A method for obtaining permeability of heterogeneous reservoirs based on inverse transformation sampling

Abstract

The present invention discloses a method for obtaining the permeability of a heterogeneous storage layer based on inverse transformation sampling, and relates to the technical field of underground fluid seepage heat transfer. The method comprises: S1, obtaining geological data of the area to be measured, constructing a three-dimensional rectangular coordinate system of the study area, determining the size and number of structural grids, the length of the relevant distance in each direction, and constructing a correlation matrix; S2, determining the number of random seeds, and using a random standard normal sequence to preliminarily generate a random field; S3, determining the permeability mean and coefficient of variation of the study area; S4, performing inverse transformation sampling on each structural grid; S5, importing an unstructured grid to obtain permeability data. The present invention realizes that the generated permeability random field is randomized again inside each structural grid on the basis of ensuring that it obeys the log-normal distribution, so as to obtain a more ideal heterogeneous reservoir that can be used in an unstructured grid.

Description

Technical Field

[0001] The present invention relates to the technical field of underground fluid seepage heat transfer, and in particular to a method for acquiring the permeability of a heterogeneous storage layer based on inverse transformation sampling. Background Art

[0002] Numerical simulation methods occupy an important position in the fields of geothermal energy utilization, carbon dioxide storage and underground energy storage that cannot be replaced by indoor experiments and field tests. They are an important means to characterize reservoir characteristics and study the flow and heat transfer laws of underground fluids. In order to accurately characterize the heterogeneity of hydrogeological parameters of geological bodies, the commonly used method of numerical simulation is to import the geological data obtained on site into the numerical model to construct heterogeneous strata, but this requires a high degree of integrity of the relevant data and is difficult to obtain. To this end, it is necessary to construct a spatially distributed random field of relevant geological parameters, so as to achieve the modeling of heterogeneous reservoirs in the absence of detailed geological data.

[0003] One of the methods for realizing the numerical model of heterogeneous reservoirs is to simply divide the geometric model of a certain size according to the degree of lithological similarity, and then assign values ​​to each area separately. This method is highly subjective and less precise. Another commonly used method is to divide the structured grid and construct a correlation matrix, considering the correlation between different units that is inversely proportional to the distance, so as to generate a spatially distributed random field that meets the conditions. This method is based on the divided structured grid for calculation. The smaller the grid volume and the more grids there are, the more computing resources are consumed. Therefore, in the calculation of the model of thousands of meters, the length of a single grid is nearly 100 meters, which means that a certain hydrogeological parameter is consistent in an area of ​​tens of thousands of square meters, which is obviously not in line with the actual geological conditions.

[0004] A large number of studies have been conducted at home and abroad on the relevant applications of heterogeneous reservoirs. This heterogeneity is often manifested as heterogeneity in permeability and porosity. Taking permeability as an example, it is currently believed that its spatial distribution obeys a log-normal distribution, and the correlation distance and coefficient of variation are different for different lithologies. How to consider the correlation distance between different units under the premise of obeying the above distribution law, while refining the heterogeneous distribution of relevant hydrogeological parameters as much as possible, so that the random field obtained by the structured grid can be better applied to the unstructured grid, is crucial for the subsequent construction of heterogeneous formation models and the characterization of underground fluid migration and distribution characteristics. Therefore, it is an urgent problem for those skilled in the art to propose a method for obtaining the permeability of heterogeneous storage layers based on inverse transform sampling to solve the difficulties existing in the prior art. Summary of the invention

[0005] In view of this, the present invention provides a method for obtaining the permeability of a heterogeneous storage layer based on inverse transform sampling. The permeability field that obeys the log-normal distribution inside a single structured grid can be obtained through the inverse transform sampling method, while meeting the requirements of the heterogeneous distribution inside the structured grid and the correlation requirements between different grids, so that it can be used in models composed of non-structured grids established by other digital modeling software.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for obtaining the permeability of a heterogeneous storage layer based on inverse transformation sampling comprises the following steps:

[0008] S1. Structural grid construction step: obtain geological data of the current study area, construct a three-dimensional rectangular coordinate system of the study area based on the geological data, determine the size, number and relevant distance length of the structural grids in each direction, and construct a correlation matrix obtained by calculating the distance between each structural grid;

[0009] S2, random field generation step: determine the number of random seeds, use the correlation matrix obtained in the previous step to decompose the lower triangular matrix, and then calculate and generate the random field;

[0010] S3, random field conversion step: obtain the permeability mean and coefficient of variation of the current study area, and convert the random field generated in S2 into a permeability random field;

[0011] S4, inverse transformation step: performing inverse transformation sampling on each structured grid to obtain the permeability random field after inverse transformation;

[0012] S5, spatial distribution import step: import the inverse transformed permeability random field obtained in S4 into the unstructured grid to obtain permeability data.

[0013] The above method optionally constructs a correlation matrix in S1:

[0014]

[0015] L.L T =ρ (2)

[0016] Where ρ is the m×m correlation matrix, which is calculated by the spatial distance between each grid and other grids, where m is the total number of grids; Δx, Δy and Δz are the distances between different grids in three directions, respectively; δ x , δ y and δ z are the relevant distances in three directions respectively; they are set by different lithology and strata, and are related to the number of grids and grid size; L and L Tare the lower triangular matrix and its transposed matrix obtained by Cholesky decomposition of the correlation matrix ρ.

[0017] In the above method, optionally, a random standard normal sequence is used in S2 to initially generate a random field:

[0018]

[0019] Where G is the initially generated random field and Z is the random standard normal sequence.

[0020] In the above method, optionally, the coefficient of variation in S3 is the ratio of the permeability standard deviation to the mean, and the random field is converted into the permeability random field using the following formula:

[0021] κ=exp(μ+σ·G) (4)

[0022]

[0023]

[0024] Where κ is the permeability field available on the generated structured grid; μ is the mean of the lognormal distribution; σ is the variance of the lognormal distribution; μ N is the mean permeability of the entire simulation area; σ N is the standard deviation of the permeability values ​​in the area.

[0025] In the above method, optionally, the specific contents of S4 include:

[0026] S401 obtains a probability density function f(x) of permeability distribution;

[0027]

[0028] Where x is the independent variable, which is the permeability in this case; μ' is the mean of the lognormal distribution; and σ' is the variance of the lognormal distribution.

[0029] S402 calculates the cumulative distribution function F(x) of the probability density function f(x) to obtain a function of the probability value changing with the permeability;

[0030]

[0031] In the formula, erf is the error function, the independent variable is the permeability, and the dependent variable is the probability value

[0032] S403 Calculate the inverse cumulative distribution function F -1 (x), and obtain the function of permeability changing with probability value.

[0033]

[0034]

[0035]

[0036] Where κ' is the final unstructured permeability field; erfinv is the inverse error function; at this time, the dependent variable is the permeability, and the independent variable is the probability value obtained through u(x, y, z). u(x, y, z) is a random function with a uniform distribution of 0 to 1 in a three-dimensional space. It is directly generated by COMSOL software and the corresponding probability value is uniformly randomly extracted from each node in the spatial coordinate system.

[0037] It can be seen from the above technical solutions that, compared with the prior art, the present invention provides a method for obtaining the permeability of a heterogeneous storage layer based on inverse transformation sampling, which has the following beneficial effects:

[0038] 1. This method can be used to generate a permeability random field that follows a log-normal distribution and is used to simulate heterogeneous reservoirs. This random field takes into account the correlation between different geological units and flexibly sets the correlation distance, permeability mean, and coefficient of variation according to the characteristics of different research areas.

[0039] 2. The random field is applicable to both structured and unstructured grids, and can more finely characterize the heterogeneity of reservoirs in simulations of larger geological scales; it is applicable to two-dimensional and three-dimensional geometric models;

[0040] 3. The permeability generated by this method makes up for the smooth interpolation characteristics of other heterogeneous methods, and some extreme values ​​generated within a reasonable range are more in line with the actual formation conditions; in addition, this method greatly reduces the amount of calculation caused by the traditional method of increasing the number of grids to generate a finer heterogeneous field;

[0041] 4. This method can be used to draw a more accurate geological model using less data, which is more conducive to the study of heterogeneous reservoirs and the exploitation of underground energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0043] Figure 1 A flow chart of a method for obtaining permeability of a heterogeneous storage layer based on inverse transformation sampling disclosed in the present invention;

[0044] Figure 2Schematic diagrams of structural and non-structural permeability random fields disclosed in the present invention, wherein 2(a) is a schematic diagram of a structural permeability random field with a correlation distance: model length of 0.1; 2(b) is a schematic diagram of a structural permeability random field with a correlation distance: model length of 1; 2(c) is a schematic diagram of a non-structural permeability random field with a correlation distance: model length of 0.1; 2(d) is a schematic diagram of a non-structural permeability random field with a correlation distance: model length of 1;

[0045] Figure 3 It is a schematic diagram of the calculation of the structural grid correlation matrix disclosed in the present invention. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] In this application, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, the elements defined by the sentence "comprise one..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0048] Reference Figure 1 As shown, the present invention discloses a method for obtaining the permeability of a heterogeneous storage layer based on inverse transformation sampling, comprising the following steps:

[0049] S1. Structural grid construction step: obtain geological data of the current study area, construct a three-dimensional rectangular coordinate system of the study area based on the geological data, determine the size, number and relevant distance length of the structural grids in each direction, and construct a correlation matrix obtained by calculating the distance between each structural grid;

[0050] S2, random field generation step: determine the number of random seeds, use the correlation matrix obtained in the previous step to decompose the lower triangular matrix, and then calculate and generate the random field;

[0051] S3, random field conversion step: obtain the permeability mean and coefficient of variation of the current study area, and convert the random field generated in S2 into a permeability random field;

[0052] S4, inverse transformation step: performing inverse transformation sampling on each structured grid to obtain the permeability random field after inverse transformation;

[0053] S5, spatial distribution import step: import the inverse transformed permeability random field obtained in S4 into the unstructured grid to obtain permeability data.

[0054] Furthermore, the correlation matrix is ​​constructed in S1:

[0055]

[0056] L.L T =ρ (2)

[0057] Where ρ is the m×m correlation matrix, which is calculated by the spatial distance between each grid and other grids, where m is the total number of grids; Δx, Δy and Δz are the distances between different grids in three directions, respectively; δ x ,δ y and δ z are the relevant distances in three directions respectively; they are set by different lithology and strata, and are related to the number of grids and grid size; L and L T are the lower triangular matrix and its transposed matrix obtained by Cholesky decomposition of the correlation matrix ρ. Figure 3 .

[0058] Furthermore, a random standard normal sequence is used in S2 to preliminarily generate a random field:

[0059]

[0060] Where G is the initially generated random field and Z is the random standard normal sequence.

[0061] Furthermore, the coefficient of variation in S3 is the ratio of the permeability standard deviation to the mean, and the random field is converted into the permeability random field using the following formula:

[0062] κ=exp(μ+σ·G) (4)

[0063]

[0064]

[0065] Where κ is the permeability field available on the generated structured grid; μ is the mean of the lognormal distribution; σ is the variance of the lognormal distribution; μ N is the mean permeability of the entire simulation area; σN is the standard deviation of the permeability values ​​in the area.

[0066] Furthermore, the specific contents of S4 include:

[0067] S401 obtains a probability density function f(x) of permeability distribution;

[0068]

[0069] In the formula, x is the independent variable, which is the permeability in this case; μ' is the mean of the lognormal distribution; σ' is the variance of the lognormal distribution;

[0070] S402 calculates the cumulative distribution function F(x) of the probability density function f(x) to obtain a function of the probability value changing with the permeability;

[0071]

[0072] In the formula, erf is the error function, the independent variable is the permeability, and the dependent variable is the probability value;

[0073] S403 Calculate the inverse cumulative distribution function F -1 (x), and obtain the function of permeability changing with probability value;

[0074]

[0075]

[0076]

[0077] Where κ' is the final unstructured permeability field; erfinv is the inverse error function; at this time, the dependent variable is the permeability, and the independent variable is the probability value obtained through u(x, y, z). u(x, y, z) is a random function with a uniform distribution of 0 to 1 in a three-dimensional space. It is directly generated by COMSOL software and the corresponding probability value is uniformly randomly extracted from each node in the spatial coordinate system.

[0078] Specifically, the permeability random field generated in this way can be randomized again within each structured grid on the basis of ensuring that it obeys the log-normal distribution, thus obtaining a more ideal heterogeneous reservoir that can be used in unstructured grids. Figure 2 .in Figure 2 (a) is a schematic diagram of the structural permeability random field with a correlation distance: model length of 0.1; Figure 2 (b) is the schematic diagram of the structural permeability random field with correlation distance: model length of 1; Figure 2 (c) is a schematic diagram of the random field of non-structural permeability with a correlation distance: model length of 0.1; Figure 2(d) Schematic diagram of the non-structural permeability random field with correlation distance: model length 1.

[0079] Among them, the comparison between Figure ab and Figure cd shows that the method adopted by the present invention does more finely depict the heterogeneity of the reservoir space, while ensuring the overall distribution characteristics;

[0080] Comparing Figure ac with Figure bd, we can see that the stronger the correlation between different structural grids, the more uniform the overall permeability distribution, that is, the weaker the heterogeneity. This correlation is related to the geological characteristics of different study areas and requires specific analysis and reasonable settings. It is usually characterized by the ratio of correlation distance: model length. The larger the ratio, the stronger the correlation.

[0081] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can refer to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can refer to the partial description of the method embodiment. The system and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without creative work.

[0082] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for obtaining the permeability of a heterogeneous reservoir layer based on inverse transformation sampling, characterized in that: The following steps are involved: S1. Structural grid construction step: obtain geological data of the current study area, construct a three-dimensional rectangular coordinate system of the study area based on the geological data, determine the size, number and relevant distance length of the structural grids in each direction, and construct a correlation matrix obtained by calculating the distance between each structural grid; S2, random field generation step: determine the number of random seeds, use the correlation matrix obtained in S1 to decompose the lower triangular matrix, and then calculate and generate the random field; S3, random field conversion step: obtain the permeability mean and coefficient of variation of the current study area, and convert the random field generated in S2 into a permeability random field; S4, inverse transformation step: performing inverse transformation sampling on each structured grid to obtain the permeability random field after inverse transformation; S5, spatial distribution import step: importing the inverse transformed permeability random field obtained in S4 into the unstructured grid to obtain permeability data; The specific contents of S4 include: S401 obtains a probability density function f(x) of permeability distribution; In the formula, x is the independent variable, which is the permeability in this case; μ' is the mean of the lognormal distribution; σ' is the variance of the lognormal distribution; S402 calculates the cumulative distribution function F(x) of the probability density function f(x) to obtain a function of the probability value changing with the permeability; In the formula, erf is the error function, the independent variable is the permeability, and the dependent variable is the probability value; S403 Calculate the inverse cumulative distribution function F -1 (x), and obtain the function of permeability changing with probability value; Where κ' is the final unstructured permeability field; erfinv is the inverse error function; at this time, the dependent variable is the permeability, and the independent variable is the probability value obtained through u(x, y, z). u(x, y, z) is a random function with a uniform distribution of 0 to 1 in a three-dimensional space. It is directly generated by COMSOL software and the corresponding probability value is uniformly randomly extracted from each node in the spatial coordinate system.

2. The method for obtaining the permeability of a heterogeneous reservoir layer based on inverse transformation sampling according to claim 1, characterized in that: Construct the correlation matrix in S1: L·L T =p (2) Where ρ is the m×m correlation matrix, which is calculated by the spatial distance between each grid and other grids, where m is the total number of grids; Δx, Δy and Δz are the distances between different grids in three directions, respectively; δ x , δ y and δ z are the relevant distances in three directions, which are set by different lithology and strata and are related to the number of grids and grid size; L and L T are the lower triangular matrix and its transposed matrix obtained by Cholesky decomposition of the correlation matrix ρ.

3. The method for obtaining the permeability of a heterogeneous reservoir layer based on inverse transformation sampling according to claim 1, characterized in that: In S2, a random standard normal sequence is used to initially generate a random field: Where G is the initially generated random field and Z is the random standard normal sequence.

4. The method for obtaining the permeability of a heterogeneous reservoir layer based on inverse transformation sampling according to claim 1, characterized in that: The coefficient of variation in S3 is the ratio of the permeability standard deviation to the mean. The random field is converted into the permeability random field using the following formula: κ=exp(μ+σ·G) (4) Where κ is the permeability field available on the generated structured grid; μ is the mean of the lognormal distribution; σ is the variance of the lognormal distribution; μ N is the mean permeability of the entire simulation area; σ N is the standard deviation of the regional permeability values.

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