CN107578152B - Evaluation method of multi-branch horizontal well gas extraction scheme - Google Patents
Evaluation method of multi-branch horizontal well gas extraction scheme Download PDFInfo
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Abstract
The invention provides an evaluation method of a multi-branch horizontal well gas extraction scheme, and relates to the technical field of mine gas treatment and utilization. A method for evaluating a gas extraction scheme of a multi-branch horizontal well comprises the steps of expressing and operating a fuzzy number based on a fuzzy structural element theory, and constructing a fuzzy productivity calculation formula of the multi-branch horizontal well; the evaluation indexes are subjected to combined weighting by using an entropy weight method and a judgment matrix method, the experience accumulated by experts for many years is associated with objective data, the comprehensive influence of each evaluation index on the evaluation result and the ambiguity problem of the evaluation index are fully considered, and the evaluation result of the multi-branch horizontal well gas extraction scheme is more real and reliable. The evaluation method of the multi-branch horizontal well gas extraction scheme provided by the invention applies a fuzzy mathematic method, gets rid of the accuracy requirement on data, and can select the extraction scheme which is most suitable for working face gas treatment.
Description
Technical Field
The invention relates to the technical field of mine gas treatment and utilization, in particular to an evaluation method for a multi-branch horizontal well gas extraction scheme.
Background
The gas is one of important factors for restricting the production safety of coal in China, and the problem is increasingly prominent as the coal mining depth is increased and the gas in a coal bed is increased. Mine gas has certain two-sidedness, coal and gas outburst and mine gas explosion can be caused in the coal production process, the main component of the gas is methane, the methane is one of main greenhouse gases, the greenhouse effect of the methane is 20 times of that of carbon dioxide, and strong greenhouse benefit can be generated when the methane is directly discharged into the air; meanwhile, gas is also a clear energy source, along with the improvement of living standard of people, the demand on the energy source is increased, the gas can be used as fuel, and huge energy caused by gas explosion energy can be used for power generation. The mine gas extraction in China can be divided into three categories: gas extraction before mining and gas extraction after mining in the tunneling process, wherein the gas extraction before mining comprises three types: gas extraction before ground drilling, gas extraction before coal seam mining and gas extraction before adjacent layer mining. The gas concentration of the gas extracted before ground drilling and extraction is highest in various gas extraction methods, and the application range is widest.
The multi-branch horizontal well gas extraction is a main arrangement method for gas extraction drilling by a gas extraction method before ground drilling and extraction, and in the construction process of the multi-branch horizontal well, because the multi-branch horizontal well has a complex structure and a drilling horizontal section needs to be kept in a coal bed all the time, the requirements on the capacity of a drilling machine and the technical level of an engineer are very high. Due to the influence of a geological structure, a large number of development mechanisms and cracks often exist in a coal seam, the pressure of coal bodies around a drill hole is relieved in the drilling process, the drill hole begins to deform, tensile stress appears around the drill hole along with the increase of the deformation, the cracks of the coal bodies grow, and finally the collapse of the drill hole is easily caused, so that great economic loss is caused.
In conclusion, the multi-branch horizontal well can increase the control area of a shaft and improve the gas extraction rate, and has the characteristics of large engineering investment and large drilling risk. Therefore, the method has very important significance for the comprehensive evaluation of the gas extraction scheme of the multi-branch horizontal well before construction. However, at present, the evaluation of the gas extraction scheme of the multi-branch horizontal well is determined by one or two indexes, the discussion and the evaluation are carried out on one aspect of the well drilling, the coal rock parameters are also ignored, and certain ambiguity is achieved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an evaluation method of a multi-branch horizontal well gas extraction scheme, which fully considers the ambiguity problem of evaluation indexes and the comprehensive influence of each evaluation index on an evaluation result, and selects an optimal gas extraction scheme from the gas extraction schemes to be selected.
A method for evaluating a gas extraction scheme of a multi-branch horizontal well comprises the following steps:
step 1: constructing an evaluation index system of a multi-branch horizontal well gas extraction scheme;
the evaluation indexes of the multi-branch horizontal well gas extraction scheme comprise: coal seam gas treatment effect, gas extraction time, well drilling output, well drilling construction difficulty, environmental impact and engineering cost;
step 2: calculating the fuzzy capacity of the multi-branch horizontal well gas extraction to-be-evaluated scheme:
obtaining target coal seam gas extraction parameters and coal rock parameters by referring to coal mine data or by a measuring method, wherein the target coal seam gas extraction parameters and the coal rock parameters comprise coal seam gas pressure at a constant pressure boundary
Permeability of coal bed in horizontal direction
Permeability of coal bed in vertical direction
Coal bed permeability proportionality coefficient
Coefficient of kinetic viscosity of gas
Thickness of coal seam
And distance from the drilling well to the coal seam roof
All the parameters are triangular fuzzy numbers, and simultaneously, the standard state temperature T and the coal bed temperature T are includedscGas compression factor Z and standard gas compression factor Z in coal bedsc；
Obtaining the fuzzy productivity of the multi-branch horizontal well gas extraction scheme according to the target coal seam gas extraction parameter, the coal rock parameter and the drilling parameter of the gas extraction to-be-evaluated scheme
Fuzzy capacity
The formula of (c) is shown as follows:
the drilling parameters of the gas extraction to-be-evaluated scheme comprise the number n of shaft branches and the length L of a main wellmainLength L of branch wellbAngle alpha between branch well and main well, supply radius reWell drilling radius rwAnd bottom hole flowing pressure Pw；
Calculated and obtained fuzzy capacity of multi-branch horizontal well gas extraction to-be-evaluated scheme
The fuzzy triangular structure element E is included in the formula, and the values of the fuzzy triangular structure element E in the formula are-1, 0 and 1, so that the fuzzy capacity is obtained
Infimum, nuclear and supremum, will obscure productivity
Simplifying into triangular fuzzy numbers;
and step 3: the method comprises the following steps of constructing a fuzzy evaluation index value matrix of a multi-branch horizontal well gas extraction to-be-evaluated scheme, and specifically comprises the following steps:
assuming that the multi-branch horizontal well gas extraction has n schemes to be evaluated, evaluating the gas extraction schemes by using an evaluation index system of each scheme to be evaluated, and obtaining a fuzzy evaluation index value matrix of the multi-branch horizontal well gas extraction schemes according to evaluation values of drilling yield evaluation index values, coal seam gas treatment effects, gas extraction time, drilling construction difficulty, environmental influences and engineering cost in the evaluation index system, wherein the fuzzy evaluation index value matrix is expressed as:
wherein the content of the first and second substances,
the method comprises the steps that fuzzy evaluation index values of the ith evaluation index of the jth gas extraction scheme to be evaluated are set to be 1, … and 6, j is set to be 1, … and n, and the fuzzy evaluation index values are triangular fuzzy numbers;
the drilling yield evaluation index value in the evaluation index system of each scheme to be evaluated is determined by the fuzzy capacity of the multi-branch horizontal well of each scheme
The evaluation values of the coal seam gas treatment effect, the gas extraction time, the drilling construction difficulty, the environmental impact and the engineering cost are calculated and obtained by calculation, and the expert group performs fuzzy evaluation and scoring according to the actual experience to giveAn evaluation value in a triangular fuzzy number form is obtained;
and 4, step 4: the method comprises the following steps of carrying out normalization processing on a fuzzy evaluation index value matrix of a multi-branch horizontal well gas extraction to-be-evaluated scheme according to a normalization formula, wherein the method specifically comprises the following steps:
fuzzy evaluation index values in gas extraction to-be-evaluated index value matrix
Is shown as (a)ij,bij,cij) In the form of (1), wherein aij、bijAnd cijAre respectively triangular fuzzy numbers
The infimum, the kernel and the supremum are normalized by a normalization formula to obtain a normalized fuzzy evaluation index value matrix, which is expressed as:
wherein the content of the first and second substances,
the fuzzy evaluation index value is the ith evaluation index of the normalized jth gas extraction scheme to be evaluated;
and 5: subjectively weighting each evaluation index of the multi-branch horizontal well gas extraction scheme by adopting a judgment matrix method to obtain a subjective weight ratio matrix, carrying out matrix compatibility test on the matrix to finally obtain a subjective weight vector w ═ w'1,w′2,…,w′6)；
Step 6: the normalized fuzzy evaluation index value matrix obtained in the step 4
Further standardizing each fuzzy standard evaluation index value to obtain a standard fuzzy evaluation index value matrix
And then objectively weighting the evaluation indexes of each scheme to be evaluated in the gas extraction of the multi-branch horizontal well by adopting an entropy weight method to obtain objective weight vectors of each evaluation index
And 7: the subjective weight vector w' and the objective weight vector of the evaluation index are calculated
Linear combination is carried out to obtain a combination weight vector of the evaluation index
Combination weight of ith evaluation index
The formula of (c) is shown as follows:
in the formula, theta is the proportion of the subjective weight to the combined weight;
and 8: calculating the comprehensive evaluation value vector of each scheme to be evaluated of the gas extraction of the multi-branch horizontal well, and sequencing the comprehensive evaluation values of the schemes to be evaluated to obtain the multi-branch well gas extraction scheme which is most suitable for working face gas control, wherein the specific method comprises the following steps:
step 8.1: evaluating the index value matrix of the standard fuzzy
Combined weight vector with each evaluation index
Multiplying to obtain a comprehensive evaluation value vector of each scheme, and specifically calculating as shown in the following formula:
wherein the content of the first and second substances,
the comprehensive evaluation value of the jth scheme to be evaluated;
step 8.2: comparing every two comprehensive evaluation values of each scheme to be evaluated for gas extraction to obtain an optimal gas extraction scheme;
the comprehensive evaluation values of all schemes to be evaluated in gas extraction are triangular fuzzy numbers, and the comparison of the triangular fuzzy numbers is compared by adopting the following formula:
in the formula (I), the compound is shown in the specification,
for the comprehensive evaluation value of the jth gas extraction scheme to be evaluated,
j ' is a comprehensive evaluation value of the jth gas extraction scheme to be evaluated, j ' is 1, …, n, j is not equal to j ', pj(x) And pj′(x) Are respectively as
And
corresponding to the value of [ -1,1 [)]A homosequential monotonic function within the interval;
if it is
Then
Balance
Is to be less than
If it is
Then
Balance
Is to be greater than
If it is
Then
Balance
Is to be equal to
Comprehensive evaluation value of each evaluation scheme of gas extraction according to the formula
Fuzzy number sorting based on fuzzy structural elements is carried out,
the bigger the corresponding multilateral well gas extraction scheme is, the more suitable the working face is for gas control.
Further, the drilling yield evaluation index values of the gas extraction schemes to be evaluated in the step 3 are determined by the fuzzy capacity of the multi-branch horizontal well of each scheme
And (4) calculating to obtain evaluation values of coal seam gas treatment effect, gas extraction time, drilling construction difficulty, environmental influence and engineering cost of each scheme, and performing fuzzy evaluation scoring by an expert group according to actual experience to give an evaluation value in a triangular fuzzy number form.
Further, the normalization formula in step 4 is different according to different types of evaluation indexes, and specifically includes:
if the numerical value of the evaluation index is larger, the evaluation result is better, the evaluation index is a benefit type evaluation index, also called a forward index, and the formula for normalizing the fuzzy evaluation index value matrix is as follows:
wherein the content of the first and second substances,
and
respectively representing the maximum infimum limit, the maximum kernel and the maximum infimum limit of the ith evaluation index in all gas extraction to-be-evaluated schemes;
if the numerical value of the evaluation value index is smaller, the evaluation result is better, the evaluation index is a cost-type evaluation index, also called a reverse index, and the formula for normalizing the fuzzy evaluation index value matrix is as follows:
wherein the content of the first and second substances,
and
respectively indicate all gas extraction to be evaluatedThe minimum infimum, the minimum kernel and the minimum supremum of the ith evaluation index in the price scheme.
Further, in step 5, obtaining the subjective weight vector of each evaluation index specifically includes:
step 5.1: comparing every two evaluation indexes in a multi-branch horizontal well gas extraction evaluation system in pairs by an expert, and giving a subjective weight ratio of each pair of evaluation indexes, wherein the value of the subjective weight ratio is an integer of 1-9 or the reciprocal of the integer;
step 5.2: constructing a subjective weight ratio matrix of the multi-branch horizontal well gas extraction scheme according to the comparison result, wherein the subjective weight ratio matrix is expressed as:
wherein r isii′The subjective weight ratio of the ith evaluation index to the ith' evaluation index is 1, … and 6;
step 5.3: calculating eigenvalues and eigenvectors of a subjective weight ratio matrix of a multi-branch horizontal well gas extraction scheme, and calculating the maximum eigenvalue lambdamaxThe corresponding feature vector is represented by w '═ w'1,w′2,…,w′6)；
Step 5.4: performing matrix compatibility inspection on the subjective weight ratio matrix of the multi-branch horizontal well gas extraction scheme, and judging the maximum eigenvalue lambda of the subjective weight ratio matrixmaxWhether the corresponding feature vector w' can be used as a subjective weight vector of each evaluation index is specifically determined as follows:
the compatibility of the subjective weight ratio matrix is checked using an incompatibility index C (R), the calculation formula of which is shown below:
in the formula, m is the order number of the weight ratio matrix, and m is 6;
if the incompatibility degree index C (R) is less than or equal to 0.1, thenThe compatibility of the subjective weight ratio matrix R of the multi-branch horizontal well gas extraction scheme is good, and the maximum eigenvalue lambda of the matrix R ismaxThe corresponding feature vector w' can be used as a subjective weight vector of each evaluation index, and step 6 is executed; if C (R)>0.1, returning to the step 5.1, adjusting the subjective weight ratio of each pair of evaluation indexes in the multi-branch horizontal well gas extraction scheme, reconstructing a subjective weight ratio matrix, and then executing the steps 5.2-5.4.
Further, in step 6, obtaining the objective weight vector of each evaluation index specifically includes:
step 6.1: the normalized fuzzy evaluation index value matrix obtained in the step 4
Further normalizing each fuzzy standard evaluation index value, wherein the formula is as follows:
and obtaining a standard fuzzy evaluation index value matrix, wherein the standard fuzzy evaluation index value matrix is represented as:
wherein the content of the first and second substances,
the standard fuzzy evaluation index value is the ith evaluation index of the normalized jth gas extraction scheme to be evaluated;
step 6.2: the fuzzy entropy of the ith evaluation index is obtained by the definition of the entropy and the standard fuzzy evaluation index value of the ith evaluation index in each gas extraction to-be-evaluated scheme, and the calculation formula is as follows:
step 6.3: calculating objective weight vector of each evaluation index according to entropy weight method and fuzzy entropy of ith evaluation index
Wherein the objective weight value of the ith evaluation index
The formula of (c) is shown as follows:
according to the technical scheme, the invention has the beneficial effects that: the evaluation method for the gas extraction scheme of the multi-branch horizontal well, provided by the invention, applies a fuzzy mathematic method, and gets rid of the accuracy requirement on data. The method is characterized in that fuzzy numbers are expressed and operated based on a fuzzy structural element theory, and a fuzzy productivity calculation formula of the multi-branch horizontal well is constructed; the entropy weight method and the judgment matrix method are selected for combined weighting, the experience accumulated by experts for many years is linked with objective data, the comprehensive influence of each evaluation index on the evaluation result and the ambiguity problem of the evaluation index are fully considered, the evaluation result of the multi-branch horizontal well gas extraction scheme is more real and reliable, and the extraction scheme which is most suitable for working face gas treatment can be selected.
Drawings
Fig. 1 is a flowchart of an evaluation method for a multilateral well gas extraction scheme according to an embodiment of the present invention.
Detailed description of the preferred embodiments
In this embodiment, a working face of a certain mine 4307 is used as a research object, a multilateral well gas extraction scheme evaluation method is used to evaluate the gas extraction scheme, and an extraction scheme most suitable for gas control of the working face of the coal seam is selected.
A method for evaluating a multilateral well gas extraction scheme is shown in figure 1 and comprises the following steps.
Step 1: constructing an evaluation index system of a multi-branch horizontal well gas extraction scheme;
the evaluation indexes of the multi-branch horizontal well gas extraction scheme comprise: coal bed gas control effect C1Gas extraction time C2Well production C3Well drilling construction difficulty C4Environmental impact C5And engineering cost C6。
Step 2: calculating the fuzzy productivity of each scheme of gas extraction of the multi-branch horizontal well:
obtaining target coal seam gas extraction parameters and coal rock parameters by referring to coal mine data or by a measuring method, wherein the target coal seam gas extraction parameters and the coal rock parameters comprise coal seam gas pressure at a constant pressure boundary
Permeability of coal bed in horizontal direction
Permeability of coal bed in vertical direction
Coal bed permeability proportionality coefficient
Coefficient of kinetic viscosity of gas
Thickness of coal seam
And distance from the drilling well to the coal seam roof
All the parameters are triangular fuzzy numbers, and simultaneously, the standard state temperature T and the coal bed temperature T are includedscGas compression factor Z and standard gas compression factor Z in coal bedsc；
Representing the triangular blur number as
Of the form (b), then there is a function f (x) such that
Wherein f (x) is a number satisfying the interval [ -1,1 [ ]]A monotonically bounded function with a monotonically bounded upper bound, E being a fuzzy triangle structure element, and a monotonically bounded function f (x) as shown in the following equation:
wherein a, b and c are triangular fuzzy numbers
Infimum, nuclear and supremum;
triangular fuzzy number
Using the fuzzy triangle structure element E, we denote as:
the membership function of the fuzzy triangle structure element E is as follows:
obtaining the fuzzy productivity of the multi-branch horizontal well gas extraction scheme according to the target coal seam gas extraction parameter, the coal rock parameter and the drilling parameter of the gas extraction to-be-evaluated scheme
Fuzzy capacity
The formula of (c) is shown as follows:
the drilling parameters of the gas extraction to-be-evaluated scheme comprise the number n of shaft branches and the length L of a main wellmainLength L of branch wellbAngle alpha between branch well and main well, supply radius reWell drilling radius rwAnd bottom hole flowing pressure Pw；
Calculated and obtained fuzzy capacity of multi-branch horizontal well gas extraction to-be-evaluated scheme
The fuzzy triangular structure element E is included in the formula, and the values of the fuzzy triangular structure element E in the formula are-1, 0 and 1, so that the fuzzy capacity is obtained
Infimum, nuclear and supremum, will obscure productivity
Simplifying into triangular fuzzy numbers;
the coal rock parameters of the working surface of a certain mine 4307 in the embodiment are shown in Table 1, and some parameters are
A triangular fuzzy number of forms;
TABLE 1 coal rock parameters of a certain mine working face
| Coal rock parameters | Coal petrography parameter value |
| Thickness of coal seam/m | (3.60,4.00,4.40) |
| Porosity/mum of coal bed in horizontal direction2 | (0.55,0.60,0.64) |
| Coal bed permeability proportionality coefficient | (8.70,9.30,10.00) |
| Coal bed gas pressure/MPa | (1.10,1.30,1.40) |
| Distance/m from drilling to coal seam roof | (1.8,4.00,4.40) |
| Bottom hole flowing pressure/MPa | (0.13,0.15,0.16) |
| Viscosity coefficient of gas dynamic/(mPas) | (9.70,10.80,12.00) |
| temperature/K of standard state | 273.15 |
| Coal bed temperature/K | 303.15 |
| Gas compression factor in coal seam | 0.973 |
| Standard gas compression factor | 0.97 |
In the embodiment, the gas extraction alternative schemes of the multi-branch horizontal well comprise a first gas extraction scheme to be evaluated, a second gas extraction scheme to be evaluated and a third gas extraction scheme to be evaluated, wherein the drilling parameters of each scheme are shown in a table 2;
TABLE 2 drilling parameters for alternatives for gas extraction in a multi-branch horizontal well
Fuzzy capacity according to multi-branch horizontal well gas extraction scheme
The fuzzy capacity of each to-be-evaluated scheme of gas extraction is obtained by the calculation formula of (1), the coal rock parameters of the working face and the drilling parameters of each to-be-evaluated scheme of the multi-branch horizontal well gas extraction, and the fuzzy capacity of each to-be-evaluated scheme of the gas extraction is respectively as follows: the fuzzy capacity of the first gas extraction to-be-evaluated scheme is
The fuzzy capacity of the second gas extraction to-be-evaluated scheme is
The fuzzy capacity of the third gas extraction to-be-evaluated scheme is
And step 3: the method comprises the following steps of constructing a fuzzy evaluation index value matrix of a multi-branch horizontal well gas extraction to-be-evaluated scheme, and specifically comprises the following steps:
assuming that the multi-branch horizontal well gas extraction has n schemes to be evaluated, evaluating the gas extraction scheme by using an evaluation index system of each scheme to be evaluated to obtain a fuzzy evaluation index value matrix of the multi-branch horizontal well gas extraction scheme, wherein the fuzzy evaluation index value matrix is expressed as follows:
wherein the content of the first and second substances,
the method comprises the steps that fuzzy evaluation index values of the ith evaluation index of the jth gas extraction scheme to be evaluated are set to be 1, … and 6, j is set to be 1, … and n, and the fuzzy evaluation index values are triangular fuzzy numbers;
the drilling yield C3 of each gas extraction scheme to be evaluated evaluates the fuzzy capacity of the index value of the multi-branch horizontal well in each scheme
And (3) calculating to obtain evaluation values of the coal seam gas control effect C1, the gas extraction time C2, the drilling construction difficulty C4, the environmental impact C5 and the engineering cost C6 of each scheme, and performing fuzzy evaluation and scoring by an expert group according to actual experience to give an evaluation value in a triangular fuzzy number form.
In this embodiment, the effect of inviting experts to treat each multi-branch horizontal well evaluation scheme is shown as C1Extraction time C2Construction difficulty C4Environmental impact C5And engineering cost C6Grading, and combining the fuzzy capacity of each gas extraction scheme obtained in the step 2 to obtain the well drilling yield C of each gas extraction scheme3Obtaining a fuzzy evaluation index value matrix
As shown in the following formula:
and 4, step 4: the method comprises the following steps of carrying out normalization processing on fuzzy evaluation index values of a multi-branch horizontal well gas extraction to-be-evaluated scheme according to a normalization formula, and specifically comprises the following steps:
fuzzy evaluation index values in gas extraction to-be-evaluated index value matrix
Is shown as (a)ij,bij,cij) In the form of (1), wherein aij、bijAnd cijAre respectively triangular fuzzy numbers
The infimum, the kernel and the supremum are normalized by a normalization formula to obtain a normalized fuzzy evaluation index value matrix, which is expressed as:
wherein the content of the first and second substances,
the fuzzy evaluation index value is the ith evaluation index of the normalized jth gas extraction scheme to be evaluated;
the normalization formulas adopted by different types of evaluation indexes are different, and the specific use method is as follows:
if the numerical value of the evaluation index is larger, the evaluation result is better, the evaluation index is a benefit type evaluation index, also called a forward index, and the formula for normalizing the fuzzy evaluation index value matrix is as follows:
wherein the content of the first and second substances,
and
respectively representing the maximum infimum limit, the maximum kernel and the maximum infimum limit of the ith evaluation index in all gas extraction to-be-evaluated schemes;
if the numerical value of the evaluation value index is smaller, the evaluation result is better, the evaluation index is a cost-type evaluation index, also called a reverse index, and the formula for normalizing the fuzzy evaluation index value matrix is as follows:
wherein the content of the first and second substances,
and
and respectively representing the minimum infimum boundary, the minimum kernel and the minimum infimum boundary of the ith evaluation index in all the gas extraction to-be-evaluated schemes.
In the embodiment, the more the evaluation index value is, the more the branch horizontal well scheme is, the better the evaluation index is, and therefore, a formula is adopted
Normalizing the fuzzy index value matrix to finally obtain a normalized fuzzy evaluation index value matrix, wherein the normalized fuzzy evaluation index value matrix is shown as the following formula:
and 5: subjectively weighting each evaluation index of the multi-branch horizontal well gas extraction scheme by adopting a judgment matrix method to obtain a subjective weight ratio matrix, and carrying out matrix compatibility test on the matrix to finally obtain a subjective weight vector of each evaluation index, wherein the specific method comprises the following steps:
step 5.1: performing pairwise comparison on evaluation indexes in a multi-branch horizontal well gas extraction scheme evaluation system by experts, and giving a subjective weight ratio of each pair of evaluation indexes, wherein the value of the subjective weight ratio is an integer of 1-9 or the reciprocal of the integer;
step 5.2: constructing a subjective weight ratio matrix of the multi-branch horizontal well gas extraction scheme according to the comparison result, wherein the subjective weight ratio matrix is expressed as:
wherein r isii′The subjective weight ratio of the ith evaluation index to the ith' evaluation index is 1, … and 6;
step 5.3: calculating eigenvalues and eigenvectors of a subjective weight ratio matrix of a multi-branch horizontal well gas extraction scheme, and calculating the maximum eigenvalue lambdamaxThe corresponding feature vector is represented by w '═ w'1,w′2,…,w′6)；
Step 5.4: performing matrix compatibility inspection on the subjective weight ratio matrix of the multi-branch horizontal well gas extraction scheme, and judging the maximum eigenvalue lambda of the subjective weight ratio matrixmaxWhether the corresponding feature vector w' can be used as a subjective weight vector of each evaluation index is specifically determined as follows:
the compatibility of the matrix R is checked using the incompatibility index C (R), which is calculated as follows:
in the formula, m is the order number of the weight ratio matrix, and m is 6;
if the incompatibility degree index C (R) is less than or equal to 0.1, the compatibility of the subjective weight ratio matrix R of the multi-branch horizontal well gas extraction scheme is good, and the maximum characteristic value lambda of the matrix R ismaxThe corresponding feature vector w' can be used as a subjective weight vector of each evaluation index, and step 6 is executed; if C (R)>0.1, returning to the step 5.1, adjusting the subjective weight ratio of each pair of evaluation indexes in the multi-branch horizontal well gas extraction scheme, reconstructing a subjective weight ratio matrix, and then executing the step 5.2-step 5.4;
in the embodiment, the experts compare every two evaluation indexes of each scheme to be evaluated for gas extraction of the multi-branch horizontal well in pairs, and give a subjective weight ratio of each pair of evaluation indexes, as shown in table 3;
TABLE 3 subjective weight ratio of each pair of evaluation indices
| Evaluation index | C1 | C2 | C3 | C4 | C5 | C6 |
| C1 | 1 | 6 | 4 | 2 | 7 | 3 |
| C2 | 1/6 | 1 | 1/3 | 1/5 | 1/2 | 1/4 |
| C3 | 1/4 | 3 | 1 | 1/4 | 3 | 1 |
| C4 | 1/2 | 5 | 4 | 1 | 4 | 3 |
| C5 | 1/7 | 2 | 1/3 | 1/4 | 1 | 1/2 |
| C6 | 1/3 | 4 | 1 | 1/3 | 2 | 1 |
Constructing a subjective weight ratio matrix of the gas extraction scheme of the multi-branch horizontal well according to a subjective weight ratio given by an expert on an evaluation index of the gas extraction scheme of the multi-branch horizontal well, wherein the subjective weight ratio matrix is as shown in the following formula:
finding the maximum eigenvalue of the matrix as lambdamax＝6.205, the corresponding feature vector is w ═ 0.389,0.042,0.113,0.278,0.059, 0.119;
according to an incompatibility degree index detection formula, calculating to obtain an incompatibility degree detection index C (R) of a subjective weight ratio matrix of the multi-branch horizontal well gas extraction scheme, wherein the incompatibility degree detection index C (R) is 0.041 or less than 0.1, and indicating that the subjective weight ratio matrix R has good compatibility and the maximum characteristic value lambda of the matrix ismaxThe corresponding feature vector w' can be used as a subjective weight vector of each evaluation index.
Step 6: objectively weighting the evaluation indexes of each scheme to be evaluated in the gas extraction of the multi-branch horizontal well by adopting an entropy weight method to obtain objective weight vectors of each evaluation index, wherein the specific method comprises the following steps:
step 6.1: the normalized fuzzy evaluation index value matrix obtained in the step 4
Further normalizing each fuzzy standard evaluation index value, wherein the formula is as follows:
and obtaining a standard fuzzy evaluation index value matrix, wherein the standard fuzzy evaluation index value matrix is expressed as:
wherein the content of the first and second substances,
the standard fuzzy evaluation index value is the ith evaluation index of the j gas extraction to-be-evaluated scheme after the standardization processing;
solving each standard fuzzy evaluation index value in the standard fuzzy evaluation index value matrix according to the formula and the standardized formula of the triangular fuzzy number and the triangular structural element E in the step 2, wherein the calculation process is as follows:
the above formula solves each evaluation index inStandard fuzzy evaluation index values in the three gas extraction to-be-evaluated schemes are obtained, and therefore a standard fuzzy evaluation value matrix of the three gas extraction to-be-evaluated schemes is obtained
Step 6.2: the fuzzy entropy of the ith evaluation index is obtained by the definition of the entropy and the standard fuzzy evaluation index value of the ith evaluation index in each gas extraction to-be-evaluated scheme, and the calculation formula is as follows:
step 6.3: calculating objective weight vector of each evaluation index according to entropy weight method and fuzzy entropy of ith evaluation index
Wherein the objective weight value of the ith evaluation index
The formula of (c) is shown as follows:
and 7: the subjective weight vector w' and the objective weight vector of the evaluation index are calculated
Linear combination is carried out to obtain a combination weight vector of the evaluation index
Combination weight of ith evaluation index
The formula of (c) is shown as follows:
in the formula, θ is a ratio of the subjective weight to the combined weight, and in this embodiment, θ is 0.5.
And 8: calculating the comprehensive evaluation value vector of each scheme to be evaluated of the gas extraction of the multi-branch horizontal well, and sequencing the comprehensive evaluation values of the schemes to be evaluated to obtain the multi-branch well gas extraction scheme which is most suitable for working face gas control, wherein the specific method comprises the following steps:
step 8.1: evaluating the index value matrix of the standard fuzzy
Combined weight vector with each evaluation index
And multiplying to obtain a comprehensive evaluation value vector of each scheme, and specifically calculating as shown in the following formula:
wherein the content of the first and second substances,
a comprehensive evaluation value of the jth evaluation scheme;
step 8.2: comparing every two comprehensive evaluation values of the gas extraction evaluation schemes to obtain an optimal gas extraction scheme;
the comprehensive evaluation values of all the evaluation schemes of the gas extraction are triangular fuzzy numbers, and the comparison of the triangular fuzzy numbers is compared by adopting the following formula:
in the formula (I), the compound is shown in the specification,
is the comprehensive evaluation value of the jth scheme to be evaluated,
is the comprehensive evaluation value of the j ' th scheme to be evaluated, j ' is 1, …, n, j is not equal to j ', pj(x) And pj′(x) Are respectively as
And
corresponding to the value of [ -1,1 [)]A homosequential monotonic function within the interval;
if it is
Then
Balance
Is to be less than
If it is
Then
Balance
Is to be greater than
If it is
Then
Balance
Is to be equal to
Comprehensive evaluation value of each evaluation scheme of gas extraction according to the formula
Fuzzy number sorting based on fuzzy structural elements is carried out,
the bigger the corresponding multilateral well gas extraction scheme is, the more suitable the working face is for gas control.
The vector of the comprehensive evaluation value of each gas extraction scheme obtained in this embodiment is
Comparing comprehensive evaluation values according to a triangular fuzzy number comparison size formula
And
the calculation process is as follows:
from the sorting rule of the triangular fuzzy number, obtain
Comprehensive consideration of coal seam gas treatment effect C of multi-branch horizontal well1Gas extraction time C2Well production C3Well drilling construction difficulty C4Environmental impact C5And engineering cost C6In this embodiment, the first gas extraction scheme is preferably adopted for the mine to treat the gas on the working face.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (3)
1. A method for evaluating a multi-branch horizontal well gas extraction scheme is characterized by comprising the following steps: the method comprises the following steps:
step 1: constructing an evaluation index system of a multi-branch horizontal well gas extraction scheme;
the evaluation indexes of the multi-branch horizontal well gas extraction scheme comprise: coal seam gas treatment effect, gas extraction time, well drilling output, well drilling construction difficulty, environmental impact and engineering cost;
step 2: calculating the fuzzy capacity of the multi-branch horizontal well gas extraction to-be-evaluated scheme:
obtaining target coal seam gas extraction parameters and coal rock parameters by referring to coal mine data or by a measuring method, wherein the target coal seam gas extraction parameters and the coal rock parameters comprise coal seam gas pressure at a constant pressure boundary
Permeability of coal bed in horizontal direction
Permeability of coal bed in vertical direction
Coal bed permeability proportionality coefficient
Coefficient of kinetic viscosity of gas
Thickness of coal seam
And distance from the drilling well to the coal seam roof
All the parameters are triangular fuzzy numbers, and simultaneously, the standard state temperature T and the coal bed temperature T are includedscGas compression factor Z and standard gas compression factor Z in coal bedsc；
Obtaining the fuzzy productivity of the multi-branch horizontal well gas extraction scheme according to the target coal seam gas extraction parameter, the coal rock parameter and the drilling parameter of the gas extraction to-be-evaluated scheme
Fuzzy capacity
The formula of (c) is shown as follows:
the drilling parameters of the gas extraction to-be-evaluated scheme comprise the number n of shaft branches and the length L of a main wellmainLength L of branch wellbAngle alpha between branch well and main well, supply radius reWell drilling radius rwAnd bottom hole flowing pressure Pw；
Calculated and obtained fuzzy capacity of multi-branch horizontal well gas extraction to-be-evaluated scheme
The fuzzy triangular structure element E is included in the formula, and the values of the fuzzy triangular structure element E in the formula are-1, 0 and 1, so that the fuzzy capacity is obtained
Infimum, nuclear and supremum, will obscure productivity
Simplifying into triangular fuzzy numbers;
and step 3: the method comprises the following steps of constructing a fuzzy evaluation index value matrix of a multi-branch horizontal well gas extraction to-be-evaluated scheme, and specifically comprises the following steps:
assuming that the multi-branch horizontal well gas extraction has n schemes to be evaluated, evaluating the gas extraction schemes by using an evaluation index system of each scheme to be evaluated, and obtaining a fuzzy evaluation index value matrix of the multi-branch horizontal well gas extraction schemes according to evaluation values of drilling yield evaluation index values, coal seam gas treatment effects, gas extraction time, drilling construction difficulty, environmental influences and engineering cost in the evaluation index system, wherein the fuzzy evaluation index value matrix is expressed as:
wherein the content of the first and second substances,
the method comprises the steps that fuzzy evaluation index values of the ith evaluation index of the jth gas extraction scheme to be evaluated are set to be 1, … and 6, j is set to be 1, … and n, and the fuzzy evaluation index values are triangular fuzzy numbers;
the drilling yield evaluation index value in the evaluation index system of each scheme to be evaluated is determined by the fuzzy capacity of the multi-branch horizontal well of each scheme
Calculating to obtain the coal seam gas treatment effect, gas extraction time, drilling construction difficulty, environmental influence and engineeringThe evaluation value of the cost is subjected to fuzzy evaluation and scoring by an expert group according to actual experience, and an evaluation value in a triangular fuzzy number form is given;
and 4, step 4: the method comprises the following steps of carrying out normalization processing on a fuzzy evaluation index value matrix of a multi-branch horizontal well gas extraction to-be-evaluated scheme according to a normalization formula, wherein the method specifically comprises the following steps:
fuzzy evaluation index values in gas extraction to-be-evaluated index value matrix
Is shown as (a)ij,bij,cij) In the form of (1), wherein aij、bijAnd cijAre respectively triangular fuzzy numbers
The infimum, the kernel and the supremum are normalized by a normalization formula to obtain a normalized fuzzy evaluation index value matrix, which is expressed as:
wherein the content of the first and second substances,
the fuzzy evaluation index value is the ith evaluation index of the normalized jth gas extraction scheme to be evaluated;
the normalization formula is different according to different types of evaluation indexes, and the specific selection method is as follows:
if the numerical value of the evaluation index is larger, the evaluation result is better, the evaluation index is a benefit type evaluation index, also called a forward index, and the formula for normalizing the fuzzy evaluation index value matrix is as follows:
wherein the content of the first and second substances,
and
respectively representing the maximum infimum limit, the maximum kernel and the maximum infimum limit of the ith evaluation index in all gas extraction to-be-evaluated schemes;
if the numerical value of the evaluation value index is smaller, the evaluation result is better, the evaluation index is a cost-type evaluation index, also called a reverse index, and the formula for normalizing the fuzzy evaluation index value matrix is as follows:
wherein the content of the first and second substances,
and
respectively representing the minimum infimum, the minimum kernel and the minimum infimum of the ith evaluation index in all gas extraction to-be-evaluated schemes;
and 5: subjectively weighting each evaluation index of the multi-branch horizontal well gas extraction scheme by adopting a judgment matrix method to obtain a subjective weight ratio matrix, carrying out matrix compatibility test on the matrix to finally obtain a subjective weight vector w ═ w'1,w′2,…,w′6)；
Step 6: the normalized fuzzy evaluation index value matrix obtained in the step 4
Further standardizing each fuzzy standard evaluation index value to obtain a standard fuzzy evaluation index value matrix
And then objectively weighting the evaluation indexes of each scheme to be evaluated in the gas extraction of the multi-branch horizontal well by adopting an entropy weight method to obtain objective weight vectors of each evaluation index
And 7: the subjective weight vector w' and the objective weight vector of the evaluation index are calculated
Linear combination is carried out to obtain a combination weight vector of the evaluation index
Combination weight of ith evaluation index
The formula of (c) is shown as follows:
in the formula, theta is the proportion of the subjective weight to the combined weight;
and 8: calculating the comprehensive evaluation value vector of each scheme to be evaluated of the gas extraction of the multi-branch horizontal well, and sequencing the comprehensive evaluation values of the schemes to be evaluated to obtain the multi-branch well gas extraction scheme which is most suitable for working face gas control, wherein the specific method comprises the following steps:
step 8.1: evaluating the index value matrix of the standard fuzzy
Combined weight vector with each evaluation index
Multiplying to obtain the comprehensive evaluation value vector of each scheme,the specific calculation is shown as the following formula:
wherein the content of the first and second substances,
the comprehensive evaluation value of the jth scheme to be evaluated;
step 8.2: comparing every two comprehensive evaluation values of each scheme to be evaluated for gas extraction to obtain an optimal gas extraction scheme;
the comprehensive evaluation values of all schemes to be evaluated in gas extraction are triangular fuzzy numbers, and the comparison of the triangular fuzzy numbers is compared by adopting the following formula:
in the formula (I), the compound is shown in the specification,
for the comprehensive evaluation value of the jth gas extraction scheme to be evaluated,
j ' is a comprehensive evaluation value of the jth gas extraction scheme to be evaluated, j ' is 1, …, n, j is not equal to j ', pj(x) And pj′(x) Are respectively as
And
corresponding to the value of [ -1,1 [)]A homosequential monotonic function within the interval;
if it is
Then
Balance
Is to be less than
If it is
Then
Balance
Is to be greater than
If it is
Then
Balance
Is to be equal to
Comprehensive evaluation value of each evaluation scheme of gas extraction according to the formula
Fuzzy number sorting based on fuzzy structural elements is carried out,
the bigger the corresponding multilateral well gas extraction scheme is, the more suitable the working face is for gas control.
2. The method for evaluating the gas extraction scheme of the multi-branch horizontal well according to claim 1, which is characterized by comprising the following steps: step 5, obtaining the subjective weight vector of each evaluation index, wherein the specific method comprises the following steps:
step 5.1: comparing every two evaluation indexes in a multi-branch horizontal well gas extraction evaluation system in pairs by an expert, and giving a subjective weight ratio of each pair of evaluation indexes, wherein the value of the subjective weight ratio is an integer of 1-9 or the reciprocal of the integer;
step 5.2: constructing a subjective weight ratio matrix of the multi-branch horizontal well gas extraction scheme according to the comparison result, wherein the subjective weight ratio matrix is expressed as:
wherein r isii′The subjective weight ratio of the ith evaluation index to the ith' evaluation index is 1, … and 6;
step 5.3: calculating eigenvalues and eigenvectors of a subjective weight ratio matrix of a multi-branch horizontal well gas extraction scheme, and calculating the maximum eigenvalue lambdamaxThe corresponding feature vector is represented by w '═ w'1,w′2,…,w′6)；
Step 5.4: performing matrix compatibility inspection on the subjective weight ratio matrix of the multi-branch horizontal well gas extraction scheme, and judging the maximum eigenvalue lambda of the subjective weight ratio matrixmaxWhether the corresponding feature vector w' can be used as a subjective weight vector of each evaluation index is specifically determined as follows:
the compatibility of the subjective weight ratio matrix is checked using an incompatibility index C (R), the calculation formula of which is shown below:
in the formula, m is the order number of the weight ratio matrix, and m is 6;
if the incompatibility degree index C (R) is less than or equal to 0.1, the compatibility of the subjective weight ratio matrix R of the multi-branch horizontal well gas extraction scheme is good, and the maximum characteristic value lambda of the matrix R ismaxThe corresponding feature vector w' can be used as a subjective weight vector of each evaluation index, and step 6 is executed; if C (R)>0.1, returning to the step 5.1, adjusting the subjective weight ratio of each pair of evaluation indexes in the multi-branch horizontal well gas extraction scheme, reconstructing a subjective weight ratio matrix, and then executing the steps 5.2-5.4.
3. The method for evaluating the gas extraction scheme of the multi-branch horizontal well according to claim 1, which is characterized by comprising the following steps: step 6, obtaining objective weight vectors of each evaluation index, wherein the specific method comprises the following steps:
step 6.1: the normalized fuzzy evaluation index value matrix obtained in the step 4
Further normalizing each fuzzy standard evaluation index value, wherein the formula is as follows:
and obtaining a standard fuzzy evaluation index value matrix, wherein the standard fuzzy evaluation index value matrix is represented as:
wherein the content of the first and second substances,
the standard fuzzy evaluation index value is the ith evaluation index of the normalized jth gas extraction scheme to be evaluated;
step 6.2: the fuzzy entropy of the ith evaluation index is obtained by the definition of the entropy and the standard fuzzy evaluation index value of the ith evaluation index in each gas extraction to-be-evaluated scheme, and the calculation formula is as follows:
step 6.3: calculating objective weight vector of each evaluation index according to entropy weight method and fuzzy entropy of ith evaluation index
Wherein the objective weight value of the ith evaluation index
The formula of (c) is shown as follows:
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