A method for describing the distribution of residual gas considering the time-varying reservoir permeability

Abstract

The present invention relates to a method for describing the distribution of residual gas taking into account the time-varying permeability of the reservoir, and belongs to the field of gas reservoir engineering; the technical scheme is to select at least 10 cores with different original permeabilities to conduct permeability stress sensitivity experiments to obtain dimensionless permeabilities under different pressures; construct and train an artificial neural network dimensionless permeability prediction model based on experimental data; and grid the reservoir, establish a two-dimensional matrix of original permeability and formation pressure according to well logging, formation static pressure test and RFT test data, and predict dimensionless permeability in combination with the artificial neural network dimensionless permeability prediction model; further calculate the pressure gradient, seepage capacity and residual gas quantitative value. Finally, through normalization processing, a dimensionless residual gas distribution map is drawn to clarify the residual gas level in different regions. The method of the present invention takes into account the time-varying permeability and provides an important theoretical basis and technical support for gas reservoir management and development.

Description

Technical Field

[0001] The invention relates to a residual gas distribution description method considering the time-varying reservoir permeability, and belongs to the field of gas reservoir engineering. Background Art

[0002] The description of the remaining gas distribution is to analyze the distribution characteristics of natural gas in different areas of the reservoir, so as to guide the secondary or tertiary potential tapping and improve the recovery rate of gas reservoirs. In loose sandstone, tight gas, shale gas and other gas reservoirs, changes in formation pressure will lead to changes in pore structure, affecting the seepage capacity, and then affecting the distribution of remaining gas. At present, the description of the remaining gas distribution is usually carried out through geological modeling and numerical simulation methods. However, this type of method assumes that the reservoir properties remain unchanged, which limits the accuracy of the remaining gas description and takes a long time for historical fitting. The remaining gas distribution can also be described by dynamic monitoring methods, but this method is expensive. Summary of the invention

[0003] The purpose of the present invention is to overcome the shortcomings of the prior art, establish an artificial neural network dimensionless permeability prediction model based on permeability stress sensitivity experimental data, characterize the residual gas distribution by combining the original permeability, pressure gradient and recovery degree, and provide a residual gas distribution description method that takes into account the time-varying reservoir permeability.

[0004] To achieve the above object, the present invention provides a method for describing the residual gas distribution taking into account the time-varying reservoir permeability, the method comprising the following steps:

[0005] S1. Randomly select at least 10 cores with different original permeabilities to conduct permeability stress sensitivity experiments, obtain dimensionless permeabilities of cores with different original permeabilities under different pressures, and integrate the data of original permeability, pressure and dimensionless permeability into a data set; the upper limit of pressure is the original formation pressure, the lower limit is the abandoned formation pressure, and the interval is 1MPa; dimensionless permeability refers to the ratio of permeability under pressure to original permeability;

[0006] S2. Build an artificial neural network dimensionless permeability prediction model. Randomly divide the data set in step S1 into a training set and a test set at a ratio of 8:2. Use the original permeability and pressure as input parameters and the dimensionless permeability as output parameter. Use 5-fold cross validation to train the training set. Use the test set to evaluate the prediction effect of the artificial neural network dimensionless permeability prediction model. When the determination coefficient R 2 When >0.8, the dimensionless permeability prediction model of artificial neural network meets the requirements;

[0007] S3, gridding the reservoir with equal step length, where the number of grids in the x direction is m and the number of grids in the y direction is n;

[0008] S4. Based on the single-well logging data, establish the original two-dimensional permeability matrix K = (k ij ) n×m , where k ij is the original permeability of the grid in the i-th row and j-th column, with the unit of mD;

[0009] S5. Based on the formation static pressure test data and RFT test data in the t-th year, establish the formation pressure two-dimensional matrix P t = (p tij ) n×m , where p tij is the formation pressure of the grid in the i-th row and j-th column in the t-th year, with the unit of MPa; The gas reservoir has been produced for T years, and t takes values of 1, 2,..., T;

[0010] S6. Input k ij and the corresponding p tij , and use the dimensionless permeability prediction model of the artificial neural network in step S2 to predict the dimensionless permeability at the corresponding position, and establish the dimensionless permeability two-dimensional matrix K Dtm = (k Dtij ) n×m , where k Dtij is the dimensionless permeability of the grid in the i-th row and j-th column in the t-th year, which is a dimensionless quantity;

[0011] S7. Establish the pressure gradient two-dimensional matrix Gt = (g tij ) n×m , where, when 1 < i < n and 1 < j < m

[0012]

[0013] In the formula, p t(i-1) j is the formation pressure of the grid in the (i - 1)-th row and j-th column in the t-th year, with the unit of MPa; p t(i+1)j is the formation pressure of the grid in the (i + 1)-th row and j-th column in the t-th year, with the unit of MPa; p ti(j-1) is the formation pressure of the grid in the i-th row and (j - 1)-th column in the t-th year, with the unit of MPa; p ti(j+1) is the formation pressure of the grid in the i-th row and (j + 1)-th column in the t-th year, with the unit of MPa; L is the grid step length, with the unit of m; g tij is the pressure gradient of the grid in the i-th row and j-th column in the t-th year, with the unit of MPa / m;

[0014] When i = 0 or i = n or j = 0 or j = m, g tij is the average value of the pressure gradients of adjacent grids;

[0015] S8. The product of the dimensionless permeability and the original permeability in the tth year is the permeability in the tth year. The product of the permeability and the pressure gradient in the tth year represents the seepage capacity in the tth year. The two-dimensional matrix D of the seepage capacity in the tth year is established. t =(d tij ) n×m ,in,

[0016] d tij =k ij ·g tij ·k Dtij

[0017] Where, d tij is the seepage capacity of the grid in the i-th row and j-th column in the t-th year, in mD·MPa·m -1 ;

[0018] S9. Perform maximum and minimum normalization on all elements of the two-dimensional matrix of seepage capacity in the tth year, and establish the dimensionless two-dimensional matrix D of seepage capacity in the tth year. Dt =(d Dtij ) n×m ;

[0019] S10, taking the annual recovery degree in year t as the weight, perform weighted summation on the dimensionless seepage capacity of each year, multiply the difference between 1 and the summation result by the original gas saturation, and obtain the remaining gas quantitative value S = (s ij ) n×m :

[0020]

[0021] In the formula, s ij It is the quantitative value of residual gas, the unit is mD·MPa·m -1 ; S gi is the initial gas saturation, dimensionless quantity; R t is the annual extraction degree in year t, a dimensionless quantity;

[0022] S11. Perform maximum and minimum normalization on the residual gas quantization value, and draw a dimensionless residual gas distribution map based on the normalized result. The part greater than or equal to 0.8 is a high residual gas area, the area less than 0.6 is a low residual gas area, and the part greater than or equal to 0.6 and less than 0.8 is a medium residual gas area.

[0023] Compared with the prior art, the present invention has the following beneficial effects: (1) a dimensionless permeability prediction model taking into account pressure and original permeability is established based on an artificial neural network, thereby improving the prediction accuracy and having intelligent characteristics; (2) the dimensionless seepage capacity is weightedly summed by the annual recovery degree, and the calculation method is convenient and effective, with high work efficiency; (3) it has strong scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is the technical roadmap of this method;

[0025] Figure 2 This is the permeability distribution map in 2006;

[0026] Figure 3 This is the penetration rate distribution map in 2016;

[0027] Figure 4 This is the penetration distribution map in 2024;

[0028] Figure 5 It is a dimensionless residual gas distribution diagram. DETAILED DESCRIPTION

[0029] The present invention is further described below in conjunction with the embodiments and drawings.

[0030] The present invention provides a method for describing the residual gas distribution taking into account the time-varying permeability of the reservoir. Figure 1 For the technical roadmap of this method, for a domestic gas reservoir that was put into production in 2006 and has been in production for 19 years until 2024, the following steps are implemented:

[0031] S1. Randomly select 10 cores with different original permeabilities to conduct permeability stress sensitivity experiments. The experimental pressure range is 4MPa~22MPa, with an interval of 1MPa, to obtain the dimensionless permeability of the cores with different original permeabilities, and integrate the data of original permeability, pressure and dimensionless permeability into a data set;

[0032] S2. Build an artificial neural network dimensionless permeability prediction model. Randomly divide the data set in step S1 into a training set and a test set at a ratio of 8:2. Use the original permeability and pressure as input parameters and the dimensionless permeability as output parameter. Use 5-fold cross validation to train the training set. Use the test set to evaluate the prediction effect of the artificial neural network dimensionless permeability prediction model. When the determination coefficient R 2 When >0.8, the dimensionless permeability prediction model of artificial neural network meets the requirements;

[0033] S3, with a step size of 50 m, the reservoir is gridded with equal step size, where the number of grids in the x direction is 195 and the number of grids in the y direction is 87;

[0034] S4. According to the single well logging data, establish the original permeability two-dimensional matrix K = (k ij ) 87×195 , where k ij is the original permeability of the grid in row i and column j, in mD;

[0035] S5. Establish a two-dimensional formation pressure matrix \(P\) for the \(t\)th year based on the formation static pressure test data and RFT test data in the \(t\)th year. t =(p tij ) 87×195 , where \(p tij \) is the formation pressure of the \(i\)th row and \(j\)th column grid in the \(t\)th year, with the unit of MPa; \(t\) takes values of 1, 2, …, 19.

[0036] S6. Input \(k ij \) and the corresponding \(p tij \), and use the dimensionless permeability prediction model of the artificial neural network in step S2 to predict the dimensionless permeability at the corresponding position, and establish a two-dimensional dimensionless permeability matrix \(K Dtm =(k Dtij ) 87×195 , where \(k Dtij \) is the dimensionless permeability of the \(i\)th row and \(j\)th column grid in the \(t\)th year, which is a dimensionless quantity.

[0037] S7. Establish a two-dimensional pressure gradient matrix \(G t =(g tij ) 87×195 , where when 1 < \(i\) < 87 and 1 < \(j\) < 195

[0038]

[0039] In the formula, \(p t(i-1)j \) is the formation pressure of the \((i - 1)\)th row and \(j\)th column grid in the \(t\)th year, with the unit of MPa; \(p t(i+1)j \) is the formation pressure of the \((i + 1)\)th row and \(j\)th column grid in the \(t\)th year, with the unit of MPa; \(p ti(j-1) \) is the formation pressure of the \(i\)th row and \((j - 1)\)th column grid in the \(t\)th year, with the unit of MPa; \(p ti(j+1) \) is the formation pressure of the \(i\)th row and \((j + 1)\)th column grid in the \(t\)th year, with the unit of MPa; \(L\) is the grid step length, with the unit of m; \(g tij \) is the pressure gradient of the \(i\)th row and \(j\)th column grid in the \(t\)th year, with the unit of MPa / m.

[0040] When \(i = 0\) or \(i = 87\) or \(j = 0\) or \(j = 195\), \(g tij \) is the average value of the pressure gradients of adjacent grids.

[0041] S8. The product of the dimensionless permeability in the \(t\)th year and the original permeability is the permeability in the \(t\)th year. To visually observe the change of permeability, draw a permeability distribution map, such as Figure 2 , Figure 3 and Figure 4 , Figure 2 is the permeability distribution map in 2006, Figure 3 is the permeability distribution map in 2016. Figure 4 is the permeability distribution map in 2024; the product of the permeability and the pressure gradient in the tth year represents the seepage capacity in the tth year, and the two-dimensional matrix D of the seepage capacity in the tth year is established t =(d tij ) 87×195 ,in,

[0042] d tij =k ij ·g tij ·k Dtij

[0043] Where, d tij is the seepage capacity of the grid in the i-th row and j-th column in the t-th year, in mD·MPa·m -1 ;

[0044] S9. All elements of the two-dimensional matrix of seepage capacity in the tth year are normalized to the maximum and minimum values, and the dimensionless two-dimensional matrix D of seepage capacity in the tth year is established. Dt =(d Dtij ) 87×195 ;

[0045] S10, taking the annual recovery degree in year t as the weight, perform weighted summation on the dimensionless seepage capacity of each year, multiply the difference between 1 and the summation result by the original gas saturation, and obtain the remaining gas quantitative value S = (s ij ) 87×195 :

[0046]

[0047] In the formula, s ij It is the quantitative value of residual gas, the unit is mD·MPa·m -1 ; S gi is the initial gas saturation, dimensionless quantity; R t is the annual extraction degree in year t, a dimensionless quantity;

[0048] S11. Perform maximum and minimum normalization on the residual gas quantization value, and draw a dimensionless residual gas distribution diagram based on the normalized result, such as Figure 5 , Figure 5 It is a dimensionless residual gas distribution diagram, in which the part greater than or equal to 0.8 is a high residual gas area, the area less than 0.6 is a low residual gas area, and the part greater than or equal to 0.6 and less than 0.8 is a medium residual gas area.

[0049] It is obvious to those skilled in the art that any modification or partial replacement of the present invention that does not depart from the spirit and scope of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for describing the distribution of residual gas considering the time-varying reservoir permeability, characterized in that: The method comprises the following steps: S1. Randomly select at least 10 cores with different original permeabilities to conduct permeability stress sensitivity experiments, obtain dimensionless permeabilities of cores with different original permeabilities under different pressures, and integrate the data of original permeability, pressure and dimensionless permeability into a data set; S2. Build an artificial neural network dimensionless permeability prediction model. Randomly divide the data set in step S1 into a training set and a test set at a ratio of 8:

2. Use the original permeability and pressure as input parameters and the dimensionless permeability as output parameter. Use 5-fold cross validation to train the training set. Use the test set to evaluate the prediction effect of the artificial neural network dimensionless permeability prediction model. When the determination coefficient R 2 When >0.8, the dimensionless permeability prediction model of artificial neural network meets the requirements; S3, gridding the reservoir with equal step length, where the number of grids in the x direction is m and the number of grids in the y direction is n; S4. According to the single well logging data, establish the original permeability two-dimensional matrix K = (k ij ) n×m , where k ij is the original permeability of the grid in row i and column j, in mD; S5. Based on the formation static pressure test data and RFT test data in year t, establish the two-dimensional formation pressure matrix P in year t t =(p tij ) n×m , where p tij is the formation pressure in the tth year of the grid in the i-th row and j-th column, in MPa; the gas reservoir is in production for T years, and t is 1, 2, …, T; S6. Input k ij The corresponding position p tij , use the artificial neural network dimensionless permeability prediction model in step S2 to predict the dimensionless permeability of the corresponding position, and establish the dimensionless permeability two-dimensional matrix K of the tth year Dtm =(k Dtij ) n×m , where k Dtij is the dimensionless permeability of the grid in row i and column j in year t, a dimensionless quantity; S7. Establish the two-dimensional matrix G of the pressure gradient for the t-th year t =(g tij ) n×m , where when 1 < i < n and 1 < j < m In the formula, p t(i-1)j is the formation pressure in the tth year of the grid in the i-1th row and jth column, in MPa; p t(i+1)j is the formation pressure in the tth year of the grid in the i+1th row and jth column, in MPa; p ti(j-1) is the formation pressure in the tth year of the grid in the i-th row and j-1th column, in MPa; p ti(j+1) is the formation pressure in the tth year of the grid in the i-th row and j+1th column, in MPa; L is the grid step size, in m; g tij is the pressure gradient in the tth year of the grid in the i-th row and j-th column, in MPa / m; When i=0 or i=n or j=0 or j=m, g tij is the average pressure gradient of adjacent grids; S8. The product of the dimensionless permeability and the original permeability in the tth year is the permeability in the tth year. The product of the permeability and the pressure gradient in the tth year represents the seepage capacity in the tth year. The two-dimensional matrix D of the seepage capacity in the tth year is established. t =(d tij ) n×m ,in, d tij =k ij ·g tij ·k Dtij Where, d tij is the seepage capacity of the grid in the i-th row and j-th column in the t-th year, in mD·MPa·m -1 ; S9. Perform maximum and minimum normalization on all elements of the two-dimensional matrix of seepage capacity in the tth year, and establish the dimensionless two-dimensional matrix D of seepage capacity in the tth year. Dt =(d Dtij ) n×m ; S10, taking the annual recovery degree in year t as the weight, perform weighted summation on the dimensionless seepage capacity of each year, multiply the difference between 1 and the summation result by the original gas saturation, and obtain the remaining gas quantitative value S = (s ij ) n×m : In the formula, s ij It is the quantitative value of residual gas, the unit is mD·MPa·m -1 ; S gi is the initial gas saturation, dimensionless quantity; R t is the annual extraction degree in year t, a dimensionless quantity; S11. Perform maximum and minimum normalization on the residual gas quantization value, and draw a dimensionless residual gas distribution map based on the normalized result. The part greater than or equal to 0.8 is a high residual gas area, the area less than 0.6 is a low residual gas area, and the part greater than or equal to 0.6 and less than 0.8 is a medium residual gas area.

2. A method for describing the residual gas distribution considering the time-varying reservoir permeability according to claim 1, characterized in that: In step S1, the upper limit of pressure is taken as the original formation pressure, and the lower limit is taken as the abandoned formation pressure, with an interval of 1 MPa; Dimensionless permeability refers to the ratio of the permeability under the influence of pressure to the original permeability.

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