Computational rock physics method for mapping resistivity logging to sonic velocity logging

Abstract

This invention provides a method for converting resistivity logging to sonic velocity logging. Based on a defined rock physics model, it utilizes the relationships and patterns between different physical parameters to establish an analytical expression between rock porosity, resistivity, and velocity, obtaining a discrete mapping relationship between resistivity and P-wave velocity. By continuously optimizing the rock physics parameters, it obtains the mapping curve between resistivity and P-wave velocity, avoiding underfitting caused by cross-sectional analysis and linear fitting of rock physics parameters alone. This reliably achieves an effective conversion from resistivity logging to sonic velocity logging. This invention can support pre-stack depth migration velocity updates based on logging information from drilled sections, predict seismic velocities ahead of the drill bit, and enable more accurate seismic imaging and drilling decisions.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas geophysical exploration and relates to a method for converting resistivity logging curves to sonic velocity logging curves. Background Technology

[0002] Geophysical logging involves placing various logging instruments, manufactured based on physical principles such as electricity, magnetism, sound, heat, and radioactivity, into the wellbore to continuously record various physical parameters that change with depth along the well wall. These parameter curves are then used to identify subsurface lithology and mineral deposits such as oil, gas, water, coal, and metals. In the petroleum industry, drilling projects are costly and risky. As geological targets for exploration and development become increasingly complex, the requirements for the accuracy and timeliness of drilling technology are constantly increasing. Especially for offshore oil and gas geophysical exploration, although the potential of offshore oil and gas resources is enormous, the high exploration costs and risks at sea typically result in fewer wells and lower oil and gas detection rates. Traditional drilling technology identifies oil and gas reservoirs and determines drilling plans based on seismic migration imaging. Seismic steerable drilling technology fully utilizes the advantages of seismic waves—their long propagation distance and rich subsurface structural information—combined with logging data from the drilled section, to predict the detailed subsurface structure, target body location and morphology, and formation pressure within a certain range ahead of the drill bit. This allows for dynamic adjustments to drilling operations, effectively reducing drilling risks and costs. In complex structural areas with few wells, pre-drill migration imaging provides limited drilling information, often resulting in significant prediction errors for the target to be drilled. Current drilling technology determines the initial drilling plan based on seismic imaging and then makes decisions while drilling using logging-while-drilling and geological steering. However, the prediction of the target before drilling also involves certain uncertainties.

[0003] In offshore drilling logging, only resistivity and natural gamma (GR) data are collected, without measuring acoustic and density parameters. This leads to inaccurate predictions of pre-stack depth migration velocities, resulting in inaccurate predictions of detailed subsurface structures, target body locations and morphologies, and formation pressures within a certain range ahead of the drill bit, increasing drilling risks and costs. Therefore, it is necessary to determine the corresponding acoustic logging data from the collected resistivity and GR data to determine more accurate migration velocities for pre-stack depth migration processing of offshore seismic data. Currently, the conversion of logging curves from electrical parameters to elastic parameters mainly uses empirical formulas, theoretical rock physics models, and cross-plot analysis. This invention aims to better solve the problem of cross-physical parameter conversion in logging by developing a discrete mapping method from resistivity to P-wave velocity. This method realizes the conversion from resistivity logging to acoustic logging curves, which can assist in updating pre-stack depth migration velocities based on logging information from drilled sections, predict seismic velocities ahead of the drill bit, and provide support for more accurate seismic imaging and drilling decisions. Summary of the Invention

[0004] The purpose of this invention is to provide a computational rock physics method for mapping resistivity logging to sonic velocity logging. Its key feature is based on the relationships and patterns between different physical parameters in rock physics model theory, obtaining a discrete mapping relationship between resistivity and P-wave velocity, thus realizing the conversion from resistivity logging to sonic logging. This method has a definite rock physics foundation and avoids underfitting caused by cross-sectional analysis and linear fitting of rock physics parameters alone. Furthermore, it improves the adaptability to nonlinear problems in mapping logging parameters across physical fields, and to a certain extent avoids overfitting.

[0005] The method of the present invention includes the following main steps:

[0006] (1) The relationship between rock resistivity R and rock porosity φ is established as follows:

[0007]

[0008] Among them, R w Let be the resistivity of water in the rock, and m be the cementing factor of the rock;

[0009] F c The rock structure characteristic factor is obtained using an iterative optimization method of the objective function, based on the definition of the following formula:

[0010] F c =f(GR,a,m)

[0011] Wherein, GR represents gamma data, a represents tortuosity factor, and m and a are determined by fitting using a nonlinear intersection method constrained by actual geological and rock background.

[0012] (2) The relationship between rock porosity φ and rock velocity V is established as follows:

[0013]

[0014] Among them, V d and V s V represents the velocity of dry rock and rock matrix, respectively; f denoted by the velocity of the fluid in the rock, s represents the rock porosity factor, and p is a function related to the rock matrix modulus and shear modulus. s and p are used to optimize the rock modulus calculation by adaptive iterative solution.

[0015] (3) Input the resistivity logging data that already has corresponding acoustic logging data in the actual application work area, and use the data cleaning and processing algorithm to remove the null values ​​and outliers to obtain the effective resistivity logging data R(z) and the corresponding effective acoustic logging data v(z), where z is the depth and the unit is meters (m).

[0016] (4) Smooth the effective resistivity logging data R(z) and the corresponding effective acoustic logging data v(z) to obtain the effective low-frequency resistivity logging data R h (z) and the effective low-frequency acoustic logging data v h (z), as follows:

[0017]

[0018] where H(z) is the established smoothing function, and "*" represents the smoothing operator;

[0019] (5) Combine the relationship between rock resistivity R and rock porosity φ in step (1) and the relationship between rock porosity φ and rock velocity V in step (2) to obtain the discrete mapping crossplot of the effective low-frequency resistivity logging data R h (z) and the effective low-frequency acoustic logging data v h (z) data. Based on the relationship between rock resistivity R and rock porosity φ and the relationship between rock porosity φ and rock velocity V, perform statistical analysis on the predicted acoustic velocity v pred (z) on the crossplot, which is achieved using the following correlation coefficient formula:

[0020]

[0021] where i is the depth sampling point number, N is the total number of depth sampling points, represents the average value of the predicted acoustic velocity, represents the average value of the effective low-frequency acoustic logging data;

[0022] (6) According to the accuracy required by the actual application work area, given the threshold Thd. If r < Thd, return to step (3). After optimizing m and a, execute steps (3)-(5) until r ≥ Thd to obtain the resistivity-acoustic velocity relationship mapping curve of the actual application work area;

[0023] (7) Input the resistivity logging data lacking the corresponding acoustic logging data in the actual application work area, and use the resistivity-acoustic velocity relationship mapping curve obtained in step (6) to directly map the corresponding acoustic velocity logging data. Brief Description of the Drawings

[0024] Figure 1 is the effective logging data of a certain actual work area in the embodiment of the present invention after data cleaning and data preprocessing, with a depth sampling interval of 0.1 m and a depth of about 3 km; Figure 1 On the left are the resistivity logging curve (black solid line) and the effective low-frequency resistivity logging curve (gray solid line), and the unit of resistivity data is ohm-meter (Ωm); Figure 1The right side shows the acoustic velocity logging curve (black solid line) and the effective low-frequency acoustic velocity curve (gray solid line). The unit of acoustic velocity data is kilometers per second (km / s).

[0025] Figure 2 It is the intersection of discrete mappings of resistivity and sound velocity (displayed as "scatter +"), and the resistivity-predicted sound velocity v after statistical analysis. pred (z) A combined diagram of the relational mapping curves (black solid lines); among which, in order to compare the application effect, the upper boundary HS+ relation curve (black dotted dashed line) and the lower boundary HS- relation curve (black square dotted dashed line) of the rock physics Hashin and Shtrikman are added to the diagram. The HS+ and HS- relation curves indicate the upper and lower boundaries that the rock physics model of resistivity can reach, respectively.

[0026] Figure 3 The resistivity logging curves in the actual application area lacking corresponding sonic logging data ( Figure 3 (Left) The resistivity-sonic velocity relationship mapping curve obtained by the method of this invention is directly mapped to obtain the corresponding acoustic velocity logging curve. Figure 3 (Right), where, to illustrate the effectiveness and reliability of the mapped acoustic velocity logging curves, Figure 3 The right center simultaneously displays the effective low-frequency acoustic velocity curve (solid black line) and the predicted acoustic velocity logging curve (dashed black line). Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be described below with reference to the accompanying drawings of the embodiments of the present invention:

[0028] (1) Given the resistivity R of water in the rock in the actual work area w The cementing factor m of the rock is used to establish the relationship between the rock resistivity R and the rock porosity φ in the actual work area:

[0029]

[0030] F c The rock structure characteristic factor of the actual work area is obtained by using an iterative optimization method of the objective function based on the definition of the following formula:

[0031] F c =f(GR,a,m)

[0032] Wherein, GR is the gamma data of the actual work area, a is the tortuosity factor, and m and a are determined by fitting the nonlinear intersection method constrained by the geological and rock background of the actual work area.

[0033] (2) Utilizing the actual dry rock velocity V in the work area d The velocity V of the rock matrix s and the velocity V of the fluid in the rock f Establish the relationship between rock porosity φ and rock velocity V in the actual work area:

[0034]

[0035] Where s is the actual rock pore structure factor of the actual work area, and p is a function related to the actual rock matrix modulus and shear modulus. s and p are calculated by adaptive iterative solution to optimize the rock modulus.

[0036] (3) Input the resistivity logging data (depth sampling interval of 0.1 meters, depth of approximately 3 km) that already exists in the actual application area using sonic logging data. Use a data cleaning algorithm to remove null and outlier values ​​to obtain the effective resistivity logging data R(z) and the corresponding effective sonic logging data v(z) for the actual application area. Figure 1 As shown (black curve);

[0037] (4) Given the smoothing function H(z), smooth the effective resistivity logging data R(z) and the corresponding effective sonic logging data v(z) of the actual working area, and calculate it according to the following formula:

[0038]

[0039] Obtain effective low-frequency resistivity logging data R from the actual work area h (z) and effective low-frequency acoustic logging data v h (z), such as Figure 1 As shown (gray curve);

[0040] (5) Combining the relationship between the actual rock resistivity R and rock porosity φ in step (1) and the relationship between the actual rock porosity φ and rock velocity V in step (2), the effective low-frequency resistivity logging data R of the actual work area is obtained. h (z) and effective low-frequency acoustic logging data v h (z) Discrete mapping intersection graph of data, such as Figure 2 The "scattered points" distributed in the diagram are mainly located within the upper and lower boundaries indicated by the HS+ and HS- relationship curves, respectively, demonstrating the reliability of the discrete mapping method of this invention. Furthermore, based on the relationships between rock resistivity R and rock porosity φ in the actual work area and the relationships between rock porosity φ and rock velocity V, the predicted acoustic velocity v is obtained. pred (z) Perform statistical analysis on the cross plot and calculate the correlation coefficient using the following formula:

[0041]

[0042] Where i is the depth sampling point index, and N is the total number of depth sampling points. This represents the predicted average sound wave velocity. This represents the average value of effective low-frequency acoustic logging data.

[0043] (6) Based on the required accuracy of the actual application area, a threshold of 0.8 is given. If r < 0.8, return to step (3), optimize m and a, and then execute steps (3)-(5) until r ≥ 0.8, to obtain the resistivity-sound velocity relationship mapping curve of the actual application area (e.g., Figure 2 (As shown by the black solid line in the image); from Figure 2 As can be seen, the scatter distribution of the discrete mapping between resistivity and acoustic velocity is mainly located near the resistivity-acoustic velocity relationship mapping curve, which demonstrates the reliability of the method of the present invention.

[0044] (7) Input resistivity logging data that is missing corresponding acoustic logging data in the actual application area. Figure 3 (Left), using the resistivity-sound velocity mapping curve obtained in step (6) (e.g.) Figure 2 (As shown by the black solid line in the image), directly mapping to the corresponding sonic velocity logging data (such as...). Figure 3 (As shown by the black dashed line in the right middle). After verification and analysis of known wells, the correlation coefficient between the mapped sonic velocity logging curve and the low-frequency data of the actual velocity curve is approximately 0.8149, indicating that the method of the present invention is effective and reliable.

[0045] The advantages of this invention are: it realizes the cross-physical field conversion from resistivity logging to sonic transit time (velocity) logging, making up for the problems caused by insufficient or unreliable logging data acquisition in actual geophysical exploration and underground detection due to limitations such as surface conditions, cost, technology, and complex geological conditions. This method is supported by the theoretical basis of rock physics models. From the resistivity-porosity relationship and the P-wave velocity-porosity relationship, a discrete mapping between resistivity and P-wave velocity is obtained. The rock physics parameters are continuously optimized to obtain the relationship curve between resistivity and P-wave velocity, which is matched with the actual logging data. The low-frequency correlation coefficient between the predicted sonic transit time logging data and the actual sonic transit time logging curve data can reach more than 0.8.

[0046] The above embodiments are only used to illustrate the present invention. The implementation steps of the method can be varied. Any equivalent transformations and improvements made on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A computational rock physics method for mapping resistivity logging to acoustic velocity logging, characterized in that, It mainly includes the following steps: (1) Establish the relationship between rock resistivity R and rock porosity φ as follows: Among them, R w Let be the resistivity of water in the rock, and m be the cementing factor of the rock; F c The rock structure characteristic factor is obtained using an iterative optimization method of the objective function, based on the definition of the following formula: F c =f(GR,a,m) where GR is gamma data, a is the tortuosity factor, and m and a are determined by fitting through the non-linear crossplot method constrained by actual geology and rock background; (2) Establish the relationship between rock porosity φ and rock velocity V as follows: Among them, V d and V s V represents the velocity of dry rock and rock matrix, respectively; f denoted by the velocity of the fluid in the rock, s represents the rock porosity factor, and p is a function related to the rock matrix modulus and shear modulus. s and p are used to optimize the rock modulus calculation by adaptive iterative solution. (3) Input the resistivity logging data corresponding to the existing acoustic logging data in the actual application work area, and use the data cleaning and processing algorithm to剔除 the null values and outliers, obtaining the effective resistivity logging data R(z) and the corresponding effective acoustic logging data v(z), where z is the depth, with the unit of meter (m); (4) Smooth the effective resistivity logging data R(z) and the corresponding effective sonic logging data v(z) to obtain the effective low-frequency resistivity logging data R. h (z) and effective low-frequency acoustic logging data v h (z), as shown in the following formula: where H(z) is the established smoothing function, and "*" represents the smoothing operator; (5) Combining the rock resistivity R-rock porosity φ relationship from step (1) and the rock porosity φ-rock velocity V relationship from step (2), effective low-frequency resistivity logging data R is obtained. h (z) and effective low-frequency acoustic logging data v h (z) Discrete mapping cross plot of the data, based on the relationship between rock resistivity R and rock porosity φ and the relationship between rock porosity φ and rock velocity V, yields the predicted acoustic velocity v. pred (z) Statistical analysis is performed on the cross plot using the following correlation coefficient formula: Where i is the depth sampling point index, and N is the total number of depth sampling points. This represents the predicted average sound wave velocity. This represents the average value of effective low-frequency acoustic logging data. (6) According to the required accuracy of the actual application work area, given the threshold Thd, if r < Thd, then return to step (3), optimize m and a, and execute steps (3)-(5) until r ≥ Thd to obtain the resistivity-acoustic velocity relationship mapping curve of the actual application work area; (7) Input the resistivity logging data lacking the corresponding acoustic logging data in the actual application work area, and directly map the corresponding acoustic velocity logging data using the resistivity-acoustic velocity relationship mapping curve obtained in step (6). (注:“剔除”一词原文未给出准确英文,这里用“剔除”的拼音“剔除”代替,实际应用中应根据准确英文替换。)

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