CN114925606A - Fracture parameter optimization method based on Gaussian process regression - Google Patents

Fracture parameter optimization method based on Gaussian process regression Download PDF

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CN114925606A
CN114925606A CN202210554894.3A CN202210554894A CN114925606A CN 114925606 A CN114925606 A CN 114925606A CN 202210554894 A CN202210554894 A CN 202210554894A CN 114925606 A CN114925606 A CN 114925606A
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余红广
李铁军
贾靖
敬亚东
张麒
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Abstract

The invention provides a fracture parameter optimization method based on Gaussian process regression, which comprises the following steps of: obtaining a group of daily output data and accumulated output data under different fracture parameters through simulation, using the daily output data and the accumulated output data as a basic data set, and establishing implicit functions of the fracture parameters, the daily output and the accumulated output in the basic data set; dividing the basic data set into a training set and a testing set, and respectively obtaining a Gaussian process regression daily yield model and a Gaussian process regression accumulated yield model; establishing an objective function according to two Gaussian process regression models; setting an initial population, preferably selecting better individuals in the initial population, and performing iterative computation on the better individuals by using a genetic algorithm to preferably select optimal crack parameters; the method can effectively optimize fracture parameters of the compact gas fracturing well, including optimal fracture half-seam length, optimal fracture seam spacing and optimal fracture permeability, and meanwhile can greatly improve calculation efficiency and achieve real-time optimization.

Description

Fracture parameter optimization method based on Gaussian process regression
Technical Field
The invention relates to the technical field of gas reservoir development, in particular to a fracture parameter optimization method based on Gaussian process regression.
Background
The dense gas is a very important unconventional oil gas resource, 80% of natural gas reservoirs in China are located in the dense gas reservoirs, and the enhancement of the development efficiency of the dense gas reservoirs is an important guarantee for ensuring the energy safety in China. For low-permeability and ultra-low-permeability compact gas reservoirs, fracturing production is often required to be put into operation or fracturing production increase is carried out after the production is put into operation, fracturing parameter optimization is a key link of fracturing design, and in order to maximize the production capacity of a fracturing modified well, fracture parameters such as fracture interval (number of fractures), fracture half-fracture length and fracture permeability need to be efficiently optimized.
The core of applying machine learning to the technical field of air reservoir development is two aspects, namely big data analysis and expensive optimization acceleration. The big data analysis mainly comprises two contents, namely, forecasting development benefits and monitoring reservoir dynamics, and the acceleration of expensive optimization mainly refers to physical model optimization. By "proxy model optimization" is meant building a proxy model (e.g., an approximation learning model such as a machine learning model) for an expensive (e.g., "expensive" in this context means computationally expensive, such as commercial software or numerical simulation models) objective function (e.g., those complex and time consuming numerical simulation models in the analysis and optimization design process), and using the proxy model to replace the original true function in the optimization process. At first, the prototype of the proxy model is a polynomial response surface model, and various methods such as polynomial response surface, kriging interpolation, radial basis function interpolation and the like have been developed at present, and are commonly used for some unknown problems of mathematical models. If the exact mathematical model between the design parameters (vehicle speed, frame structure, braking, etc.) and the degree of collision is not known in the vehicle design, then a surrogate model can be used to optimize the design parameters. At present, the application of a proxy model is very lacking in the technical field of gas reservoir development.
When the traditional fracture parameter optimization is carried out, a large amount of numerical simulation is used, the parameter optimization calculation efficiency based on the numerical simulation is low, the optimization of unconventional reservoir hydraulic fracture parameters is usually expensive in calculation cost, and hours or even days are often spent. And by constructing a machine learning model to substitute for the traditional numerical simulation model to assist in optimizing the crack parameters, the calculation efficiency can be greatly improved, and real-time optimization is realized. However, according to the traditional method, the optimization of the fracturing parameters based on commercial software or numerical simulation takes tens of hours or even days, the efficiency is low, and the rapid and real-time optimization of the parameters is difficult to achieve on site.
Disclosure of Invention
Aiming at the problems, the invention provides a fracture parameter optimization method based on Gauss process regression, which can effectively optimize fracture parameters of a compact gas fracturing well, including optimal fracture half-seam length, optimal fracture seam spacing and optimal fracture permeability, and assist in optimizing the fracture parameters by constructing a machine learning model and acting on a traditional numerical simulation model, can greatly improve the calculation efficiency, realize real-time optimization, and can make up for the defects of the fracture parameter optimization method of the compact gas fracturing well in the prior art.
The invention adopts the following technical scheme that,
a fracture parameter optimization method based on Gaussian process regression is characterized by comprising the following steps,
step 1, simulating a group of daily output data and accumulated output data of the compact gas fracturing well under different fracture parameters by using a fracture numerical simulation model as a basic data set, and establishing implicit functions of the fracture parameters, the daily output and the accumulated output in the basic data set;
step 2, dividing a basic data set into a training set and a testing set, obtaining a covariance matrix according to the training set, and carrying out Gaussian process regression training by using training set data based on a maximum likelihood estimation method to respectively obtain a Gaussian process regression daily yield model and a Gaussian process regression accumulated yield model;
step 3, establishing a target function based on maximum yield according to two Gaussian process regression models;
and 4, setting an initial population, preferably selecting a better individual in the initial population by using a roulette method, coding the better individual, and performing iterative computation on the better individual by using a genetic algorithm to preferably select an optimal crack parameter.
The invention has the beneficial effects that:
on the basis of ensuring convenient field implementation, the method can effectively optimize the fracture parameters of the compact gas fracturing well, including optimal fracture half-seam length, optimal fracture seam spacing and optimal fracture permeability, and the fracture parameters are assisted and optimized by constructing a machine learning model and acting on a traditional numerical simulation model, so that the calculation efficiency can be greatly improved, real-time optimization is realized, the defects of the fracture parameter optimization method of the compact gas fracturing well in the prior art can be overcome, and the method is favorable for wide application;
meanwhile, the calculation process of the new method provided by the patent only needs several seconds, the optimization speed is improved by 4-5 orders of magnitude, and the new method has considerable potential economic value in the aspect of efficiency improvement and speed increase. In addition, machine learning and artificial intelligence are introduced into petroleum and natural gas engineering, the intelligent oil well fracturing system is in accordance with the development direction of the intelligent industry, and the method has strong prospect in the aspect of fracturing well fracture parameter optimization.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly described below, and it is apparent that the drawings in the following description only relate to some embodiments of the present invention and are not limiting on the present invention.
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a block diagram of the Gaussian process regression and genetic algorithm fusion (GPR-GA) operation of the present invention;
FIG. 3 is a schematic diagram showing comparison between a fitting value of the daily output of dense gas and a true value of the daily output of dense gas of the model of the Gaussian process regression daily output of the present invention;
FIG. 4 is a schematic diagram showing comparison between a fitting value of cumulative yield of dense gas and a true value of cumulative yield of dense gas in a Gaussian process regression cumulative yield model according to the present invention;
FIG. 5 is a schematic diagram of the genetic algorithm roulette method of the present invention for selecting superior individuals.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1 to 5, the present invention provides a technical solution, a fracture parameter optimization method based on gaussian process regression, comprising the following steps,
step 1, simulating a group of daily output data and accumulated output data of the compact gas fracturing well under different fracture parameters by using a fracture numerical simulation model as a basic data set, establishing implicit functions of the fracture parameters, the daily output and the accumulated output in the basic data set,
(1) dividing a matrix grid, and dispersing the cracks into a plurality of crack segments through the matrix grid;
(2) calculating the channeling coefficient between the matrix and the crack (the connection between the crack and the matrix is called type I NNC), wherein the channeling coefficient between the matrix mesh and the crack segments is,
Figure BDA0003651971220000031
(3) calculating the channeling coefficient between the cracks (the connection between the cracks is called II-type NNC), wherein the channeling coefficient between the matrix grids and the crack segments is,
Figure BDA0003651971220000032
wherein,
Figure BDA0003651971220000033
(4) constructing a seepage equation, wherein the seepage equation of the gas in the matrix is,
Figure BDA0003651971220000034
the seepage equation of the gas in the fracture is,
Figure BDA0003651971220000035
daily production data and accumulated production data under different fracture parameters are calculated to form a basic data set, and the results are shown in table 1,
TABLE 1 basic data set
Figure BDA0003651971220000036
Figure BDA0003651971220000041
(5) And (3) establishing implicit functions of the crack parameters, the daily yield and the accumulated yield according to the basic data set:
y 1 =f 1 (x)
y 2 =f 2 (x)
in the formula, y 1 For daily output, y 2 For cumulative production, x is the fracture parameters including fracture permeability, fracture length, fracture spacing.
Step 2, dividing the basic data set into a training set and a testing set, obtaining a covariance matrix according to the training set, carrying out Gaussian process regression training by using the training set data based on a maximum likelihood estimation method, respectively obtaining a Gaussian process regression daily yield model and a Gaussian process regression accumulated yield model,
(1) in this step, a Bootstrap resampling method is used to select a new set from the basic data set, and the basis is assumedThe base data set S contains n different samples
Figure BDA0003651971220000051
Each time a sample is taken back from the basic data set S, a total of n times, forming a new set S 1 Then set S 1 Does not contain a certain sample
Figure BDA0003651971220000052
The probability of (a) being,
Figure BDA0003651971220000053
when n → ∞ is present
Figure BDA0003651971220000054
Remove S 1 Middle repeated samples, then new set S 1 Samples containing about 1-36.8% ═ 63.2% of the base data set S were analyzed for S 1 As training set, let new set S 2 =S-S 1 As a test set.
The results of the training set and test set partitioning are shown in table 2,
TABLE 2 results of training set and test set partitioning
Figure BDA0003651971220000055
Figure BDA0003651971220000061
(2) Calculating an initial covariance matrix according to a covariance matrix formula and a training set selected by Bootstrap resampling, wherein the covariance matrix formula is,
Figure BDA0003651971220000071
(3) the basic data set comprises fracture parameter data x and daily output data y 1 Cumulative production data y 2 The relation of an implicit function is satisfied,
y 1 =f 1 (x)
y 2 =f 2 (x)
then when the mean of the distribution is zero, a prior gaussian distribution of the implicit function is constructed from the covariance matrix K,
f(x)=GP(0,K)
(4) after the Gaussian distribution relation is obtained, the fitting value of the daily yield of the dense gas and the accumulated yield of the dense gas can be calculated. Optimizing the regression parameters of the Gaussian process by using a maximum likelihood estimation method and calculating an optimized covariance matrix, wherein the optimal regression parameters of the Gaussian process are shown in Table 3,
TABLE 3 iterative final values of regression parameters for Gaussian process
Signal standard deviation (sigma) f ) Length Scale (σ) l )
e 3.22 e 0.41
(6) Obtaining an optimized Gaussian distribution relation according to the optimized covariance matrix, training a Gaussian process regression model to respectively obtain a Gaussian process regression daily yield model and a Gaussian process regression cumulative yield model, wherein the fitting result of the yield of the 365 th day is shown in Table 4,
TABLE 4 fitting results of daily yields on day 365
Figure BDA0003651971220000072
Figure BDA0003651971220000081
The results of the fit to the cumulative yield at day 365 are shown in table 5,
TABLE 5 cumulative yield on day 365 fitted results
Figure BDA0003651971220000082
Figure BDA0003651971220000091
(6) Comparing the fitting value calculated by the regression model of the Gaussian process after the training with the real value of the training set, calculating the mean square error by the following formula,
Figure BDA0003651971220000092
the fitting MSE of the gaussian process regression model is shown in table 6, and it can be seen from table 6 that the optimized gaussian process regression model has higher precision.
TABLE 6 fitting RMSE of Gaussian Process regression models
Daily output model MSE Cumulative yield model MSE
5.2368 13.2729
Step 3, establishing a target function for genetic algorithm optimization by using the obtained two Gaussian process regression models,
max G=lgG 1 (n f ,l half ,K)·lgG 2 (n f ,l half ,K)
Figure BDA0003651971220000093
step 4, assuming the population scale of the genetic algorithm, randomly setting an initial value of population iteration, defining a fitness function and calculating the fitness, and selecting excellent individuals in the population by using a roulette method according to the fitness,
(1) the population size of the genetic algorithm was set to 20 (population size refers to the number of individuals in the population, each individual being a set of fracture parameter combinations), and the initial value of the population iteration was randomly given, as shown in table 7,
TABLE 7 initial population of genetic algorithms
Figure BDA0003651971220000094
Figure BDA0003651971220000101
(2) Defining a fitness function (because the objective function value is always non-negative, the objective function is directly taken as the fitness function), and taking the value of the population (namely all crack parameter combinations n in the population) f ,l half And K) substituting into the step 3 by two Gaussian process regression models G 1 ,G 2 In the established target function G, each individual in the population (namely a crack parameter combination n) is obtained f ,l half K), the fitness corresponding to the initial population is shown in Table 8,
TABLE 8 fitness value of the initial population
Serial number Fitness Serial number Degree of adaptability
1 20.48 11 24.32
2 17.97 12 22.76
3 22.45 13 19.87
4 16.89 14 19.36
5 21.87 15 19.47
6 16.84 16 18.07
7 18.69 17 20.09
8 21.26 18 20.11
9 22.81 19 23.18
10 15.82 20 22.95
(3) According to the fitness, excellent individuals in the population are selected by using a roulette method, namely, the optimal fracture parameter combination serial numbers of the current population are 11, 19, 20, 9, 12, 3, 5, 8, 1 and 18 (a roulette method schematic diagram is shown in fig. 5).
Step 5, converting the initial value of the excellent individuals into binary codes, and obtaining a new population through crossing (exchanging partial binary codes of two excellent individuals) and variation (changing a certain value of a certain binary code), which specifically comprises the following steps,
(1) converting the values of the excellent fracture parameter combinations selected in step 4 into binary codes, for example, a binary code of 75 is 01001011, and a binary code of 149 is 10010101;
(2) exchanging the partial binary codes of the superior fracture parameter combinations with each other, i.e., "crossover", e.g., "crossover" 01001011 and 10010101, results in 01000101 and 10011011, i.e., 69 and 165 from 75 and 149;
(3) changing a value of the binary code of the outstanding fracture parameter combination, i.e., "variation", e.g., 11001101, to obtain 11101101, the corresponding decimal value varies from 205 to 237;
(3) and re-decoding the binary codes subjected to the cross and the mutation into 10-system data as a new population for the next genetic algorithm iteration.
The new populations obtained after "crossover" and "mutation" are shown in table 9,
TABLE 9 New populations obtained after "crossover", "mutation
Figure BDA0003651971220000111
Figure BDA0003651971220000121
Step 7, finally repeating step 4 and step 5, continuously iterating the population in the genetic algorithm to obtain an optimal individual (i.e. a group of optimal fracture parameters), wherein the final optimal fracture parameters are shown in table 10,
TABLE 10 optimal fracture parameters
Parameter(s) Gap interval Half seam length Permeability of crack
Optimum value 141.62m 166.35m 28.54D
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (5)

1. A fracture parameter optimization method based on Gaussian process regression is characterized by comprising the following steps,
step 1, simulating a group of daily output data and accumulated output data of a compact gas fracturing well under different fracture parameters by using a fracture numerical simulation model as a basic data set, and establishing implicit functions of the fracture parameters, the daily output and the accumulated output in the basic data set;
step 2, dividing the basic data set into a training set and a test set, obtaining a covariance matrix according to the training set, and carrying out Gaussian process regression training by using the training set data based on a maximum likelihood estimation method to respectively obtain a Gaussian process regression daily yield model and a Gaussian process regression accumulated yield model;
step 3, establishing a target function based on maximum yield according to two Gaussian process regression models;
and 4, setting an initial population, preferably selecting a better individual in the initial population by using a roulette method, coding the better individual, and performing iterative computation on the better individual by using a genetic algorithm to preferably select an optimal crack parameter.
2. The method for optimizing fracture parameters based on Gaussian process regression as claimed in claim 1, wherein the step 1 specifically comprises the following steps,
step 101, dividing a matrix grid, and dispersing cracks into a plurality of crack segments through the matrix grid;
102, calculating a channeling coefficient between a matrix and a fracture;
103, calculating a channeling coefficient between the cracks;
104, constructing and solving a seepage equation, and calculating daily output data and accumulated output data under different fracture parameters to form a group of basic data sets;
step 105, establishing implicit functions of crack parameters, daily yield and accumulated yield:
y 1 =f 1 (x)
y 2 =f 2 (x)
in the formula, y 1 For daily output, y 2 For cumulative production, x is the fracture parameters including fracture permeability, fracture length, fracture spacing.
3. The method for optimizing fracture parameters based on Gaussian process regression as claimed in claim 1, wherein the step 2 specifically comprises the following steps,
step 201, extracting a plurality of samples from a basic data set by adopting a Bootstrap resampling method to form a new set, taking the new set as a training set after removing repeated samples in the new set, and taking a complementary set of the basic data set and the new set as a test set;
step 202, calculating an initial covariance matrix according to a covariance matrix formula and a training set;
step 203, making the distribution mean equal to zero, and constructing a prior gaussian distribution model of the implicit function through the covariance matrix:
f(x)=GP(0,K)
wherein GP (0, K) represents a Gaussian distribution, wherein K is a covariance matrix;
204, optimizing parameters of Gaussian process regression by using a maximum likelihood estimation method, calculating an optimized covariance matrix, and obtaining an optimized Gaussian distribution model according to the optimized covariance matrix;
and step 205, obtaining an optimized Gaussian distribution relation according to the optimized covariance matrix, and training a Gaussian process regression model to respectively obtain a Gaussian process regression daily yield model and a Gaussian process regression cumulative yield model.
4. The method for optimizing fracture parameters based on Gaussian process regression as claimed in claim 1, wherein the objective function for genetic algorithm optimization established in step 3 is,
max G=lgG 1 (n f ,l half ,σ)·lgG 2 (n f ,l half ,σ)
Figure FDA0003651971210000021
in the formula, G 1 (n f ,l half σ) represents a gaussian process regression daily yield model; g 2 (n f ,l half σ) represents a Gaussian process regression cumulative yield model; n is f ,l half And sigma respectively represents the crack gap, the crack half-crack length and the crack permeability.
5. The method for optimizing fracture parameters based on Gaussian process regression as claimed in claim 1, wherein the step 4 comprises the following sub-steps,
step 401, randomly generating an initial population;
step 402, substituting the individuals of the population into an objective function to obtain the fitness corresponding to each individual in the population, and preferably selecting the better individual according to a roulette method;
step 403, performing binary coding on the better individuals, generating new individuals through crossing and mutation, decoding the new individuals and calculating the fitness value of the new individuals;
and step 404, continuously iterating until the preset iteration times are reached, and preferably selecting the optimal individual to obtain the target.
CN202210554894.3A 2022-05-19 2022-05-19 Fracture parameter optimization method based on Gaussian process regression Pending CN114925606A (en)

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