A method for predicting natural fracture line density based on interval quantization random function

Abstract

The application discloses a method for predicting natural fracture line density based on interval quantization random function, and provides an effective method for predicting natural fracture line density without the aid of third-party software and with low artificial workload when imaging logging data and core data are less. The method comprises the following steps: obtaining core data, conventional logging data, array sonic logging data and imaging logging data of a drilling well in a target layer system; calculating dynamic rock mechanics parameters of the drilling well according to the array sonic logging data and the conventional logging data; calculating natural fracture line density according to the core data or the imaging logging data; quantitatively studying the sectional correlation between the dynamic rock mechanics parameters and the natural fracture line density; and establishing an interval quantization random function model and predicting the natural fracture line density. The application is free from the limitations of great fitting difficulty and low reliability of parameters and natural fracture line density.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of reservoir geomechanics in geology. BACKGROUND

[0002] Reservoir natural fracture comprehensive characterization is the basis of reservoir natural fracture prediction and modeling, and is also an important reference for reservoir engineering sweet spot optimization and exploration and development plan formulation. At present, the natural fracture identification and characterization methods mainly include geological and petrological method, logging method, drilling and logging, and production dynamic data analysis method (Liu J S, Ding W L, Xiao Z K, et al. Reservoir fracture comprehensive characterization and prediction research progress [J]. Progress in Geophysics, 2019, 34(06): 2283-2300). Natural fracture line density calculation is an important link in natural fracture identification and characterization work. At present, the methods for calculating natural fracture line density mainly include:

[0003] Method one: based on imaging logging data or core data, etc. to carry out natural fracture identification and characterization, to count the number of natural fractures, and to calculate the natural fracture line density. This technology is the most direct and accurate, but the disadvantage is that it needs a large amount of high-cost imaging logging data or core data, which may be met in the middle and late stages of oil and gas field exploration and development, but in the early stage of oil and gas field exploration and development, when all kinds of data are scarce, it is difficult to carry out effective and large-scale natural fracture line density prediction work through this method.

[0004] Method two: a fracture line density prediction method based on imaging logging and artificial neural network has also been proposed for fracture line density calculation in recent years. This method applies imaging logging data containing fracture line density curve in single well as basic data, optimizes multiple logging curves with strong fracture sensitivity in conventional logging curves as identification samples, and through the neural network function in Petrel software, predicts the fracture line density curve for wells without fracture line density curve, and then verifies the prediction results through single well imaging logging data and core data, and finally adjusts repeatedly to predict the fracture line density development in wells without imaging logging and coring section (Han P Y, Ding W L, Yang D B, et al. Fracture line density prediction method based on imaging logging and artificial neural network [P]. Beijing: CN202311115587.6, 2024-07-12). This method can effectively predict the natural fracture line density, but still has the shortcomings of needing to rely on third-party software (Petrel) and needing to be adjusted repeatedly by artificial means. The universality and convenience of the operation of this method still have a lot of room for improvement.

[0005] Method three: Based on the numerical simulation of tectonic stress field, the plane distribution characteristics of the tectonic stress of the target layer system in the study area can be obtained, and then according to the rock failure criterion, the fracture rate of the target layer system can be calculated. The conversion model of the fracture rate and the natural fracture line density can be obtained by carrying out fitting analysis on the fracture rate and the natural fracture line density obtained from the imaging logging, and the plane and spatial distribution characteristics of the natural fracture line density of the target layer system can be further obtained (Yuntao Li, Wenlong Ding*, Jun Han, Xuyun Chen, Cheng Huang, Jingtian Li, Shihao Ding, 2024. Quantitative Prediction of the Development and Opening Sequence of Fractures in an Ultradeep Carbonate Reservoir: A Case Study of the Middle Ordovician in the Shunnan Area, Tarim Basin, China. SPE Journal. 29(06), 3091-3117. https: / / doi.org / 10.2118 / 219453-PA.), or the natural fracture line density can be directly solved according to the simulation results of the tectonic stress field and the theory of elasticity (Wang Ke, Zhang Ronghu, Dai Junsbng, et al. Research Progress of Fractures in Low Permeability Reservoirs [J]. Journal of Earth Sciences and Environment, 2015, 37(02): 44-58). However, the problem of this technology is that the formation period of natural fractures needs to be determined before carrying out the corresponding numerical simulation of tectonic stress field, which requires a large amount of natural fracture filling dating, rock mechanics and geostress experiments, and the cost is high. Moreover, the reliability of the numerical simulation of tectonic stress field needs to be improved through a large amount of work. SUMMARY

[0006] The present application provides a method for predicting natural fracture line density based on interval quantization random function, aiming to solve the problem that when the imaging logging data and core data are insufficient, an effective method for predicting natural fracture line density applicable to various stages of oil and gas field exploration and development is proposed without the aid of third-party software and with low human workload.

[0007] In a first aspect, the present application provides a method for predicting natural fracture line density based on interval quantization random function, comprising:

[0008] Step S1, determining a study area and a target layer system, and obtaining core, conventional logging, array acoustic logging and imaging logging data of each well drilled through the target layer system in the study area; and classifying the wells in the study area, if the well has only conventional logging data in the target layer system, it is determined as a first type well; if the well has both conventional logging data and array acoustic logging data in the target layer system, it is determined as a second type well; if the well has conventional logging data and core or imaging logging data in the target layer system, it is determined as a third type well;

[0009] Step S2, calculating dynamic rock mechanics parameters of each well in the target layer system according to the array acoustic logging data and the conventional logging data;

[0010] Step S3, calculating the natural fracture line density according to the core or imaging logging data;

[0011] Step S4, screening the conventional logging or dynamic rock mechanics parameter with the highest correlation with the natural fracture line density, and quantitatively studying the segmented correlation between the dynamic rock mechanics parameter and the natural fracture line density;

[0012] Step S5, establishing an interval quantization random function model and predicting the natural fracture line density.

[0013] In the above scheme, optionally, the step S2 comprises:

[0014] The first conversion model is a conversion model of acoustic time difference AC and longitudinal wave time difference DTC, and the second model is a conversion model of longitudinal wave time difference DTC and transverse wave time difference DTS;

[0015] Based on the conventional logging data, the first conversion model and the second conversion model, DTC and DTS of the first type well and the third type well are calculated;

[0016] The dynamic Young's modulus and the dynamic Poisson's ratio of the first type well, the second type well and the third type well are calculated, and the calculation formula is:

[0017]

[0018] Wherein, E d represents the dynamic Young's modulus, and the unit is GPa; μ d represents the dynamic Poisson's ratio; Δt p represents the longitudinal wave time difference DTC, and the unit is μs / ft; Δt s represents the transverse wave time difference DTS, and the unit is μs / ft; ρ represents the density, and the unit is g / cm 3 .

[0019] In the above scheme, optionally, the step S3 comprises:

[0020] The third type of well is used to identify and characterize natural fractures, and the number of natural fractures is counted to obtain the relationship between the number of natural fractures and the actual depth of a single well;

[0021] According to the relationship between the number of natural fractures and the depth of a single well, the natural fracture line density is calculated, and the calculation formula is:

[0022]

[0023] where MD represents the depth of the natural fracture line density to be calculated, in meters; FD(MD) represents the measured value of the natural fracture line density, in pieces per meter; CL represents the cumulative number curve of natural fractures, that is, the cumulative number curve made according to the obtained relationship between the number of natural fractures and the depth of a single well; and W represents the measurement window length, which is a constant greater than 1, in meters.

[0024] In the above scheme, further optionally, the identification and characterization of natural fractures for the third type of well includes: if the third type of well has imaging logging data, first, the identification and characterization of natural fractures and the statistics are carried out using the imaging logging data; otherwise,

[0025] The identification and characterization of natural fractures and the statistics are carried out using core data.

[0026] In the above scheme, optionally, the step S4 includes:

[0027] The correlation coefficient of the conventional logging or dynamic rock mechanics parameter and the natural fracture line density FD is calculated, and the dynamic rock mechanics parameter A with the highest correlation with the natural fracture line density FD is selected;

[0028] All the dynamic rock mechanics parameters A with the highest correlation with the natural fracture line density FD belonging to the third type of well are sorted to obtain the minimum value A min and the maximum value A max of the parameter A.

[0029] According to the research accuracy requirement, the numerical range of the dynamic rock mechanics parameter A is divided into several intervals, the length of each interval is (A max -A min ) / n, and the numerical range of each interval is [A min +(i-1)*(A max -A min ) / n, A min +i*(A max -A min) / n], wherein n represents the number of divided intervals, and i represents the interval number; constructing a data group FD(A), wherein each data point contains a dynamic rock mechanics parameter A and its corresponding natural fracture line density FD; for each interval, calculating the minimum value FD of the data group of the parameter A corresponding to the natural fracture line density FD belonging to the interval min (i) the average value FD ave (i) and the maximum value FD max (i).

[0030] In the above scheme, further optionally, the selecting the dynamic rock mechanics parameter A with the highest correlation with the natural fracture line density FD comprises:

[0031] The dynamic rock mechanics parameter with the highest correlation with the natural fracture line density is selected by using a correlation analysis method.

[0032] In the above scheme, further optionally, the correlation analysis method comprises a linear fitting goodness analysis, a Pearson correlation analysis and a Spearman rank correlation analysis.

[0033] The formula for using the Spearman rank correlation analysis is:

[0034]

[0035] In the formula, R s (m) represents the Spearman rank correlation coefficient; m represents the number of data sets for quantitative relationship analysis of two variables; d i represents the ranking difference of the i-th variable set (X, Y);

[0036] Each variable set (X, Y) is changed to a variable set (X', Y') by the following formula, so that there is no same rank variable in X or Y:

[0037] X' = X + Rand() / 10 8

[0038] Y' = Y + Rand() / 10 8

[0039] In the formula, Rand() represents a random number between 0 and 1.

[0040] According to the negative value and the positive value of the calculated Spearman rank correlation coefficient Rs(n), the variable group under study is negatively correlated and positively correlated, respectively, and the closer the absolute value is to 1, the stronger the negative correlation or positive correlation between the variables.

[0041] In the above scheme, optionally, the step S5 comprises:

[0042] Constructing an interval quantization random function:

[0043]

[0044] wherein, RAND represents a random number within 0-1, a i , b i and k i represent undetermined constant coefficients in the function;

[0045] FD i (0) = FD min (i) = a i *b i

[0046] FD i (1) = FD max (i) = b i +a i *b i

[0047] According to the interval statistics results minimum value FD min (i), the average value FD ave (i) and the maximum value FD max (i) of step S4, the undetermined constant coefficients a i and b i are determined, that is:

[0048]

[0049] b i = FD max (i) - FD min (i)

[0050] k i is determined by the condition of equal area:

[0051]

[0052] The equation of the interval quantization random function and the undetermined constant coefficients a i and b i is brought in, and the coefficient ki is solved as:

[0053]

[0054] Then the interval quantization random function is:

[0055]

[0056] For the first type and the second type of drilling, the natural fracture line density FD prediction based on the interval quantization random function model is carried out.

[0057] In the scheme, further alternatively, the developing the natural fracture density FD prediction based on the interval quantization random function model comprises:

[0058] For the first type and the second type of drilling, the conventional logging data or the dynamic rock mechanics parameter A thereof has been acquired;

[0059] According to the dynamic rock mechanics parameter A with the highest correlation with the natural fracture density FD determined in the step S4, the interval to which each parameter A belongs is determined;

[0060] For the interval to which each parameter A belongs, a random number RAND between 0 and 1 is generated;

[0061] Based on the random number RAND and the corresponding interval quantization random function, the natural fracture density FD corresponding to the parameter A is calculated;

[0062] For each drilling, the interval to which the parameter A belongs is determined, the random number is generated, and the FD is calculated repeatedly until the FD corresponding to the parameter A of all the drillings is calculated; in each operation, the random number RAND is newly generated.

[0063] Compared with the prior art, the present application has at least the following beneficial effects:

[0064] Based on further analysis and research on the problems of the prior art, it is realized that the existing method for predicting the natural fracture density usually needs more imaging logging data and core data, and usually a part of the data is used to construct the prediction model and a part of the data is used for verification. However, when the research area is in the initial stage of exploration and development, the data is very scarce, especially the precious data such as imaging logging and core data of the target layer system. The method proposed in the present application can be used for the prediction of the natural fracture density under such circumstances. As long as there is a very small amount of imaging logging data or core data, the method proposed in the present application can be implemented to effectively predict the natural fracture density, which is the first advantage of the present application.

[0065] Compared with the prior art, the interval quantization random function proposed in the present application takes into account the heterogeneity of the parameter with the highest correlation with the natural fracture density in different numerical intervals, and the function proposed takes into account the non-uniformity of the data distribution represented by the minimum value, the maximum value and the average value of the natural fracture density FD in different numerical intervals, which is obviously different from the overall correlation between the parameter and the natural fracture density usually considered in the prior art. Moreover, the overall correlation between the parameter and the natural fracture density is usually not obvious, and it is difficult to obtain a fitting function with high goodness of fit. Therefore, the interval quantization random function proposed in the present application has wide applicability and overcomes the limitation of difficulty in fitting and low reliability of the parameter and the natural fracture density. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 A flow chart of a method for predicting natural fracture line density based on interval quantization random function is provided for an embodiment of the present application.

[0067] Figure 2 A broken line graph of acoustic time difference AC, compressional wave time difference DTC and shear wave time difference DTS of a second type drilling well X2 in a target layer system is provided for an embodiment of the present application.

[0068] Figure 3 A broken line graph of acoustic time difference AC, compressional wave time difference DTC and shear wave time difference DTS of a second type drilling well X2 in a target layer system is provided for an embodiment of the present application.

[0069] Figure 4 A broken line graph of acoustic time difference AC, compressional wave time difference DTC and shear wave time difference DTS of a second type drilling well X3 in a target layer system is provided for an embodiment of the present application.

[0070] Figure 5 A linear conversion mathematical model of AC and DTC obtained from AC and DTC data of a second type drilling well is provided for an embodiment of the present application.

[0071] Figure 6 A linear conversion mathematical model of DTC and DTS obtained from DTC and DTS data of a second type drilling well is provided for an embodiment of the present application.

[0072] Figure 7 AC, DTC and DTS data (leftmost small graph, unit: μs / ft), density logging data (second left small graph, unit: g / cm 3 ), dynamic Young's modulus (second right small graph, unit: GPa) and dynamic Poisson's ratio (rightmost small graph, dimensionless) of a first type drilling well X4 are provided for an embodiment of the present application, and the ordinate of all small graphs is depth (m).

[0073] Figure 8 AC, DTC and DTS data (leftmost small graph, unit: μs / ft), density logging data (second left small graph, unit: g / cm 3 ), dynamic Young's modulus (second right small graph, unit: GPa) and dynamic Poisson's ratio (rightmost small graph, dimensionless) of a first type drilling well X5 are provided for an embodiment of the present application, and the ordinate of all small graphs is depth (m).

[0074] Figure 9 AC, DTC and DTS data (leftmost small graph, unit: μs / ft), density logging data (second left small graph, unit: g / cm 3Dynamic Young's modulus (right two panels, in GPa) and dynamic Poisson's ratio (rightmost panel, dimensionless), all with depth (m) as the ordinate.

[0075] Figure 10 The correlation curve of FD and depth of three types of drilling X7 provided for an embodiment of the present application.

[0076] Figure 11 The correlation curve of FD and depth of three types of drilling X8 provided for an embodiment of the present application.

[0077] Figure 12 The schematic diagram of the interval quantization random function model provided for an embodiment of the present application.

[0078] Figure 13 The FD prediction result (X1 well) based on the interval quantization random function model provided for an embodiment of the present application.

[0079] Figure 14 The FD prediction result (X2 well) based on the interval quantization random function model provided for an embodiment of the present application.

[0080] Figure 15 The FD prediction result (X3 well) based on the interval quantization random function model provided for an embodiment of the present application.

[0081] Figure 16 The FD prediction result (X4 well) based on the interval quantization random function model provided for an embodiment of the present application.

[0082] Figure 17 The FD prediction result (X5 well) based on the interval quantization random function model provided for an embodiment of the present application.

[0083] Figure 18 The FD prediction result (X6 well) based on the interval quantization random function model provided for an embodiment of the present application. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0085] In the description of this application: unless otherwise stated, "a plurality of" means two or more. The terms "first," "second," "third," etc., in this application are intended to distinguish the objects referred to and do not have any special meaning in terms of technical connotation (e.g., they should not be construed as an emphasis on importance or order). Expressions such as "comprising," "including," and "having" also mean "not limited to" (certain units, components, materials, steps, etc.).

[0086] The purpose of this application is to provide a method for predicting the linear density of natural fractures based on interval quantized random functions, in order to solve the problem in the existing technology that it is difficult to effectively predict the linear density of natural fractures based on conventional logging and array sonic logging data when limited and costly imaging logging and core data are available. This method will promote the development of oil and gas fields and the study of reservoir geomechanics.

[0087] Therefore, in one embodiment of this application, a method for predicting the line density of natural cracks based on an interval quantized random function is provided, the method comprising steps S1 to S5.

[0088] Step S1: Determine the study area and target strata, and clarify the core, conventional logging, array sonic logging, and imaging logging data of each well that penetrates the target strata within the study area.

[0089] Step S11: Determine the study area and target stratigraphic sequence based on the actual research needs of oil and gas exploration and development.

[0090] Based on the actual research needs of oil and gas exploration and development, the target stratigraphic sequence is selected, and the depth distribution characteristics of the top and bottom interfaces of the target stratigraphic sequence within the study area are clarified. This is mainly achieved by obtaining the top and bottom interface depths of the target stratigraphic sequence from drilling data within the study area. This is because the foundational data for the method proposed in this application are conventional logging, array sonic logging, and imaging logging data of the target stratigraphic sequence, all of which are correlated with the depth of the target stratigraphic sequence in a single well.

[0091] Step S12: Clarify the core, conventional logging, array sonic logging, and imaging logging data of each well that has penetrated the target layer in the study area, and classify the wells that have penetrated the target layer in the study area accordingly.

[0092] A detailed statistical analysis was conducted on the core, conventional logging, array sonic logging, and imaging logging data of each well that drilled through the target formation within the study area. The wells within the study area were then classified according to the following principles: if a well only has conventional logging data in the target formation, it is classified as a Class I well; if a well has both conventional and array sonic logging data in the target formation, it is classified as a Class II well; if a well has both conventional logging data (array sonic logging data is not required) and core or imaging logging data in the target formation, it is classified as a Class III well.

[0093] Step S2: Calculate the dynamic rock mechanics parameters of the target layer from the array acoustic logging data and conventional logging data.

[0094] Step S21: Construct a conversion model of "acoustic transit time (AC) - longitudinal wave transit time (DTC)" and a conversion model of "longitudinal wave transit time (AC) - transverse wave transit time (DTC)" based on array acoustic logging data and conventional logging data.

[0095] Dynamic rock mechanics parameters reflect the brittleness and deformation characteristics of rocks and can be highly indicative of the development of natural fractures. Therefore, in addition to the parameters from conventional logging data, dynamic rock mechanics parameters should also be incorporated into the prediction of natural fracture linear density. The two most important dynamic rock mechanics parameters are dynamic Young's modulus and dynamic Poisson's ratio. The calculation of these parameters requires density logging data (from conventional logging data), P-wave transit time (DTC), and D-wave transit time (DTS) logging data (from array acoustic logging data). Due to the high cost of array acoustic logging, it is typically only available in a subset of wells in the study, namely the Class II wells mentioned in step S12 (and Class III wells with array acoustic logging data). Therefore, a conversion model between conventional logging data and DTC and DTS needs to be constructed to enable the calculation of DTC and DTS based on conventional logging data. In conventional well logging data, acoustic transit time (AC) data, DTC and DTS are both time-difference data and are considered to have good correlation. Therefore, we first construct a conversion model between AC and DTC based on the second type of well, and then construct a conversion model between DTC and DTS based on array acoustic logging data.

[0096] In one embodiment of this application, AC, DTC, and DTS data from Class II drilling wells X1, X2, and X3 located within the study area are used for illustration, as shown in the attached figures. Figure 2 , 3 As shown in Figure 4. Based on the AC and DTC data of all Class II wells in the study area, a conversion model for AC and DTC can be constructed, as shown in the attached figure. Figure 5 As shown, using linear fitting, the goodness of fit R0 is... 2is 0.66. According to the DTC and DTS data of all the second type of wells in the study area, the conversion models of DTC and DTS can be constructed, as shown in Figs. 2 and 3, and the goodness of fit R Figure 6 is 0.86. 2

[0097] Step S22, the single-well dynamic rock mechanics parameters of the target layer system in the study area are calculated according to the acoustic travel time (AC) logging data and the two conversion models constructed in step S21.

[0098] Based on the conventional logging data and the two conversion models mentioned in step S21, the calculation of DTC and DTS can be realized, and according to the following formulas (1) and (2), the dynamic Young's modulus and dynamic Poisson's ratio of the first type and third type of wells (if there is no array acoustic logging data in the wells) in step S12 can be calculated:

[0099]

[0100] where E d is the dynamic Young's modulus, GPa; μ d is the dynamic Poisson's ratio; Δt p is the compressional wave travel time DTC, μs / ft; Δt s is the shear wave travel time DTS, μs / ft; and ρ is the density, g / cm 3 .

[0101] In an embodiment of the present application, the AC, DTC (calculated according to the AC data and the conversion model in Fig. 2) and DTS data (calculated according to the AC data and the conversion model in Fig. 3) of the first type of well X4 located in the study area are shown in Fig. 4, the leftmost small graph, and the density logging of X4 is shown in the second small graph from the left. The dynamic Young's modulus and dynamic Poisson's ratio of X4 calculated from the DTC, DTS and density logging data of X4 and formulas (1) and (2) are shown in the two small graphs on the right and the rightmost small graph, respectively. Fig. 4 shows the AC, DTC and DTS data (the leftmost small graph), the density logging data (the second small graph from the left), the dynamic Young's modulus (the two small graphs on the right) and the dynamic Poisson's ratio (the rightmost small graph) of X5, which is also a first type of well. Fig. 5 shows the AC, DTC and DTS data (the leftmost small graph), the density logging data (the second small graph from the left), the dynamic Young's modulus (the two small graphs on the right) and the dynamic Poisson's ratio (the rightmost small graph) of X6, which is also a first type of well. In Fig. 5, the AC, DTC and DTS data of X6 are calculated according to the AC data of X6 and the conversion models in Figs. 2 and 3. Figure 5 Figure 6 Figure 7 Figure 7 Figure 7 Figure 8 Figure 9 Figures 7 to 9 ​​​​​​​​In the figures, the vertical axis of all the small figures is the depth of the target formation (m), the unit of the leftmost small figure is μs / ft, the unit of density is g / cm 3 , the unit of dynamic Young's modulus is GPa, and the dynamic Poisson's ratio is dimensionless.

[0102] Step S3, calculating the natural fracture line density according to the core or imaging logging data.

[0103] Step S31, carrying out natural fracture identification and characterization on the drilling wells in the study area that have core or imaging logging data in the target formation and counting the number of natural fractures.

[0104] For the three types of drilling wells described in step S12, if the drilling well has imaging logging data, the natural fracture identification and characterization and counting are carried out based on the imaging logging data first, and if the drilling well does not have imaging logging, the natural fracture identification and characterization and counting are carried out based on the core data. The single-well natural fracture description in the target formation of the study area is carried out based on the imaging logging (core data) and the number of natural fractures is counted to obtain the relationship between the number of natural fractures and the actual depth.

[0105] Step S32, calculating the single-well natural fracture line density of the target formation in the study area.

[0106] According to the relationship between the number of single-well natural fractures and the depth obtained in step S31, the natural fracture line density is calculated according to the following formula (3):

[0107]

[0108] Wherein, MD represents the depth to be calculated for the natural fracture line density, m; FD represents the relationship curve between the number of single-well natural fractures and the depth; FD(MD) represents the measured value of the natural fracture line density, pieces / m; CL represents the cumulative number curve of natural fractures, that is, the cumulative number curve made according to the relationship between the number of single-well natural fractures and the depth obtained in step S31; W is the length of the measurement window, usually a constant greater than 1, m.

[0109] In an embodiment of the present application, the relationship between FD and depth of X7 and X8 wells, which belong to the same type of drilling wells, is shown in FIGS. 1 and 2, respectively. Figure 10 and 11 .

[0110] Step S4, selecting the conventional logging or dynamic rock mechanics parameter A with the highest correlation with the natural fracture line density FD and quantitatively studying the segmented correlation between parameter A and FD.

[0111] Step S41, calculating the correlation coefficient between the conventional logging or dynamic rock mechanics parameter and the natural fracture line density FD, and selecting the parameter A with the highest correlation with FD according to the correlation coefficient.

[0112] For the three types of drilling wells in step S12, the natural fracture linear density curve FD has been calculated according to step S32, and the dynamic rock mechanics logging data is calculated according to the array acoustic logging (if there is no array acoustic logging, it is calculated according to step S2) possessed by itself. Since these drilling wells possess FD, conventional logging and dynamic rock mechanics parameters, the sensitivity analysis of conventional logging and dynamic rock mechanics parameters to FD can be carried out. At present, the linear fitting goodness analysis, Pearson correlation analysis and Spearman rank correlation analysis are more commonly used. The three methods can be used to study the correlation between conventional logging and dynamic rock mechanics parameters and FD, and the parameters with high correlation to FD are the more sensitive parameters to the development of natural fractures.

[0113] Taking the Spearman rank correlation coefficient as an example, its formula is:

[0114]

[0115] Where R s (m) is the Spearman rank correlation coefficient; m is the number of data sets for quantitative relationship analysis of two variables; d i is the ranking difference of the i-th variable set (X, Y). Each variable set (X, Y) is changed to a variable set (X', Y') by the following formulas (7) and (8) so that there is no same rank variable in X (or Y):

[0116] X' = X + Rand() / 10 8 (5)

[0117] Y' = Y + Rand() / 10 8 (6)

[0118] Where Rand() is a random number between 0 and 1.

[0119] The Spearman rank correlation coefficient R sThe negative and positive values of (m) represent negative and positive correlations of the studied variable groups, respectively. The closer the absolute value is to 1, the stronger the negative or positive correlation between the variables (PEARSON ES, SNOW BA. Tests for rank correlation coefficients [J]. Biometrika, 1962, (1-2): 1-2; BOLAND J, HOWLETT P, PIANTADOSI J. Matching the grade correlation coefficient using a copula with maximum disorder [J]. Journal of Industrial & Management Optimization, 2017, 3(2): 305-312). Therefore, after calculating the Spearman rank correlation coefficients of the conventional logging data and dynamic rock mechanics logging data and FD, the conventional logging or dynamic rock mechanics logging parameter corresponding to the highest absolute value of the Spearman rank correlation coefficient can be selected as the optimal parameter A reflecting the development degree of natural fractures in the target layer.

[0120] In an embodiment of the present application, since the three types of drilling wells X7 and X8 do not have array acoustic logging data, DTC and DTS data are not selected for parameter optimization in this step, because DTC and DTS data are obtained through the linear fitting function conversion model in Figure 5 and 6 , which are strictly positively correlated with AC data, and the correlation of the two parameters with FD is consistent with the correlation of AC with FD. Since AC, density, dynamic Young's modulus and dynamic Poisson's ratio are data that X7 and X8 wells have, these four parameters are selected for parameter optimization. The Spearman rank correlation analysis is used for parameter optimization. The Spearman rank correlation coefficients of the four data AC, density, dynamic Young's modulus and dynamic Poisson's ratio obtained from X7 and X8 wells and FD are 0.35613, 0.05947, 0.09497 and 0.082003, respectively. The absolute value of the correlation coefficient is the largest, which is 0.35613, that is, the correlation of AC with FD is the highest, and AC is selected as the optimal parameter A in an embodiment of the present application.

[0121] Step S42, according to the actual value of parameter A in step S41 and the research precision requirement, the total number of intervals or the interval length is set.

[0122] The optimal parameter A has been determined from step S41, and all parameters A belonging to the three types of drilling wells are arranged in ascending order, and the minimum value of A is A min and the maximum value of A is A maxAccording to the research precision requirement, the parameter A is divided into n intervals, the length of each interval is (A max -A min ) / n, the value range of the i-th interval is [A min +(i-1)*(A max -A min ) / n, A min +i*(A max -A min ) / n], wherein i is a positive integer between 1 and n.

[0123] In an embodiment of the present application, the range of the AC data of the three types of drilling wells X7 and X8 is 43-83 μs / ft, the total number of intervals is set to be 20, the interval length is 2, and the value range of the i-th interval is [41+2*i, 43+2*i], wherein i is a positive integer between 1 and 20.

[0124] Step S43, the minimum value, the average value and the maximum value of the FD data group corresponding to different value intervals of the parameter A are counted.

[0125] For the parameter A and the corresponding FD (calculated from step S32) of the three types of drilling wells, the data group FD(A) is constructed. For the i-th (i is a positive integer between 1 and n) interval [A min +(i-1)*(A max -A min ) / n, A min +i*(A max -A min ) / n] in step S42, all the parameters A and the corresponding FD belonging to this interval are determined, and the minimum value FD min (i), the average value FD ave (i) and the maximum value FD max (i) of all the corresponding FD are calculated.

[0126] In an embodiment of the present application, it is judged in sequence which interval of the 20 intervals in step S42 the parameter A of the three types of drilling wells X7 and X8 belongs to, and the minimum value, the average value and the maximum value of the FD corresponding to the parameter A belonging to the same interval are calculated, and the results are shown in Table 1.

[0127] Table 1

[0128]

[0129]

[0130] Step S5, the interval quantization random function model is established and the FD is predicted.

[0131] Step S51: Construct an interval quantized random function, and calculate the undetermined coefficients in the interval quantized random function based on the minimum, average, and maximum values ​​of the FD data sets corresponding to different numerical intervals of parameter A.

[0132] Constructing an interval-quantized random function:

[0133]

[0134] Where RAND is a random number between 0 and 1, a i and b i and k i These are the coefficients of the undetermined constants in the function. The curve shape of function (7) is shown in the attached figure. Figure 12 As shown in A, the following two equations hold true:

[0135] FD i (0)=FD min (i)=a i *b i (8)

[0136] FD i (1)=FD max (i)=b i +a i *b i (9)

[0137] The minimum value of FD for the i-th interval calculated in step S43 is FD. min (i) Average FD ave (i) and maximum value FD max (i) can determine the undetermined coefficients a in formulas (7) to (9). i and b i ,Right now:

[0138]

[0139] b i =FD max (i)-FD min (i)(11)

[0140] Appendix Figure 12 In B, the red-filled area is a region with a length and width equal to 1 and FD respectively. ave The rectangle (i) has an area of ​​S2, and the green area enclosed by the curve of function (7), the horizontal axis of the coordinate system, and the lines RAND=0 and RAND=1 has an area of ​​S1, as shown in the appendix. Figure 12 As shown in A. To make these two areas equal, we have:

[0141]

[0142] Substitute function (7) and equations (10), (11) into equation (12), the coefficient k can be solved i

[0143]

[0144] Equations (10), (11) and (13) make the undetermined constant coefficients in function (7) be determined completely, and function (7) can be determined as:

[0145]

[0146] In an embodiment of the present application, the calculation results of the minimum value, the average value and the maximum value of FD in each interval in Table 1 are substituted into equations (10), (11) and (13), the constant terms a, b and k in function (7) can be calculated, and the results are shown in Table 2.

[0147] Table 2

[0148]

[0149] In step S52, for the first and second type of drilling wells in step S12, FD prediction based on the interval quantized random function model is carried out.

[0150] For the first and second type of drilling wells in step S12, their conventional logging data or dynamic rock mechanics logging data (from step S2) have been obtained, for the parameter A determined in step S41, first determine which interval the parameter A of each drilling well belongs to in step S42, then generate a random number RAND between 0 and 1, based on RAND and function (14), the FD corresponding to the parameter A can be calculated. Repeat this operation until the FD corresponding to the parameter A of all drilling wells is calculated, in each operation, the random number RAND is regenerated. Thus, the FD prediction based on the interval quantized random function model is realized.

[0151] In an embodiment of the present application, for X1, X2, X3, X4, X5 and X6 wells, the interval to which each AC data of the well belongs is determined respectively (the determination of the interval is shown in detail in step S42, and the AC data of these wells are shown in the attached Figure 2 , 3 , 4, 7, 8 and 9) and the corresponding interval quantized random function (14) (the undetermined coefficients a, b and k in the function are shown in Table 2), generate a random number RAND between 0 and 1, and based on the random number RAND and the interval quantized random function (14), the corresponding FD is calculated. The FD calculation results of the target layer of X1, X2, X3, X4, X5 and X6 wells are shown in the attached Figures 13 to 18 .

[0152] ​Any technical features in the above embodiments can be combined, and for the sake of brevity, not all possible combinations are described, however, any combination of the technical features is considered to be within the scope of the present specification.

Claims

1. A method for predicting natural fracture line density based on interval quantization random function, characterized in that, The method comprises the following steps: Step S1, determining a study area and a target layer system, and obtaining core data, conventional logging data, array acoustic logging data and imaging logging data of each well drilled through the target layer system in the study area; and classifying the wells in the study area, if the well has only conventional logging data in the target layer system, the well is determined as a first type well; if the well has both conventional logging data and array acoustic logging data in the target layer system, the well is determined as a second type well; if the well has conventional logging data and core data or imaging logging data in the target layer system, the well is determined as a third type well; Step S2, calculating dynamic rock mechanics parameters of each well in the target layer system according to the array acoustic logging data and the conventional logging data; Step S3, calculating a natural fracture line density according to the core data or the imaging logging data; Step S4, screening a conventional logging parameter or a dynamic rock mechanics parameter having the highest correlation with the natural fracture line density, and quantitatively studying a segmented correlation between the dynamic rock mechanics parameter and the natural fracture line density; Step S5, establishing an interval quantization random function model and predicting the natural fracture line density; the step S5 comprises the following steps: constructing an interval quantization random function: ； wherein represents a random number within 0-1, , and represents a constant coefficient to be determined in the function; ； ； The minimum value of the interval statistics according to step S4 The average value and the maximum value determine the pending constant coefficients and i.e. ； ； Determination by area equality condition : ； Substitute interval quantized random function, and the pending constant coefficient and into the equation, solve the coefficient is: ； the interval quantization random function is: ； for the first type well and the second type well, carrying out natural fracture line density FD prediction based on the interval quantization random function model; the natural fracture line density FD prediction comprises the following steps: for the first type well and the second type well, the conventional logging data or the dynamic rock mechanics parameter A has been obtained; determining an interval to which each parameter A belongs according to the dynamic rock mechanics parameter A having the highest correlation with the natural fracture line density FD determined in the step S4; generating a random number RAND between 0 and 1 for each interval to which the parameter A belongs; calculating the natural fracture line density FD corresponding to the parameter A based on the random number RAND and the corresponding interval quantization random function; for each well, repeating the determination of the interval to which the parameter A belongs, the generation of the random number and the calculation of the FD, until the FD corresponding to the parameter A of all the wells is calculated; in each operation, the random number RAND is newly generated.

2. The method for predicting natural fracture line density based on interval quantization random function according to claim 1, characterized in that, The step S2 comprises the following steps: constructing a first conversion model and a second conversion model by using the second type well, wherein the first conversion model is a conversion model of acoustic time difference AC and longitudinal wave time difference DTC, and the second conversion model is a conversion model of longitudinal wave time difference DTC and transverse wave time difference DTS; calculating DTC and DTS of the first type well and the third type well based on the conventional logging data, the first conversion model and the second conversion model; calculating dynamic Young's modulus and dynamic Poisson's ratio of the first type well, the second type well and the third type well, and the calculation formula is: ； ； wherein, represents the dynamic Young's modulus in GPa; represents the dynamic Poisson's ratio; represents the longitudinal wave transit time DTC in ; represents the transverse wave transit time DTS in ; represents the density in .

3. The method for predicting natural fracture line density based on interval quantization random function according to claim 1, characterized in that, The step S3 comprises the following steps: carrying out natural fracture identification and characterization on the third type well, and counting the number of natural fractures to obtain a relationship between the number of single-well natural fractures and actual depth; calculating the natural fracture line density according to the relationship between the number of single-well natural fractures and the depth, and the calculation formula is: ； wherein, represents the depth to be calculated for natural fracture line density, with the unit of m; represents the natural fracture line density value to be measured, with the unit of strip / m; represents the natural fracture cumulative quantity curve, that is, the cumulative quantity curve made according to the relationship between the obtained single-well natural fracture quantity and depth; W represents the measurement window length, which is a constant greater than 1, with the unit of m.

4. The method for predicting natural fracture line density based on interval quantization random function according to claim 3, characterized in that, the natural fracture identification and characterization on the third type well comprises the following steps: if the third type well has imaging logging data, first, the imaging logging data is used to carry out natural fracture identification and characterization and counting; otherwise, the core data is used to carry out natural fracture identification and characterization and counting.

5. The method for predicting natural fracture line density based on interval quantization random function according to claim 1, characterized in that, The step S4 comprises: calculating a correlation coefficient of a conventional logging or dynamic rock mechanics parameter and the natural fracture line density FD, and selecting a dynamic rock mechanics parameter A with the highest correlation with the natural fracture line density FD; The dynamic rock mechanics parameter A, which is most correlated with the linear density FD of natural fractures for all Class III drillings, is sorted to obtain the minimum value of parameter A. and maximum value ; According to the research precision requirement, the numerical range of the dynamic rock mechanics parameter A is divided into a plurality of intervals, the length of each interval is , and the numerical range of each interval is , wherein n represents the number of intervals, and i represents the interval number; a data group FD(A) is constructed, wherein each data point contains the dynamic rock mechanics parameter A and the corresponding natural fracture line density FD; for each interval, the minimum value , the average value , and the maximum value of the FD data group corresponding to the parameter A belonging to the interval are counted.

6. The method of predicting natural fracture line density based on interval quantization random function according to claim 5, characterized in that, The selecting the dynamic rock mechanics parameter A with the highest correlation with the natural fracture line density FD comprises: selecting the dynamic rock mechanics parameter with the highest correlation with the natural fracture line density by using a correlation analysis method.

7. The method of predicting natural fracture line density based on interval quantization random function according to claim 6, characterized in that, The correlation analysis method comprises: a linear fitting goodness analysis, a Pearson correlation analysis and a Spearman rank correlation analysis; The formula of the Spearman rank correlation analysis is: ； wherein denotes the Spearman's rank correlation coefficient; denotes the number of data sets for quantitative relationship analysis of two variables; denotes the rank difference of the i-th variable set . Each set of variables are changed to the set of variables by the following equation so that or there is no variable of the same rank in ； ； wherein represents a random number between 0 and 1; According to the calculated Spearman rank correlation coefficient The negative and positive values represent the negative and positive correlation of the variable groups studied, and the closer the absolute value is to 1, the stronger the negative or positive correlation between the variables.

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