CN114693005A - Three-dimensional underground oil reservoir dynamic prediction method based on convolution Fourier neural network - Google Patents
Three-dimensional underground oil reservoir dynamic prediction method based on convolution Fourier neural network Download PDFInfo
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Abstract
The invention discloses a three-dimensional underground oil reservoir dynamic prediction method based on a convolution Fourier neural network, which belongs to the technical field of oil reservoir engineering, and dynamically predicts the residual oil saturation or pressure of the three-dimensional underground oil reservoir by utilizing a constructed 3D convolution Fourier neural network model, and specifically comprises the following steps: collecting three-dimensional underground oil reservoir data; constructing a 3D convolution Fourier neural network, and considering time and space information simultaneously by combining with LSTM; setting hyper-parameters of a convolution Fourier network model, and training a 3D convolution Fourier network model; evaluating the performance of the 3D convolutional Fourier neural network; and after the training is finished, outputting a 3D convolution Fourier network model with good test indexes. The method realizes high-precision rapid prediction of the three-dimensional oil reservoir model, well aims at the characteristics of the space-time property and the physical system of the three-dimensional oil reservoir, and better meets the actual field requirements.
Description
Technical Field
The invention belongs to the technical field of oil reservoir engineering, and particularly relates to a three-dimensional underground oil reservoir residual oil saturation or pressure production dynamic prediction method based on a 3D convolution Fourier neural network model.
Background
Numerical simulation of multiphase flow in porous media is critical to many geoscience applications. In the field of oil reservoir engineering, an oil-water two-phase partial differential equation can accurately describe an underground flow system, and a large amount of partial differential equation solution calculation is needed for simulating underground flow, which is also the basis of a numerical simulation technology. The traditional numerical simulation solves partial differential equations based on numerical calculation methods such as finite element method, finite difference method and the like. The reservoir numerical simulation can accurately calculate reservoir states of future reservoirs such as pressure, saturation, yield and the like for dynamic evaluation of production development. The number of real three-dimensional oil reservoir models is large, the models are large and the boundaries are complex, and a large amount of time and computing resources are consumed for solving.
With the deepening of informatization and the continuous development of hardware level, artificial intelligent methods such as deep learning and the like are widely applied to scenes such as image recognition, target detection and the like. In the field of oil reservoir engineering, a data-driven machine learning method provides a faster alternative scheme for a traditional simulator by constructing a neural network proxy model. The mapping between the machine learning agent model and the numerical simulation data provides a faster choice for the traditional simulator, and the prediction time can be effectively saved. Most of the current popular agent model methods are directed at two-dimensional oil reservoirs, more grids are formed for a three-dimensional complex geological model, and meanwhile, the gravity influence is considered, and an oil well penetrates through a plurality of areas. Therefore, the three-dimensional oil reservoir prediction is more challenging and more practical than the two-dimensional oil reservoir prediction. Some existing methods applied to three-dimensional models only consider local information among images, but cannot consider physical information and space-time characteristics, and have the limitations of low precision, poor generalization performance, slow training time and the like.
Disclosure of Invention
Aiming at the problems that the residual oil saturation or pressure prediction time is too long when numerical reservoir simulation is used at present, a common machine learning agent model cannot effectively predict a three-dimensional complex oil reservoir and the like, the invention provides a production dynamic prediction method of the residual oil saturation or pressure of the three-dimensional oil reservoir based on a convolution Fourier neural network model, and the influence of the time-space property, the physical information and the gravity factor of the three-dimensional oil reservoir is considered, so that the prediction precision is effectively improved, the method is suitable for different oil reservoir conditions, and the calculation time is saved.
The technical scheme of the invention is as follows:
a three-dimensional underground oil reservoir dynamic prediction method based on a convolution Fourier neural network utilizes a built 3D convolution Fourier neural network model to dynamically predict the residual oil saturation or pressure of the three-dimensional underground oil reservoir, and specifically comprises the following steps:
step 1, collecting three-dimensional underground oil reservoir data, generating a three-dimensional permeability field according with geological characteristics by using an SGeMS geological statistical tool, solving saturation or pressure within a period of time corresponding to different permeabilities by using a numerical simulator as a sample library, dividing a data set according to a proportion, taking the permeability as input, and taking the saturation or pressure as output;
step 2, constructing a 3D convolution Fourier neural network, combining 3D convolution and Fourier transform, extracting image local information by using a 3D convolution operator, extracting a physical information approximate differential operator by using Fourier transform, and adding gravity constraint in the network; mapping from permeability to an oil reservoir state is realized by utilizing a coding and decoding network, and time and space information is considered simultaneously by combining with an LSTM;
step 3, setting hyper-parameters of the convolution Fourier network model, and training the 3D convolution Fourier network model under a training set;
step 4, evaluating the performance of the 3D convolution Fourier neural network by using the test set, and calculating the relative error between RMSE and the quantized saturation or pressure;
Further, the specific process of step 1 is as follows:
step 1.1, collecting three-dimensional underground oil reservoir data, generating a three-dimensional permeability field by using an SGeMS geological statistical model, wherein the grid size is 40 multiplied by 20, and generating 2000 permeability samples;
step 1.2, calculating an oil-water two-phase flow equation of the three-dimensional oil reservoir system by using a finite element method through a numerical simulator to obtain saturation or pressure results in all grid blocks; the oil reservoir underground oil-water flow system is three-dimensional, needs to consider the gravity effect, and consists of a mass conservation equation (1) and a facies Darcy velocity equation (2);
the mass conservation equation is expressed as (1),
wherein the content of the first and second substances,
representing a gradient operator;jindicating different phases, including oil and water phases,oby which is meant an oil,wrepresents water;
represents the density of the phase;v j represents the phase darcy speed;
representing source/sink items, superscriptlRepresenting a parameter at the well;
represents porosity;S j represents the saturation of the phase;trepresents time;
the expression of the facies darcy velocity equation is shown as (2),
wherein the content of the first and second substances,k rj which is indicative of the relative permeability of the phases,
the absolute permeability vector is represented by the absolute permeability vector,
which represents the viscosity of the phase(s),p j the pressure of the phase is indicated and,gwhich is indicative of the force of gravity,zrepresenting a depth;
step 1.3, according to 8: 2, dividing the data set and the test set in proportion; the permeability of input data is a tensor of (n, nx, ny, nz,1), the saturation or pressure of output data is a tensor of (n, nx, ny, nz,1, T), n is the number of samples, nx is the number of horizontal grids, ny is the number of vertical grids, nz is the number of grids in the depth direction, and T is the number of time steps.
Further, the specific process of step 2 is as follows:
the 3D convolution Fourier neural network mainly comprises an encoding network and a decoding network, and a cyclic neural module which takes the time sequence influence into consideration and increases the processing time; the input parameter is a permeability field of a known observed value, and the output parameter is saturation or pressure in a future period of time;
the coding network structure comprises M3D convolutional Fourier layers, each of which is structured as follows,
wherein the content of the first and second substances,xis the initial input of the parameters that are,Wis the weight of the image,
is an activation function, activated using Relu;v N+1(x) Is a convolution Fourier moduleNThe output result of the +1 layer is,v N (x) Is thatNOutputting the result of the layer;
the product is a three-dimensional Fourier integral operator used for extracting physical information;
is a fast fourier transform of the signal to be processed,
is the inverse of the fourier transform,Cthe operation of cutting off Fourier series exceeding the maximum threshold value is carried out, and the Fourier transform operation can approximate the physical rule which is met by data through the Fourier series, namely a series of sine and cosine curves;Conv3Dthe convolution method is a 3D convolution result and is used for extracting local information, the size and the step of each layer of convolution kernel can be adjusted, the sizes of the convolution kernels are 3 multiplied by 3, and the convolution steps are 1 multiplied by 1 and 2 multiplied by 2; because the Fourier transform is infinite dimension mapping, the dimension of the result extracted by using the Fourier transform is required to be consistent with that of the convolution result, the original dimension cannot be changed after the addition, and the obtained final result enters a decoding network through five layers of Fourier layers;
the decoding network structure is composed of a deconvolution layer, the input of a part of layers of the decoding network is formed by copying and splicing the output matrix corresponding to the coding network and the current input, and the purpose is to store more information and prevent the loss of characteristics in the convolution process; the decoding network is a process of decoding the intermediate result to an original data space, and the obtained result is a pressure value or saturation of a certain time step;
considering the influence of time sequence, enabling intermediate results of a plurality of time steps input through a decoding network to pass through an LSTM structure, combining time sequence information, and obtaining an output result of each time step by using a corresponding decoding network for each feature map after LSTM processing;
LSTM intThe time of day is input three: state of the cellC t-1In a hidden layer stateh t-1Current input characteristicsx t ；
C t Carrying space-time information, the calculation formula is as follows,
wherein the content of the first and second substances,f t representing forgetting gate, controlling the state of discarded cellsC t-1Some of the information in (a);
represents a new candidate cell state that is,i t representative update Gate, selection of retained candidate cell State
Some of the information in (1);
hidden layer output resulth t From the output gateo t And calculated in the previous stepC t Calculated by the tanh activation function, as follows,
forgetting doorf t Updating doori t Output dooro t And novel candidate cell states
The calculation formula is as follows, each gate has its own weight and offset, in LSTM
Is a sigmoid activation function, the activation result is between (0, 1), and the tanh activation result is between (-1, 1);
wherein the content of the first and second substances,W f 、W i 、W o andW c weights corresponding to the forgetting gate, the updating gate, the output gate and the new candidate cell state are respectively set;b f 、b i 、b o andb c biases corresponding to the forgetting gate, the updating gate, the output gate and the new candidate cell state respectively;
inputting a permeability field, obtaining hidden layer variables through a convolution Fourier coding layer, and obtaining a prediction result of saturation or pressure simultaneously containing time information and space information through an LSTM structure and a decoding network
。
Further, the specific process of step 3 is as follows:
step 3.1, setting input and output of a 3D convolution Fourier network model; the input parameter is the permeability of the three-dimensional oil reservoir; setting an output value, and predicting the oil reservoir saturation or pressure distribution in a future period of time;
step 3.2, initializing the hyper-parameters, wherein the batch processing size is 8, the activation function uses a ReLu function, and randomly initializing the weightW(ii) a The super-parameters are optimized and adjusted according to network evaluation performance, the loss function uses an MSE function to calculate loss, and the MSE loss function value is as follows during pressure training: codec networks use the same hyper-parameter setTraining is carried out to converge within 200 epochs;
loss function of saturationloss sat_MSE The following were used:
wherein the content of the first and second substances,y sat_i and
are respectively the first in the training setiThe true value of the output saturation of each sample and the saturation calculation result of the 3D convolution Fourier neural network model,n train total number of samples in training set;
for vertical wells drilled through multiple zones, at depthdWellbore pressure at formation
The junction attraction force affected by the change in depth z; the wellbore pressure at the uppermost perforation, called bottom hole pressure, continues down with depthd+1 formation depth wellbore pressure
The calculation is as in equation (12),
is the difference in depth of the image,
is the fluid mix density;
when the 3D convolution Fourier network model predicts the pressure, considering that the pressure in the depth direction is influenced by the gravity action, the pressure satisfies equation (12),
loss function of pressureloss press_MSE The following were used:
wherein the content of the first and second substances,y press_i and
are respectively the first in the training setiThe real value of the output pressure of each sample and the pressure calculation result of the 3D convolution Fourier neural network model;
at the grid of wellsdThe actual value of wellbore pressure at +1 formation depth,
at the grid of wellsdPredicted wellbore pressure values for depth of layer;
are the coefficients of the data constraints that are,
is the coefficient of the equation constraint;
the network carries out forward propagation according to the set hyper-parameters and the network iterative structure;
step 3.3, performing back propagation according to the loss error calculated in the step 3.2, and updating the weight by using an ADAM optimizerWGradually reducing the MSE loss; the initial learning rate lr =0.003 of the ADAM optimization algorithm, the batch size is 8, and the mixing weight is 1000; this process is repeated, and after 200 epochs the error falls within the acceptance range and training is complete.
Further, the specific process of step 4 is as follows:
calculating relative Root Mean Square Error (RMSE) for all test samples, and quantifying the relative error of the predicted saturation or pressure;
the RMSE calculation formula is:
wherein the content of the first and second substances,n test the total number of samples in the test set;
predicting results for the model, including
And with
；y i Solving true values for numerical simulations, includingy sat_i Andy press_i ；
the formula for calculating the saturation or pressure relative error of the three-dimensional oil reservoir is as follows:
the relative error of saturation is
The relative error of the pressure is
，n test Is the total number of samples tested and,n M is the total number of the grids,n t is the number of time steps taken,
is the first to testiA sample ofmA gridtThe result of the prediction of the saturation at the time,
is the true value for the corresponding saturation;
is the first to testiA sample ofmA gridtThe result of the prediction of the pressure at the moment,
is the true value of the corresponding pressure; the pressure normalization is performed by subtracting the minimum pressure from the maximum pressure,
is the firstiA test specimentThe maximum pressure at the moment of time is,
is the firstiA test specimentThe minimum pressure at the moment.
Further, the specific process of step 5 is as follows:
storing a 3D convolution Fourier neural network model with better performance index evaluation, storing the trained weight and the super-parameter, and rapidly predicting the future saturation or pressure state of the three-dimensional oil reservoir by using the 3D convolution Fourier neural network model; the input is the permeability field of the three-dimensional reservoir and the output is a period of timetThe internal pressure and saturation distribution are input and output can be obtained through one-time forward propagation calculation;
the yield of the oil-water well is calculated by utilizing the pressure and the saturation through a peakeman model, the calculation formula is as follows,
wherein the content of the first and second substances,
is the firstmThe rate of injection/recovery of oil/water phase from wells in each grid,k m is as followsmThe absolute permeability of the individual grids is,k r j,is composed ofk m The corresponding oil/water relative permeability rates,S w m,is as followsmPersonal netThe value of the water-containing saturation at the grid,
is the thickness of the grid or grid,
by default, to
The reservoir has equal width in both x and y directions,r w is the radius of the borehole,
is the viscosity of the water or oil and,P m andP l are respectively the firstmPressure at each grid and wellbore pressure.
The invention has the following beneficial technical effects:
the invention provides a production dynamic prediction method based on residual oil saturation or pressure of a 3D (three-dimensional) convolution Fourier model, which is characterized in that a convolution Fourier layer is utilized to simultaneously extract local information and physical information, a coding and decoding network is utilized to realize the conversion from permeability to saturation or pressure, an LSTM (least squares) structure is adopted in the network to consider the time sequence problem, and spatial information and time information are simultaneously considered in a neural network. And adding constraints in the loss function by using a physical equation when predicting the pressure, and considering the influence of gravity factors on pressure change in a neural network. The method realizes high-precision rapid prediction of the three-dimensional oil reservoir model, well aims at the characteristics of the space-time property and the physical system of the three-dimensional oil reservoir, and better meets the actual field requirements.
Drawings
FIG. 1 is a schematic flow chart of a three-dimensional reservoir residual oil saturation or pressure production dynamic prediction method based on a 3D convolution Fourier neural network according to the invention;
FIG. 2 is a schematic structural diagram of a 3D convolutional Fourier neural network model of the present invention;
FIG. 3 is a schematic diagram of the structure of the convolutional Fourier layer of the present invention;
FIG. 4 is a schematic diagram of the combination of the codec structure and LSTM of the present invention;
FIG. 5 is a detailed schematic diagram of the LSTM structure of the present invention;
FIG. 6 is a graph of relative permeability in an experiment of the present invention;
FIG. 7 is a diagram illustrating the effect of mean square error RMSE in the experiment of the present invention;
FIG. 8 is a comparison of the actual and measured values of well production for production well 1 and production well 2 in the experiment of the present invention;
FIG. 9 is a comparison of the actual and measured well production for production wells 3 and 4 in the present invention experiment.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
according to the invention, a neural network proxy model is constructed through a 3D convolution Fourier neural network, local information and physical information are simultaneously extracted by utilizing a convolution Fourier layer, and the conversion from permeability to saturation or pressure is realized by utilizing a coding and decoding network. The method can well replace a numerical simulation method for the three-dimensional oil reservoir which accords with the field reality, and can quickly carry out the dynamic prediction of oil reservoir production. Compared with the existing proxy model, the method can better process the three-dimensional oil reservoir model, and has better prediction precision and generalization.
Referring to fig. 1, the invention provides a dynamic prediction method of a three-dimensional underground oil reservoir based on a convolution Fourier neural network, which dynamically predicts the residual oil saturation or pressure of the three-dimensional underground oil reservoir by using a constructed 3D convolution Fourier neural network model, and specifically comprises the following steps:
step 1, collecting three-dimensional underground oil reservoir data, generating a three-dimensional permeability field according with geological characteristics by using an SGeMS geological statistical tool, solving oil reservoir states, namely saturation or pressure, corresponding to different permeabilities within a period of time by using a numerical simulator to serve as a sample library, dividing a training test set data set in proportion, wherein the permeabilities serve as input, and the saturation or pressure serves as output.
The specific process is as follows:
step 1.1, collecting three-dimensional underground oil reservoir data, generating a three-dimensional permeability field by using an SGeMS geological statistical model, wherein the grid size is 40 multiplied by 20, and generating 2000 permeability samples.
And step 1.2, calculating an oil-water two-phase flow equation of the three-dimensional oil reservoir system by using a finite element method through a numerical simulator to obtain saturation or pressure results in all grid blocks. The oil reservoir underground oil-water flow system is three-dimensional, needs to consider the gravity effect, and consists of a mass conservation equation (1) and a phase Darcy velocity equation (2).
The mass conservation equation is expressed as (1),
wherein, the first and the second end of the pipe are connected with each other,
representing a gradient operator;jindicating different phases, including oil and water phases,oby which is meant an oil,wrepresents water;
represents the density of the phase;v j represents the phase darcy speed;
representing source/sink items (superscript)lRepresenting a parameter at the well);
represents porosity;S j represents the saturation of the phase;trepresents time;
the expression of the facies darcy velocity equation is shown as (2),
wherein the content of the first and second substances,k rj which represents the relative permeability of the phases,
the absolute permeability vector is represented by the absolute permeability vector,
which represents the viscosity of the phase(s),p j the pressure of the phase is indicated and,gwhich is indicative of the force of gravity,zindicating the depth.
Step 1.3, according to 8: 2 to divide the data set and test set. The permeability of input data is a tensor of (n, nx, ny, nz,1), the saturation or pressure of output data is a tensor of (n, nx, ny, nz,1, T), n is the number of samples, nx is the number of horizontal grids, ny is the number of vertical grids, nz is the number of grids in the depth direction, and T is the number of time steps.
And 2, constructing a 3D convolution Fourier neural network shown in the figures 2-5, combining the 3D convolution and Fourier transform, extracting image local information by using a 3D convolution operator, extracting a physical information approximate differential operator by using the Fourier transform, and adding gravity constraint in the network. And mapping from permeability to reservoir state is realized by utilizing a coding and decoding network, and finally, the saturation or pressure of a certain period of time in the future is output by combining with the LSTM and considering time and space information. The specific process is as follows:
the 3D convolution Fourier neural network mainly comprises an encoding network and a decoding network, and a recurrent neural module (RNN) which increases the processing time in consideration of the influence of time series. The input parameter is a known observed permeability field. The output parameter is the saturation or pressure for a future period of time.
The coding network structure contains M3D convolutional fourier layers, as shown in fig. 4, each of which is structured as follows.
Wherein the content of the first and second substances,xis the initial input of the parameters that are,Wis the weight of the image,
is an activation function, activated using Relu;v N+1(x) Is a convolution Fourier moduleNThe output result of the +1 layer is,v N (x) Is thatNAnd outputting the result of the layer.
The product is a three-dimensional fourier integration operator to extract the physical information.
Is a fast fourier transform of the signal to be processed,
is the inverse of the fourier transform,Cthe operation of truncating the Fourier series exceeding the maximum threshold value is adopted, and the Fourier transform operation can approximate the physical law which is accorded by the data through the Fourier series, namely a series of sine and cosine curves.Conv3DThe convolution kernel size and the step size of each layer are adjusted possibly, the convolution kernel size is 3 × 3 × 3, and the convolution step size is 1 × 1 × 1 and 2 × 2 × 2. Since the fourier transform is infinite dimension mapped, the result of using fourier extraction here needs to be consistent with the dimension of the convolution result, without changing the original dimension after addition, through five fourier layers, i.e. layers that do not contain the information in equation (3)Conv3DThe network layer of this operation will get the final result to the decoding network.
The decoding network is implemented by deconvolution transform, while combining the advantages of LSTM on analog time series transforms. The decoding network structure is composed of a deconvolution layer, the input of a part of layers of the decoding network is formed by copying and splicing the output matrix corresponding to the coding network and the current input, and the purpose is to store more information and prevent the loss of characteristics in the convolution process. The decoding network is a process of decoding the intermediate result to the original data space, and the obtained result is the pressure value or the saturation of a certain time step. Considering the influence of time series, the intermediate results of multiple time steps input through the decoding network are passed through the LSTM structure, which is shown in fig. 2, and the output result of each time step is obtained by applying the corresponding decoding network to each feature map after the LSTM processing, in combination with the time series information.
The iterative structure of the LSTM is shown in FIG. 5, the LSTM is attThe time of day is input three: state of the cellC t-1In a hidden layer stateh t-1Current input characteristicsx t 。
C t Carrying space-time information, the calculation formula is as follows,
wherein the content of the first and second substances,f t representing forgetting gate, controlling the state of discarded cellsC t-1Some of the information in (1);
represents a new candidate cell state that is,i t representative update gate, selecting to preserve candidate cell state
Some of the information in (1);
hidden layer output resulth t From the output gateo t And calculated in the previous stepC t Calculated by the tanh activation function, as follows,
forgetting doorf t Updating doori t Output dooro t And novel candidate cell states
The calculation formula is as follows, each gate has its own weight and offset, unlike other cases in the network, in LSTM
Is a sigmoid activation function, the activation result is between (0, 1), and the tanh activation result is between (-1, 1).
Wherein the content of the first and second substances,W f 、W i 、W o andW c weights corresponding to the forgetting gate, the updating gate, the output gate and the new candidate cell state are respectively set;b f 、b i 、b o andb c biases corresponding to the forgetting gate, the updating gate, the output gate and the new candidate cell state respectively;
inputting a permeability field, obtaining hidden layer variables through a convolution Fourier coding layer, and obtaining a prediction result of saturation or pressure simultaneously containing time information and space information through an LSTM structure and a decoding network
。
Fig. 3 shows the details of the specific coding and decoding structure of a single time step, firstly, local and physical information is extracted through 6 layers of fourier convolution layers, the dimension of the intermediate variable is changed, and then, the dimension is not changed through five layers of fourier layers. In the decoding structure, the output of the corresponding coding layer with the same size and the output of the last decoding layer are copied and spliced together. The final intermediate variables are decoded to obtain the prediction result at each time step. The specific change in the shape and size values is shown in Table 1.
And 3, setting hyper-parameters of the convolution Fourier network model, and training the 3D convolution Fourier network model under a training set. The specific process is as follows:
step 3.1, setting input and output of a 3D convolution Fourier network model; the input parameter is the permeability of the three-dimensional oil reservoir; setting an output value, and predicting the oil reservoir saturation or pressure distribution in a future period of time;
step 3.2, initializing the hyper-parameters, wherein the batch processing size is 8, the activation function uses a ReLu function, and randomly initializing the weightW(ii) a The super-parameters are optimized and adjusted according to network evaluation performance, the loss function uses an MSE function to calculate loss, and the MSE loss function value is as follows during pressure training: the coding and decoding network uses the same super parameter setting and trains to converge in 200 epochs;
loss function of saturationloss sat_MSE The following were used:
wherein the content of the first and second substances,y sat_i and
are respectively the first in the training setiThe true value of the output saturation of each sample and the saturation calculation result of the 3D convolution Fourier neural network model,n train is the total number of samples in the training set.
For vertical wells drilled through multiple zones, at depthdWellbore pressure at formation
Influenced by the junction attraction varying in depth z. The uppermostThe wellbore pressure at the face perforations, called Bottom Hole Pressure (BHP), continues down with depthd+1 formation depth wellbore pressure
The calculation is as in equation (12),
is the difference in depth of the image,
is the fluid mix density.
When the 3D convolution Fourier network model predicts the pressure, in order to improve the prediction accuracy, the influence of gravity on the pressure in the depth direction needs to be considered, the pressure satisfies equation (12),
loss function of pressureloss press_MSE The following were used:
wherein the content of the first and second substances,y press_i and
are respectively the first in the training setiThe real value of the output pressure of each sample and the pressure calculation result of the 3D convolution Fourier neural network model;
at the grid of wellsdThe actual value of wellbore pressure at +1 formation depth,
at the grid of wellsdA predicted value of wellbore pressure at the depth of layer;
the inventionThe physical significance is embedded with the gravity constraint as a penalty phase in the loss function of pressure. The equations are trained so that the output meets both the data constraints and the equation constraints,
are the coefficients of the data constraint and,
the coefficients are constrained by an equation, are hyper-parameters of the network, are respectively initialized to 0.9 and 0.1, and can be automatically updated in the training process.
The network carries out forward propagation according to the set hyper-parameters and the network iterative structure;
step 3.3, performing back propagation according to the loss error calculated in the step 3.2, and updating the weight by using an ADAM optimizerWThe MSE loss is gradually reduced. The initial learning rate lr =0.003, the batch size is 8, and the mixing weight is 1000 for the ADAM optimization algorithm; the process is repeated, and the error generally falls within the acceptable range after 200 epochs, so that the training is completed.
And 4, evaluating the performance of the 3D convolution Fourier neural network by using the test set, and calculating the relative errors of RMSE and the quantization saturation or pressure. The specific process is as follows:
for all test samples, the relative root mean square error RMSE is calculated and the relative error of the predicted saturation or pressure is quantified; the RMSE calculation formula is:
wherein the content of the first and second substances,n test the total number of samples in the test set;
to evaluate the predicted solution, including
And
；y i solving true values for numerical simulations, includingy sat_i Andy press_i . The closer the RMSE value is to 0, the higher the similarity between the two parameters.
The formula for calculating the saturation or pressure relative error of the three-dimensional oil reservoir is as follows:
the relative error of saturation is
The relative error of the pressure is
，n test Is the total number of test samples 400,n M is the total number of grids 40 x 20=16000,n t it is the number of time steps that is 20,
is the first to testiA sample ofmA gridtThe result of the prediction of the saturation at the time,
is the true value for the corresponding saturation;
is the first to testiA sample ofmA gridtThe result of the prediction of the pressure at the moment,
is the true value of the corresponding pressure. The saturation range is not normalized to 0-1, the pressure is not normalized to this range, and the maximum pressure minus the minimum pressure is used for pressure normalization，
Is the firstiA test specimentThe maximum pressure at the moment of time is,
is the firstiA test specimentThe minimum pressure at the moment. The closer the relative error is to 0, the more accurate the prediction of the saturation or pressure of the three-dimensional reservoir.
And 5, outputting a 3D convolution Fourier network model with good test indexes after the training is finished. The method comprises the steps of collecting three-dimensional underground oil deposit data in real time by monitoring equipment installed on the basis of an oil deposit, generating a permeability field of the three-dimensional oil deposit on line by using a geological statistical tool, predicting oil deposit saturation or pressure field distribution of the oil deposit within a future period of time on line by using a 3D convolution Fourier network model, further calculating yield through pressure and saturation, and providing visual reference for formulating a production strategy. The specific process is as follows:
and (3) storing the 3D convolution Fourier neural network model with better performance index evaluation, namely storing the trained weight and the hyper-parameter, and rapidly predicting the future saturation or pressure state of the three-dimensional oil reservoir by using the 3D convolution Fourier neural network model. The input is the permeability field of the three-dimensional oil reservoir and the output is a period of timetThe internal pressure and saturation distribution are input and output can be obtained through one-time forward propagation calculation.
The yield of the oil-water well is calculated by utilizing the pressure and the saturation through a peakeman model, the calculation formula is as follows,
wherein the content of the first and second substances,
is the firstmThe oil/water phase injection/recovery rate of the wells in each grid, which is also the injection and recovery result to be calculated,k m is as followsmPersonal netThe absolute permeability of the grid is determined,k r j,is composed ofk m The corresponding oil/water relative permeability,S w m,is as followsmThe value of the water saturation at each grid,
is the thickness of the grid or grid,
by default, to
The reservoir has equal width in both x and y directions,r w is the radius of the borehole,
is the viscosity of the water or oil and,P m and withP l Are respectively the firstmPressure at each grid and wellbore pressure. According to the prediction result, the future state of the oil reservoir can be further analyzed, and visual reference is provided for formulating a production strategy.
To demonstrate the feasibility of the present invention, the following experiments were performed.
The experimental data was derived from a three-dimensional field block in a region, and the model contained 40 x 20 grid blocks, each grid block having dimensions of 20m in the lower x, y, z directions. Four producing wells, two water injection wells, one water injection well and two producing wells jet the upper 10 layers of the reservoir, and the other water injection well and two producing wells jet the bottom 10 layers of the reservoir. All wells were produced under constant pressure conditions, with the bottom pressure of the producing well set at 33.5Mpa and the bottom pressure of the water injection well set at 31.0 Mp. The permeability in each direction x, y, z is assumed to be equal.
Initially 0.25, initial oil saturation was set to 0.90 and initial water saturation was set to 0.10. The relative permeability curve represents the relationship between water saturation and relative permeability, as shown in FIG. 6, respectivelyThe relative permeability curves of the water and oil phases are shown. The oil-water flow state of the oil reservoir in 1000 days in the future is simulated, the production period of each section is 50 days, and 20 time steps are total. Firstly, a random three-dimensional osmotic field with the sample number of 2000 and the grid number of 40 multiplied by 20 is generated by sequential Gaussian simulation, a numerical simulator is used for calculating an oil-water two-phase partial differential equation to calculate a high-fidelity residual oil saturation or pressure field result for a period of time to be used as a data set, 1600 samples are randomly selected to be used as a training set, and the rest 400 samples are used as a testing set. The network comprises an encoding structure, a decoding structure and an LSTM structure, the specific structure is shown in table 1, and the sizes of convolution kernels are all 3 x 3. Setting a network hyper-parameter initial value, initializing hyper-parameters (weight and bias of a Fourier convolutional coding decoding network and an LSTM network, contribution coefficient in a loss function and the like) in a network, and using an ADAM optimization algorithm, wherein the initial learning rate lr =0.003, the batch size is 8, and the mixing weight is 1000. The neural network model trains 200 epochs. And testing the neural network model after the training is completed. In the experiment, a saturation field and pressure field map with 50 time steps and 30 days of each time step is output by training a 3D convolution Fourier neural network agent model.
Table 1 fourier convolution network architecture details table
As shown in fig. 7, the mean square error RMSE of the test for the 3D convolved nerves after 200 epoch training was 0.0651, which is close to the training loss and did not produce an overfitting.
Table 2 shows the saturation field and pressure prediction results of the three-dimensional oil reservoir produced by using a grid of 40 × 40 × 20 at constant pressure, and it can be seen that the RMSE values of the saturation field and the pressure prediction results are both close to 0, the fitting regression effect is good, and the accuracy is high. Relative error of saturation quantified by equation (15)
Relative error with pressure
5% and 0.67%, respectively, and the relatively low error performance indicates that the neural network has high prediction precision on the three-dimensional reservoir model. The Fourier convolution structure well extracts spatial information in a three-dimensional space, and meanwhile, the LSTM structure well considers time sequence characteristics.
TABLE 2 three-dimensional reservoir saturation or pressure prediction results
FIGS. 8 (production well 1 and production well 2) and 9 (production well 3 and production well 4) show the comparison of the yield calculated by the peakeman equation to the true yield, the predicted yield and the true yield being very close to each other throughout the production cycle, and the well yield being 750m3Day to 1000m3The fitting between the/day ranges is good, which shows that the 3D convolution Fourier neural network model has good prediction effect.
The experiment can effectively prove that the method can effectively improve the residual oil and pressure prediction speed of the three-dimensional oil reservoir. The Fourier convolution structure and the LSTM structure are adopted in the network to combine the spatiotemporal and physical significance, and meanwhile, the gravity constraint is also considered. The method has better effect on treating the three-dimensional oil reservoir, higher training speed, higher precision, better generalization and more on-site practical value.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (6)
1. A three-dimensional underground oil reservoir dynamic prediction method based on a convolution Fourier neural network is characterized in that a built 3D convolution Fourier neural network model is used for dynamically predicting the residual oil saturation or pressure of the three-dimensional underground oil reservoir, and the method specifically comprises the following steps:
step 1, collecting three-dimensional underground oil reservoir data, generating a three-dimensional permeability field according with geological characteristics by using an SGeMS geological statistical tool, solving saturation or pressure within a period of time corresponding to different permeabilities by using a numerical simulator as a sample library, dividing a data set according to a proportion, taking the permeability as input, and taking the saturation or pressure as output;
step 2, constructing a 3D convolution Fourier neural network, combining 3D convolution and Fourier transform, extracting image local information by using a 3D convolution operator, extracting a physical information approximate differential operator by using Fourier transform, and adding gravity constraint in the network; mapping from permeability to an oil reservoir state is realized by utilizing a coding and decoding network, and time and space information is considered simultaneously by combining with an LSTM;
step 3, setting hyper-parameters of the convolution Fourier network model, and training the 3D convolution Fourier network model under a training set;
step 4, evaluating the performance of the 3D convolution Fourier neural network by using the test set, and calculating the relative error between RMSE and the quantized saturation or pressure;
step 5, outputting a 3D convolution Fourier network model with good test indexes after the training is finished; the method comprises the steps of collecting three-dimensional underground oil deposit data in real time by monitoring equipment installed on the basis of an oil deposit, generating a permeability field of the three-dimensional oil deposit on line by using a geological statistical tool, predicting oil deposit saturation or pressure field distribution of the oil deposit within a future period of time on line by using a 3D convolution Fourier network model, further calculating yield through pressure and saturation, and providing visual reference for formulating a production strategy.
2. The method for dynamically predicting the three-dimensional underground oil reservoir based on the convolutional Fourier neural network as claimed in claim 1, wherein the specific process of the step 1 is as follows:
step 1.1, collecting three-dimensional underground oil reservoir data, generating a three-dimensional permeability field by using an SGeMS geological statistical model, wherein the grid size is 40 multiplied by 20, and generating 2000 permeability samples;
step 1.2, calculating an oil-water two-phase flow equation of the three-dimensional oil reservoir system by using a finite element method through a numerical simulator to obtain saturation or pressure results in all grid blocks; the oil reservoir underground oil-water flow system is three-dimensional, needs to consider the gravity effect and consists of a mass conservation equation (1) and a phase Darcy velocity equation (2);
the mass conservation equation is expressed as (1),
wherein the content of the first and second substances,
representing a gradient operator;jindicating different phases, including oil and water phases,oby which is meant an oil,wrepresents water;
represents the density of the phase;v j represents the phase darcy speed;
representing source/sink items, superscriptlRepresenting a parameter at the well;
represents porosity;S j represents the saturation of the phase;trepresents time;
the expression of the facies darcy velocity equation is shown as (2),
wherein, the first and the second end of the pipe are connected with each other,k rj which represents the relative permeability of the phases,
the absolute permeability vector is represented by the absolute permeability vector,
the viscosity of the phase is expressed in terms of,p j the pressure of the phase is indicated and,gwhich is indicative of the force of gravity,zrepresenting a depth;
step 1.3, according to 8: 2, dividing the data set and the test set in proportion; the permeability of input data is a tensor of (n, nx, ny, nz,1), the saturation or pressure of output data is a tensor of (n, nx, ny, nz,1, T), n is a sample number, nx is a transverse grid number, ny is a longitudinal grid number, nz is a grid number in a depth direction, and T is a time step number.
3. The method for dynamically predicting the three-dimensional underground oil reservoir based on the convolutional Fourier neural network as claimed in claim 2, wherein the specific process of the step 2 is as follows:
the 3D convolution Fourier neural network mainly comprises an encoding network and a decoding network, and a cyclic neural module which takes the time sequence influence into consideration and increases the processing time; the input parameter is a permeability field of a known observed value, and the output parameter is saturation or pressure in a future period of time;
the coding network structure comprises M3D convolutional Fourier layers, each of which is structured as follows,
wherein the content of the first and second substances,xis the initial input of the parameters that are,Wis the weight of the image,
is an activation function, activated using Relu;v N+1(x) Is a convolution Fourier moduleNThe output result of the +1 layer is,v N (x) Is thatNOutputting the result of the layer;
the product is a three-dimensional Fourier integral operator used for extracting physical information;
is a fast fourier transform of the signal to be processed,
is the inverse of the fourier transform,Cthe operation of cutting off Fourier series exceeding the maximum threshold value, and the Fourier transform operation can approximate the physical law which is accorded with the data through the Fourier series, namely a series of sine and cosine curves;Conv3Dthe convolution method is a 3D convolution result and is used for extracting local information, the size and the step of each layer of convolution kernel can be adjusted, the sizes of the convolution kernels are 3 multiplied by 3, and the convolution steps are 1 multiplied by 1 and 2 multiplied by 2; because the Fourier transform is infinite dimension mapping, the dimension of the result extracted by using the Fourier transform is required to be consistent with that of the convolution result, the original dimension cannot be changed after the addition, and the obtained final result enters a decoding network through five layers of Fourier layers;
the decoding network structure is composed of a deconvolution layer, the input of a part of layers of the decoding network is formed by copying and splicing the output matrix corresponding to the coding network and the current input, and the purpose is to store more information and prevent the loss of characteristics in the convolution process; the decoding network is a process of decoding the intermediate result to an original data space, and the obtained result is a pressure value or saturation of a certain time step;
considering the influence of time sequence, enabling intermediate results of a plurality of time steps input through a decoding network to pass through an LSTM structure, combining time sequence information, and obtaining an output result of each time step by using a corresponding decoding network for each feature map after LSTM processing;
LSTM attThe time of day is input three: state of the cellC t-1In a hidden layer stateh t-1Current input characteristicsx t ；
C t Carrying space-time information, the calculation formula is as follows,
wherein the content of the first and second substances,f t representing forgetting gate, controlling the state of discarded cellsC t-1Some of the information in (a);
represents a new candidate cell state that is,i t representative update gate, selecting to preserve candidate cell state
Some of the information in (a);
hidden layer output resulth t Output gateo t And calculated in the previous stepC t Calculated by the tanh activation function, as follows,
forgetting doorf t Updating doori t Output dooro t And novel candidate cell states
The calculation formula is as follows, each gate has its own weight and offset, in LSTM
Is a sigmoid activation function, the activation result is between (0, 1), and the tanh activation result is between (-1, 1);
wherein, the first and the second end of the pipe are connected with each other,W f 、W i 、W o andW c weights corresponding to the forgetting gate, the updating gate, the output gate and the new candidate cell state are respectively set;b f 、b i 、b o andb c biases corresponding to the forgetting gate, the updating gate, the output gate and the new candidate cell state respectively;
inputting a permeability field, obtaining hidden layer variables through a convolution Fourier coding layer, and obtaining a prediction result of saturation or pressure simultaneously containing time information and space information through an LSTM structure and a decoding network
。
4. The method for dynamically predicting the three-dimensional underground oil reservoir based on the convolutional Fourier neural network as claimed in claim 3, wherein the specific process of the step 3 is as follows:
step 3.1, setting input and output of a 3D convolution Fourier network model; the input parameter is the permeability of the three-dimensional oil reservoir; setting an output value, and predicting the oil reservoir saturation or pressure distribution in a future period of time;
step 3.2, initialize the hyper-parameter, batch size 8, laserLiving function uses ReLu function, randomly initializing weightsW(ii) a The super-parameters are optimized and adjusted according to network evaluation performance, the loss function uses an MSE function to calculate loss, and the MSE loss function value is as follows during pressure training: the coding and decoding network uses the same super parameter setting and trains to converge in 200 epochs;
loss function of saturationloss sat_MSE The following were used:
wherein the content of the first and second substances,y sat_i and
are respectively the first in the training setiThe true value of the output saturation of each sample and the saturation calculation result of the 3D convolution Fourier neural network model,n train total number of samples in training set;
for vertical wells drilled through multiple zones, at depthdWellbore pressure at formation
The junction attraction force affected by the change in depth z; the wellbore pressure at the uppermost perforation, called bottom hole pressure, continues down with depthd+1 formation depth wellbore pressure
The calculation is as in equation (12),
is the difference in depth of the image,
is the fluid mix density;
when the 3D convolution Fourier network model predicts the pressure, considering that the pressure in the depth direction is influenced by the gravity action, the pressure satisfies equation (12),
loss function of pressureloss press_MSE The following were used:
wherein the content of the first and second substances,y press_i and
are respectively the first in the training setiThe real value of the output pressure of each sample and the pressure calculation result of the 3D convolution Fourier neural network model;
at the grid of wellsdThe actual value of wellbore pressure at +1 formation depth,
at the grid of wellsdA predicted value of wellbore pressure at the depth of layer;
are the coefficients of the data constraint and,
is the coefficient of the equation constraint;
the network carries out forward propagation according to the set hyper-parameters and the network iterative structure;
step 3.3, performing back propagation according to the loss error calculated in the step 3.2, and updating the weight by using an ADAM optimizerWGradually reducing the MSE loss; the initial learning rate lr =0.003, the batch size is 8, and the mixing weight is 1000 for the ADAM optimization algorithm; repetition ofThis process, after 200 epochs the error falls within the acceptance range and training is complete.
5. The method for dynamically predicting the three-dimensional underground oil reservoir based on the convolutional Fourier neural network as claimed in claim 4, wherein the specific process of the step 4 is as follows:
calculating relative Root Mean Square Error (RMSE) for all test samples, and quantifying the relative error of the predicted saturation or pressure;
the RMSE calculation formula is:
wherein the content of the first and second substances,n test the total number of samples in the test set;
predicting results for the model, including
And
；y i solving true values for numerical simulations, includingy sat_i Andy press_i ；
the formula for calculating the saturation or pressure relative error of the three-dimensional oil reservoir is as follows:
the relative error of saturation is
The relative error of the pressure is
，n test Is the total number of samples tested and,n M is the total number of the grids,n t is the number of time steps that the user can take,
is the first to testiA sample ofmA gridtThe result of the prediction of the saturation at the time,
is the true value for the corresponding saturation;
is the first to testiA sample ofmA gridtThe result of the prediction of the pressure at the moment,
is the true value of the corresponding pressure; the pressure normalization is performed by subtracting the minimum pressure from the maximum pressure,
is the firstiA test specimentThe maximum pressure at the moment of time is,
is the firstiA test specimentThe minimum pressure at the moment.
6. The method for dynamically predicting the three-dimensional underground oil reservoir based on the convolutional Fourier neural network as claimed in claim 5, wherein the specific process of the step 5 is as follows:
storing the 3D convolution Fourier neural network model with better performance index evaluation, storing the trained weight and the hyperparameter, and rapidly predicting the future saturation or pressure state of the three-dimensional oil reservoir by using the 3D convolution Fourier neural network model(ii) a The input is the permeability field of the three-dimensional reservoir and the output is a period of timetThe internal pressure and saturation distribution are input and output can be obtained through calculation of one-time forward propagation;
the yield of the oil-water well is calculated by utilizing the pressure and the saturation through a peakeman model, the calculation formula is as follows,
wherein the content of the first and second substances,
is the firstmThe rate of injection/recovery of oil/water phase from wells in each grid,k m is as followsmThe absolute permeability of the individual grids is,k r j,is composed ofk m The corresponding oil/water relative permeability,S w m,is as followsmThe value of the water saturation at each grid,
is the thickness of the grid or grid,
by default, to
The reservoir has equal width in both x and y directions,r w is the radius of the borehole,
is the viscosity of the water or oil and,P m andP l are respectively the firstmPressure at each grid and wellbore pressure.
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