Fractured horizontal well perforation position optimization method based on dynamic programming solution

Abstract

The invention relates to the technical field of oil and gas yield increase, in particular to a fractured horizontal well perforation position optimization method based on dynamic programming solution, which comprises the following steps: 1) selecting sweet spot evaluation parameters, normalizing the sweet spot evaluation parameters, and establishing a sweet spot index model; 2) establishing a perforation position optimization model in the single fracturing section, wherein the perforation position meets the cluster spacing constraint and the maximum cluster number constraint; and 3) dividing the whole horizontal well fracturing section into a plurality of fracturing sections, and then repeatedly iterating the perforation position optimization process of the single fracturing section to complete the perforation position optimization of the whole horizontal section. According to the method, the state transition equation is constructed by applying a dynamic planning idea to solve the perforation cluster position optimization model, so that the perforation position of the shale gas horizontal well is quickly optimized, and the defects of manual perforation cluster division are overcome.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas production increase, and in particular relates to a method for optimizing perforation positions of a fractured horizontal well based on dynamic programming solution. Background Art

[0002] The efficient development of shale gas reservoirs must rely on the horizontal well multi-cluster large-scale volume fracturing technology. The selection of perforation positions is an important part of the horizontal well staged fracturing design, and the reasonable optimization of perforation positions is the basis for achieving better transformation effects. In the horizontal well section, the perforation cluster positions are usually optimized based on the designed fracturing segment positions, cluster spacing, cluster number, physical parameters of the reservoir in the horizontal well section, and the compressibility. However, when there are many horizontal well fracturing sections, the manual optimization is time-consuming, the factors are not fully considered, and it is difficult to obtain the optimal perforation position distribution under the constraints of cluster spacing, cluster number, etc.

[0003] In order to remedy the above problems existing in the prior art when artificially dividing perforation clusters, the present invention provides a method for optimizing perforation positions for fractured horizontal wells based on dynamic programming solution. Summary of the invention

[0004] The purpose of the present invention is to solve the defects existing in artificially dividing perforation clusters and to provide a method for optimizing perforation positions of fractured horizontal wells based on dynamic programming solution.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for optimizing perforation positions of fractured horizontal wells based on dynamic programming solution, characterized by comprising the following steps:

[0007] 1) selecting a dessert evaluation parameter, normalizing the dessert evaluation parameter, and establishing a dessert index model;

[0008] 2) establishing a perforation position optimization model within a single fracturing stage, wherein the perforation position satisfies the cluster spacing constraint and the maximum cluster number constraint;

[0009] 3) Within the entire horizontal well fracturing section, after dividing into multiple fracturing sections, the perforation position optimization process of a single fracturing section is iterated repeatedly to complete the perforation position optimization of the entire horizontal section.

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

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

[0012] For the positive sweet spot evaluation parameters:

[0013]

[0014] Evaluation parameters for the reverse sweet spot:

[0015]

[0016] Where: y is the normalized dessert evaluation parameter; x is the original dimensioned dessert evaluation parameter; x max is the maximum value of the sweet spot evaluation parameter in a certain well section; x min It is the minimum value of the sweet spot evaluation parameter in a certain well section.

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

[0018] Determine the weights of each dessert evaluation parameter and establish a dessert index model.

[0019] Preferably, in step 1), the weight of each dessert rating parameter is determined by using a coefficient of variation method that measures the size of difference information within the indicator.

[0020] Preferably, establishing a dessert index model in step 1) comprises:

[0021] Determine the weights for each dessert rating parameter:

[0022]

[0023] In the formula, w k is the weight value of the kth sweet spot evaluation parameter; C k is the coefficient of variation of the kth sweet spot evaluation parameter; σ k The standard deviation of the parameters evaluated for a single dessert; is the mean of the evaluation parameters of a single sweet spot; n is the number of sweet spot evaluation parameters;

[0024] Calculate the sweet spot index:

[0025]

[0026] Where DI is the sweet spot index, y is the normalized sweet spot evaluation parameter, and k represents the sequence number.

[0027] Preferably, the perforation position optimization model in step 2) is:

[0028]

[0029] Where MD is the depth, DI is the sweet spot index, c is the number of clusters, L is 1、 L2 is the sounding range, and a and b are the left and right endpoints of the cluster spacing range.

[0030] Preferably, in step 3), dynamic programming is used to solve the single fracturing stage perforation optimization model.

[0031] Preferably, the state transition equation of dynamic programming is:

[0032]

[0033] Preferably, the minimum segment spacing also needs to be considered in step 3). Assuming that the minimum segment spacing between two adjacent fracturing segments is ΔL, for a fracturing segment with a top depth of TD and a bottom depth of BD, the top depth and bottom depth L1 and L2 of the well segment actually used for optimizing the perforation position are:

[0034]

[0035] The present invention uses a comprehensive sweet spot evaluation index that considers reservoir physical parameters and compressibility conditions. In the horizontal well fracturing section, the present invention considers the constraints of segmentation position, minimum segment spacing, length of the fracturing section, spacing between perforation clusters, number of clusters, etc., and takes the maximum value of the sum of comprehensive sweet spot values ​​corresponding to all the selected perforation clusters as the goal to construct a perforation cluster location optimization model. The state transfer equation is constructed using the dynamic programming concept to solve the perforation cluster location optimization model, which realizes the rapid optimization of the perforation position of shale gas horizontal wells, makes up for the shortcomings of artificial division of perforation clusters, and simplifies the fracturing design process. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0037] Figure 2 This is a diagram showing the optimization result of the segmented perforation cluster of Well A in an embodiment of the present invention;

[0038] Figure 3 This is a comparison diagram of the 9th fracturing stage DI and the preferred perforation positions in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0040] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0041] like Figure 1 As shown, the present invention provides a method for optimizing perforation positions of fractured horizontal wells based on dynamic programming solution, comprising the following steps:

[0042] 1) selecting a dessert evaluation parameter, normalizing the dessert evaluation parameter, and establishing a dessert index model;

[0043] 2) establishing a perforation position optimization model within a single fracturing stage, wherein the perforation position satisfies the cluster spacing constraint and the maximum cluster number constraint;

[0044] 3) Within the entire horizontal well fracturing section, after dividing into multiple fracturing sections, the perforation position optimization process of a single fracturing section is iterated repeatedly to complete the perforation position optimization of the entire horizontal section.

[0045] In step 1), the continuous sweet spot distribution along the wellbore profile is required for the division of fracturing stages and the optimization of perforation cluster locations. The geological sweet spot evaluation parameters such as total organic carbon content, porosity, and gas content interpreted by logging data with good continuity, as well as the geomechanical characteristic parameters such as rock Young's modulus, Poisson's ratio, and horizontal stress difference are standardized and the weights are determined by the coefficient of variation method. The comprehensive sweet spot index DI (dessert index) is constructed by the weighted method.

[0046] Since different sweet spot evaluation parameters have different dimensions, it is necessary to normalize the data such as organic carbon content, porosity, gas content, Young's modulus, Poisson's ratio, horizontal stress difference, etc. to make the data reach the same magnitude. The range transformation method is used to normalize the data. For the positive sweet spot evaluation parameters:

[0047]

[0048] Evaluation parameters for the reverse sweet spot:

[0049]

[0050] Where: y is the normalized sweet spot parameter; x is the original dimensioned sweet spot parameter; x max is the maximum value of the sweet spot parameter in a certain well section; x min It is the minimum value of the sweet spot parameter in a certain well section.

[0051] In the process of comprehensive evaluation of geological engineering sweet spots, weight is a particularly critical factor. For the sweet spot parameters of the continuous profile of the horizontal section well section, the greater the difference in the horizontal well section, the priority should be given to its difference in the fracturing segmentation design, and the maximum weight should be given to make a more targeted design; on the contrary, if a certain sweet spot parameter has a small difference in the horizontal well section, then the sweet spot parameter can be regarded as the same type in the entire well section, and there is no need to consider it in a targeted manner. This is also the basic principle of difference segmentation. To this end, the present invention adopts the coefficient of variation method of measuring the size of the difference information in the indicator to determine the weight of the sweet spot evaluation parameter:

[0052]

[0053] In the formula, w k is the weight value of the kth sweet spot evaluation parameter; C k is the coefficient of variation of the kth sweet spot evaluation parameter; σk The standard deviation of the parameters evaluated for a single dessert; is the mean of the evaluation parameters of a single sweet spot; n is the number of sweet spot evaluation parameters.

[0054] The sweet spot index DI is calculated as follows:

[0055]

[0056] Step 2) establishing a perforation position optimization model within a single fracturing stage, wherein the perforation position satisfies a cluster spacing constraint and a maximum cluster number constraint;

[0057] Perforation cluster optimization requires selecting the location with better results within the fracturing stage based on the comprehensive sweet spot evaluation results, while considering factors such as the fracturing stage length, the number of perforation clusters, and the cluster spacing.

[0058] Assume that the measured depth of the fracturing stage for the optimal perforation position ranges from L1 to L2, the cluster spacing range is fixed to a to b, the number of designed perforation clusters is c, and the measured depth of the optimal perforation position is MD i , the corresponding comprehensive dessert index is DI i The selected fracturing location MD i The following constraints are met:

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

[0060] a≤MD i+1 -MD i ≤b(6)

[0061] Where: 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 number of clusters constraint:

[0063] Starting from the beginning of the fracturing stage, the maximum number of clusters is determined by selecting with the minimum cluster spacing:

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

[0065] The solution is:

[0066]

[0067] This allows us to determine the range of cluster numbers:

[0068] 0<c≤c max (9)

[0069] The depth MD, sweet spot index DI and cluster number c are used as decision variables, and the sum of the closeness of the selected perforation points is used as the The maximum is the target, and the cluster spacing constraint requirements are met in the target segment. The optimization point selection model is constructed as follows:

[0070]

[0071] By solving the above optimization model, the fracturing perforation positions that meet the requirements of cluster spacing and cluster number within a single fracturing stage can be obtained.

[0072] 3) Within the entire horizontal well fracturing section, after dividing into multiple fracturing sections, the perforation position optimization process of a single fracturing section is iterated repeatedly to complete the perforation position optimization of the entire horizontal section.

[0073] In the process of perforation location optimization, due to the constraint of cluster spacing, the perforation location optimization problem is a multi-stage decision problem, which can be solved by constructing the state transition equation of the dynamic programming problem. ij It means that when there are i sweet spots in total, the optimal value is obtained when the jth position is selected. For each d ij , there are two options: one is not to choose the i-th position, then d ij =d i-1,j , the second is to select the i-th position, at this time, choose one state from the range of ib to ia to transfer, that is, d ij =max(d m,j-1 +DI i ), where m is between ib and ia. Thus, the state transition equation of the dynamic programming problem can be constructed:

[0074]

[0075] The optimal solution to the above optimization problem can be obtained by iterative calculation based on the state transfer equation. At the same time, the compressibility value DI of each selected sweet spot is recorded during the calculation. i and its corresponding depth measurement, we can obtain the optimal perforation position distribution under the constraints of equations (10) and (11).

[0076] In the entire horizontal well fracturing section, after dividing multiple fracturing sections, the single-section perforation position optimization process can be repeated and iterated to complete the optimization of the entire horizontal section perforation position. For two adjacent fracturing sections, it is necessary to set a reasonable section spacing to insert segmentation tools such as bridge plugs for segmented fracturing. Therefore, when optimizing the perforation position of multiple fracturing sections, it is necessary to consider the minimum section spacing to determine the well section actually used for perforation position optimization of each fracturing section. Assuming that the minimum section spacing between two adjacent fracturing sections is ΔL, for a fracturing section with a top depth of TD and a bottom depth of BD, the top depth and bottom depth L1 and L2 of the well section actually used for perforation position optimization are:

[0077]

[0078] Example Application

[0079] There is a shale gas horizontal well A with a horizontal section length of 2200 meters and 32 sections of fracturing. The comprehensive sweet spot index DI is constructed by using the well logging, seismic and other data of the well considering the 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 well is designed with a cluster spacing of 8-10 meters, 4-6 clusters in a single section, and a minimum section spacing of 16 meters. Table 1 shows the fracturing section positions of the well and the single section actually used for perforation position optimization considering the minimum section spacing.

[0080] Table 1: The segmented positions of the fracturing section and the preferred well section range of the perforation cluster in Well A

[0081]

[0082]

[0083] Table 2 Optimization results of perforation cluster positions in Well A

[0084]

[0085]

[0086] The horizontal well multi-fracture stage perforation position optimization model constructed by the present invention was used to iteratively solve the perforation cluster positions of Well A. A total of 190 perforation clusters were optimized in the well section actually used for perforation position optimization. Table 2 shows the perforation position optimization results of Well A. Figure 2 This is a comparison chart of the sweet spot index DI, the location of the sub-fracture stage, and the preferred perforation cluster location of the 32nd stage of Well A. Figure 3 The optimal perforation cluster position in the 9th fracturing stage of Well A is the comparison of the comprehensive sweet spot index DI of this stage. Figure 3 It can be seen that the selected perforation cluster position corresponds well to the high value of the sweet spot index DI, and at the same time meets the requirements of cluster number and cluster spacing, realizing the optimal perforation cluster position selection within the segment.

[0087] It can be seen that the present invention provides a method for optimizing the perforation positions of fractured horizontal wells based on dynamic programming, in which the state transfer equation is constructed using the dynamic programming idea to solve the perforation position optimization model, thereby realizing the rapid optimization of the perforation positions of shale gas horizontal wells, making up for the shortcomings of artificial division of perforation clusters, and having important field application value.

[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for optimizing perforation positions for fractured horizontal wells based on dynamic programming, characterized in that: The following steps are involved: 1) selecting a dessert evaluation parameter, normalizing the dessert evaluation parameter, and establishing a dessert index model; 2) establishing a perforation position optimization model within a single fracturing stage, wherein the perforation position satisfies the cluster spacing constraint and the maximum cluster number constraint; 3) Within the entire horizontal well fracturing section, after dividing into multiple fracturing sections, the single fracturing section perforation position optimization process is iterated repeatedly to complete the perforation position optimization of the entire horizontal section.

2. The method for optimizing perforation positions for fractured horizontal wells as described in claim 1, wherein the sweet spot evaluation parameters in step 1) include organic carbon content, porosity, gas content, Young's modulus, Poisson's ratio, and horizontal stress difference.

3. The method for optimizing perforation positions for fractured horizontal wells according to claim 1, wherein the normalization processing method in step 1) comprises: For the positive sweet spot evaluation parameters: Evaluation parameters for the reverse sweet spot: Where: y is the normalized dessert evaluation parameter; x is the original dimensioned dessert evaluation parameter; x max is the maximum value of the sweet spot evaluation parameter in a certain well section; x min It is the minimum value of the sweet spot evaluation parameter in a certain well section.

4. The method for optimizing perforation positions for a fractured horizontal well according to claim 1, wherein the step 1) further comprises: Determine the weights of each dessert evaluation parameter and establish a dessert index model.

5. The method for optimizing perforation positions for hydraulically fractured horizontal wells as claimed in claim 1, wherein in step 1), the weights of the sweet spot rating parameters are determined by using a coefficient of variation method that measures the size of difference information within a metric.

6. The method for optimizing perforation positions for hydraulically fractured horizontal wells according to claim 1, wherein the step 1) of establishing a sweet spot index model comprises: Determine the weights for each dessert rating parameter: In the formula, w k is the weight value of the kth sweet spot evaluation parameter; C k is the coefficient of variation of the kth sweet spot evaluation parameter; σ k The standard deviation of the parameters evaluated for a single dessert; is the mean of the evaluation parameters of a single sweet spot; n is the number of sweet spot evaluation parameters; Calculate the sweet spot index: Where DI is the sweet spot index, y is the normalized sweet spot evaluation parameter, and k represents the sequence number.

7. The method for optimizing perforation positions in a horizontal well under hydraulic fracturing according to claim 1, wherein the optimization model for perforation positions in step 2) is: in, MD is the depth measurement, DI is the sweet spot index, c is the number of clusters, L is the 1、 L2 is the sounding range, and a and b are the left and right endpoints of the cluster spacing range.

8. The method for optimizing perforation positions for fractured horizontal wells according to claim 1, wherein in step 3), dynamic programming is used to solve the single fracturing stage perforation optimization model.

9. The method for optimizing perforation positions for hydraulically fractured horizontal wells according to claim 8, wherein the state transition equation for dynamic programming is:

10. The method for optimizing perforation positions for a horizontal well under hydraulic fracturing as claimed in claim 1, wherein the minimum segment spacing must also be considered in step 3), and assuming that the minimum segment spacing between two adjacent hydraulic fracturing segments is ΔL, then for a hydraulic fracturing segment with a top depth of TD and a bottom depth of BD, the top depth and bottom depth L1 and L2 of the well segment actually used for optimizing perforation positions are:

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