CN110020453B - Three-dimensional decomposition simulator for formation permeability - Google Patents
Three-dimensional decomposition simulator for formation permeability Download PDFInfo
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Abstract
A stratum permeability three-dimensional decomposition simulator belongs to the field of numerical simulation of petroleum industry. The method has the advantages that three-dimensional space X, Y and Z permeability values in underground oil reservoirs are obtained by innovatively applying a Ward cluster analysis method in geostatistics and combining space geometric transformation, the accuracy of the permeability values in the three directions can reach more than 95% of underground real numerical values, an oil field development scheme (recovery ratio, recoverable reserve and the like) is simulated by using the obtained accurate permeability in the numerical simulation process, the accuracy of the oil field development scheme is ensured, powerful guarantee is provided for reasonable and efficient development of an oil field, and the method has quite high practical value in oil field development.
Description
Technical Field
A brand new method for obtaining permeability in three-dimensional direction in an underground oil reservoir is characterized by comprising the following steps: the permeability values in the three directions of X, Y and Z in the three-dimensional space of the underground oil reservoir can be obtained through the innovative method, the accuracy of the permeability values in the three directions can reach more than 95% of the underground real numerical value, an oil field development scheme (recovery efficiency, recoverable reserves and the like) is simulated by using the obtained accurate permeability in the numerical simulation process, the accuracy of the oil field development scheme is ensured, and powerful guarantee is provided for reasonable and efficient development of the oil field. Belongs to the field of numerical simulation in the petroleum industry.
Background
Permeability is a very important geological parameter in numerical modeling in oilfield development research, whether in history fitting or production prediction: the accuracy of the horizontal and vertical permeability in the history fit directly affects the degree of fit of oil and water production for individual wells and the whole area. In reality, permeability data of all directions are difficult to obtain, and determination of the magnitude of the permeability of the anisotropic medium in the directions is important and difficult work. Therefore, the permeability of many geological modeling simulations is only numerical and has no direction, however, the permeability in the x, y and z directions is needed when the numerical simulation is performed. The method is that an empirical formula is used for assigning values to model permeability data in three directions, and the directions of all horizontal fractures of an oil reservoir are considered to be consistent artificially, so that the horizontal permeability of the oil reservoir is the same as the grid model value. It equates the planar permeability directions to the original scalar permeability, i.e. PERMx = PERMy = permm, and the vertical permeability PERMz = aPERM (a is a coefficient). However, it is now common practice to assign permeability values in three different directions by empirical methods, which is inaccurate. In order to overcome the inaccuracy and obtain a more accurate, more real and more reasonable thickened oil simulation prediction result, the principle of cluster analysis in geostatistics is used for carrying out three-dimensional space conversion, and based on the idea, the thickened oil simulation prediction method is compiled into a computer program language, so that accurate permeability values in different directions required in numerical simulation can be obtained more conveniently and rapidly.
Disclosure of Invention
In order to obtain a permeability grid data volume relatively accurately, the permeability is classified by applying the Ward clustering analysis idea in geological statistics and utilizing a nine-grid model with the minimum permeability data volume, so that data sets sensitive to direction changes are combined into one type, and then three-dimensional space geometric operation is utilized, so that the permeability value is decomposed into x, y and z directions.
In view of the above considerations, we perform normalized transformation on data and cluster by using Ward's method, which always results in the smallest intra-class dispersion square sum increment of the clustered data, and the larger inter-class dispersion square sum. The choice of distance formula and the choice of clustering parameters are also very important. Calculating the similarity degree between data by using an Euclidean distance formula; parameters such as an inclination angle, an azimuth angle, a distance and a permeability value are comprehensively considered in the clustering time variable selection.
There are three key points in this process:
(1) The nine-square lattice body is used under the condition of establishing a layer small-layer model which is fine enough, namely, in order to obtain more accurate vertical permeability, a small-layer model is established, and the layer thickness of the small-layer model is not more than 3m;
(2) Selecting a clustering method;
(3) Special processing is required if the following situations are met in the clustering operation: 1) 26 points around the central point of the permeability grid are the same, and in this case, value assignment is carried out according to an empirical formula; 2) Clustering the central points of the permeability grids to form two main directions with opposite directions, wherein the default permeability is higher.
According to a clustering analysis algorithm, a search range comprises 27 grid values in a nine-square body, two types are separated, the value of permeability is similar to a central point and is a type, and other values are b types. The direction of permeability can be determined by pointing the coordinates of the center point to the center of gravity of other points in the class a except the center point.
The nine-square grid body is moved along the directions of x, y and z in turn, and the above steps are repeated, so that permeability values (permx, permy and permz) of each grid in three directions are obtained. Compared with the traditional artificial matrix assignment operation, the algorithm integrates the mathematical geological thought, and performs matrix reassignment closer to the actual geological condition under the condition of more stable data change speed.
Drawings
FIG. 1 is a technical route diagram of the method
FIG. 2 is a schematic diagram of points where the permeability in a nine-square lattice is close to a round point
FIG. 3 Experimental data volume
FIG. 4 is a graph showing the classification result pedigree
FIG. 5 is a three-dimensional projection view
Detailed Description
The method is that an empirical formula is used for assigning values to model permeability data in three directions, and the directions of all horizontal fractures of an oil reservoir are considered to be consistent artificially, so that the horizontal permeability of the oil reservoir is the same as the grid model value. The vertical permeability is considered to be equal to the value of the model permeability multiplied by 0.1 in the longitudinal direction according to empirical formulas. However, this method lacks scientificity and accuracy, and only roughly estimates the permeability at anisotropy. In order to establish a relatively correct mathematical oil-gas-water seepage motion model, a penetration data volume derived from petrel modeling software is processed by a ward clustering analysis method, and an angle conversion formula is derived by using three-dimensional space geometric operation, so that the penetration value is decomposed into x, y and z directions, and a technical flow chart is shown in FIG. 1. Through the treatment of the permeability, the precision of numerical simulation is greatly improved, and a powerful basis is provided for the development of oil fields.
Principles and methods of cluster analysis selection
A finding the distance between data
When the permeability value changes not very severely, an Euclidean distance calculation formula is adopted to analyze the degree of affinity and sparseness among data points, systematic clustering analysis is carried out according to the degree of affinity and sparseness, and a method is adopted to carry out clustering when the method is selected for analysis.
Distance coefficient statistics are typically employed for sample clustering (Q-clustering). The smaller the distance, the smaller the distance between samples, and the smaller the difference. Points that are further away should belong to different classes. Because the Ward method based on the analysis of variance requires that the distance between samples must be the Euclidean distance, the Euclidean distance formula is adopted for calculation in the research, and the calculation formula is as follows:
selection of B clustering method
Ward least squares sum of dispersion was obtained according to the principle of ANOVA [1]. Because the intra-class dispersion square sum of the ward dispersion square sum method is small, and the inter-class dispersion square sum is large, the geological rule classification is more in line with. Thus, the cluster center in which the variation of the external condition is within the normal range can be obtained.
The Ward method firstly combines the least-difference square sum into one class when calculating, so that the intra-class dispersion square sum is increased least until all samples are gathered into one class, always leads the intra-class dispersion square sum increment caused by clustering to be minimum, and the inter-class dispersion square sum is relatively large.
D ij Is the distance between the ith sample and the jth sample
The distance between the 1 st sample and the two i, j samples combined into one class is:
experimental design by using cluster analysis method
A experiment model establishment and process
The data derived from the petrel modeling software contains a "PERMEABILITY" key, under which is contained a model-derived PERMEABILITY data volume, each value representing the PERMEABILITY value in each mesh, but which has no directionality. The actual geological situation is that it should have directionality (permx, permy, permz), and the traditional approach is to artificially assign values: permx = perm; permy = perm; permz =1/10perm, which is a meaningful empirical assignment but is still not scientific.
The permeability value in the grid is positioned by an xyz three-dimensional coordinate, different grids have different coordinate values and grid values, a search range includes 27 grid values in a nine-square body according to a clustering analysis algorithm, two types are separated, the permeability value close to a central point is a type, and other values are b types (shown in fig. 2). The direction of permeability can be determined by pointing the coordinates of the center point to the center of gravity of other points in the class a except the center point. And the magnitude of the permeability value in this direction can be found by a weighted average method. And respectively solving permeability values decomposed to the X/Y coordinate direction and the Z direction by a sine formula and a cosine formula. And moving the nine-square grid body along the directions of x, y and z in turn, and repeating the steps to obtain permeability values (permx, permy and permz) of each grid in three directions. Compared with the traditional artificial matrix assignment operation, the algorithm integrates the mathematical geological thought, and performs matrix reassignment closer to the actual geological condition under the condition of more stable data change speed.
B Experimental data preparation
The data types of each column of permeability grid data are required to be the same, each permeability value is respectively positioned at the upper left corner of the grid, the Sudoku is taken as a unit to perform clustering analysis once, after the operation is finished, the center automatically moves to the next grid, and the moving sequence is in the directions of x, y and z. Considering that the examined samples generally have different dimensions, in order to enable the data in different dimensions and different value ranges to be put together for comparison, the data is firstly subjected to normalized transformation, that is, the average value of each column of data in the data matrix is 0, the variance is 1, and the experimental data is as shown in fig. 3.
C clustering analysis algorithm application
Calculating the similarity between data by using an Euclidean distance formula; parameters such as an inclination angle, an azimuth angle, a distance and a permeability value are comprehensively considered in the clustering time variable selection. Euclidean distance between the variables after the standardized transformation is calculated by adopting an Euclidean distance formula, and the calculation process is realized by SPSS statistical analysis software and is expressed by a distance similarity coefficient matrix. And (3) performing cluster analysis by using SPSS software, and classifying by using a ward method when selecting method analysis after the number of cluster classifications is given. After the distance matrix or the correlation matrix is calculated, we often use a pedigree chart to represent the classification results (as shown in fig. 4) in order to more intuitively see the relationship between the samples or variables.
It can be clearly seen from the pedigree diagram that B230, B330, B220 and C33-1 are classified into one class, and the other points are classified into one class, which is completely consistent with the original permeability data classification, so that the clustering analysis can cluster the data more safely and stably without deviating from the original permeability value grid distribution rule.
Three-dimensional space geometric angle transformation for solving permeability values in three directions
A, calculating the main direction permeability value
After the cluster analysis method finds out the type which meets the condition, the main direction of the permeability and the magnitude of the permeability value in the main direction are obtained in the next step. Finding out n values belonging to the same class as the central value by a clustering method, and calculating the permeability value in the main direction by an arithmetic mean value method (such as formula 1)
B finding the main direction of permeability
Knowing that three points which accord with the data form a triangular surface in space, knowing the space coordinates of the three points, firstly calculating the coordinates of the middle point in each side by using a middle point formula, then calculating the gravity center M (x 0, y0 and z 0) by using a fixed ratio interior point formula, and calculating the gravity center formula as follows
x 0 ＝(x 1 +λx 2 )/(1+λ)，y 0 ＝(y 1 +λy 2 )/(1+λ)，y 0 ＝(y 1 +λy 2 )/(1+λ) (5)
Wherein =1/2.
After the coordinates M (x 0, y0, z 0) of the gravity center point are obtained, the direction in which the center points to the gravity center is known as the permeability main direction. If the number of the points in the class is 4, the permeability direction can be obtained by obtaining the centroid coordinate, and if the number of the points in the class n exceeds 4, the dip angle and the azimuth angle are weighted averages of the dip angles and the azimuth angles of the points, so that the main direction of permeability is determined.
C three-dimensional angle transformation for solving permeability in x, y and z directions
Firstly, projecting the main direction of permeability in three-dimensional space onto xz plane and yz plane respectively (as shown in figure 5), and determining theta according to the three-dimensional space coordinates of the central point and the gravity center point M yz 、θ xz 。
CoSθ yz ＝(y 0 -y j )/[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 (6)
Cosθ xz ＝(x 0 -x i )/[(x 0 -x i ) 2 +(z 0 -z k ) 2 ] 1/2 (7)
θ yz ＝arccos(y 0 -y j )/[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 (8)
θ xz ＝arccos(y 0 -y j )/[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 (9)
Wherein theta is yz 、θ xz Respectively the included angles between the line projected on the surface and the coordinate axes y and z.
Length value projected onto yz plane = [ (y) 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 (10)
Length of three-dimensional space principal direction line = [ (x) 0 -x i ) 2 +(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 (11)
CosΦ yz ＝[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 /[(x 0 -x i ) 2 +(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 (12)
Where Φ yz is the angle between the principal direction line of permeability and the line projected onto the yz plane.
K yz ＝CosΦ yz *K＝[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 /[(x 0 -x i ) 2 +(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 *K (13)
K z ＝sinθ yz *K yz ＝sinarccos(y 0 -y j )/[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 *[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 /[(x 0 -x i ) 2 +(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 *K (14)
K y ＝Cosθ yz *K yz ＝(y 0 -y j )/[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 *[(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 /[(x 0 -x i ) 2 +(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 *K (15)
In the same way, K can be obtained x ＝(x 0 -x i )/[(x 0 -x i ) 2 +(z 0 -z k ) 2 ] 1/2 *[(x 0 -x i ) 2 +(z 0 -z k ) 2 ] 1/2 /[(x 0 -x i ) 2 +(y 0 -y j ) 2 +(z 0 -z k ) 2 ] 1/2 *K (16)
Wherein K yz Permeability as projected onto the yz plane, K z 、K y 、K x Permeability values in three directions are respectively.
And then, the permeability of the next grid can be calculated until the grid calculation of the work area is finished.
Claims (1)
1. A method for obtaining permeability in a three-dimensional direction in an underground oil reservoir is characterized by comprising the following steps: the permeability values of the three-dimensional space X, Y and the Z direction in the underground oil reservoir can be obtained by the method; in order to relatively accurately obtain a permeability grid data body, applying Ward cluster analysis thought in geology statistics, classifying permeability by using a nine-square grid model with the smallest permeability data body, so that data sets sensitive to direction changes are combined into one class, according to a cluster analysis method, searching 27 grid values in the nine-square grid body in a range, separating two classes, wherein the permeability value is close to a central point and is a class a, other values are b classes, the direction of the permeability can be determined by pointing the coordinate of the central point to the gravity centers of other points except the central point in the class a, and the nine-square grid body sequentially moves along the directions x, y and z, and repeating the steps to obtain the permeability values (permx, permy and permz) of each grid in three directions; after the class which meets the condition is found out by a clustering analysis method, the main direction of the permeability and the magnitude of the permeability value in the main direction are obtained next, n values which belong to the same class with the central value are found out by the clustering method, the permeability value in the main direction is obtained by an arithmetic mean value method, three points which meet the class of data are known to form a triangular surface in space, the space coordinates of the three points are also known, the coordinates of the middle points in each side are firstly obtained by a middle point formula, then the gravity center M (x 0, y0 and z 0) is obtained by a point formula in definite ratio, after the coordinates M (x 0, y0 and z 0) of the gravity center point are obtained, the direction of the gravity center pointed by the center is known to be the main direction of the permeability, the main direction of the permeability in the three-dimensional space is respectively projected onto xz and yz planes, theta yz and theta xz are determined according to the three-dimensional space coordinates of the center point and the gravity center point M, and finally the permeability in the three-dimensional space is obtained by geometric calculation.
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