CN114934770A - Method for evaluating reservoir deployment feasibility of tight gas reservoir horizontal well - Google Patents
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Abstract
The invention relates to a method for evaluating the feasibility of a compact gas reservoir horizontal well for deploying a reservoir, which comprises the following steps: sequentially establishing a reservoir parameter matrix and a fuzzy equivalent matrix; establishing a significance vector, forming a maximum significance class by using the elements with the maximum significance in the significance vector, and solving the unique maximum significance element in the maximum significance class; if the only element with the maximum significance degree is 0, the reservoir feasibility that horizontal well deployment cannot be achieved in each reservoir in the reservoir parameter matrix is shown; conversely, the existence of a unique maximum saliency element is represented, and the unique maximum saliency element corresponds to a unique maximum saliency reservoir; judging whether the development condition of the reservoir with the unique maximum significance is superior to that of other reservoirs; and if the development condition of the unique reservoir with the maximum significance degree is superior to that of other reservoirs, the unique reservoir with the maximum significance degree in the reservoir parameter matrix has reservoir feasibility of horizontal well deployment. The method has important value for effective development of the dense gas reservoir.
Description
Technical Field
The invention relates to the technical field of oil and gas field development, in particular to a method for evaluating reservoir deployment feasibility of a compact gas reservoir horizontal well.
Background
Horizontal wells are very important development modes in oil and gas field development, and compared with vertical wells and directional wells, the horizontal wells can generally adopt fewer wells to obtain higher yield, but the investment cost is generally higher. The reservoir feasibility of horizontal well deployment is reasonably demonstrated, the deployment risk can be effectively reduced, and the foundation for realizing successful development of the horizontal well is provided.
The reservoir of the tight gas reservoir is generally represented by multilayer superposition, and the main principle of horizontal well deployment is as follows: when the development condition of a certain reservoir is obviously superior to that of other reservoirs, a horizontal well can be deployed at the layer for development. The research on the feasibility of deploying the reservoir in the multilayer overlapped compact gas reservoir horizontal well is equivalent to evaluating the relative development conditions of different reservoirs, and the development conditions of the reservoirs are mainly evaluated by a main control parameter method at present, wherein the main control parameters comprise thickness, reserve abundance, gas saturation, permeability and the like. The parameters influencing the development condition of the reservoir layer comprise a plurality of non-main control parameters besides the main control parameters, wherein in the non-main control parameters, the influence of a single parameter on the development condition of the reservoir layer is not large, and when a plurality of non-main control parameters act simultaneously, the influence of the non-main control parameters on the development condition of the reservoir layer cannot be ignored. The more the parameters are considered, the more accurate evaluation is performed on the development condition of the reservoir, but the evaluation difficulty is increased greatly, the method for evaluating the feasibility of deploying the reservoir in the compact gas reservoir horizontal well is established by considering the parameters, and the method has important significance on the development of the compact gas reservoir.
Disclosure of Invention
The invention aims to provide a method for evaluating the reservoir deployment feasibility of a compact gas reservoir horizontal well aiming at the problems.
The technical scheme of the invention is as follows:
a method for evaluating reservoir deployment feasibility of a tight gas reservoir horizontal well comprises the following steps:
step 1: establishing a reservoir parameter matrix X, and establishing a fuzzy equivalent matrix R according to the reservoir parameter matrix X * ；
The specific process is as follows:
1) establishing a reservoir parameter matrix X of nxm;
in the formula: each 1 row of the reservoir parameter matrix X represents 1 reservoir, n rows are counted, and n is more than or equal to 2;
each 1 column of the reservoir parameter matrix X represents 1 parameter, m columns are counted, and m is more than or equal to 2;
2) calculating the elements in the formula (1) by using a translation and range conversion formula (2)
Wherein:
in the formula: x is the number of ik The element of the ith row and the kth column in the reservoir parameter matrix X is i-1, 2 … n, k-1, 2 … m;
s k the standard deviation of the kth column element in the reservoir parameter matrix X is shown;
x" ik for the elements in row i and column k in the fuzzy matrix X', 0 ≦ X " ik Less than or equal to 1, and no dimension;
obtaining a fuzzy matrix X' of n × m:
3) the elements in equation (3) are calculated using the following equation
In the formula: r is ij In order to blur the elements in the ith row and the jth column in the similarity matrix R, i is 1,2 … n, j is 1,2 … n;
x" ik to blur the elements, X, of row i, column k in matrix X ″. lk In order to blur the elements in the ith row and kth column of the matrix X ", there is no dimension, i is 1,2 … n, k is 1,2 … m, and l is j; 0 is less than or equal to x " ik ≤1，0≤x" lk ≤1；
Obtaining an n × n fuzzy similarity matrix R:
4) the elements in equation (5) are calculated using the following equation
In the formula: r 2 The matrix is an n multiplied by n matrix and represents the synthesis of the fuzzy similar matrix R and the fuzzy similar matrix R;
r ip ∧r qj represents taking r ip And r qj 1,2 … n, q ═ p;
sequentially calculating by formula (6)
Up to
Wherein s is meterNumber of calculations, s is less than or equal to log 2 n+1；
Obtaining an n multiplied by n fuzzy equivalent matrix R * ：
And 2, step: based on fuzzy equivalence matrix R * Establishing a significance vector; forming a maximum significance class by using the elements with the maximum significance in the significance vector, and solving a unique maximum significance element in the maximum significance class;
if the only element with the maximum significance degree is 0, the fact that the only element with the maximum significance degree does not exist is shown, namely the reservoir with the maximum significance degree is not unique, and all reservoirs in the reservoir parameter matrix X do not have reservoir feasibility of horizontal well deployment; otherwise, the unique maximum significance element is represented to exist, the unique maximum significance element corresponds to the unique maximum significance reservoir and is further judged by combining a development condition classification decision function;
the specific process is as follows:
fuzzy equivalence matrix R of n x n * Saliency vector r converted to n × 1:
r＝(r 1 ,…,r i ,…,r n ) T (9)
in the formula: r is a saliency vector;
t is transposition operation of the vector;
r i the development significance of the ith reservoir is r is more than or equal to 0 i 1, i is equal to or less than 1,2 … n and is dimensionless;
wherein:
in the formula: r is ij * Is a fuzzy equivalence matrix R * The element in the ith row and the jth column, i is 1,2 … n, j is 1,2 … n, and is dimensionless;
establishing a calculation formula of the maximum degree of significance class:
in the formula: g ∨ The reservoir is the type with the maximum significance degree and is formed by the reservoir with the maximum significance degree in the reservoir parameter matrix X;
r t is the element with the maximum significance in the significance vector r, and r is more than or equal to 0 t 1, t is 1,2 … n, and is dimensionless;
finding class G with the greatest significance ∨ The only most significant element in (1):
in the formula: r is a radical of hydrogen ∨ The unique maximum significance element corresponds to the unique maximum significance reservoir in the reservoir parameter matrix X;
sgn (x) is a mathematical function; sgn (x) -1 when x < 0; sgn (x) 0 when x is 0; sgn (x) 1 when x > 0;
if the only element of maximum significance r ∨ When the number of the elements is 0, the maximum significance element does not exist, namely the maximum significance reservoir is not unique, and each reservoir in the reservoir parameter matrix X does not have reservoir feasibility of horizontal well deployment; if the only element of maximum significance r ∨ Class G with maximum significance ∨ Indicates that there is a unique maximum element of significance r in the reservoir parameter matrix X ∨ Correspond toThe reservoir is the only most significant reservoir.
And step 3: judging whether the development condition of the unique reservoir with the maximum significance degree is superior to other reservoirs according to a development condition classification decision function;
if the development condition of the unique maximum-significance reservoir is superior to that of other reservoirs, the unique maximum-significance reservoir in the reservoir parameter matrix X has reservoir feasibility of horizontal well deployment; and otherwise, each reservoir in the reservoir parameter matrix X does not have reservoir feasibility of horizontal well deployment.
The specific process is as follows:
the only maximum element r of significance is calculated by adopting the formula (11) ∨ Then, the only maximum significant element r needs to be further judged ∨ Whether the development condition of the corresponding reservoir is better than that of other reservoirs or not; establishing a unique maximum element r of significance ∨ And (3) classifying decision functions corresponding to the development conditions of the reservoirs:
in the formula: c ∨ Classifying decision functions for developmental conditions, C ∨ ＝-1,1；
Ω (i) Reserve abundance for the ith reservoir, 10 8 m 3 /Km 2 ；
Ω (∨) The reserve abundance of the only most significant reservoir is proportional to the reservoir development, 10 8 m 3 /Km 2 ；
R sg(i) Is the sand-land ratio of the ith reservoir without dimension;
R sg(∨) the sand-to-ground ratio of the reservoir with the only maximum significance degree is in direct proportion to the development condition of the reservoir and is dimensionless;
V k(∨) the reservoir variation coefficient is the only maximum reservoir variation coefficient with significance, is inversely proportional to the reservoir development condition and is dimensionless;
V k(i) coefficient of variation for the ith reservoir, dimensionless;
sign (x) is a mathematical function; sign (x) is-1 when x is less than 0; sign (x) is 1 when x is more than or equal to 0;
calculating to obtain a development condition classification decision function C ∨ ：
If C ∨ The development condition of the unique reservoir with the maximum significance degree is not superior to that of other reservoirs, and each reservoir in the reservoir parameter matrix X does not have reservoir feasibility of horizontal well deployment; if C ∨ The development condition of the unique reservoir with the maximum significance degree is superior to that of other reservoirs when being 1, and the unique reservoir with the maximum significance degree in the reservoir parameter matrix X has reservoir feasibility of horizontal well deployment.
The invention has the technical effects that:
according to the reservoir feasibility evaluation method for the deployment of the compact gas reservoir horizontal well, a reservoir parameter matrix, a fuzzy equivalent matrix, a development condition significance, a development condition classification decision function, the reservoir deployment feasibility of the horizontal well and the like are constructed, and the reservoir feasibility evaluation method for the deployment of the compact gas reservoir horizontal well can consider multiple parameters when evaluating the reservoir feasibility of the horizontal well deployment, and has important value for the effective development of the compact gas reservoir.
Detailed Description
Specific Experimental example 1
The Ordos basin southeast develops a plurality of layers of superposed compact gas reservoirs, but the development conditions of different reservoirs in different areas have certain difference, reservoir parameters of 3 adjacent areas are collected, and the reservoir feasibility of deploying horizontal wells in the 3 adjacent areas and different reservoirs is calculated by adopting the method provided by the invention.
Step 1: establishing a reservoir parameter matrix X, and establishing a fuzzy equivalent matrix R according to the reservoir parameter matrix X * ；
1) Establishing a reservoir parameter matrix X;
selecting the porosity phi, the permeability K and the gas saturation S of 4 reservoirs gi Reservoir thickness h, reservoir pressure p i Reservoir temperature T i Relative density of gamma g Critical pressure p pc Critical temperature T pc Storage abundance omega and variation coefficient V k Coefficient of surging T k Grade difference J k Coefficient of homogeneity K p Sandstone layer number n sl Sand to ground ratio R sg Number n of interlayer layers il Thick interlayerDegree h il And (3) waiting 18 parameters, and establishing a reservoir parameter matrix X when n is more than or equal to 4 and more than or equal to 2 and m is more than or equal to 18 and more than or equal to 2:
2) calculating elements of a reservoir parameter matrix X by using a translation and range transformation formula (2) to obtain a fuzzy matrix X':
3) calculating elements in the fuzzy matrix X' by using a formula (4) to obtain a fuzzy similarity matrix R:
4) calculating the elements in the fuzzy similar matrix R by using a formula (6) to obtain a fuzzy equivalent matrix R * ：
Step 2: fuzzy equivalence matrix R by using formula (8) * Calculating the elements in the sequence to obtain a significance vector r:
r＝(0.646,0.646,0.654,0.654) T
calculating elements in the significance vector r to obtain the class G with the maximum significance ∨ ：
G ∨ ＝{0.654,0.654}
Class G with the greatest significance ∨ Number of elements in
Calculating by adopting a formula (11) to obtain a unique maximum element r of significance ∨ ＝0；
Unique maximum element of significance r ∨ When 0, it means that there is no only element with the greatest significance, i.e., the reservoir with the greatest significanceThe reservoir parameter matrix X is not unique, a reservoir suitable for horizontal well deployment does not exist in the reservoir parameter matrix X, and each reservoir in the reservoir parameter matrix X does not have reservoir feasibility of horizontal well deployment.
Specific Experimental example 2
Step 1: establishing a reservoir parameter matrix X, and establishing a fuzzy equivalent matrix R according to the reservoir parameter matrix X * ；
Selecting the porosity phi, the permeability K and the gas saturation S of 4 reservoirs gi Reservoir thickness h, reservoir pressure p i Reservoir temperature T i Relative density of gamma g Critical pressure p pc Critical temperature T pc Abundance omega, coefficient of variation V k Coefficient of surging T k Grade difference J k Coefficient of homogeneity K p Sandstone layer number n sl Sand to ground ratio R sg Number of interlayer layers n il Thickness h of the interlayer il And (3) waiting 18 parameters, and establishing a reservoir parameter matrix X when n is more than or equal to 4 and more than or equal to 2 and m is more than or equal to 18 and more than or equal to 2:
2) calculating elements of a reservoir parameter matrix X by using a translation and range transformation formula (2) to obtain a fuzzy matrix X':
3) calculating elements in the fuzzy matrix X' by using a formula (4) to obtain a fuzzy similarity matrix R:
4) calculating the elements in the fuzzy similar matrix R by using a formula (6) to obtain a fuzzy equivalent matrix R * ：
And 2, step: fuzzy equivalence matrix R by using formula (8) * Calculating the elements in the sequence to obtain a significance vector r:
r＝(0.67,0.76,0.67,0.71) T
calculating elements in the saliency vector r to obtain the maximum saliency class G ∨ ：
G ∨ ＝{0.76}
Class G with the greatest significance ∨ Number of middle element
Calculating by adopting a formula (11) to obtain a unique maximum element r of significance ∨ ＝G ∨ ；
Indicates that there is a unique maximum element of saliency r ∨ The corresponding reservoir is the layer 2 in the reservoir parameter matrix X, and the development significance of the corresponding reservoir is 0.76; the decision function of the development condition classification is combined for further judgment.
And step 3: calculating the elements in the reservoir parameter matrix X by using a formula (12) to obtain a development condition classification decision function C ∨ ＝-1。
Unique maximum element of significance r ∨ The corresponding reservoir (the 2 nd reservoir in the reservoir parameter matrix X) is the only reservoir with the largest significance, but the development condition of the corresponding reservoir (the 2 nd reservoir in the reservoir parameter matrix X) is not better than that of other reservoirs according to the decision result of the development condition, so that the reservoir suitable for deploying the horizontal well does not exist in the reservoir parameter matrix X, the calculation is finished, and the calculation result is that the reservoir in the reservoir parameter matrix X does not have the reservoir feasibility of horizontal well deployment.
Specific Experimental example 3
Step 1: establishing a reservoir parameter matrix X, and establishing a fuzzy equivalent matrix R according to the reservoir parameter matrix X * ；
Selecting the porosity phi, the permeability K and the gas saturation S of 4 reservoirs gi Reservoir thickness h, reservoir pressure p i Reservoir temperature T i Relative density of gamma g Critical pressure p pc Critical temperature T pc Abundance omega, coefficient of variation V k Coefficient of surging T k Grade difference J k Coefficient of homogeneity K p Sandstone layer number n sl Sand to ground ratio R sg Number n of interlayer layers il Thickness h of the interlayer il And (3) waiting 18 parameters, and establishing a reservoir parameter matrix X when n is more than or equal to 4 and more than or equal to 2 and m is more than or equal to 18 and more than or equal to 2:
2) calculating elements of a reservoir parameter matrix X by using a translation and range transformation formula (2) to obtain a fuzzy matrix X':
3) calculating elements in the fuzzy matrix X' by using a formula (4) to obtain a fuzzy similarity matrix R:
4) calculating the elements in the fuzzy similar matrix R by using a formula (6) to obtain a fuzzy equivalent matrix R * ：
Step 2: fuzzy equivalence matrix R by formula (8) * Calculating the elements in the sequence to obtain a significance vector r:
r＝(0.59,0.59,0.78,0.73) T
calculating elements in the saliency vector r to obtain the maximum saliency class G ∨ ；
G ∨ ＝{0.78}
Class G with the greatest significance ∨ Number of middle element
Calculating by adopting a formula (11) to obtain a unique maximum element r of significance ∨ ＝G ∨ ；
Indicating that there is a unique maximum element of saliency, r ∨ The corresponding reservoir is the 3 rd layer in the reservoir parameter matrix X, and the development significance of the reservoir is 0.78; the decision function of the development condition classification is combined for further judgment.
And step 3: calculating elements in the reservoir parameter matrix X by using a formula (12) to obtain a development condition classification decision function C ∨ ＝1。
Unique maximum element of significance r ∨ The corresponding reservoir (the 3 rd reservoir in the reservoir parameter matrix X) is the only reservoir with the largest significance, the development condition is superior to other reservoirs according to the decision result of the development condition, the 3 rd reservoir in the reservoir parameter matrix X is the reservoir suitable for horizontal well deployment, the calculation is finished, and the 3 rd reservoir in the reservoir parameter matrix X has reservoir feasibility of horizontal well deployment according to the calculation result.
Claims (7)
1. A method for evaluating the reservoir deployment feasibility of a compact gas reservoir horizontal well comprises the following steps:
step 1: establishing a reservoir parameter matrix X, and establishing a fuzzy equivalent matrix R according to the reservoir parameter matrix X * ；
The reservoir parameter matrix X is an n multiplied by m matrix and consists of n reservoirs containing m parameters;
fuzzy equivalence matrix R * A symmetric matrix of n × n;
the method is characterized in that:
step 2: based on fuzzy equivalence matrix R * Establishing a significance vector; forming a maximum significance class by using the elements with the maximum significance in the significance vector, and solving a unique maximum significance element in the maximum significance class;
if the only element with the maximum significance degree is 0, the fact that the only element with the maximum significance degree does not exist is shown, namely the reservoir with the maximum significance degree is not unique, and all reservoirs in the reservoir parameter matrix X do not have reservoir feasibility of horizontal well deployment; otherwise, the unique maximum significance element is represented to exist, the unique maximum significance element corresponds to the unique maximum significance reservoir and is further judged by combining a development condition classification decision function;
and step 3: judging whether the development condition of the only reservoir with the maximum significance is superior to other reservoirs according to a development condition classification decision function;
if the development condition of the unique maximum-significance reservoir is superior to that of other reservoirs, the unique maximum-significance reservoir in the reservoir parameter matrix X has reservoir feasibility of horizontal well deployment; and on the contrary, the reservoir feasibility that each reservoir in the reservoir parameter matrix X does not have horizontal well deployment is shown.
2. The method for evaluating the feasibility of deploying the reservoir in the tight gas reservoir horizontal well according to claim 1, which is characterized by comprising the following steps of: the specific process of the step 1 is as follows:
1) establishing a reservoir parameter matrix X of nxm;
in the formula: each 1 row of the reservoir parameter matrix X represents 1 reservoir, n rows are counted, and n is more than or equal to 2;
each 1 column of the reservoir parameter matrix X represents 1 parameter, m columns are counted, and m is more than or equal to 2;
2) converting the n × m reservoir parameter matrix X into an n × m fuzzy matrix X ":
3) converting the fuzzy matrix X' of n multiplied by m into a fuzzy similar matrix R of n multiplied by n;
4) converting the fuzzy similarity matrix R of n x n into the fuzzy equivalent matrix R of n x n * ：
3. The method for evaluating the feasibility of deploying the reservoir in the tight gas reservoir horizontal well according to claim 2, which is characterized by comprising the following steps of: the specific process of the step 2 is as follows:
fuzzy equivalence matrix R of n x n * Saliency vector r converted to n × 1:
r＝(r 1 ,…,r i ,…,r n ) T (9)
in the formula: r is a saliency vector;
t is the transposition operation of the vector;
r i the development significance of the ith reservoir is r is more than or equal to 0 i 1, i is equal to or less than 1,2 … n and is dimensionless;
wherein:
in the formula: r is ij * Is a fuzzy equivalence matrix R * The element in the ith row and the jth column, i is 1,2 … n, j is 1,2 … n, and is dimensionless;
establishing a calculation formula of the maximum class of the significance degree:
in the formula: g ∨ The reservoir is the type with the maximum significance degree and is formed by the reservoir with the maximum significance degree in the reservoir parameter matrix X;
r t is made apparent byThe element with the largest significance in the degree vector r, r is more than or equal to 0 t 1, t is 1,2 … n, and is dimensionless;
finding class G with the greatest significance ∨ The only most significant element in (1):
in the formula: r is ∨ The single maximum significance element corresponds to the single maximum significance reservoir in the reservoir parameter matrix X;
4. The method for evaluating the feasibility of deploying the reservoir in the tight gas reservoir horizontal well according to claim 3, which is characterized by comprising the following steps of: the specific process of the step 3 is as follows:
establishing a development condition classification decision function:
in the formula: c ∨ Classifying decision functions for developmental conditions, C ∨ ＝-1,1；
Ω (i) Reserve abundance for the ith reservoir, 10 8 m 3 /Km 2 ；
Ω (∨) The reserve abundance of the only most significant reservoir is proportional to the reservoir development, 10 8 m 3 /Km 2 ；
R sg(i) The sand-to-ground ratio of the ith reservoir is dimensionless;
R sg(∨) the sand-to-ground ratio of the reservoir with the maximum significance is only in direct proportion to the development condition of the reservoir and is dimensionless;
V k(∨) the reservoir variation coefficient is the only maximum reservoir variation coefficient with significance, is inversely proportional to the reservoir development condition and is dimensionless;
V k(i) coefficient of variation for the ith reservoir, dimensionless;
calculating to obtain a development condition classification decision function C ∨ ：
If C ∨ The development condition of the unique reservoir with the maximum significance degree is not superior to that of other reservoirs, and each reservoir in the reservoir parameter matrix X does not have reservoir feasibility of horizontal well deployment; if C ∨ And (2) 1, the development condition of the unique reservoir with the maximum significance degree is superior to that of other reservoirs, and the unique reservoir with the maximum significance degree in the reservoir parameter matrix X has reservoir feasibility of horizontal well deployment.
5. The method for evaluating the feasibility of deploying the reservoir in the tight gas reservoir horizontal well according to claim 4, which is characterized by comprising the following steps of: the specific process of converting the n × m reservoir parameter matrix X into the n × m fuzzy matrix X ″ is as follows:
the elements in equation (1) are calculated using the following formula:
wherein:
in the formula: x is the number of ik The element of the ith row and the kth column in the reservoir parameter matrix X is i-1, 2 … n, k-1, 2 … m;
s k the standard deviation of the kth column element in the reservoir parameter matrix X is shown;
x″ ik 0 ≦ X ″, which is the element in the ith row and the kth column in the blur matrix X ″ ik Less than or equal to 1, and no dimension;
a blur matrix X "is obtained.
6. The method for evaluating the feasibility of deploying the reservoir in the tight gas reservoir horizontal well according to claim 5, wherein the method comprises the following steps: the specific process of converting the n × m fuzzy matrix X ″ into the n × n fuzzy similar matrix R is as follows:
the elements in equation (3) are calculated using the following equation
In the formula: r is ij In order to blur the elements in the ith row and jth column of the similarity matrix R, i is 1,2 … n, j is 1,2 … n;
x″ ik to obscure the element in row i and column k in matrix X', X ″ lk In order to blur the elements in the ith row and kth column of the matrix X ″, there is no dimension, i is 1,2 … n, k is 1,2 … m, and l is j; x is more than or equal to 0 ≦ x ″) ik ≤1，0≤x″ lk ≤1；
An nxn fuzzy similarity matrix R is obtained.
7. The method for evaluating the feasibility of deploying the reservoir in the tight gas reservoir horizontal well according to claim 6, wherein the method comprises the following steps: the conversion of the n × n fuzzy similar matrix R into the n × n fuzzy equivalent matrix R * The specific process comprises the following steps:
the elements in equation (5) are calculated using the following equation
In the formula: r 2 The matrix is an n multiplied by n matrix and represents the synthesis of the fuzzy similar matrix R and the fuzzy similar matrix R;
r ip ∧r qj represents taking r ip And r qj 1,2 … n, q ═ p;
sequentially calculating by formula (6)
Up to
Wherein s is the number of calculation times, and s is less than or equal to log 2 n+1；
Obtaining an n multiplied by n fuzzy equivalent matrix R * 。
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