Method for determining a static effective stress coefficient of a layered formation
By measuring the density and acoustic velocity of layered formations, combined with VRH model and uniaxial compression test, the problem of low efficiency in existing technologies has been solved, enabling rapid and accurate determination of the static effective stress coefficient of layered formations, which is suitable for downhole applications.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA NAT PETROLEUM CORP
- Filing Date
- 2022-12-16
- Publication Date
- 2026-07-24
AI Technical Summary
Existing technologies are insufficient for quickly and accurately determining the static effective stress coefficient of layered formations. Furthermore, existing methods are inefficient, produce discrete data, and are not applicable to layered formations, thus failing to meet the needs of downhole applications.
By measuring the density and acoustic velocity of vertical and parallel bedding in layered strata, and combining the VRH model and uniaxial compression tests, the static bulk modulus and Young's modulus of the rock are calculated, and the static effective stress coefficient is determined.
It enables rapid and accurate acquisition of the static effective stress coefficient of layered formations, improves acquisition efficiency, is applicable to any lithological formation, and simplifies downhole applications.
Smart Images
Figure CN116106118B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of oil and gas field development technology, and in particular to a method for determining rock mechanical coefficients, and more specifically, to a method for determining the static effective stress coefficient of layered strata. Background Technology
[0002] The effective stress coefficient of rock, also known as the Biot coefficient, can be obtained from the rock bulk modulus and the bulk modulus of the matrix mineral particles. This coefficient is a fundamental parameter describing porous elastic rock media and plays an important role in oil reservoir geomechanical formation pressure prediction, horizontal stress calculation, wellbore stability analysis after drilling and completion, sand production prediction, hydraulic fracturing design, reservoir permeability analysis and stress sensitivity research in oil and gas reservoir engineering, and reservoir depletion. According to the effective stress principle, an accurate and reliable effective stress coefficient of rock determines the reliability of formation effective stress and plays a key role in the above-mentioned studies. For layered strata, due to layer-by-layer deposition and directional arrangement of mineral particles, layered strata exhibit obvious bedding characteristics, resulting in significant differences in rock physical and mechanical properties in the direction perpendicular to and parallel to bedding. The effective stress coefficient of rock also shows differences, requiring separate acquisition of the effective stress coefficient perpendicular to and parallel to bedding to improve the reliability of layered strata mechanical property analysis.
[0003] Currently, the effective stress coefficient of rocks is mainly obtained through direct or indirect laboratory testing methods and rock physics modeling methods. For the first category of methods, there are mainly drainage tests, cross-plotting, and acoustic parameter methods. Drainage tests and cross-plotting primarily use plunger rock samples with different combinations of pore pressure and confining pressure. While these two methods can obtain accurate and reliable effective stress coefficients, they suffer from drawbacks such as difficulty in obtaining downhole cores, long testing times, and low efficiency. Furthermore, the obtained test data is discrete and cannot provide a continuous effective stress coefficient profile of the formation, limiting their application. Acoustic parameter methods indirectly calculate the effective stress coefficient of the formation by obtaining the acoustic wave velocity of the formation rock. Continuous effective stress coefficients of the formation can be obtained using well logging data or seismic velocity. However, this method obtains a dynamic effective stress coefficient, which needs to be corrected and converted to a static effective stress coefficient before it can be used for calculation. The second type of rock physics modeling method mainly involves using a suitable rock physics model for the target formation to obtain the corresponding rock bulk modulus and matrix particle modulus, and then calculating the effective stress coefficient. This type of method considers many factors, has complex models, and is difficult to solve, limiting its practical application. Furthermore, some rock physics parameters must be obtained through laboratory testing, which is not only inefficient but also introduces uncertain errors. This is especially true for layered formations, which require more complex rock physics models and numerous laboratory tests to obtain the required effective stress coefficient. Therefore, there is an urgent need for a method that can quickly and accurately determine the static effective stress coefficient of layered formations, fully utilize existing well logging data, facilitate widespread application, and is applicable to layered formations with any lithology. Summary of the Invention
[0004] To address the problems and shortcomings of the existing technology, this application proposes a method for determining the static effective stress coefficient of layered strata. This method only requires density measurement and acoustic wave velocity testing of rocks perpendicular to and parallel to bedding in layered strata to conveniently obtain the static effective stress coefficient of rocks perpendicular to and parallel to bedding, thus improving the efficiency of acquisition.
[0005] To achieve the above-mentioned objectives, the technical solution of this application is as follows:
[0006] A method for determining the static effective stress coefficient of layered strata includes the following steps:
[0007] Obtain the dynamic bulk modulus and dynamic Young's modulus of vertical and parallel bedding of the target layered strata;
[0008] Based on the conversion relationship between the dynamic and static Young's moduli of rocks with vertical and parallel bedding in layered strata, the static bulk modulus of rocks with vertical and parallel bedding in the target layered strata is calculated.
[0009] The VRH model was used to calculate the bulk modulus of the target layered strata rock matrix.
[0010] Calculate the static effective stress coefficient of the rock with vertical and parallel bedding in the target layered strata.
[0011] Preferably, obtaining the dynamic bulk modulus and dynamic Young's modulus of the target layered strata perpendicular and parallel bedding includes:
[0012] Standard plunger rock samples were drilled from the target layered strata, both perpendicular and parallel to bedding. Density measurements and acoustic wave velocity tests were performed on both samples to obtain their bulk density, P-wave velocity, and S-wave velocity. The dynamic bulk modulus and dynamic Young's modulus of the perpendicular and parallel bedding standard plunger rock samples were calculated using the following formulas.
[0013]
[0014]
[0015]
[0016]
[0017]
[0018] in, and The dynamic bulk modulus of rocks are those of standard plunger rock samples with vertical bedding and those with parallel bedding, respectively. and The dynamic Young's modulus of rocks, V, is measured for standard plunger samples with vertical bedding and those with parallel bedding, respectively. p,v and V p,h The P-wave velocities of the rocks are those of standard plunger samples with vertical bedding and those with parallel bedding, respectively; V s,v and V s,h The rock shear wave velocities are ρ for standard plunger samples with vertical bedding and standard plunger samples with parallel bedding, respectively. b ρ represents the average volume density of the target layered strata. b,v and ρ b,h The volumetric densities are those of vertically bedding standard plunger samples and parallel-bedding standard plunger samples, respectively.
[0019] Preferably, the calculation expression for the static bulk modulus of rocks perpendicular to and parallel to bedding, based on the conversion relationship between the dynamic and static Young's moduli of the target layered strata, is as follows:
[0020]
[0021]
[0022]
[0023]
[0024] in, and These are the static bulk moduli of rocks with perpendicular bedding and parallel bedding, respectively. and , respectively, are the static Young's modulus of rocks with vertical bedding and parallel bedding; m, n, m′, and n′ are all undetermined coefficients.
[0025] Preferably, the dynamic and static Young's modulus conversion relationship of the target layered strata with vertical and parallel bedding is an empirical relationship applicable to the target strata rocks.
[0026] Preferably, the dynamic and static Young's modulus conversion relationship of the target layered strata perpendicular to and parallel to bedding is obtained through the following method:
[0027] Uniaxial compression tests were conducted on standard plunger rock samples with perpendicular and parallel bedding. The dynamic Young's modulus of the standard plunger rock samples with perpendicular and parallel bedding, calculated from acoustic wave velocity measurements, was cross-fitted with the static Young's modulus of the same samples obtained from the uniaxial compression tests. The final result was the conversion relationship between the dynamic and static Young's moduli of perpendicular and parallel bedding. The fitting method can be linear, exponential, or polynomial fitting, or other conventional fitting methods.
[0028] Preferably, the calculation of the rock matrix bulk modulus using the VRH model includes:
[0029] XRD analysis was performed on rock samples with vertical and parallel bedding of the target layered strata to obtain the mineral composition and percentage content of the rock with vertical and parallel bedding. For the same mineral composition, its average percentage content was calculated. Then, based on the bulk modulus of each matrix mineral, the VRH model was used to calculate the bulk modulus of the target layered strata rock matrix.
[0030] Preferably, the calculation expression for the bulk modulus of the rock matrix using the VRH model is as follows:
[0031]
[0032]
[0033]
[0034] Where K0 is the bulk modulus of the rock matrix; K V K is the average modulus of Voigt; R f is the Reussian mean modulus; i K represents the volume percentage of the i-th mineral component in the rock; i Let be the bulk modulus of the i-th mineral component in the rock.
[0035] Preferably, the calculation expression for the static effective stress coefficient of the rock perpendicular to and parallel to the bedding of the target layered strata is as follows:
[0036]
[0037]
[0038] in, and The static effective stress coefficients of rocks with vertical and parallel bedding are given.
[0039] Preferably, the dynamic bulk modulus and dynamic Young's modulus of the target layered strata rock can also be calculated using P-wave transit time and S-wave transit time, as shown in the following expressions.
[0040]
[0041]
[0042]
[0043]
[0044]
[0045]
[0046]
[0047]
[0048] Where, Δt p,v Δt represents the P-wave transit time of rocks perpendicular to bedding. s,v Δt represents the transverse wave transit time of rocks perpendicular to bedding. p,h Δt represents the P-wave transit time of rocks with parallel bedding; s,h This represents the transverse wave time of rocks perpendicular to bedding.
[0049] The beneficial effects of this application are:
[0050] This application only requires density measurement and acoustic wave velocity testing of vertically and parallelly bedding rocks to conveniently obtain the static effective stress coefficient of rock in layered strata with vertical and parallel bedding, which improves the efficiency of obtaining the static effective stress coefficient of rock compared with existing technologies. Attached Figure Description
[0051] The foregoing and hereinafter detailed description of this application becomes clearer when read in conjunction with the following figures, in which:
[0052] Figure 1 This is a flowchart of the method in this application;
[0053] Figure 2 This is a schematic diagram of standard plunger rock samples with vertical and parallel bedding in this application;
[0054] Figure 3 This is a cross-fit diagram of the dynamic and static Young's modulus of the rock perpendicular to the bedding direction in this application;
[0055] Figure 4 This is a cross-fit diagram of the dynamic and static Young's modulus of rocks parallel to the bedding direction in this application. Detailed Implementation
[0056] To enable those skilled in the art to better understand the technical solutions in this application, the following will further illustrate the technical solutions for achieving the inventive objectives of this application through several specific embodiments. It should be noted that the technical solutions claimed in this application include, but are not limited to, the following embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without inventive effort should fall within the scope of protection of this application.
[0057] Currently, the effective stress coefficient of rocks is mainly obtained through direct or indirect laboratory testing methods and rock physics modeling methods. For the first category of methods, there are mainly drainage tests, cross-plotting, and acoustic parameter methods. Drainage tests and cross-plotting primarily use plunger rock samples with different combinations of pore pressure and confining pressure. While these two methods can obtain accurate and reliable effective stress coefficients, they suffer from drawbacks such as difficulty in obtaining downhole cores, long testing times, and low efficiency. Furthermore, the obtained test data is discrete and cannot provide a continuous effective stress coefficient profile of the formation, limiting their application. Acoustic parameter methods indirectly calculate the effective stress coefficient of the formation by obtaining the acoustic wave velocity of the formation rock. Continuous effective stress coefficients of the formation can be obtained using well logging data or seismic velocity. However, this method obtains a dynamic effective stress coefficient, which needs to be corrected and converted to a static effective stress coefficient before it can be used for calculation. The second type of rock physics modeling method mainly involves using a suitable rock physics model for the target formation to obtain the corresponding rock bulk modulus and matrix particle modulus, and then calculating the effective stress coefficient. This type of method considers many factors, has complex models, and is difficult to solve, limiting its practical application. Furthermore, some rock physics parameters must be obtained through laboratory testing, which is not only inefficient but also introduces uncertain errors. This is especially true for layered formations, which require more complex rock physics models and numerous laboratory tests to obtain the required effective stress coefficient. Therefore, there is an urgent need for a method that can quickly and accurately determine the static effective stress coefficient of layered formations, fully utilize existing well logging data, facilitate widespread application, and is applicable to layered formations with any lithology.
[0058] Based on this, this application proposes a method for determining the static effective stress coefficient of layered strata. The method of this application only requires density measurement and acoustic wave velocity testing of rocks with vertical and parallel bedding to conveniently obtain the static effective stress coefficient of rocks with vertical and parallel bedding, thereby improving the efficiency of obtaining the static effective stress coefficient of rocks.
[0059] This embodiment discloses a method for determining the static effective stress coefficient of layered strata, as shown in the appendix to the specification. Figure 1 The method includes the following steps.
[0060] Step S1. Obtain the dynamic bulk modulus and dynamic Young's modulus of the vertical and parallel bedding of the target layered strata.
[0061] Refer to the instruction manual appendix Figure 2 As shown, based on the structure of the layered strata, standard plunger rock samples were drilled for the vertical bedding and parallel bedding of the target layered strata, respectively, to obtain the corresponding vertical bedding standard plunger rock samples and parallel bedding standard plunger rock samples.
[0062] Density measurements and acoustic wave velocity tests were conducted on standard plunger rock samples with perpendicular bedding and those with parallel bedding to obtain the bulk density, P-wave velocity, and S-wave velocity of the corresponding rock samples. The dynamic bulk modulus and dynamic Young's modulus of the standard plunger rock samples with perpendicular bedding and those with parallel bedding were calculated using the following formulas:
[0063]
[0064]
[0065]
[0066]
[0067]
[0068] In the above calculation expression, The dynamic bulk modulus of rock for a standard vertically bedding plunger sample; The dynamic bulk modulus of the rock is given by the standard plunger sample with parallel bedding. The dynamic Young's modulus of a standard plunger rock sample with vertical bedding; The dynamic Young's modulus of a standard stud rock sample with parallel bedding; V p,v V represents the longitudinal wave velocity of a standard plunger rock sample with vertical bedding; p,h The longitudinal wave velocity of a standard plunger rock sample with parallel bedding; V s,v V represents the shear wave velocity of a standard plunger rock sample with vertical bedding; s,h The shear wave velocity of a standard plunger rock sample with parallel bedding; ρ b ρ is the average volume density of the layered strata. b,v The bulk density of a standard plunger rock sample with vertical bedding; ρ b,h The volume density of a standard plunger rock sample with parallel bedding is given.
[0069] In this embodiment, it should be noted that the size of the standard plunger rock sample is...
[0070] Step S2. Based on the conversion relationship between the dynamic and static Young's moduli of the rock perpendicular to and parallel to the bedding of the target layered strata, calculate the static bulk modulus of the rock perpendicular to and parallel to the bedding of the target layered strata. The specific calculation expression is as follows:
[0071]
[0072]
[0073]
[0074]
[0075] in, The static bulk modulus of rock perpendicular to bedding; The static bulk modulus of rock with parallel bedding; The static Young's modulus of rock perpendicular to bedding; is the static Young's modulus of the rock with parallel bedding; m, n, m′, and n′ are all undetermined coefficients.
[0076] In this embodiment, it should be noted that the conversion relationship between the dynamic and static Young's modulus of the layered rocks with vertical and parallel bedding, i.e., the determination of the undetermined coefficients m, n, m′, n′ in the above calculation expression, can be an empirical relationship applicable to the target strata rocks, or it can be obtained by uniaxial compression tests on the plunger rock samples with vertical and parallel bedding.
[0077] In this embodiment, the conversion relationship between the dynamic and static Young's moduli of layered rocks with perpendicular and parallel bedding is obtained through uniaxial compression tests as follows:
[0078] Uniaxial compression tests were conducted on standard plunger rock samples with vertical bedding and standard plunger rock samples with parallel bedding. The dynamic Young's modulus of the standard plunger rock samples with vertical bedding and parallel bedding, calculated by acoustic wave velocity measurement, was cross-fitted with the static Young's modulus of the standard plunger rock samples with vertical bedding and parallel bedding, obtained by uniaxial compression tests. Finally, the conversion relationship between the dynamic and static Young's modulus of vertical bedding and parallel bedding was obtained.
[0079] In this embodiment, it should be noted that when conducting uniaxial compression tests on standard plunger rock samples, at least three standard plunger rock samples with perpendicular bedding and three standard plunger rock samples with parallel bedding are required.
[0080] For example, regarding vertical bedding, the two undetermined coefficients m and n are determined as follows:
[0081] The dynamic Young's modulus is calculated using well logging data or indoor acoustic wave velocity tests, and then the static Young's modulus is obtained through uniaxial compression tests. Refer to the appendix of the instruction manual. Figure 3 As shown, after plotting the intersection of these two values, the undetermined coefficients m and n are obtained by linear fitting, where m is the slope of the fitting formula and n is the y-intercept of the fitting formula.
[0082] In this embodiment, the fitting method can be a simple linear fitting, or other fitting methods, such as exponential fitting or polynomial fitting. The fitting method is a conventional technique and will not be elaborated further here.
[0083] In this embodiment, the determination method for the undetermined coefficients m′ and n′ of parallel bedding is the same as that for perpendicular bedding, and the fitting results are as per the appendix of the specification. Figure 4 As shown.
[0084] Step S3. Calculate the bulk modulus of the rock matrix using the VRH model.
[0085] XRD analysis was performed on rock samples perpendicular to and parallel to the bedding of the target layered strata to obtain the mineral composition and percentage content of the rocks with perpendicular and parallel bedding. Then, based on the bulk modulus of each matrix mineral, the VRH model was used to calculate the matrix bulk modulus of the target layered strata rocks. The specific expression for calculating the matrix bulk modulus of the target layered strata rocks is as follows:
[0086]
[0087]
[0088]
[0089] Where K0 is the bulk modulus of the rock matrix; K V K is the average modulus of Voigt; R f is the Reussian mean modulus; i K represents the volume percentage of the i-th mineral component in the rock; i Let be the bulk modulus of the i-th mineral component in the rock.
[0090] In this embodiment, it should be noted that for the same mineral components, their average percentage content is calculated.
[0091] In this embodiment, it should also be noted that the VRH model is known to those skilled in the art and will not be described in detail here.
[0092] Step S4. Calculate the static effective stress coefficient of the rock perpendicular to and parallel to the bedding of the target layered strata. The specific calculation expression is as follows:
[0093]
[0094]
[0095] in, The static effective stress coefficient of rock perpendicular to bedding; The static effective stress coefficient of rock with parallel bedding is given.
[0096] The above description is merely a preferred embodiment of this application and does not constitute any limitation on this application. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of this application shall fall within the protection scope of this application.
Claims
1. A method for determining the static effective stress coefficient of layered strata, characterized in that, Includes the following steps: Obtain the dynamic bulk modulus and dynamic Young's modulus of the target layered strata perpendicular to and parallel to bedding, including: Standard plunger rock samples were drilled from the target layered strata, both perpendicular and parallel to bedding. Density measurements and acoustic wave velocity tests were conducted on both samples to obtain their bulk density, P-wave velocity, and S-wave velocity. The dynamic bulk modulus and dynamic Young's modulus of the rock samples were then calculated using the following formulas. （1） （2） （3） （4） （5） in, and The dynamic bulk modulus of rocks are those of standard plunger rock samples with vertical bedding and those with parallel bedding, respectively. and The dynamic Young's modulus of rocks is represented by standard plunger rock samples with vertical bedding and standard plunger rock samples with parallel bedding, respectively. and The P-wave velocities of the rock are shown in the standard plunger rock samples with vertical bedding and those with parallel bedding, respectively. and The shear wave velocities of rock samples are shown in the standard plunger samples with vertical bedding and those with parallel bedding, respectively. The average volume density of the target layered strata; and The volumetric densities are those of standard plunger rock samples with vertical bedding and those with parallel bedding, respectively. Based on the conversion relationship between the dynamic and static Young's moduli of rocks with vertical and parallel bedding in the target layered strata, the static bulk modulus of rocks with vertical and parallel bedding in the target layered strata is calculated. The specific calculation expression is as follows: （6）； （7）； （8）； （9）； in, and These are the static bulk moduli of rocks with perpendicular bedding and parallel bedding, respectively. and The static Young's modulus of rocks with perpendicular bedding and parallel bedding are respectively. , , , All are undetermined coefficients; The VRH model was used to calculate the bulk modulus of the target layered strata rock matrix. The static effective stress coefficients of the target layered strata, perpendicular to and parallel to bedding, are calculated using the following expressions: （13）； （14）； in, and The static effective stress coefficients of rocks with perpendicular and parallel bedding are given. This represents the bulk modulus of the rock matrix.
2. The method for determining the static effective stress coefficient of layered strata according to claim 1, characterized in that, The calculation of the target layered strata rock matrix bulk modulus using the VRH model includes: XRD analysis was performed on rock samples with vertical and parallel bedding of the target layered strata to obtain the mineral composition and percentage content of the rock with vertical and parallel bedding. Based on the bulk modulus of each matrix mineral, the bulk modulus of the target layered strata rock matrix was calculated using the VRH model.
3. The method for determining the static effective stress coefficient of layered strata according to claim 2, characterized in that, For the same mineral composition, calculate its average percentage content.
4. The method for determining the static effective stress coefficient of layered strata according to claim 2, characterized in that, The calculation expression for the bulk modulus of the target layered strata rock matrix using the VRH model is as follows: （10）； （11）； （12）； in, Bulk modulus of the rock matrix; Voigt's average modulus; It is the Reussian average modulus; For the first in the rock Volume percentage of a mineral component; For the first in the rock The bulk modulus of a mineral component.
5. The method for determining the static effective stress coefficient of layered strata according to claim 1, characterized in that, The dynamic and static Young's modulus conversion relationship of the target layered strata with vertical and parallel bedding is an empirical relationship applicable to the target layered strata rocks.
6. The method for determining the static effective stress coefficient of layered strata according to claim 1, characterized in that, The dynamic and static Young's modulus conversion relationships of the target layered strata perpendicular and parallel bedding were obtained through the following methods: Uniaxial compression tests were conducted on standard plunger rock samples with vertical bedding and standard plunger rock samples with parallel bedding. The dynamic Young's modulus of the standard plunger rock samples with vertical bedding and parallel bedding, calculated by acoustic wave velocity measurement, was cross-fitted with the static Young's modulus of the standard plunger rock samples with vertical bedding and parallel bedding, obtained by uniaxial compression tests. Finally, the conversion relationship between the dynamic and static Young's modulus of vertical bedding and parallel bedding was obtained.