CN116205164B - Multi-agent injection and production optimization method based on self-adaptive basis function selection - Google Patents

Multi-agent injection and production optimization method based on self-adaptive basis function selection Download PDF

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CN116205164B
CN116205164B CN202310465041.7A CN202310465041A CN116205164B CN 116205164 B CN116205164 B CN 116205164B CN 202310465041 A CN202310465041 A CN 202310465041A CN 116205164 B CN116205164 B CN 116205164B
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王嘉林
张黎明
张凯
付文豪
辛国靖
王鑫炎
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China University of Petroleum East China
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Abstract

The invention discloses a multi-agent injection and production optimization method based on self-adaptive basis function selection, and relates to the technical field of oil reservoir production optimization. According to the method, an initial sample is obtained based on Latin hypercube sampling, a net present value of the initial sample is calculated by utilizing an oil reservoir numerical simulator to build a database, a radial basis function network proxy model is built by utilizing samples in the database by adopting a plurality of basis functions, root mean square errors are calculated, a basis function with highest prediction precision in a current optimization stage is selected to serve as an optimal basis function to build a plurality of proxy models, an initial population in an optimization stage is built, multi-agent optimization is carried out based on a non-dominant ranking genetic algorithm, after a child population suitable for the plurality of proxy models is obtained, a new individual update database is generated by calculating an average value of the child population in each dimension, repeated iterative optimization is carried out until the preset times are reached, an optimal development scheme and the net present value are output, and the oil reservoir development scheme is accurately predicted while the injection and production optimization efficiency is improved.

Description

Multi-agent injection and production optimization method based on self-adaptive basis function selection
Technical Field
The invention relates to the technical field of oil reservoir production optimization, in particular to a multi-agent injection and production optimization method based on self-adaptive basis function selection.
Background
Injection and production optimization is an important component of oil reservoir management, and aims to fully develop oil reservoir potential by searching an optimal development scheme (namely bottom hole pressure or flow rate of each well) so as to realize maximum economic benefit. In the injection and production optimization process, a numerical simulator is often used for evaluating the quality of candidate development schemes, and a better development scheme is selected. However, the injection and production optimization simulation using a numerical simulator takes a long time, such as tens of minutes or even hours, and when the control variables and the objective function are in a highly nonlinear relationship, the simulation time required for a real reservoir model with a large number of grids and wells is longer, so that injection and production optimization becomes an expensive optimization problem. Therefore, consideration should be given to how to obtain a development scheme with high economic benefits in limited numerical simulation.
The agent model based on data driving trains by taking the production state as input and the known economic benefit response as output, and replaces a numerical simulator to rapidly forecast and evaluate candidate development schemes by establishing a mathematical model, so that the evaluation times of the numerical simulation are greatly reduced, and the agent model has been frequently applied to injection and production optimization.
The radial basis function network model in the proxy model approximates the objective function of reservoir injection and production optimization by weighting the sum of the basis functions. By virtue of the robustness, the method is widely applied to oil reservoir development with a large number of wells and a long production period. However, radial basis function network models are built based on data, and models built based on different basis functions will make different predictions without physical significance. Some of the basis function agents have higher prediction accuracy in the early optimization stage, while others have better performance in the later optimization stage. Therefore, it is not clear what basis function construction model should be selected at each stage to obtain the best prediction result for the current optimization problem of the new reservoir. In addition, the candidate solutions generated in the optimization stage are often obtained by evaluating a proxy model, and prediction bias is easy to generate, so that the search direction is poor.
Disclosure of Invention
Aiming at the problems that in the prior art, the prediction deviation is caused by the fact that the radial basis function network model is built by the basis function with highest prediction precision in the current optimization stage and a single agent is difficult to adaptively select in the injection and production optimization process, the invention provides the multi-agent injection and production optimization method based on the self-adaptive basis function selection, which has the characteristics of high-precision global searching capability and rapid positioning of the optimal oil reservoir development scheme, improves the injection and production optimization efficiency, and simultaneously realizes the accurate prediction of the optimal oil reservoir development scheme.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a multi-agent injection and production optimization method based on self-adaptive basis function selection comprises the following steps:
step 1, according to geological data of a research area, utilizing geological modeling software to construct a geological model of the research area, inputting the constructed geological model into an oil reservoir numerical simulator, and establishing an oil reservoir numerical simulation model in the oil reservoir numerical simulator;
step 2, an oil reservoir injection and production optimization model is established, initial samples are obtained through Latin hypercube sampling, the net present value of each initial sample is calculated by utilizing an oil reservoir numerical simulator according to the initial value of each initial sample, the initial value and the net present value of each initial sample are obtained, and a database is constructed;
step 3, dividing samples in a database into a training set and a testing set, constructing a radial basis function network proxy model by adopting different basis functions based on the samples in the training set, and determining a first radial basis function network proxy model, a second radial basis function network proxy model and a third radial basis function network proxy model;
step 4, obtaining root mean square error of each radial basis function network proxy model based on samples in the test set, and selecting a basis function with highest prediction precision in the current optimization stage as an optimal basis function according to the root mean square error of each radial basis function network proxy model;
Step 5, constructing a plurality of proxy models composed of optimal basis functions based on a bootstrap sampling method;
step 6, constructing a global diversity subset as an initial population of an optimization stage;
step 7, carrying out multi-agent optimization based on a non-dominant ordering genetic algorithm to obtain a child population suitable for a plurality of agent models;
step 8, calculating the average value of the child population in each dimension, generating a new individual, carrying out numerical simulation on the new sample, and updating a database;
step 9, utilizing the updated databaseAnd (3) continuing to perform iterative optimization, repeating the steps (3) to (8) until the iterative optimization times reach the maximum evaluation times preset in the oil reservoir numerical simulator, recording samples output by the oil reservoir numerical simulator and net present values of the samples during each iterative optimization, and outputting the samples obtained by each iterative optimization and the net present values corresponding to the samples by the oil reservoir numerical simulator after the iterative optimization is finished, so as to obtain the optimal development scheme and the net present values of the optimal development scheme.
Preferably, in the step 2, the method specifically includes the following steps:
step 2.1, setting an injection and production optimization target to obtain maximum economic benefit by controlling development schemes of a production well and a water injection well, setting a net present value as an objective function of injection and production optimization, and establishing an oil reservoir injection and production optimization model by combining boundary constraint conditions of decision variables, wherein the oil reservoir injection and production optimization model is shown in a formula (1):
（1）
Wherein,,
（2）
in the method, in the process of the invention,for sequence number of time step->For the total number of time steps>Time intervals being time steps;find a function for maximum value +_>Optimizing the objective function for injection and production->For decision variables +.>For the dimension of the decision variable, the dimension of the decision variable +.>，/>For the number of wells to be optimized in the reservoir +.>Calculating state variables of reservoir characteristic information for the reservoir numerical simulator; />For the lower boundary of the decision variable, +.>Is the upper boundary of the decision variable;for the time step->The unit of daily oil production of (1) is STB/D; />For the time step->The unit of daily water yield of (1) is STB/D; />For the time step->The daily water injection amount is expressed as STB/D; />The unit is USD/STB; />The cost of water production is treated for unit volume, and the unit is USD/STB; />The unit is USD/STB; />Is the discount rate;
step 2.2, collecting initial samples in a constraint range of decision variables based on Latin hypercube sampling to obtain an initial sample setInitial sample set->Wherein->Is numbered (I)>For the number of initial samples, +.>Is->A filling and sampling system of each sample;
step 2.3, inputting the initial sample set into an oil reservoir numerical simulator, presetting maximum evaluation times in the oil reservoir numerical simulator, and calculating net present values of all samples in the initial sample set by using the oil reservoir numerical simulator to obtain a sample set corresponding to the initial sample set Corresponding net present value data set +.>Net present value dataset +.>，/>Is->Net present values for the individual samples;
step 2.4, according to the initial sample setInitial sample set +.>Corresponding net present value data set +.>Obtaining initial value and net present value of each initial sample, constructing database +.>Database->。
Preferably, the step 3 specifically includes the following steps:
step 3.1, obtaining the number N of samples in a database, randomly selecting 0.8N samples in the database to form a training set, and forming a test set by the rest samples;
step 3.2, a radial basis function network model is established, and the sum of weighted basis functions is utilized to approach an objective function of injection and production optimization, as shown in a formula (3):
（3）
in the method, in the process of the invention,for the predicted value of the radial basis function network model, < +.>Is->Weight coefficient of individual samples, +.>Is European norm, ++>As a basis function +.>Is->Injection and collection regimen of each sample,/->Is a decision variable;
step 3.3, constructing a radial basis function network proxy model based on the training set samples;
setting a basis function in a radial basis function network model as a cubic spline function, a Gaussian function and an inverse polynary quadratic function in sequence, and constructing a first radial basis function network proxy model based on samples in a training set when the basis function in the radial basis function network model is set as the cubic spline function The method comprises the steps of carrying out a first treatment on the surface of the When the basis function in the radial basis function network model is set to be GaussianWhen the number is counted, a second radial basis function network proxy model is built based on samples in the training set>The method comprises the steps of carrying out a first treatment on the surface of the When the basis function in the radial basis function network model is set as an inverse multi-element quadratic function, a third radial basis function network proxy model is constructed based on samples in the training set +.>；
The cubic spline function is shown in a formula (4):
（4）
in the method, in the process of the invention,is a cubic spline function;
the gaussian function is shown in formula (5):
（5）
wherein,,
（6）
in the method, in the process of the invention,as a Gaussian function +.>For shape parameters +.>For maximum distance between input decision variables, +.>Is the dimension of the decision variable;
the inverse polynary quadratic function is shown in formula (7):
（7）
in the method, in the process of the invention,is an inverse multiple quadratic function.
Preferably, the step 4 specifically includes the following steps:
step 4.1, substituting the samples in the test set into a first radial basis function network proxy model, a second radial basis function network proxy model and a third radial basis function network proxy model respectively, and calculating root mean square errors of the radial basis function network proxy models respectively;
the root mean square error calculation formula is as follows:
（8）
in the method, in the process of the invention,sequence number for proxy model of radial basis function network, +. >When=1, the first radial basis function network proxy model is represented, +.>When=2, the second radial basis function network proxy model is represented, +.>When=3, the third radial basis function network proxy model is represented; />For the number of samples of the test set, +.>Is->Net present value of individual samples,/->The expression number is->Is calculated by the radial basis function network proxy model>Predicted values for the individual samples;
and 4.2, selecting a radial basis function network proxy model with the minimum root mean square error from the first radial basis function network proxy model, the second radial basis function network proxy model and the third radial basis function network proxy model, taking the basis function adopted by the radial basis function network proxy model with the minimum root mean square error as an optimal basis function, wherein the optimal basis function is the basis function with the highest prediction precision in the current optimization stage.
Preferably, the step 5 specifically includes the following steps:
step 5.1, setting the number of proxy models to be built based on the optimal basis functionsAnd bootstrap sample ratio->Setting the total number of loop calculations equal to the number of agent models to be built +.>Performing cyclic calculation;
step 5.2, setting an empty set correspondingly for each cycle calculation ，Traversing the database every time a loop is calculated>Randomly generating a random number ++1 within a range of 0-1>If random number->Less than bootstrap sampling ratio->Then put the sample into the empty set +.>Until the database is traversed>After all samples in (1), use the set +.>Establishing a proxy model based on an optimal basis function until the cyclic calculation is finished, and entering a step 5.3;
step 5.3, after the cyclic calculation is finished, obtaining the adoptionIndividual data sets are trained separately +.>A proxy model consisting of optimal basis functions.
Preferably, in the step 6, the method specifically includes the following steps:
step 6.1, setting an empty setIn database->Selecting the sample with the largest net present value and placing the sample in the empty set +.>In (a) and (b);
step 6.2, determining the number of samples in the initial population in the optimization stageSetting the total number of loop calculation as +.>The calculation of the database is carried out every time the calculation of the cycle is carried out>Samples and collections->Cumulative Euclidean distance between samples in (3) and database +.>Middle and Collection->The sample with the largest accumulated Euclidean distance between the samples is taken out and placed in the collectionUntil the cycle calculation is finished, entering a step 6.3;
step 6.3, after the cycle calculation is completed, obtaining the optimal individual including 1 Global diversity subset of individual compositions with good spatial properties +.>And subset of global diversity +.>As an initial population for the optimization phase.
Preferably, in the step 7, the method specifically includes the following steps:
step 7.1, subset the global diversityInitializing to obtain optimized population->Optimizing populationWherein->To optimize the%>A subject; setting maximum iterative calculation times->；
Setting an objective function to be optimized asAgent model consisting of optimal basis functions +.>，And sets the optimization problem as follows:
（9）；
step 7.2, starting multi-agent optimization iterative computation, utilizingAfter the agent models formed by the optimal basis functions evaluate the fitness values of all samples in the optimized population respectively, the method enters a step 7.3 for rapid non-dominant sorting;
step 7Thirdly, setting empty sets for each body in the optimized population respectivelyAnd the dominant number, empty set->For storing other individuals subjected to individual control, the initial value of the controlled number is set to 0, and the empty set corresponding to each individual is +.>And an evolution formula of the dominant number, as shown in formula (10):
（10）
in the method, in the process of the invention,、/>are individuals in the optimized population;
aiming at all individuals in the optimized population, the pareto grades of the individuals are respectively divided based on a formula (10), and the division basis is as follows:
Selection of individuals from an optimized populationAnd->If the empty set corresponding to the individual +.>And the evolution process of the dominant number satisfies the formula (10), then the individual is called +>Dominating individuals->Individual(s)/>Corresponding set->Update to original empty set->Is in charge of individuals>Is the union of individuals->Corresponding dominant number->Updated to->；
Respectively divide the individualComparing the agent model fitness value with other individuals in the optimized population, and if the individualsCorresponding dominant number->Still 0, it means that none of the other individuals in the optimized population is able to dominate the individual +.>Thereby giving individuals->Set to non-dominant solution, at which time individual +.>The pareto grade of (2) is set to 1; if individuals are->Corresponding dominant numberIs not 0, indicating individual->Other +.>Individual innervation, according to individual->Corresponding dominant number->Individuals are treated with->The pareto grades of (2) are classified as +.>；
Step 7.4, respectively calculating crowding distances of all individuals in the optimized population;
evaluating the fitness value of each sample in the optimized population according to each agent model consisting of the optimal basis functions, sorting the individuals in the optimized population according to the sequence of the fitness values from small to large, setting the crowding distance between the individual with the largest fitness value and the individual with the smallest fitness value to infinity after sorting, and calculating the crowding distance of each individual in the optimized population by using the optimized objective functions respectively aiming at all the individuals in the optimized population, wherein the crowding distance is shown in a formula (11):
（11）
In the method, in the process of the invention,to optimize the%>Sample utilization->Personal objective function->A calculated crowding distance; />Is->Personal objective function->For->Adaptation evaluation value of neighboring individuals in front of each sample, < >>Is->Personal objective function->For->An fitness evaluation value of an adjacent individual behind the individual samples; />To utilize->Personal objective function->Evaluating the maximum evaluation value obtained for all individuals in the optimized population,/->To utilize->Personal objective function->Evaluating the minimum evaluation values obtained by all individuals in the optimized population;
after the crowding distances of all samples in the optimized population under the control of each objective function are calculated, the crowding distances under the control of each objective function are accumulated and summed to obtain the crowding degree of all individuals in the optimized population, and the crowding degree of the individuals in the optimized population is shown as a formula (12):
（12）
in the method, in the process of the invention,is->Final crowding of individual individuals;
step 7.5, selecting the pareto grade in the optimized population to be positioned in front according to the pareto grade and the crowding degree of the individuals in the optimized populationIs located before the individual and crowding degree>Is obtained by randomly selecting parent individuals from the parent population>And parent individuals->Generating parent individuals based on cross mutation calculation >And parent individuals->Is a progeny individual of (a); by carrying out cross mutation calculation on all father individuals in the father population, the offspring individuals obtained by all calculation form offspring population +.>Offspring population->Wherein->Is the>A child generation individual;
the cross calculation formula is as follows:
（13）
wherein,,
（14）
in the method, in the process of the invention,for parent individuals->Generating the +.sub.individual by crossover calculation>Wei (dimension)>As father individualsGenerating the +.sub.individual by crossover calculation>Wei (dimension)>Is a crossing factor->Is a random number between 0 and 1, < >>Is a crossover parameter;
the variance calculation formula is as follows:
（15）
wherein,,
（16）
in the method, in the process of the invention,for offspring individuals->Variation calculation of the final offspring individual +.>Wei (dimension)>As a variant factor, cryptophan officinalis L>Is a variation parameter;
step 7.6, for offspring populationsRepeating the steps 7.2 to 7Step 7.5, performing iterative computation until the iterative computation times reach the preset maximum iterative computation times +.>Thereafter, a population of offspring is obtained that fits the plurality of agent models.
Preferably, in the step 8, an average value of all individuals in each dimension in the offspring population suitable for the plurality of agent models is calculated, and a new sample is generated, as shown in formula (17):
（17）
In the method, in the process of the invention,for new sample->Is>Wei (dimension)>Is the>Individual->Dimension; />The number of sample points in the offspring population;
new samples to be generatedInputting the sample into a reservoir numerical simulator, and calculating a new sample by using the reservoir numerical simulatorNet present value->And new sample->And the net present value of the new sample +.>Add to database->In updating database->Is a sample of (b).
The invention has the beneficial effects that:
aiming at the problems that the calculation time of the existing oil reservoir injection and production optimization method is long and the development scheme with the highest economic benefit is difficult to accurately acquire, the invention provides a multi-agent injection and production optimization method based on self-adaptive basis function selection.
Meanwhile, the conventional oil deposit injection and production optimization method only adopts one agent model to evaluate the oil deposit development scheme during the oil deposit injection and production optimization period, the oil deposit development scheme determined by the single agent model has larger error and is difficult to accurately predict the optimal oil deposit development scheme, and the method combines the self-adaptive basis function selection with the pareto sampling criterion, so that the optimization method based on the multi-agent model is realized, the probability of misleading the searching direction is greatly reduced by introducing the global diversity subset and the average sampling method into the multi-agent optimization process, the injection and production optimization efficiency is obviously improved, the capacity of optimizing the population to escape from local optimal is improved, and the injection and production optimization method with high-precision global searching capacity and rapid positioning of the optimal oil deposit development scheme is formed, so that the method has extremely high popularization and application values.
Drawings
FIG. 1 is a flow chart of a multi-agent injection and production optimization method based on adaptive basis function selection in accordance with the present invention.
FIG. 2 is a flow chart of the present invention for building multiple proxy models based on bootstrap sampling methods.
FIG. 3 is a flow chart of the present invention for multi-agent optimization to determine offspring populations based on non-dominant ranking genetic algorithms.
FIG. 4 is a graph showing the net present value versus the number of evaluations during the optimizing process according to the present invention.
FIG. 5 is a box plot of the best net present value distribution after optimization in accordance with an embodiment of the present invention.
FIG. 6 shows the cumulative oil production provided by the best-effort development of the present invention.
FIG. 7 shows the cumulative water yield provided by the best-effort development scheme in accordance with the present invention.
FIG. 8 shows the cumulative water injection provided by the best development scheme in the embodiment of the invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and detailed description:
the invention provides a multi-agent injection and production optimization method based on self-adaptive basis function selection, as shown in fig. 1, a study block in the embodiment adopts a water injection development mode, 8 water injection wells and 4 production wells are arranged in the study block, and the multi-agent injection and production optimization method based on self-adaptive basis function selection provided by the invention is used for determining the optimal development scheme of the study block, and specifically comprises the following steps:
And 1, constructing a geologic model of the research block by using geologic modeling software Petrel according to geologic data of the research block, including layer depth, initial pressure, porosity, oil-water compression coefficient, rock compression coefficient, crude oil viscosity and initial water saturation, inputting the constructed geologic model into an oil reservoir numerical simulator Eclipse, and establishing an oil reservoir numerical simulation model in the oil reservoir numerical simulator Eclipse.
Step 2, an oil reservoir injection and production optimization model is established, initial samples are obtained through Latin hypercube sampling, the net present value of each initial sample is calculated by utilizing an oil reservoir numerical simulator according to the initial value of each initial sample, the initial value and the net present value of each initial sample are obtained, and a database is constructed, specifically comprising the following steps:
step 2.1, setting an injection and production optimization target to obtain maximum economic benefit by controlling development schemes of a production well and a water injection well, setting a net present value as an objective function of injection and production optimization, and establishing an oil reservoir injection and production optimization model by combining boundary constraint conditions of decision variables, wherein the oil reservoir injection and production optimization model is shown in a formula (1):
（1）
wherein,,
（2）
in the method, in the process of the invention,for sequence number of time step->For the total number of time steps>Time intervals being time steps; Find a function for maximum value +_>Optimizing the objective function for injection and production->For decision variables +.>For the dimension of the decision variable, the dimension of the decision variable +.>，/>For the number of wells to be optimized in the reservoir +.>Calculating state variables of reservoir characteristic information for the reservoir numerical simulator; />For the lower boundary of the decision variable, +.>Is the upper boundary of the decision variable;for the time step->The unit of daily oil production of (1) is STB/D; />For the time step->The unit of daily water yield of (1) is STB/D; />For the time step->The daily water injection amount is expressed as STB/D; />The unit is USD/STB; />The cost of water production is treated for unit volume, and the unit is USD/STB; />Is a unit bodyThe water accumulation and injection cost is expressed as USD/STB; />Is the discount rate.
Injection and production optimization objective function in this embodimentFor the net present value, since the production well pressure is constant at 395bar in this embodiment, only the water injection rate of 8 water injection wells needs to be optimized, i.e., decision variable +.>The water injection quantity is the water injection quantity of the water injection well; the total number of time steps in this embodiment +.>Set to 20, time interval of time step +.>180 days, production period of 3600 days, and unit volume of oil production income +.>Set to 20, per unit volume of treatment water production cost +. >Set to 3, water injection cost per unit volume +.>Set to 1, discount rate->Set to 0. Since 8 water injection wells are to be optimized in this embodiment, the dimension of the decision variable in this embodiment is +.>160, lower boundary of decision variable +.>0, upper boundary of decision variable +.>73m 3 。
Step 2.2, collecting initial samples in a constraint range of decision variables based on Latin hypercube sampling to obtain an initial sample setInitial sample set->Wherein->Is numbered (I)>For the number of initial samples, 200, # is set in this embodiment>Is->Injection and extraction system of each sample.
Step 2.3, inputting the initial sample set into an oil reservoir numerical simulator, presetting maximum evaluation times in the oil reservoir numerical simulator, wherein the preset maximum evaluation times in the oil reservoir numerical simulator are 1000 times in the embodiment, and calculating the net present value of each sample in the initial sample set by using the oil reservoir numerical simulator to obtain the initial sample setCorresponding net present value data set +.>Net present value dataset +.>，/>Is->Net present value of each sample.
Step 2.4, according to the initial sample setInitial sample set +.>Corresponding net present value data set +.>Obtaining initial value and net present value of each initial sample, constructing database +. >Database->。
Step 3, dividing samples in a database into a training set and a testing set, constructing a radial basis function network proxy model by adopting different basis functions based on the samples in the training set, and determining a first radial basis function network proxy model, a second radial basis function network proxy model and a third radial basis function network proxy model, wherein the method specifically comprises the following steps:
and 3.1, acquiring the number N of samples in a database, randomly selecting 0.8N samples in the database to form a training set, and forming a test set by the rest samples.
Step 3.2, a radial basis function network model is established, and the sum of weighted basis functions is utilized to approach an objective function of injection and production optimization, as shown in a formula (3):
（3）
in the method, in the process of the invention,for the predicted value of the radial basis function network model, < +.>Is->Weight coefficient of individual samples, +.>Is European norm, ++>As a basis function +.>Is->Injection and collection regimen of each sample,/->Is a decision variable.
Step 3.3, constructing a radial basis function network proxy model based on the training set samples;
setting a basis function in a radial basis function network model as a cubic spline function, a Gaussian function and an inverse polynary quadratic function in sequence, and constructing a first radial basis function network proxy model based on samples in a training set when the basis function in the radial basis function network model is set as the cubic spline function The method comprises the steps of carrying out a first treatment on the surface of the When the basis function in the radial basis function network model is set to be a gaussian function, a second radial basis function network proxy model is constructed based on samples in the training set>The method comprises the steps of carrying out a first treatment on the surface of the When the basis function in the radial basis function network model is set as an inverse multi-element quadratic function, a third radial basis function network proxy model is constructed based on samples in the training set +.>；
In this embodiment, the cubic spline function is as shown in formula (4):
（4）
in the method, in the process of the invention,is a cubic spline function;
the gaussian function is shown in formula (5):
（5）
wherein,,
（6）
in the method, in the process of the invention,as a Gaussian function +.>For shape parameters +.>For maximum distance between input decision variables, +.>Is the dimension of the decision variable;
the inverse polynary quadratic function is shown in formula (7):
（7）
in the method, in the process of the invention,is an inverse multiple quadratic function.
And step 4, acquiring root mean square errors of the radial basis function network proxy models based on samples in the test set, and selecting a basis function with highest prediction precision in the current optimization stage as an optimal basis function according to the root mean square errors of the radial basis function network proxy models, wherein the method specifically comprises the following steps:
step 4.1, respectively bringing samples in the test set into a first radial basis function network proxy model, a second radial basis function network proxy model and a third radial basis function network proxy model, respectively calculating root mean square errors of the radial basis function network proxy models by using a formula (8), and obtaining the first radial basis function network proxy model Root mean square error of>Second radial basis function network proxy model +.>Root mean square error of>And a third radial basis function network proxy modelRoot mean square error of>。
And 4.2, selecting a radial basis function network proxy model with the minimum root mean square error from the first radial basis function network proxy model, the second radial basis function network proxy model and the third radial basis function network proxy model, taking the basis function adopted by the radial basis function network proxy model with the minimum root mean square error as an optimal basis function, wherein the optimal basis function is the basis function with the highest prediction precision in the current optimization stage.
Step 5, based on the bootstrap sampling method, constructing a plurality of proxy models composed of optimal basis functions, as shown in fig. 2, specifically including the following steps:
step 5.1, setting the number of proxy models to be built based on the optimal basis functionsAnd bootstrap sample ratio->The number of agent models in this embodiment +.>The value is 2, bootstrapping sampling proportion->The value is 0.8, and the total number of cyclic calculation is set to be equal to the number of agent models to be built +.>And (5) performing cyclic calculation.
Step 5.2, setting an empty set correspondingly for each cycle calculation ，Traversing the database every time a loop is calculated>Randomly generating a random number ++1 within a range of 0-1>If random number->Less than bootstrap sampling ratio->Then put the sample into the empty set +.>Until the database is traversed>After all samples in (1), use the set +.>The agent model based on the optimal basis function is established until the loop calculation is finished, and the step 5.3 is entered.
Step 5.3, after the cyclic calculation is finished, obtaining the adoptionIndividual data sets are trained separately +.>A proxy model consisting of optimal basis functions.
Step 6, constructing a global diversity subset as an initial population of an optimization stage, and specifically comprising the following steps:
step 6.1, setting an empty setIn database->Selecting the sample with the largest net present value and placing the sample in the empty set +.>Is a kind of medium.
Step 6.2, determining the number of samples in the initial population in the optimization stageThe number of samples in the initial population in this embodiment +.>Setting 100, setting the total number of loop calculation to +.>Performing cyclic calculation every timeCalculation database for loop calculation>Samples and collections->Cumulative Euclidean distance between samples in (3) and database +.>Middle and Collection->Sample taking out with the largest cumulative Euclidean distance between the samples is placed in the collection +. >Until the loop calculation is completed, step 6.3 is entered.
Step 6.3, after the cycle calculation is completed, obtaining the optimal individual including 1Global diversity subset of individual compositions with good spatial properties +.>And subset of global diversity +.>As an initial population for the optimization phase.
Step 7, performing multi-agent optimization based on a non-dominant ordering genetic algorithm to obtain a child population suitable for a plurality of agent models, as shown in fig. 3, specifically including the following steps:
step 7.1, subset the global diversityInitializing to obtain optimized population->Optimizing populationWherein->To optimize the%>A subject; setting maximum iterative calculation times->Maximum number of iterative calculations +.>Set to 100.
Setting an objective function to be optimized asAgent model consisting of optimal basis functions +.>，And sets the optimization problem as follows:
（9）。
step 7.2, starting multi-agent optimization iterative computation, utilizingAnd after the agent models formed by the optimal basis functions evaluate the fitness values of all samples in the optimized population respectively, the method enters a step 7.3 for rapid non-dominant sorting.
Step 7.3, setting empty sets for each body in the optimized population respectively And the dominant number, empty set->For storing other individuals subjected to individual control, the initial value of the controlled number is set to 0, and the empty set corresponding to each individual is +.>And an evolution formula of the dominant number, as shown in formula (10):
（10）
in the method, in the process of the invention,、/>are individuals in the optimized population.
Aiming at all individuals in the optimized population, the pareto grades of the individuals are respectively divided based on a formula (10), and the division basis is as follows:
selection of individuals from an optimized populationAnd->If the empty set corresponding to the individual +.>And the evolution process of the dominant number satisfies the formula (10), then the individual is called +>Dominating individuals->Individual->Corresponding set->Update to original empty set->Is in charge of individuals>Is the union of individuals->Corresponding dominant number->Updated to->；
Respectively divide the individualComparing the agent model fitness value with other individuals in the optimized population, and if the individualsCorresponding dominant number->Still 0, it means that none of the other individuals in the optimized population is able to dominate the individual +.>Thereby giving individuals->Set to non-dominant solution, at which time individual +.>The pareto grade of (2) is set to 1; if individuals are->Corresponding dominant numberIs not 0, indicating individual->Other +.>Individual innervation, according to individual- >Corresponding dominant number->Individuals are treated with->The pareto grades of (2) are classified as +.>。
Step 7.4, respectively calculating crowding distances of all individuals in the optimized population;
evaluating the fitness value of each sample in the optimized population according to each agent model consisting of the optimal basis functions, sorting the individuals in the optimized population according to the sequence of the fitness values from small to large, setting the crowding distance between the individual with the largest fitness value and the individual with the smallest fitness value to infinity after sorting, and calculating the crowding distance of each individual in the optimized population by using the optimized objective functions respectively aiming at all the individuals in the optimized population, wherein the crowding distance is shown in a formula (11):
（11）
in the method, in the process of the invention,to optimize the%>Sample utilization->Personal objective function->A calculated crowding distance; />Is->Personal objective function->For->Adaptation evaluation value of neighboring individuals in front of each sample, < >>Is->Personal objective function->For->An fitness evaluation value of an adjacent individual behind the individual samples; />To utilize->Personal objective function->Evaluating the maximum evaluation value obtained for all individuals in the optimized population,/->To utilize->Personal objective function->Evaluating the minimum evaluation values obtained by all individuals in the optimized population;
after the crowding distances of all samples in the optimized population under the control of each objective function are calculated, the crowding distances under the control of each objective function are accumulated and summed to obtain the crowding degree of all individuals in the optimized population, and the crowding degree of the individuals in the optimized population is shown as a formula (12):
（12）
In the method, in the process of the invention,is->Final crowding of individual individuals.
Step 7.5, selecting the pareto grade in the optimized population to be positioned in front according to the pareto grade and the crowding degree of the individuals in the optimized populationIs located before the individual and crowding degree>Is obtained by randomly selecting parent individuals from the parent population>And parent individuals->Generating parent individuals based on cross mutation calculation>And parent individuals->Is a progeny individual of (a); by performing cross variation calculation on all father individuals in the father population, obtaining by using all calculationOffspring individuals make up the offspring population->Offspring population->Wherein->Is the>A child generation individual;
the cross calculation formula is as follows:
（13）
wherein,,
（14）
in the method, in the process of the invention,for parent individuals->Generating the +.sub.individual by crossover calculation>Wei (dimension)>As father individualsGenerating the +.sub.individual by crossover calculation>Wei (dimension)>Is a crossing factor->Is a random number between 0 and 1, < >>As crossing parameter, crossing parameter +.>The value is 2./>
The variance calculation formula is as follows:
（15）
wherein,,
（16）
in the method, in the process of the invention,for offspring individuals->Variation calculation of the final offspring individual +.>Wei (dimension)>As a variant factor, cryptophan officinalis L >As the variation parameter, the variation parameter in this embodiment +.>The value is 5.
Step 7.6, for offspring populationsRepeating the steps 7.2 to 7.5 for iterative computation until the iterative computation times reach the preset maximum iterative computation times ++>Thereafter, a population of offspring is obtained that fits the plurality of agent models.
And 8, calculating the average value of the child population in each dimension, generating a new individual, carrying out numerical simulation on the new sample, and updating a database.
In this embodiment, a new sample is generated by calculating the average value of all the individuals in each dimension in the child population suitable for the multiple agent models, as shown in formula (17):
（17）
in the method, in the process of the invention,for new sample->Is>Wei (dimension)>Is the>Individual->Dimension; />Is the number of sample points in the offspring population.
New samples to be generatedInput into a numerical reservoir simulatorCalculation of new samples with reservoir numerical simulatorNet present value->And new sample->And the net present value of the new sample +.>Add to database->In updating database->Is a sample of (b).
Step 9, utilizing the updated databaseAnd (3) continuing to perform iterative optimization, repeating the steps (3) to (8) until the iterative optimization times reach the maximum evaluation times preset in the oil reservoir numerical simulator, recording samples output by the oil reservoir numerical simulator and net present values of the samples during each iterative optimization, and outputting the samples obtained by each iterative optimization and the net present values corresponding to the samples by the oil reservoir numerical simulator after the iterative optimization is finished, so as to obtain the optimal development scheme and the net present values of the optimal development scheme.
In order to verify the evaluation effect of the optimal development scheme of the method, the conventional single-agent model optimizing method and the method are respectively utilized to carry out iterative optimization to determine the optimal injection-production scheme of the research block, namely the optimal development scheme of the research block, a change curve of net present values along with the iterative optimization times is output, as shown in fig. 4, the net present values corresponding to the injection-production scheme obtained by the method of the invention can be greatly improved from fig. 4, and the optimal net present value distribution box type diagram obtained by carrying out 10 times of optimization on the research block by adopting the conventional single-agent model optimizing method and the method of the invention is further compared, as shown in fig. 5, the method of the invention is found to be more stable compared with the conventional single-agent model optimizing method.
Fig. 6 is a cumulative oil yield of an optimal injection and production scheme determined by the method of the present invention and the conventional single-agent model optimizing method, fig. 7 is a cumulative water yield of an optimal injection and production scheme determined by the method of the present invention and the conventional single-agent model optimizing method, and fig. 8 is a cumulative water injection amount of an optimal injection and production scheme determined by the method of the present invention and the conventional single-agent model optimizing method. The accumulated oil yield is a benefit item, and the accumulated water yield and the accumulated water injection quantity are cost items. As can be obtained by analyzing fig. 6 to 8, the injection and production scheme determined by the method can improve the accumulated oil yield and reduce the investment cost in the aspects of accumulated water yield and accumulated water injection, and has higher economic benefit.
The foregoing description is, of course, merely illustrative of preferred embodiments of the present invention, and it should be understood that the present invention is not limited to the above-described embodiments, but is intended to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

Claims (7)

1. The multi-agent injection and production optimization method based on the self-adaptive basis function selection is characterized by comprising the following steps of:
step 1, according to geological data of a research area, utilizing geological modeling software to construct a geological model of the research area, inputting the constructed geological model into an oil reservoir numerical simulator, and establishing an oil reservoir numerical simulation model in the oil reservoir numerical simulator;
step 2, an oil reservoir injection and production optimization model is established, initial samples are obtained through Latin hypercube sampling, the net present value of each initial sample is calculated by utilizing an oil reservoir numerical simulator according to the initial value of each initial sample, the initial value and the net present value of each initial sample are obtained, and a database is constructed;
step 3, dividing samples in a database into a training set and a testing set, constructing a radial basis function network proxy model by adopting different basis functions based on the samples in the training set, and determining a first radial basis function network proxy model, a second radial basis function network proxy model and a third radial basis function network proxy model;
Step 4, obtaining root mean square error of each radial basis function network proxy model based on samples in the test set, and selecting a basis function with highest prediction precision in the current optimization stage as an optimal basis function according to the root mean square error of each radial basis function network proxy model;
step 5, constructing a plurality of proxy models composed of optimal basis functions based on a bootstrap sampling method;
step 6, constructing a global diversity subset as an initial population of an optimization stage;
step 7, carrying out multi-agent optimization based on a non-dominant ordering genetic algorithm to obtain a child population suitable for a plurality of agent models;
step 8, calculating the average value of the child population in each dimension, generating a new individual, carrying out numerical simulation on the new sample, and updating a database;
step 9, utilizing the updated databaseContinuing to perform iterative optimization, repeating the steps 3 to 8 until the iterative optimization times reach the maximum evaluation times preset in the oil reservoir numerical simulator, recording samples output by the oil reservoir numerical simulator and net present values of the samples during each iterative optimization, and outputting the samples obtained by each iterative optimization and the net present values corresponding to the samples by the oil reservoir numerical simulator after the iterative optimization is finished, so as to obtain an optimal development scheme and the net present values of the optimal development scheme;
The step 2 specifically includes the following steps:
step 2.1, setting an injection and production optimization target to obtain maximum economic benefit by controlling development schemes of a production well and a water injection well, setting a net present value as an objective function of injection and production optimization, and establishing an oil reservoir injection and production optimization model by combining boundary constraint conditions of decision variables, wherein the oil reservoir injection and production optimization model is shown in a formula (1):
（1）
wherein,,
（2）
in the method, in the process of the invention,for sequence number of time step->For the total number of time steps>Time intervals being time steps; />Find a function for maximum value +_>Optimizing the objective function for injection and production->For decision variables +.>For the dimension of the decision variable, the dimension of the decision variable +.>，/>For the number of wells to be optimized in the reservoir +.>Calculating state variables of reservoir characteristic information for the reservoir numerical simulator; />For the lower boundary of the decision variable, +.>Is the upper boundary of the decision variable; />For the time step->The unit of daily oil production of (1) is STB/D; />For the time step->The unit of daily water yield of (1) is STB/D; />For the time step->The daily water injection amount is expressed as STB/D; />The unit is USD/STB; />The cost of water production is treated for unit volume, and the unit is USD/STB; />The unit is USD/STB; / >Is the discount rate;
step 2.2, based on Latin hypercube sampling within the constraint range of the decision variableCollecting an initial sample to obtain an initial sample setInitial sample set->Wherein->Is numbered (I)>For the number of initial samples,is->A filling and sampling system of each sample;
step 2.3, inputting the initial sample set into an oil reservoir numerical simulator, presetting maximum evaluation times in the oil reservoir numerical simulator, and calculating net present values of all samples in the initial sample set by using the oil reservoir numerical simulator to obtain a sample set corresponding to the initial sample setCorresponding net present value data set +.>Net present value dataset +.>，/>Is->Net present values for the individual samples;
step 2.4, according to the initial sample setInitial sample set +.>Corresponding net present value data set +.>Obtaining initial value and net present value of each initial sample, constructing database +.>Database->。
2. The multi-agent injection and production optimization method based on the adaptive basis function selection according to claim 1, wherein the step 3 specifically comprises the following steps:
step 3.1, obtaining the number N of samples in a database, randomly selecting 0.8N samples in the database to form a training set, and forming a test set by the rest samples;
step 3.2, a radial basis function network model is established, and the sum of weighted basis functions is utilized to approach an objective function of injection and production optimization, as shown in a formula (3):
（3）
In the method, in the process of the invention,for the predicted value of the radial basis function network model, < +.>Is->Weights of individual samplesCoefficient of->Is European norm, ++>As a basis function +.>Is->Injection and collection regimen of each sample,/->Is a decision variable;
step 3.3, constructing a radial basis function network proxy model based on the training set samples;
setting a basis function in a radial basis function network model as a cubic spline function, a Gaussian function and an inverse polynary quadratic function in sequence, and constructing a first radial basis function network proxy model based on samples in a training set when the basis function in the radial basis function network model is set as the cubic spline functionThe method comprises the steps of carrying out a first treatment on the surface of the When the basis function in the radial basis function network model is set to be a gaussian function, a second radial basis function network proxy model is constructed based on samples in the training set>The method comprises the steps of carrying out a first treatment on the surface of the When the basis function in the radial basis function network model is set as an inverse multi-element quadratic function, a third radial basis function network proxy model is constructed based on samples in the training set +.>；
The cubic spline function is shown in a formula (4):
（4）
in the method, in the process of the invention,is a cubic spline function;
the gaussian function is shown in formula (5):
（5）
wherein,,
（6）
in the method, in the process of the invention,as a Gaussian function +.>For shape parameters +. >For maximum distance between input decision variables, +.>Is the dimension of the decision variable;
the inverse polynary quadratic function is shown in formula (7):
（7）
in the method, in the process of the invention,is an inverse multiple quadratic function.
3. The multi-agent injection and production optimization method based on the adaptive basis function selection according to claim 2, wherein the step 4 specifically includes the following steps:
step 4.1, substituting the samples in the test set into a first radial basis function network proxy model, a second radial basis function network proxy model and a third radial basis function network proxy model respectively, and calculating root mean square errors of the radial basis function network proxy models respectively;
the root mean square error calculation formula is as follows:
（8）
in the method, in the process of the invention,sequence number for proxy model of radial basis function network, +.>When=1 represents the first radial basis function network proxy model,when=2, the second radial basis function network proxy model is represented, +.>When=3, the third radial basis function network proxy model is represented; />For the number of samples of the test set, +.>Is->Net present value of individual samples,/->The expression number is->Is calculated by the radial basis function network proxy model>Predicted values for the individual samples;
and 4.2, selecting a radial basis function network proxy model with the minimum root mean square error from the first radial basis function network proxy model, the second radial basis function network proxy model and the third radial basis function network proxy model, taking the basis function adopted by the radial basis function network proxy model with the minimum root mean square error as an optimal basis function, wherein the optimal basis function is the basis function with the highest prediction precision in the current optimization stage.
4. The multi-agent injection and production optimization method based on adaptive basis function selection according to claim 3, wherein the step 5 specifically comprises the following steps:
step 5.1, setting the number of proxy models to be built based on the optimal basis functionsAnd bootstrap sample ratio->Setting the total number of loop calculations equal to the number of agent models to be built +.>Performing cyclic calculation;
step 5.2, setting an empty set correspondingly for each cycle calculation，Traversing the database every time a loop is calculated>Randomly generating a random number ++1 within a range of 0-1>If random number->Less than bootstrap sampling ratio->Then put the sample into the empty set +.>Until the database is traversed>After all samples in (1), use the set +.>Establishing a proxy model based on an optimal basis function until the cyclic calculation is finished, and entering a step 5.3;
step 5.3, after the cyclic calculation is finished, obtaining the adoptionIndividual data sets are trained separately +.>A proxy model consisting of optimal basis functions.
5. The multi-agent injection and production optimization method based on adaptive basis function selection according to claim 4, wherein in the step 6, the method specifically comprises the following steps:
Step 6.1, setting an empty setIn database->Selecting the sample with the largest net present value and placing the sample in the empty set +.>In (a) and (b);
step 6.2, determining the number of samples in the initial population in the optimization stageSetting the total number of loop calculation as +.>The calculation of the database is carried out every time the calculation of the cycle is carried out>Samples and collections->Cumulative Euclidean distance between samples in (3) and database +.>Middle and Collection->Sample taking out with the largest cumulative Euclidean distance between the samples is placed in the collection +.>Until the cycle calculation is finished, entering a step 6.3;
step 6.3, after the cycle calculation is completed, obtaining the optimal individual including 1Global diversity subset of individual compositions with good spatial properties +.>And subset of global diversity +.>As an initial population for the optimization phase.
6. The multi-agent injection and production optimization method based on adaptive basis function selection according to claim 5, wherein in step 7, the method specifically comprises the following steps:
step 7.1, subset the global diversityInitializing to obtain optimized population->Optimizing populationWherein->To optimize the%>A subject; setting maximum iterative calculation times->；
Setting an objective function to be optimized as Agent model consisting of optimal basis functions +.>，And sets the optimization problem as follows:
（9）；
step 7.2, starting multi-agent optimization iterative computation, utilizingAfter the agent models formed by the optimal basis functions evaluate the fitness values of all samples in the optimized population respectively, the method enters a step 7.3 for rapid non-dominant sorting;
step 7.3, setting empty sets for each body in the optimized population respectivelyAnd the dominant number, empty set->For storing other individuals subjected to individual control, the initial value of the controlled number is set to 0, and the empty set corresponding to each individual is +.>And an evolution formula of the dominant number, as shown in formula (10):
（10）
in the method, in the process of the invention,、/>are individuals in the optimized population;
aiming at all individuals in the optimized population, the pareto grades of the individuals are respectively divided based on a formula (10), and the division basis is as follows:
selection of individuals from an optimized populationAnd->If the empty set corresponding to the individual +.>And the evolution process of the dominant number satisfies the formula (10), then the individual is called +>Dominating individuals->Individual->Corresponding set->Update to original empty set->Is in charge of individuals>Is the union of individuals->Corresponding dominant number->Updated to->；
Will respectivelyIndividual bodyComparing the agent model fitness value with other individuals in the optimized population, and if the individuals are + >Corresponding dominant number->Still 0, it means that none of the other individuals in the optimized population is able to dominate the individual +.>Thereby giving individuals->Set to non-dominant solution, at which time individual +.>The pareto grade of (2) is set to 1; if individuals are->Corresponding dominant number->Is not 0, indicating individual->Other +.>Individual innervation, according to individual->Corresponding dominant number->Individuals are treated with->The pareto grades of (2) are classified as +.>；
Step 7.4, respectively calculating crowding distances of all individuals in the optimized population;
evaluating the fitness value of each sample in the optimized population according to each agent model consisting of the optimal basis functions, sorting the individuals in the optimized population according to the sequence of the fitness values from small to large, setting the crowding distance between the individual with the largest fitness value and the individual with the smallest fitness value to infinity after sorting, and calculating the crowding distance of each individual in the optimized population by using the optimized objective functions respectively aiming at all the individuals in the optimized population, wherein the crowding distance is shown in a formula (11):
（11）
in the method, in the process of the invention,to optimize the%>Sample utilization->Personal objective function->A calculated crowding distance; />Is->Personal objective function->For->Adaptation evaluation value of neighboring individuals in front of each sample, < > >Is->Personal objective function->For->An fitness evaluation value of an adjacent individual behind the individual samples;to utilize->Personal objective function->The maximum evaluation value obtained by all individuals in the optimized population is evaluated,to utilize->Personal objective function->Evaluating the minimum evaluation values obtained by all individuals in the optimized population;
after the crowding distances of all samples in the optimized population under the control of each objective function are calculated, the crowding distances under the control of each objective function are accumulated and summed to obtain the crowding degree of all individuals in the optimized population, and the crowding degree of the individuals in the optimized population is shown as a formula (12):
（12）
in the method, in the process of the invention,is->Final crowding of individual individuals;
step 7.5, selecting the pareto grade in the optimized population to be positioned in front according to the pareto grade and the crowding degree of the individuals in the optimized populationIs located before the individual and crowding degree>Is obtained by randomly selecting parent individuals from the parent population>And parent individuals->Generating parent individuals based on cross mutation calculation>And parent individuals->Is a progeny individual of (a); by carrying out cross mutation calculation on all father individuals in the father population, the offspring individuals obtained by all calculation form offspring population +. >Offspring population->Wherein->Is the>A child generation individual;
the cross variation calculation formula in the cross variation calculation is as follows:
（13）
wherein,,
（14）
in the method, in the process of the invention,for parent individuals->Generating the +.sub.individual by crossover calculation>Wei (dimension)>For parent individuals->Generating the +.sub.individual by crossover calculation>Wei (dimension)>Is a crossing factor->Is a random number between 0 and 1, < >>Is a crossover parameter;
the variance calculation formula in the cross variance calculation is as follows:
（15）
wherein,,
（16）
in the method, in the process of the invention,for offspring individuals->Variation calculation of the final offspring individual +.>Wei (dimension)>As a variant factor, cryptophan officinalis L>Is a variation parameter;
step 7.6, for offspring populationsRepeating steps 7.2 to 7.5Performing iterative computation until the iterative computation times reach the preset maximum iterative computation times +.>Thereafter, a population of offspring is obtained that fits the plurality of agent models.
7. The multi-agent injection and production optimization method based on adaptive basis function selection according to claim 6, wherein in the step 8, an average value of all individuals in each dimension in the child population suitable for the plurality of agent models is calculated, and a new sample is generated, as shown in formula (17):
（17）
in the method, in the process of the invention,for new sample- >Is>Wei (dimension)>Is the>Individual->Dimension; />The number of sample points in the offspring population;
new samples to be generatedInputting the sample into a reservoir numerical simulator, and calculating a new sample by using the reservoir numerical simulator>Net present value->And new sample->And the net present value of the new sample +.>Add to database->In updating database->Is a sample of (b).
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