A fracturing horizontal well perforation position optimization method based on dynamic programming solution

Abstract

The present application relates to the technical field of oil and gas stimulation, in particular to a fracturing horizontal well perforation position optimization method based on dynamic programming solution, comprising the following steps: 1) selecting a sweet spot evaluation parameter, normalizing the sweet spot evaluation parameter, and establishing a sweet spot index model; 2) establishing a single fracturing section perforation position optimization model, wherein the perforation position meets the cluster spacing constraint and the maximum cluster number constraint; 3) after dividing multiple fracturing sections in the entire horizontal well fracturing section, repeating the single fracturing section perforation position optimization process, and completing the entire horizontal section perforation position optimization. The present application uses the dynamic programming idea to construct the state transition equation to solve the perforation cluster position optimization model, realizes the rapid optimization of the shale gas horizontal well perforation position, and makes up for the shortcomings of the artificial division of the perforation cluster.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of oil and gas production, and particularly relates to a fracturing horizontal well perforation position optimization method based on dynamic programming solution. BACKGROUND

[0002] Beneficial development of shale gas reservoirs needs to be assisted by horizontal well staged multi-cluster large-scale volume fracturing technology. Perforation position selection is an important link in horizontal well pressure staged fracturing design, and reasonable optimization of perforation position is the basis for achieving good transformation effect. In the horizontal well section, perforation cluster positions are usually artificially optimized according to the designed fracturing staged position, cluster interval and cluster number, and according to the physical parameters and pressureability of the horizontal well section reservoir. However, when the horizontal well fracturing section is divided into more sections, artificial division and optimization have problems such as time consumption, incomplete consideration of factors, and difficulty in obtaining the optimal perforation position distribution under the restrictions of cluster interval and cluster number.

[0003] In order to make up for the above problems in the prior art when perforation clusters are artificially divided, the application provides a fracturing horizontal well perforation position optimization method based on dynamic programming solution. SUMMARY

[0004] The application aims to solve the defects in artificial division of perforation clusters and provide a fracturing horizontal well perforation position optimization method based on dynamic programming solution.

[0005] In order to achieve the above purpose, the technical scheme adopted by the application is as follows:

[0006] A fracturing horizontal well perforation position optimization method based on dynamic programming solution, characterized by comprising the following steps:

[0007] 1) Selecting a sweet spot evaluation parameter, normalizing the sweet spot evaluation parameter, and establishing a sweet spot index model;

[0008] 2) Establishing a single fracturing section perforation position optimization model, wherein the perforation position meets the cluster interval constraint and the maximum cluster number constraint;

[0009] 3) After dividing multiple fracturing sections in the entire horizontal well fracturing section, repeating the single fracturing section perforation position optimization process to complete the entire horizontal section perforation position optimization.

[0010] Preferably, the sweet spot evaluation parameter in step 1) includes organic carbon content, porosity, gas content, Young's modulus, Poisson's ratio and horizontal stress difference.

[0011] Preferably, the normalization method in step 1) includes:

[0012] For forward sweet spot evaluation parameters:

[0013]

[0014] For reverse dessert evaluation parameters:

[0015]

[0016] wherein y is the normalized dessert evaluation parameter; x is the original dessert evaluation parameter with dimension; x max is the maximum value of the dessert evaluation parameter in a certain interval; x min is the minimum value of the dessert evaluation parameter in a certain interval.

[0017] Preferably, the step 1) further comprises:

[0018] determining the weight of each dessert evaluation parameter to establish a dessert index model.

[0019] Preferably, the step 1) determines the weight of each dessert evaluation parameter by the coefficient of variation method which measures the size of the difference information.

[0020] Preferably, the step 1) establishes the dessert index model, which comprises:

[0021] determining the weight of each dessert evaluation parameter:

[0022]

[0023] wherein w k is the weight value of the kth dessert evaluation parameter; C k is the coefficient of variation of the kth dessert evaluation parameter; σ k is the standard deviation of the single dessert evaluation parameter; is the mean value of the single dessert evaluation parameter; and n is the number of the dessert evaluation parameters.

[0024] calculating the dessert index:

[0025]

[0026] wherein DI is the dessert index, y is the normalized dessert evaluation parameter, and k represents the serial number.

[0027] Preferably, the step 2) is a perforation position optimization model, which comprises:

[0028]

[0029] wherein MD is the depth, DI is the dessert index, c is the cluster number, L 1、 L2 is the depth range, and a and b are the left and right endpoints of the cluster interval range.

[0030] Preferably, the step 3) adopts dynamic programming to solve the single fracture perforation optimization model.

[0031] The preferred state transition equation for dynamic programming is:

[0032]

[0033] Preferably, in step 3), the minimum segment spacing also needs to be considered. Let the minimum segment spacing between two adjacent fracturing segments be ΔL. Then, for a fracturing segment with a top depth of TD and a bottom depth of BD, the actual top depth, bottom depth L1, and bottom depth L2 of the well section used for perforation location selection are:

[0034]

[0035] This invention utilizes a comprehensive sweet spot evaluation index that considers reservoir physical parameters and compressibility conditions. Within the fractured section of a horizontal well, it considers constraints such as segment location, minimum segment spacing, fracture section length, perforation cluster spacing, and cluster number. The objective is to construct an optimal perforation cluster location model by maximizing the sum of the comprehensive sweet spot values ​​corresponding to all optimized perforation clusters. Dynamic programming is employed to construct state transition equations for solving the perforation cluster location optimization model, enabling rapid optimization of perforation locations in shale gas horizontal wells. This overcomes the shortcomings of manually dividing perforation clusters and simplifies the fracturing design process. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0037] Figure 2 This is a diagram showing the preferred results of the segmented perforation cluster in Well A in this embodiment of the invention;

[0038] Figure 3 This is a comparison diagram of the 9th fracturing section DI and the preferred perforation position in an embodiment of the present invention. Detailed Implementation

[0039] The present invention will now be described in detail with reference to the accompanying drawings.

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] like Figure 1 As shown, this invention provides a method for optimizing the perforation location in a fracturing horizontal well based on dynamic programming, comprising the following steps:

[0042] 1) Select dessert evaluation parameters, normalize the dessert evaluation parameters, and establish a dessert index model;

[0043] 2) Establish a single fracture section within the perforation location optimization model, the perforation location meets the cluster spacing constraint and the maximum cluster number constraint;

[0044] 3) In the whole horizontal well fracturing section, after dividing multiple fracturing sections, repeat the single fracturing section perforation location optimization process to complete the whole horizontal section perforation location optimization.

[0045] In step 1), when the fracturing section is divided and the perforation cluster location is optimized, the continuous dessert distribution along the wellbore profile is needed, the total organic carbon content, porosity, gas content and other geological dessert evaluation parameters interpreted by the logging data with good continuity are standardized, and the weight is determined by using the coefficient of variation method, and the comprehensive dessert index DI (dessert index) is constructed by using the weighted method.

[0046] Since different dessert evaluation parameters have different dimensions, the organic carbon content, porosity, gas content, Young's modulus, Poisson's ratio, and horizontal stress difference need to be normalized to make the data reach the same order of magnitude. The range transformation method is used for data normalization. For positive dessert evaluation parameters:

[0047]

[0048] For reverse dessert evaluation parameters:

[0049]

[0050] In the formula, y is the normalized dessert parameter, x is the original dessert parameter with dimension, x max is the maximum value of the dessert parameter in the well section, and x min is the minimum value of the dessert parameter in the well section.

[0051] In the process of comprehensive evaluation of geological engineering dessert, the weight is a key factor. For the dessert parameters of the continuous profile of the horizontal section, the greater the difference is, the more the difference should be considered in the fracturing section design, and the greater the weight is, so as to make more targeted design; on the contrary, if the difference of a dessert parameter in the horizontal section is small, the dessert parameter can be regarded as the same type in the whole well section, and it is not necessary to consider it specifically, which is also the basic principle of difference segmentation. Therefore, the variation coefficient method which measures the size of the difference information of the index is used to determine the weight of the dessert evaluation parameter:

[0052]

[0053] In the formula, w k is the weight value of the kth dessert evaluation parameter, C k is the variation coefficient of the kth dessert evaluation parameter, and σk standard deviation of the parameter for individual dessert evaluation; average value of the parameter for individual dessert evaluation; n is the number of dessert evaluation parameters.

[0054] The dessert index DI is calculated as follows:

[0055]

[0056] Step 2) Establish a single-pressure fracture segment perforation location optimization model, which meets the cluster spacing constraint and the maximum cluster number constraint;

[0057] The perforation cluster optimization needs to be based on the comprehensive dessert evaluation results to optimize the position with better results in the fracture segment, while considering factors such as fracture segment length, perforation cluster number, cluster spacing, etc.

[0058] Let the fracture segment depth range for perforation location optimization be L1 to L2, the cluster spacing range be a to b, the designed perforation cluster number be c, and the depth of the optimized perforation location be MD i The corresponding comprehensive dessert index is DI i The selected fracture location MD i satisfies the following constraints:

[0059] (1) Cluster spacing constraint, that is:

[0060] a≤MD i+1 -MD i ≤b(6)

[0061] In the formula: a, b are the left and right endpoints of the cluster spacing range, m; MD i+1 -MD i is the cluster spacing, m.

[0062] (2) Maximum cluster number constraint:

[0063] Starting from the beginning of the fracture segment, the maximum cluster number can be determined by selecting the minimum cluster spacing:

[0064] L1+a(c max -1)=L2(7)

[0065] The solution is:

[0066]

[0067] From this, the cluster number range can be determined:

[0068] 0<c≤c max (9)

[0069] Taking the depth MD, the dessert index DI, and the cluster number c as decision variables, and taking the sum of the closeness of the selected perforation points The maximum is the target, and the cluster spacing constraint requirement is met in the target section. The optimization point selection model is constructed as follows:

[0070]

[0071] Solving the above optimization model can obtain the fracturing perforation position that meets the cluster spacing and cluster number requirements in a single fracturing section.

[0072] 3) In the entire horizontal well fracturing section, after dividing multiple fracturing sections, the single fracturing section perforation position optimization process is repeated and iterated to complete the entire horizontal section perforation position optimization.

[0073] In the perforation position optimization process, due to the constraint of cluster spacing, the perforation position optimization problem is a multi-stage decision problem, which can be solved by constructing the state transition equation of the dynamic programming problem. Let d ij represent the optimal value when the jth position value is selected when there are a total of i dessert positions. For each d ij , there are two choices: one is not to select the i-th position, then d ij = d i-1,j , the second is to select the i-th position, then select one from the states in the range of i-b to i-a to transfer, that is, d ij = max(d m,j-1 + DI i ), where m is between i-b and i-a. Thus, the state transition equation of the dynamic programming problem can be constructed as follows:

[0074]

[0075] According to the iterative calculation of the state transition equation, the optimal solution of the above optimization problem can be obtained, and the crushability value DI i and the corresponding depth of each selected dessert can be recorded to obtain the optimal perforation position distribution under the constraints of formula (10) and formula (11).

[0076] In the entire horizontal well fracturing section, after dividing multiple fracturing sections, the single section perforation position optimization process is repeated and iterated to complete the entire horizontal section perforation position optimization. For adjacent two fracturing sections, a reasonable section spacing needs to be set to perform segmented fracturing by setting a bridge plug segmentation tool. Therefore, when optimizing the perforation position of multiple fracturing sections, the minimum section spacing needs to be considered to determine the actual well section used for perforation position optimization of each fracturing section. Let the minimum section spacing between adjacent two fracturing sections be ΔL, and for a fracturing section with a top depth of TD and a bottom depth of BD, the actual well section used for perforation position optimization is L1 and L2:

[0077]

[0078] Example application

[0079] There is a shale gas horizontal well A with a horizontal section length of 2200 meters, 32 sections of fracturing, and a comprehensive sweet spot index DI is constructed by using the logging, seismic and other data of the well, considering porosity (POR), total organic carbon content (TOC), gas content (GAS), Young's modulus (E), Poisson's ratio (v), and horizontal principal stress difference (ΔH). The cluster spacing of the well is designed to be 8-10 meters, the single section is 4-6 clusters, and the minimum section spacing is 16 meters. Table 1 gives the fracturing section position of the well and the well section considering the minimum section spacing for the actual perforation position optimization.

[0080] Table 1A Well fracturing section position and perforation cluster optimization well section range

[0081]

[0082]

[0083] Table 2A Well perforation cluster position optimization result table

[0084]

[0085]

[0086] The horizontal well multi-fracturing section perforation position optimization model constructed by the application is used to iteratively solve the perforation cluster position of the well A, and a total of 190 clusters of perforation are optimized in the well section actually used for perforation position optimization. Table 2 gives the perforation position optimization results of the well A, Figure 2 A comparison chart of the 32 section sweet spot index DI of the well A, the fracturing section position and the optimized perforation cluster position, Figure 3 The comparison of the optimized perforation cluster position in the 9th fracturing section of the well A and the comprehensive sweet spot index DI of the section, Figure 3 It can be seen from the comparison that the optimized perforation cluster position corresponds well to the high value of the sweet spot index DI, and at the same time meets the requirements of the cluster number and the cluster spacing, and realizes the optimization of the perforation cluster position in the section.

[0087] Therefore, the application provides a fracturing horizontal well perforation position optimization method based on dynamic programming solution, wherein the dynamic programming idea is used to construct a state transition equation to solve the perforation position optimization model, the rapid optimization of the shale gas horizontal well perforation position is realized, the deficiencies of the artificial division of the perforation cluster are made up, and the method has important field application value.

[0088] The above only describes the preferred embodiments of the application and should not be used to limit the application. Any modification, equivalent replacement and improvement made within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. A method for optimizing the perforation location in a fracturing horizontal well based on dynamic programming, characterized in that, Includes the following steps: 1) Select dessert evaluation parameters, normalize the dessert evaluation parameters, and establish a dessert index model; The dessert evaluation parameters mentioned in step 1) include organic carbon content, porosity, gas content, Young's modulus, Poisson's ratio, and horizontal stress difference; 2) Establish an optimal perforation location model within a single fracturing section, wherein the perforation location satisfies cluster spacing constraints and maximum cluster number constraints; The preferred model for the perforation location in step 2) is as follows: （10） （11） in, MD For depth measurement, DI For dessert index, c For the number of clusters, L 1、 L 2 represents the depth measurement range. a , b These represent the left and right endpoints of the cluster spacing range; 3) Within the entire horizontal well fracturing section, after dividing it into multiple fracturing sections, the perforation location optimization process for each single fracturing section is iterated repeatedly to complete the optimization of the perforation location for the entire horizontal section. In step 3), dynamic programming is used to solve the single fracturing section perforation optimization model. set up d ij Indicates a total of i When choosing a dessert spot, select the first one. j The optimal value is found at position _ , and the state transition equation for dynamic programming is: （12）。 2. The method for optimizing the perforation location in a fractured horizontal well as described in claim 1, wherein the normalization process in step 1) includes: For positive dessert evaluation parameters: （1） For the evaluation parameters of reverse desserts: （2） In the formula: y is the normalized dessert evaluation parameter; x These are the original, dimensionless dessert evaluation parameters; x max This represents the maximum value of the sweet spot evaluation parameter within a certain well section. x min This represents the minimum value of the sweet spot evaluation parameter within a certain well section.

3. The method for selecting the perforation location in a fractured horizontal well as described in claim 1, wherein step 1) further includes: Determine the weights of each dessert evaluation parameter and establish a dessert index model.

4. In the method for selecting the perforation location of a fractured horizontal well as described in claim 3, the weight of each sweet spot rating parameter in step 1) is determined by the coefficient of variation method, which measures the magnitude of differences in information within the index.

5. The method for optimizing the perforation location of a fractured horizontal well as described in claim 4, wherein establishing the sweet spot index model in step 1) includes: Determine the weight of each dessert rating parameter: （3） （4） In the formula, w k For the first k The weight values ​​of each dessert evaluation parameter; C k For the first k The coefficient of variation of the dessert evaluation parameters; σ k The standard deviation of a single dessert evaluation parameter; This represents the mean of the evaluation parameters for a single dessert. n The number of evaluation parameters for desserts; Calculate the dessert index: （5） In the formula, DI For dessert index, y These are the normalized dessert evaluation parameters. k Indicates the serial number.

6. The method for optimizing the perforation location in a fractured horizontal well as described in claim 1, wherein step 3) further requires consideration of the minimum segment spacing, assuming the minimum segment spacing between two adjacent fractured segments is... Then for a certain top depth of TD The bottom depth is BD The preferred depth of the fractured section at the top of the well. L 1. Bottom depth L 2 are respectively: （13） （14）。

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