A method for optimizing crack parameters based on Gaussian process regression

Abstract

The present invention provides a method for optimizing fracture parameters based on Gaussian process regression, comprising the following steps: obtaining a set of daily production data and cumulative production data under different fracture parameters through simulation as a basic data set, and establishing an implicit function of fracture parameters, daily production and cumulative production in the basic data set; dividing the basic data set into a training set and a test set, and respectively obtaining a Gaussian process regression daily production model and a Gaussian process regression cumulative production model; establishing an objective function according to the two Gaussian process regression models; setting an initial population, selecting better individuals in the initial population, and performing iterative calculations on them using a genetic algorithm to select the optimal fracture parameters; the present invention can effectively optimize the fracture parameters of a tight gas fracturing well, including the optimal fracture half-fracture length, the optimal fracture seam spacing, and the optimal fracture permeability, and can also greatly improve the calculation efficiency and realize real-time optimization.

Description

Technical Field

[0001] The invention relates to the technical field of gas reservoir development, and in particular to a fracture parameter optimization method based on Gaussian process regression. Background Art

[0002] Tight gas is a very important unconventional oil and gas resource. 80% of my country's natural gas reservoirs are located in tight gas reservoirs. Improving the development efficiency of tight gas reservoirs is an important guarantee for ensuring my country's energy security. For low-permeability and ultra-low-permeability tight gas reservoirs, fracturing is often required before or after production. Fracturing parameter optimization is a key link in fracturing design. In order to maximize the production capacity of fracturing wells, fracture parameters such as fracture spacing (number of fractures), fracture half-fracture length and fracture permeability need to be efficiently optimized.

[0003] The core of applying machine learning to the field of gas reservoir development technology is two aspects: big data analysis and accelerated expensive optimization. Big data analysis mainly includes two aspects: predicting development benefits and monitoring reservoir dynamics, while accelerated expensive optimization mainly refers to proxy model optimization. The so-called "proxy model optimization" is to establish a proxy model (approximate learning model such as machine learning model) for the expensive (here "expensive" refers to expensive calculations, such as commercial software or numerical simulation models) objective function (complex and time-consuming numerical simulation models in the analysis and optimization design process), and use the proxy model to replace the original real function in the optimization process. At first, the prototype of the proxy model was the polynomial response surface model. So far, many methods such as polynomial response surface, Kriging interpolation, radial basis function interpolation have been developed, which are often used for some problems with unknown mathematical models. For example, in automobile design, if the accurate mathematical model between design parameters (vehicle speed, frame structure, brakes, etc.) and collision degree is unknown, the proxy model can be used to optimize the design parameters. At present, there is still a lack of application of proxy models in the field of gas reservoir development technology.

[0004] When performing traditional fracture parameter optimization, a large number of numerical simulations are required. The calculation efficiency of parameter optimization based on numerical simulation is low. The optimization of hydraulic fracture parameters in unconventional reservoirs is usually computationally expensive and takes hours or even days. By building a machine learning model to proxy the traditional numerical simulation model to assist in optimizing fracture parameters, the calculation efficiency can be greatly improved and real-time optimization can be achieved. However, according to traditional methods, fracturing parameter optimization based on commercial software or numerical simulation often takes dozens of hours or even days, which is inefficient and difficult to achieve fast and real-time optimization of parameters on site. Summary of the invention

[0005] In response to the above problems, the present invention provides a fracture parameter optimization method based on Gaussian process regression, which can effectively optimize the fracture parameters of tight gas fracturing wells, including the optimal fracture half-length, the optimal fracture spacing, and the optimal fracture permeability. By constructing a machine learning model to replace the traditional numerical simulation model to assist in optimizing the fracture parameters, the calculation efficiency can be greatly improved, and real-time optimization can be achieved, which can make up for the shortcomings of the existing method for optimizing fracture parameters of tight gas fracturing wells.

[0006] The present invention adopts the following technical solutions:

[0007] A method for optimizing crack parameters based on Gaussian process regression, characterized in that it comprises the following steps:

[0008] Step 1: Use a fracture numerical simulation model to simulate a set of daily production data and cumulative production data of tight gas fracturing wells under different fracture parameters as a basic data set, and establish an implicit function between the fracture parameters and the daily production and cumulative production in the basic data set;

[0009] Step 2: divide the basic data set into a training set and a test set, and obtain the covariance matrix based on the training set. Perform Gaussian process regression training using the training set data based on the maximum likelihood estimation method to obtain a Gaussian process regression daily production model and a Gaussian process regression cumulative production model;

[0010] Step 3, establishing an objective function based on maximum output according to two Gaussian process regression models;

[0011] Step 4, set the initial population, use the roulette method to select the better individuals in the initial population, encode the better individuals, and use the genetic algorithm to iteratively calculate them to select the optimal crack parameters.

[0012] The beneficial effects of the present invention are:

[0013] The present invention can effectively optimize the fracture parameters of tight gas fracturing wells, including the optimal fracture half length, the optimal fracture spacing, and the optimal fracture permeability, on the basis of ensuring the convenience of on-site implementation. Moreover, by constructing a machine learning model to replace the traditional numerical simulation model to assist in optimizing the fracture parameters, the calculation efficiency can be greatly improved, and real-time optimization can be achieved. This can make up for the shortcomings of the existing method for optimizing fracture parameters of tight gas fracturing wells, and is conducive to wide use.

[0014] At the same time, the new method proposed in this patent only takes a few seconds to calculate, which increases the optimization speed by 4-5 orders of magnitude, and has considerable potential economic value in terms of efficiency and speed. In addition, the patent of this invention introduces machine learning and artificial intelligence into oil and gas engineering, which is in line with the industry development direction of "intelligentization" and has strong foresight in optimizing fracture parameters of fracturing wells. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings in the following description only relate to some embodiments of the present invention, but are not intended to limit the present invention.

[0016] Figure 1 It is a schematic diagram of the process of the present invention;

[0017] Figure 2 Schematic diagram of the framework of the Gaussian process regression and genetic algorithm fusion (GPR-GA) operation of the present invention;

[0018] Figure 3 It is a schematic diagram for comparing the tight gas daily production fitting value and the tight gas daily production real value of the Gaussian process regression daily production model of the present invention;

[0019] Figure 4 It is a schematic diagram for comparing the fitted value of the tight gas cumulative production of the Gaussian process regression cumulative production model of the present invention and the actual value of the tight gas cumulative production;

[0020] Figure 5 Schematic diagram of selecting excellent individuals using the genetic algorithm roulette method of the present invention. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] like Figures 1 to 5 As shown, the present invention provides a technical solution, a crack parameter optimization method based on Gaussian process regression, comprising the following steps:

[0023] Step 1: Use the fracture numerical simulation model to simulate a set of daily production data and cumulative production data of tight gas fracturing wells under different fracture parameters as the basic data set, and establish an implicit function of fracture parameters in the basic data set with daily production and cumulative production.

[0024] (1) Dividing the matrix grid, and discretizing the fracture into several fracture segments through the matrix grid;

[0025] (2) Calculate the translocation coefficient between the matrix and the fracture (the connection between the fracture and the matrix is ​​called type I NNC). The translocation coefficient between the matrix grid and the fracture segment is,

[0026]

[0027] (3) Calculate the crossover coefficient between fractures (the connection between fractures is called type II NNC). The crossover coefficient between the matrix grid and the fracture fragment is,

[0028]

[0029] in,

[0030]

[0031] (4) Construct the seepage equation. The seepage equation of gas in the matrix is:

[0032]

[0033] The flow equation of gas in the crack is:

[0034]

[0035] The daily production data and cumulative production data under different fracture parameters are calculated to form a basic data set. The results are shown in Table 1.

[0036] Table 1 Basic data set

[0037]

[0038]

[0039] (5) Based on the above basic data set, the implicit function of fracture parameters and daily production and cumulative production is established:

[0040] y 1 =f 1 (x)

[0041] y 2 =f 2 (x)

[0042] In the formula, y 1 is the daily output, y 2 is the cumulative production, x is the fracture parameters, and the fracture parameters include fracture permeability, fracture length, and fracture spacing.

[0043] Step 2: divide the basic data set into a training set and a test set, and obtain the covariance matrix based on the training set. Use the training set data to train Gaussian process regression based on the maximum likelihood estimation method to obtain the Gaussian process regression daily production model and the Gaussian process regression cumulative production model.

[0044] (1) In this step, the Bootstrap resampling method is used to select a new set from the basic data set. Assume that the basic data set S contains n different samples. Each time, a sample is extracted from the basic data set S with replacement, and a total of n samples are extracted to form a new set S 1 , then the set S 1 A sample is not included in The probability is,

[0045]

[0046] When n→∞, we have

[0047]

[0048] Remove S 1 The new set S 1 The sample size of the basic dataset S is about 1-36.8% = 63.2%. 1 As a training set, let the new set S 2 =SS 1 as a test set.

[0049] The training set and test set division results are shown in Table 2.

[0050] Table 2. Training set and test set division results

[0051]

[0052]

[0053] (2) Calculate the initial covariance matrix according to the covariance matrix formula and the training set selected by Bootstrap resampling. The covariance matrix formula is:

[0054]

[0055] (3) The fracture parameter data x and daily production data y in the basic data set 1 , cumulative production data y 2 Satisfies the implicit function relationship,

[0056] y 1 =f 1 (x)

[0057] y 2 =f 2 (x)

[0058] When the mean of the distribution is zero, the covariance matrix K is used to construct the prior Gaussian distribution of the implicit function.

[0059] f(x)=GP(0,K)

[0060] (4) After obtaining the Gaussian distribution relationship, the fitting values ​​of tight gas daily production and tight gas cumulative production can be calculated. The maximum likelihood estimation method is used to optimize the parameters of Gaussian process regression and calculate the optimized covariance matrix. The optimal Gaussian process regression parameters are shown in Table 3.

[0061] Table 3 Final values ​​of Gaussian process regression parameter iteration

[0062] <![CDATA[Signal standard deviation (σ f )]]> <![CDATA[Length scale (σ l )]]> <![CDATA[e 3.22 ]]> <![CDATA[e 0.41 ]]>

[0063] (6) The optimized Gaussian distribution relationship is obtained according to the optimized covariance matrix, and the Gaussian process regression model is trained to obtain the Gaussian process regression daily production model and the Gaussian process regression cumulative production model. The fitting results of the daily production on the 365th day are shown in Table 4.

[0064] Table 4 Fitting results of daily production on the 365th day

[0065]

[0066]

[0067] The fitting results of the cumulative output on the 365th day are shown in Table 5.

[0068] Table 5 Fitting results of cumulative production on the 365th day

[0069]

[0070]

[0071] (6) Compare the fitted value calculated by the Gaussian process regression model after the training with the true value of the training set to calculate the mean square error. The mean square error is calculated by the following formula:

[0072]

[0073] The fitting MSE of the Gaussian process regression model is shown in Table 6. It can be seen from Table 6 that the optimized Gaussian process regression model has a higher accuracy.

[0074] Table 6 Fitting RMSE of Gaussian process regression model

[0075] Daily production model MSE Cumulative production model MSE 5.2368 13.2729

[0076] Step 3, using the two obtained Gaussian process regression models to establish the objective function for genetic algorithm optimization:

[0077] max G=lgG 1 (n f ,l half ,K)·lgG2 (n f ,l half ,K)

[0078]

[0079] Step 4, assuming the population size of the genetic algorithm, and randomly setting the initial value of the population iteration, defining the fitness function and calculating the fitness, and selecting the excellent individuals in the population using the roulette method according to the fitness, specifically including the following steps:

[0080] (1) The population size of the genetic algorithm is set to 20 (the population size refers to the number of individuals in the population, and each individual is a set of crack parameter combinations), and the initial value of the population iteration is randomly given, as shown in Table 7.

[0081] Table 7 Initial population of genetic algorithm

[0082]

[0083]

[0084] (2) Define the fitness function (since the objective function value is always non-negative, the objective function is directly taken as the fitness function), and set the value of the population (that is, all the crack parameter combinations n in the population) f , l half , K) into the step 3 by two Gaussian process regression models G 1 , G 2 In the established objective function G, each individual in the population (i.e., the crack parameter combination n f , l half , K) corresponds to the fitness of the initial population as shown in Table 8.

[0085] Table 8 Fitness values ​​of the initial population

[0086] Serial number Fitness Serial number Fitness 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

[0087] (3) According to the fitness, the roulette method is used to select the best individuals in the population. That is, the optimal crack parameter combination number under the current population is 11, 19, 20, 9, 12, 3, 5, 8, 1, 18 (the roulette method diagram is shown in Figure 5 shown).

[0088] Step 5, convert the initial value of the excellent individuals into binary code, and obtain a new population through "crossover" (exchanging part of the binary code of two excellent individuals) and "mutation" (changing a certain value of a binary code), which specifically includes the following steps:

[0089] (1) Convert the values ​​of the excellent crack parameter combinations screened out in step 4 into binary codes, for example, the binary code of 75 is 01001011, and the binary code of 149 is 10010101;

[0090] (2) exchanging some binary codes of the excellent crack parameter combinations, i.e., “crossing”. For example, if 01001011 and 10010101 are “crossed”, 01000101 and 10011011 will be obtained, i.e., 69 and 165 will be obtained from 75 and 149;

[0091] (3) Changing a certain value of the binary code of the optimal crack parameter combination, i.e., “mutation”, for example, 11001101 is mutated to 11101101, and the corresponding decimal value mutates from 205 to 237;

[0092] (3) The binary code that has undergone "crossover" and "mutation" is re-decoded into decimal data and used as a new population for the next genetic algorithm iteration.

[0093] The new population obtained after "crossover" and "mutation" is shown in Table 9.

[0094] Table 9 New populations obtained after "crossover" and "mutation"

[0095]

[0096]

[0097] Step 7, finally repeating steps 4 and 5, continuously iterating the population in the genetic algorithm to obtain an optimal individual (i.e., a set of optimal crack parameters), and the final optimized crack parameters are shown in Table 10.

[0098] Table 10 Optimal crack parameters

[0099] parameter Seam spacing Half seam length Fracture permeability Optimal value 141.62m 166.35m 28.54D

[0100] 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 variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A crack parameter optimization method based on Gaussian process regression, characterized in that: The following steps are included: Step 1: Use a fracture numerical simulation model to simulate a set of daily production data and cumulative production data of tight gas fracturing wells under different fracture parameters as a basic data set, and establish an implicit function between the fracture parameters and the daily production and cumulative production in the basic data set; Step 2: divide the basic data set into a training set and a test set, and obtain the covariance matrix based on the training set. Perform Gaussian process regression training using the training set data based on the maximum likelihood estimation method to obtain a Gaussian process regression daily production model and a Gaussian process regression cumulative production model; Step 3, establishing an objective function based on maximum output according to two Gaussian process regression models; Step 4, setting the initial population, using the roulette method to select the better individuals in the initial population, encoding the better individuals, and using the genetic algorithm to iteratively calculate them to select the optimal crack parameters; The objective function for genetic algorithm optimization established in step 3 is: max G=lgG1(n f ,l half ,σ)·lgG2(n f ,l half ,s) In the formula, G1(n f ,l half ,σ) represents the Gaussian process regression daily production model; G2(n f ,l half ,σ) represents the Gaussian process regression cumulative production model; n f , l half , σ represent the crack spacing, crack half length, and crack permeability, respectively.

2. The crack parameter optimization method based on Gaussian process regression according to claim 1 is characterized in that: The step 1 specifically includes the following steps: Step 101, dividing the matrix grid, and discretizing the crack into a plurality of crack segments through the matrix grid; Step 102, calculating the crossflow coefficient between the matrix and the crack; Step 103, calculating the crossflow coefficient between cracks; Step 104, constructing and solving the seepage equation, calculating the daily production data and cumulative production data under different fracture parameters to form a set of basic data sets; Step 105, establish an implicit function of fracture parameters, daily production and cumulative production: y1=f1(x) y2=f2(x) Where y1 is the daily production, y2 is the cumulative production, and x is the fracture parameters, which include fracture permeability, fracture length, and fracture spacing.

3. The crack parameter optimization method based on Gaussian process regression according to claim 1 is characterized in that: The step 2 specifically includes the following steps: Step 201, using the Bootstrap resampling method, extracting multiple samples from the basic data set to form a new set, removing duplicate samples in the new set, using the new set as a training set, and using the complement of the basic data set and the new set as a test set; Step 202, calculating an initial covariance matrix according to the covariance matrix formula and the training set; Step 203, set the distribution mean equal to zero, and construct a priori Gaussian distribution model of the implicit function through the covariance matrix: f(x)=GP(0,K) In the formula, GP(0,K) represents Gaussian distribution, where K is the covariance matrix; Step 204, using the maximum likelihood estimation method, optimizing the parameters of the Gaussian process regression and calculating the optimized covariance matrix, and obtaining an optimized Gaussian distribution model according to the optimized covariance matrix; Step 205, obtaining an optimized Gaussian distribution relationship according to the optimized covariance matrix, and training the Gaussian process regression model to obtain a Gaussian process regression daily production model and a Gaussian process regression cumulative production model.

4. The crack parameter optimization method based on Gaussian process regression according to claim 1 is characterized in that: The step 4 specifically includes the following sub-steps: Step 401, randomly generate an initial population; Step 402, substitute the individuals of the population into the objective function, obtain the fitness corresponding to each individual in the population, and select the better individual according to the roulette method; Step 403, binary-encode the better individuals, generate new individuals through "crossover" and "mutation", decode the new individuals and calculate their fitness values; Step 404, continue iterating until a preset number of iterations is reached, and the best individual is selected.

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