CN109558613B - Inversion method and system of anisotropic rock physical model - Google Patents
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Abstract
The invention discloses an inversion method and system of an anisotropic rock physical model, wherein the inversion method comprises the following steps: establishing a rock physical model with transverse isotropic elastic characteristics; based on Bayes theory, posterior probability distribution is obtained; establishing an inverted target function based on the rock physical model and the posterior probability distribution; and obtaining an optimal solution of the fracture density parameter based on the target function. The invention has the advantages that: the method can comprehensively consider the influence of anisotropic clay and directionally arranged microcracks on the anisotropy of the shale, and carries out rock physics inversion by using prior information and logging parameters as constraints based on a Bayesian framework to obtain the elastic parameters of clay minerals and the density of directionally arranged microcracks, thereby further discussing the anisotropy characteristics.
Description
Technical Field
The invention relates to the technical field of oil and gas geophysical, in particular to an inversion method and system of an anisotropic rock physical model.
Background
Shale petrophysical modeling aims to relate shale components, structures and packing fluids to their elastic parameters and further analyze their elastic properties. Shale has a relatively complex mineral composition and structure, which makes the work of shale relatively difficult. The research on the shale petrophysical model can be traced back to the petrophysical modeling problem of the North American Bakken shale belonging to the organic-rich black shale type based on the anisotropic Backus average theory, such as vernier and Nur (1992), vernier and Liu (1997) in the early period. Meanwhile, Hornby et al (1994) used anisotropic self-consistent approximation (SCA) and Differential Equivalent Medium (DEM) theory for shale petrophysical modeling.
In recent years, many scholars have discussed the composition of shale and its fine structure, and analyzed its anisotropic properties, using petrophysical modeling methods: mba and Prasad (2010) analyzed the relationship of mineral components in shale to elastic anisotropy; spikes (2011) studies the uncertainty of fracture density parameters and the influence of pore morphology on shale elasticity parameters based on a statistical method; jiang (2013) establishes a petrophysical model by using a self-consistent model and a Chapman theory to carry out parameter estimation on Hayns Vill shale. The factors causing the shale anisotropy are complex, and the influence of all the factors cannot be considered by the existing rock physics modeling means, so that the factor causing the shale anisotropy is considered as comprehensively as possible, which is an important development direction of the shale rock physics modeling at present.
Most of the existing technologies discuss one or two factors causing shale anisotropy, such as clay anisotropy, organic matter distribution, horizontal bedding, cracks and the like. Contrary to considering as many influencing factors as possible, the constraints are not sufficient, i.e. corresponding data is lacking. In addition, clay minerals are important components of shale, and the content of the clay minerals can even reach over 50 percent in some regions, so the estimation of elastic parameters of the clay minerals determines the quality of rock physical modeling. The clay mineral has complex components and the characteristic of directional arrangement, so that the elasticity parameters of the clay in different regions are different, and the existing research is mostly based on the elasticity parameters of the clay measured by the previous experiment, and the influence caused by the component difference and the directional arrangement is ignored.
Therefore, there is a need to develop an anisotropic rock physical modeling method and system, which can comprehensively consider the influence of anisotropic clay and directionally arranged microcracks on the anisotropy of the shale, and directly invert to obtain the elastic parameters of the clay minerals without directly using the elastic parameters measured by the predecessors in the process of considering the clay minerals.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention provides an inversion method and an inversion system of an anisotropic rock physical model, which can comprehensively consider the influence of anisotropic clay and directionally arranged microcracks on the anisotropy of shale, and perform rock physical inversion by taking prior information and logging parameters as constraints based on a Bayesian framework to obtain the elastic parameters of clay minerals and the density of directionally arranged cracks, thereby further discussing the anisotropic characteristics.
According to an aspect of the present invention, an inversion method of an anisotropic petrophysical model is provided, the inversion method comprising:
establishing a rock physical model with transverse isotropic elastic characteristics;
based on Bayes theory, posterior probability distribution is obtained;
establishing an inverted target function based on the petrophysical model and the posterior probability distribution;
and acquiring an optimal solution of the fracture density parameter based on the target function.
Preferably, establishing the petrophysical model comprises:
based on a Hashi-Shtrikman limit theory, calculating isotropic elastic parameters of non-clay minerals and organic kerogen;
mixing clay mineral with the non-clay mineral and kerogen based on Backus average theory, calculating the elastic modulus of the solid matrix with VTI anisotropy, and considering the heterogeneity of the elastic parameters of the clay mineral;
solving the elastic parameter of the mixed fluid in the pore-fracture space based on the Wood formula;
introducing a multi-scale pore-fracture system into a solid matrix based on a Chapman theory to obtain shale reservoir elastic parameters with VTI anisotropy;
and calculating the TTI elastic anisotropy parameter of the shale reservoir under the condition of stratum inclination based on the Bond transformation.
Preferably, the TTI elastic anisotropy parameter matrix of the shale reservoir is:
in the formula (I), the compound is shown in the specification,
an elastic anisotropy parameter coefficient matrix of the TTI model;
vpclaythe longitudinal wave velocity of the clay mineral;
vsclaythe transverse wave velocity of the clay mineral;
ε is the density of parallel-layered pores or microcracks.
Preferably, according to the petrophysical definition, the density epsilon of the parallel-bedding pores or microcracks is, with known log porosity phi:
then formula (1) is:
where α is the pore aspect ratio and is the base 10 logarithm.
Preferably, the posterior probability distribution is:
P(B∣A)∝P(A∣B)P(B) (4)
wherein P (B) is the prior probability of occurrence of event B;
p (A | B) is a likelihood function;
p (B | A) is the posterior probability.
Preferably, three parameters vp to be invertedclay，vsclayAnd α follows a ternary gaussian distribution:
wherein x is a parameter vector consisting of the logarithm of the base 10 of the longitudinal and transverse wave speeds and the pore aspect ratio of the clay mineral;
μ1a vector consisting of the mean values of the parameters;
Σ1is a covariance matrix of the parameter vectors.
Preferably, the likelihood function satisfies a two-dimensional gaussian distribution:
in the formula, y is a vector formed by vertical longitudinal wave speed and transverse wave speed of the TTI model;
μ2the vector is composed of longitudinal and transverse wave speeds of the logging;
Σ2determining the tolerance degree of the model solution deviating from the actual logging speed for the covariance matrix;
then equation (4) is:
preferably, the objective function obtained according to equation (7) is:
in the formula, JiAn objective function of the ith logging point;
yiforming a vector for longitudinal and transverse wave velocities obtained by rock physical modeling of the ith logging point;
xithe vector is composed of longitudinal and transverse wave speeds of clay and the aspect ratio of pores at the ith logging point;
Preferably, the optimal solution of the fracture density parameter is obtained when the objective function is minimum.
According to another aspect of the present invention, there is provided an inversion system of an anisotropic petrophysical model, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
establishing a rock physical model with transverse isotropic elastic characteristics;
based on Bayes theory, posterior probability distribution is obtained;
establishing an inverted target function based on the petrophysical model and the posterior probability distribution;
and obtaining the optimal solution of the objective function.
According to the inversion method and the inversion system of the anisotropic rock physical model, the advantages are that: the method can comprehensively consider the influence of anisotropic clay and directionally arranged microcracks on the anisotropy of the shale, and carries out rock physics inversion by using prior information and logging parameters as constraints based on a Bayesian framework to obtain the elastic parameters of clay minerals and the density of directionally arranged microcracks, thereby further discussing the anisotropy characteristics.
The method and system of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings.
FIG. 1 shows a flow chart of steps of a method of inversion of an anisotropic petrophysical model according to an exemplary embodiment of the present invention.
FIG. 2 shows a schematic diagram of establishing a petrophysical model according to an exemplary embodiment of the present invention.
Figures 3a and 3b show schematic diagrams comparing TTI model compressional and shear velocity versus actual velocity logs, respectively, according to an exemplary embodiment of the invention.
FIG. 4 shows a schematic of fracture aspect ratio curves obtained from inversion of a petrophysical model according to an exemplary embodiment of the present invention.
Fig. 5a and 5b show schematic diagrams of longitudinal wave velocity and transverse wave velocity, respectively, of a clay mineral obtained by inversion of a petrophysical model according to an exemplary embodiment of the present invention.
FIG. 6 shows a schematic diagram of a fracture density profile according to an exemplary embodiment of the present invention.
Fig. 7 shows a schematic diagram of the compressional wave anisotropy parameter epsilon and shear wave anisotropy parameter gamma curves according to an exemplary embodiment of the invention.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
The invention provides an inversion method of an anisotropic rock physical model, which comprises the following steps:
establishing a rock physical model with transverse isotropic elastic characteristics;
based on Bayes theory, posterior probability distribution is obtained;
establishing an inverted target function based on the rock physical model and the posterior probability distribution;
and obtaining an optimal solution of the fracture density parameter based on the target function.
And establishing a rock physical model through the shale reservoir with transverse isotropy parameter characteristics.
Preferably, the establishing of the petrophysical model comprises:
based on a Hashi-Shtrikman limit theory, isotropic elastic parameters of non-clay minerals (quartz, dolomite, limestone and pyrite) and organic matter kerogen are calculated, and based on previous researches, the kerogen is assumed to be distributed in a random block shape in space;
mixing clay minerals with the above non-clay minerals and kerogen based on Backus' average theory, calculating the elastic modulus of the solid matrix having VTI (Transversell isotopy with a vertical axis) anisotropy, and considering the heterogeneity of the elastic parameters of the clay minerals;
solving the elasticity parameter of the mixed fluid (gas and water) in the pore-fracture space based on the Wood formula;
introducing a multi-scale pore-fracture system into a solid matrix based on a Chapman theory to obtain shale reservoir elastic parameters with VTI anisotropy;
and calculating the TTI elastic anisotropy parameter of the shale reservoir under the condition of stratum inclination based on the Bond transformation.
The method can comprehensively consider the influence of anisotropic clay and directionally arranged microcracks on the anisotropy of the shale, and carries out rock physics inversion by using prior information and logging parameters as constraints based on a Bayesian framework to obtain the elastic parameters of clay minerals and the density of directionally arranged microcracks, thereby further discussing the anisotropy characteristics.
In the above petrophysical model, the clay mineral longitudinal wave velocity, transverse wave velocity and pore or fracture density are undetermined parameters, and other parameters can be determined or estimated from the well logging data, so that for the convenience of designing the inversion method of the petrophysical model, the TTI elastic anisotropy parameter matrix of the shale reservoir is:
in the formula (I), the compound is shown in the specification,
an elastic anisotropy parameter coefficient matrix of the TTI model;
vpclayis the longitudinal wave velocity of the clay mineral;
vsclayis the transverse wave velocity of the clay mineral;
ε is the density of parallel-layered pores or microcracks.
Preferably, according to the petrophysical definition, in the case of a known well-logging porosity φ, the density ε of parallel-bedding pores or microcracks is:
then formula (1) is:
where α is the pore aspect ratio and is the base 10 logarithm.
And calculating three parameters of longitudinal wave velocity, transverse wave velocity and pore aspect ratio of the clay minerals through logging data, and designing an inversion algorithm of the rock physical model.
And taking the clay longitudinal wave velocity, the clay transverse wave velocity and the pore aspect ratio in the modeling process as fitting parameters, and taking the longitudinal wave velocity and the transverse wave velocity obtained by well logging as constraints to carry out inversion of the rock physical model.
As a preferred scheme, the posterior probability distribution is:
P(B∣A)∝P(A∣B)P(B) (4)
wherein P (B) is the prior probability of occurrence of event B;
p (A | B) is a likelihood function;
p (B | A) is the posterior probability.
According to the invention, the longitudinal wave velocity and the transverse wave velocity of the clay mineral are supposed to meet Gaussian distribution, the average value of the longitudinal wave velocity and the transverse wave velocity is the result of previous measurement, the pore aspect ratio alpha is a logarithm with the base of 10 and also meets the Gaussian distribution, the pore aspect ratio has larger change along with lithology in different areas, and larger variance is selected. Thus, the three parameters to be inverted conform to a ternary gaussian distribution, which satisfies the formula:
wherein x is a parameter vector consisting of the logarithm of the base 10 of the longitudinal and transverse wave speeds and the pore aspect ratio of the clay mineral;
μ1a vector consisting of the mean values of the parameters;
Σ1is a covariance matrix of the parameter vectors.
The covariance matrix not only reflects the degree of deviation of each variable from the mean value, but also reflects the correlation among different variables. The invention assumes that the longitudinal wave velocity and the transverse wave velocity of the clay mineral are in positive correlation, namely the longitudinal wave velocity is increased, the transverse wave velocity is also increased, the covariance is obtained by the clay velocity statistics measured by the predecessor, and meanwhile, the aspect ratio of the pores is assumed to have no correlation with the longitudinal wave velocity and the transverse wave velocity of the clay, namely the covariance is 0.
In order to establish an inverse objective function, it is assumed that a residual error between a forward modeling result of the model and logging constraint parameters (measured compressional velocity and shear velocity), i.e., a likelihood function, also satisfies a two-dimensional gaussian distribution.
Preferably, the likelihood function satisfies a two-dimensional gaussian distribution:
in the formula, y is a vector formed by vertical longitudinal wave speed and transverse wave speed of the TTI model;
μ2the vector is composed of longitudinal and transverse wave speeds of the logging;
Σ2determining the tolerance degree of the model solution deviating from the actual logging speed for the covariance matrix;
then equation (4) is:
the point with the maximum posterior probability density corresponds to the optimal solution, and therefore, the objective function can be obtained as follows:
in the formula, JiAn objective function of the ith logging point;
yilongitudinal and transverse waves obtained by rock physical modeling of ith logging pointThe velocity constitutes a vector;
xithe vector is composed of longitudinal and transverse wave speeds of clay and the aspect ratio of pores at the ith logging point;
As a preferred scheme, the optimal solution of the fracture density parameter is obtained when the objective function is minimum.
The method can establish the relation between rock components, porosity, pore morphology, fluid properties and overall rock elastic parameters by utilizing the inversion method of the rock physical model, further analyzes the anisotropic characteristics of the rock components, the porosity, the pore morphology and the fluid properties, and has important reference significance for finding shale oil and gas reservoirs. Meanwhile, the fractures in the shale are important oil and gas migration channels and storage spaces, the higher the fracture density is, the higher the storage space is, and the fracture density parameter obtained through rock physics inversion is one of important parameters for evaluating the storage capacity of the reservoir.
The invention also provides an inversion system of the anisotropic rock physical model, which is characterized by comprising the following components:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
establishing a rock physical model with transverse isotropic elastic characteristics;
based on Bayes theory, posterior probability distribution is obtained;
establishing an inverted target function based on the rock physical model and the posterior probability distribution;
and obtaining the optimal solution of the objective function.
Examples
FIG. 1 shows a flow chart of steps of a method of inversion of an anisotropic petrophysical model according to an exemplary embodiment of the present invention.
As shown in fig. 1, an inversion method of an anisotropic petrophysical model of the present embodiment includes:
establishing a rock physical model with transverse isotropic elastic characteristics;
based on Bayes theory, posterior probability distribution is obtained;
establishing an inverted target function based on the rock physical model and the posterior probability distribution;
and obtaining an optimal solution of the fracture density parameter based on the target function.
FIG. 2 shows a schematic diagram of establishing a petrophysical model according to an exemplary embodiment of the present invention.
As shown in fig. 2, establishing the petrophysical model includes:
based on a Hashi-Shtrikman limit theory, isotropic elastic parameters of non-clay minerals (quartz, dolomite, limestone and pyrite) and organic matter kerogen are calculated, and based on previous researches, the kerogen is assumed to be distributed in a random block shape in space;
mixing clay minerals with the above non-clay minerals and kerogen based on Backus' average theory, calculating the elastic modulus of the solid matrix having VTI (Transversell isotopy with a vertical axis) anisotropy, and considering the heterogeneity of the elastic parameters of the clay minerals;
solving the elasticity parameter of the mixed fluid (gas and water) in the pore-fracture space based on the Wood formula;
introducing a multi-scale pore-fracture system into a solid matrix based on a Chapman theory to obtain shale reservoir elastic parameters with VTI anisotropy;
and calculating the TTI elastic anisotropy parameter of the shale reservoir under the condition of stratum inclination based on the Bond transformation.
In China, a certain well logging shop one by one carries out inversion of the petrophysical model by using the method.
Figures 3a and 3b show schematic diagrams comparing TTI model compressional and shear velocity versus actual velocity logs, respectively, according to an exemplary embodiment of the invention.
As shown in fig. 3a and fig. 3b, the dark line segments represent vertical longitudinal wave velocity (shown in fig. 3 a) and transverse wave velocity (shown in fig. 3 b) of the TTI petrophysical model, and the light line segments represent measured longitudinal wave velocity and transverse wave velocity of the logging tool. Therefore, by using the target function to carry out constraint and particle swarm inversion methods, the well logging curve is well fitted, the fitting residual error is small, and the target function has strong constraint force.
The particle swarm inversion aims to obtain the optimal solution of the model parameters when the objective function is minimum.
FIG. 4 shows a schematic diagram of pore aspect ratio curves obtained from inversion of a petrophysical model according to an exemplary embodiment of the present invention.
As shown in FIG. 4, the aspect ratio of the shale interval is concentrated between 0.1 and 0.3, and the overall aspect ratio of the shale interval meets the statistical result of the former people on the aspect ratio of the shale interval in the area.
Fig. 5a and 5b are schematic diagrams respectively illustrating longitudinal wave velocity and transverse wave velocity of a clay mineral obtained by inversion of a petrophysical model according to an exemplary embodiment of the present invention.
As shown in fig. 5a and 5b, the inverted clay longitudinal wave velocity (shown in fig. 5 a) and transverse wave velocity (shown in fig. 5 b) are greater than those of the predecessors, and the reason for this may be that the clay component in the shale has a higher content of illite than that of the predecessors' clay, which has higher longitudinal and transverse wave velocities. The inversion result further illustrates that the inversion strategy provided by the invention can reflect the influence of the speed caused by the change of the components in the clay minerals.
FIG. 6 shows a schematic diagram of a fracture density profile according to an exemplary embodiment of the present invention. Fig. 7 shows a schematic diagram of the compressional wave anisotropy parameter epsilon and shear wave anisotropy parameter gamma curves according to an exemplary embodiment of the invention.
As shown in fig. 7, VTI anisotropy of a horizontal fracture-enhanced formation parallel to the bedding plane, which shows a parameter epsilon of longitudinal wave anisotropy and a parameter gamma of transverse wave anisotropy, can be used for analyzing the anisotropy characteristics of shale in the region, where the parameter epsilon represents the difference of longitudinal wave velocities in the horizontal direction and the vertical direction caused by anisotropy, and the parameter gamma represents the difference of longitudinal wave velocities in the horizontal direction and the vertical direction caused by anisotropy.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the illustrated embodiments. The terminology used herein is chosen in order to best explain the principles of the embodiments, the practical application, or improvements made to the technology in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.
Claims (6)
1. An inversion method of an anisotropic petrophysical model, the inversion method comprising:
establishing a rock physical model with transverse isotropic elastic characteristics;
based on Bayes theory, posterior probability distribution is obtained;
establishing an inverted target function based on the petrophysical model and the posterior probability distribution;
obtaining an optimal solution of a fracture density parameter based on the objective function;
wherein, establishing the petrophysical model comprises:
based on a Hashi-Shtrikman limit theory, calculating isotropic elastic parameters of non-clay minerals and organic kerogen;
mixing clay mineral with the non-clay mineral and kerogen based on Backus average theory, calculating the elastic modulus of the solid matrix with VTI anisotropy, and considering the heterogeneity of the elastic parameters of the clay mineral;
solving the elastic parameter of the mixed fluid in the pore-fracture space based on the Wood formula;
introducing a multi-scale pore-fracture system into a solid matrix based on a Chapman theory to obtain shale reservoir elastic parameters with VTI anisotropy;
calculating a TTI elastic anisotropy parameter of the shale reservoir under the condition of stratum inclination based on Bond transformation;
wherein the TTI elastic anisotropy parameter matrix of the shale reservoir is as follows:
in the formula (I), the compound is shown in the specification,
an elastic anisotropy parameter coefficient matrix of the TTI model;
vpclaythe longitudinal wave velocity of the clay mineral;
vsclaythe transverse wave velocity of the clay mineral;
α is the pore aspect ratio, logarithmic to the base 10;
three parameters vp to be invertedclay，vsclayAlpha is in accordance with the ternary Gaussian distribution, and the residual error between the forward result of the model and the logging constraint parameter, namely the likelihood function, meets the two-dimensional Gaussian distribution, so as to obtain the posterior probability;
wherein, the point with the maximum posterior probability density corresponds to the optimal solution, and the obtained objective function is as follows:
in the formula, JiAn objective function of the ith logging point;
yiforming a vector for longitudinal and transverse wave velocities obtained by rock physical modeling of the ith logging point;
xithe vector is composed of longitudinal and transverse wave speeds of clay and the aspect ratio of pores at the ith logging point;
Σ1a covariance matrix which is a parameter vector;
Σ2determining the tolerance degree of the model solution deviating from the actual logging speed for the covariance matrix;
and obtaining the optimal solution of the fracture density parameter when the objective function is minimum.
2. The method of inverting an anisotropic petrophysical model of claim 1, wherein equation (3) is obtained according to the following steps:
the TTI elastic anisotropy parameter matrix of the shale reservoir is as follows:
wherein epsilon is the density of pores or microcracks with parallel layers;
according to the petrophysical definition, the density epsilon of pores or microcracks in parallel bedding is:
then formula (1) is:
3. the method of inverting an anisotropic petrophysical model of claim 2, wherein the posterior probability distribution is:
P(B∣A)∝P(A∣B)P(B) (4)
wherein P (B) is the prior probability of occurrence of event B;
p (A | B) is a likelihood function;
p (B | A) is the posterior probability.
4. Method of inversion of an anisotropic petrophysical model according to claim 3, wherein three parameters to be inverted vpclay，vsclayAnd α follows a ternary gaussian distribution:
wherein x is a parameter vector consisting of the logarithm of the base 10 of the longitudinal and transverse wave speeds and the pore aspect ratio of the clay mineral;
μ1a vector consisting of the mean values of the parameters.
5. The method of inverting an anisotropic petrophysical model of claim 4, wherein the likelihood function satisfies a two-dimensional Gaussian distribution:
in the formula, y is a vector formed by vertical longitudinal wave speed and transverse wave speed of the TTI model;
μ2the vector is composed of longitudinal and transverse wave speeds of the logging;
then equation (4) is:
6. an inversion system for an anisotropic petrophysical model, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
establishing a rock physical model with transverse isotropic elastic characteristics;
based on Bayes theory, posterior probability distribution is obtained;
establishing an inverted target function based on the petrophysical model and the posterior probability distribution;
obtaining an optimal solution of the objective function;
wherein, establishing the petrophysical model comprises:
based on a Hashi-Shtrikman limit theory, calculating isotropic elastic parameters of non-clay minerals and organic kerogen;
mixing clay mineral with the non-clay mineral and kerogen based on Backus average theory, calculating the elastic modulus of the solid matrix with VTI anisotropy, and considering the heterogeneity of the elastic parameters of the clay mineral;
solving the elastic parameter of the mixed fluid in the pore-fracture space based on the Wood formula;
introducing a multi-scale pore-fracture system into a solid matrix based on a Chapman theory to obtain shale reservoir elastic parameters with VTI anisotropy;
calculating a TTI elastic anisotropy parameter of the shale reservoir under the condition of stratum inclination based on Bond transformation;
wherein the TTI elastic anisotropy parameter matrix of the shale reservoir is as follows:
in the formula (I), the compound is shown in the specification,
an elastic anisotropy parameter coefficient matrix of the TTI model;
vpclaythe longitudinal wave velocity of the clay mineral;
vsclaythe transverse wave velocity of the clay mineral;
α is the pore aspect ratio, logarithmic to the base 10;
three parameters vp to be invertedclay，vsclayAlpha is in accordance with the ternary Gaussian distribution, and the residual error between the forward result of the model and the logging constraint parameter, namely the likelihood function, meets the two-dimensional Gaussian distribution, so as to obtain the posterior probability;
wherein, the point with the maximum posterior probability density corresponds to the optimal solution, and the obtained objective function is as follows:
in the formula, JiAn objective function of the ith logging point;
yiforming a vector for longitudinal and transverse wave velocities obtained by rock physical modeling of the ith logging point;
xithe vector is composed of longitudinal and transverse wave speeds of clay and the aspect ratio of pores at the ith logging point;
Σ1a covariance matrix which is a parameter vector;
Σ2determining the tolerance degree of the model solution deviating from the actual logging speed for the covariance matrix;
and obtaining the optimal solution of the fracture density parameter when the objective function is minimum.
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| CN110135112A (en) * | 2019-06-04 | 2019-08-16 | 南京信息工程大学 | A kind of shale anisotropy estimation method based on particle filter algorithm |
| CN110512622B (en) * | 2019-08-23 | 2021-07-13 | 郑州安源工程技术有限公司 | Vertical crack filling and grouting method for slope rock mass |
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| CN114280670A (en) * | 2021-12-13 | 2022-04-05 | 华能煤炭技术研究有限公司 | Multi-physical-model well logging shear wave velocity curve reconstruction method and system and electronic equipment |
| CN117420202A (en) * | 2023-10-18 | 2024-01-19 | 中国地质大学（北京） | Shale type determining method, shale type determining device, shale type determining terminal and shale type storing medium |
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