the constraint phase, and the specific numerical value is obtained by a grid searching method.
The advantages of the present invention can be further illustrated by the following experiments:
1. conditions of the experiment
The oil field block is provided with 5 wells, wherein 1 water injection well and 4 production wells, the well position layout adopts a reverse five-point method mode, and the wells are all mined in a full-jet open mode. The experiment adopts constant pressure exploitation, and the bottom hole flowing pressure is fixed. The permeability field size is 60 x 60 with a relative permeability dimension of 6. The experiment generates 2000 samples, 1500 samples are used for training, and 500 samples are used for testing. The example outputs saturation field and pressure field images of 60 × 60 at 15 time steps, each time step being 360 days, by training the neural network proxy model of the deep convolutional encoder decoder.
2. Results of the experiment
The output results are displayed by selecting 5 plots in 15 time steps. FIG. 6 is a graph comparing the results of a numerical simulation calculation of the saturation field of a sample of a test set, which is randomly drawn in the test set, with the results of a prediction by a surrogate model; FIG. 7 is a graph comparing the results of the numerical simulation calculation of the saturation field of the sample with the results of the proxy model prediction; FIG. 8 is a comparison graph of the real production well yield, the proxy model predicted yield, and the corrected proxy model yield of the sample; FIG. 9 is a plot of the effect of mean square error for the entire test set; fig. 10 is a graph of correlation coefficient effects for all test sets. It can be observed from the figure that the error gradually stabilizes and reaches a lower level with the iterative training, and the decision coefficient gradually increases to a constant value with the increase of the number of iterations.
The invention has been described in an illustrative manner, and it is to be understood that any simple variations, modifications or other equivalent changes which can be made by one skilled in the art without departing from the spirit of the invention fall within the scope of the invention.

Claims (7)

1. A history fitting prediction method based on dual dimensionality of time and space is characterized in that: the method comprises the following steps:
step 1, constructing a sample library by using a numerical simulator: the input data of the sample are permeability field images and relative permeability vectors, the output data are saturation field images and pressure field images of a plurality of time steps, and a sample library is divided into 3: 1, dividing a training set and a test set in proportion;
step 2, constructing a proxy model based on a neural network of a decoder of the depth convolution encoder, considering dual dimensionality of time and space, and capturing a complex nonlinear mapping relation between input data and output data;
step 3, training the constructed neural network model in the training set;
step 4, using the root mean square error RMSE and the decision coefficient R in the test sample set2Evaluating the performance of the trained agent model;
and 5, optimizing the proxy model by a method of adding constraint on the well point on a loss function of the neural network model, and further calculating the oil well yield by using the Peacheman model according to the pressure value and the saturation value of the well point obtained through prediction.
2. The method of claim 1, wherein the prediction method comprises: the specific method of step 1: using an open source packet SGeMS to generate a permeability field image, using a power law model to generate relative permeability vectors with the same quantity, using a numerical simulator to calculate an oil-water two-phase flow equation of an oil reservoir, wherein the calculation principle is a finite element and finite volume principle, inputting data, namely the permeability field image and the corresponding relative permeability vector, calculating to obtain corresponding saturation field images and pressure field images at multiple time steps, using the calculated data as a model label, and using the input and output data pair according to the ratio of 3: a scale of 1 divides the training data set and the test data set.
3. The method of claim 1, wherein the prediction method comprises: the specific method of step 2:
step 2.1, establishing a mapping relation between input and output: y ═ f (x, θ)
Wherein: y represents the output data-saturation field and pressure field images at multiple time steps, x represents the input data-permeability field images and relative permeability field vectors,
Figure FDA0003396673520000011
Ncthe equations governing the oil-water flow system are solved in a regular grid, N, representing the number of channelsHAnd NWRepresenting the height and width of a spatial domain, namely the number of grids in the horizontal direction and the longitudinal direction of each sample image, and representing model parameters including convolution kernel weight, scaling translation parameters and the like by theta;
step 2.2, designing a neural network model of a deep convolutional coder decoder to capture the mapping relation: the network selects a dense connection convolutional neural network (DenseNet), which is proved to have a cascade characteristic structure so as to effectively relieve the gradient disappearance problem, and the calculation steps of the neural network model are as follows: firstly, inputting input data into a convolutional layer (Conv) of an encoder network, performing convolution operation on an image by each convolutional core in a sliding mode from left to right and from top to bottom to extract input features, further extracting the features from an extracted feature map into the encoder network consisting of a plurality of dense blocks and a down-sampling connecting layer, after the feature extraction is completed, enabling the feature map to enter a decoder network consisting of a plurality of dense blocks and an up-sampling connecting layer to gradually restore feature images, and directly outputting a reconstructed image from the last layer in the decoder network.
4. The method of claim 1, wherein the prediction method comprises: the specific method of step 3:
step 3.1, aiming at all samples in the training data set, carrying out forward calculation on input data by a neural network to obtain the calculation output of a neural network model;
step 3.2, using a regularization MSE function to carry out error comparison between the calculation result of the neural network model and the calculation result of the numerical simulation, wherein the MSE loss function value is as follows:
Figure FDA0003396673520000021
wherein n is the total number of training set samples, yiAnd
Figure FDA0003396673520000022
respectively calculating results of the numerical simulator in the ith grid and the neural network model;
and 3.3, updating the iterative weights of the network model by adopting a back propagation and gradient descent algorithm according to the MSE error calculated in the step 2 until the preset training times are reached or the error is smaller than the expected value, stopping the iterative updating of the weights, and storing the trained neural network model.
5. The method of claim 1, wherein the prediction method is based on dual time and space dimensionsThe method is characterized in that: the specific method of step 4: using the test set to verify the performance of the trained neural network model, the loss value of the Root Mean Square Error (RMSE) and the decision coefficient R2Is used for evaluating the performance of the system, and the specific calculation formula is as follows:
Figure FDA0003396673520000023
wherein n is the total number of training set samples, yiAnd
Figure FDA0003396673520000024
RMSE was used to measure L between two images, the result of the numerical simulator in the ith mesh and the result of the neural network model, respectively2The closer the distance and the value are to 0, the higher the similarity between two images, and the decision coefficient is an important index for measuring the linear correlation relationship between two variables:
Figure FDA0003396673520000025
wherein n is the total number of training set samples, yiAnd
Figure FDA0003396673520000026
the calculation results of a plurality of time steps of the numerical simulator in the ith grid and the calculation results of the neural network model are respectively, and the closer the value is to 1, the better the linear correlation between the two variables is.
6. The method of claim 1, wherein the prediction method comprises: the specific method of step 5: and calculating the yield of the production well according to the saturation value and the pressure value of the well point obtained by calculation of the neural network model, wherein the calculation is based on a Peaceman model, and the calculation formula is as follows:
Figure FDA0003396673520000031
wherein k isiIs the absolute permeability, k, of the ith meshr,αIs the relative permeability of water or oil, S, at the ith cellw,iIs the value of water saturation at the ith grid, Δ z is the grid width, PiAnd PwellRespectively the pressure at the ith grid and the wellbore pressure,
Figure FDA0003396673520000032
Δ x and Δ y are the widths of the model mesh in both x and y directions, rwIs the borehole radius, μαIs the viscosity of water or oil.
7. The method of claim 6, wherein the prediction method comprises: correction method of calculation formula: adding the constraint at the well hole on the basis of the neural network model loss function, and the modified loss function formula is as follows:
Figure FDA0003396673520000033
wherein n is the total number of training set samples, m is the number of wells in the model, yiAnd with
Figure FDA0003396673520000034
The calculation results of a plurality of time steps of the numerical simulator in the ith grid and the calculation result of the neural network model are respectively obtained, w is the weight coefficient of the constraint phase, and the specific numerical value of the weight coefficient is obtained by a grid searching method.
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Cited By (2)

* Cited by examiner, † Cited by third party
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CN115204530A (en) * 2022-09-16 2022-10-18 中科数智能源科技(深圳)有限公司 Oil reservoir prediction method based on Fourier neural operator and cyclic neural network
CN115204531A (en) * 2022-09-16 2022-10-18 中科数智能源科技(深圳)有限公司 Oil reservoir prediction method, device and medium based on Fourier nerve operator

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115204530A (en) * 2022-09-16 2022-10-18 中科数智能源科技(深圳)有限公司 Oil reservoir prediction method based on Fourier neural operator and cyclic neural network
CN115204531A (en) * 2022-09-16 2022-10-18 中科数智能源科技(深圳)有限公司 Oil reservoir prediction method, device and medium based on Fourier nerve operator
CN115204531B (en) * 2022-09-16 2022-12-27 中科数智能源科技(深圳)有限公司 Oil reservoir prediction method, equipment and medium based on Fourier neural operator

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