CN113176614A - Reservoir effective pressure prestack inversion prediction method based on rock physics theory - Google Patents

Reservoir effective pressure prestack inversion prediction method based on rock physics theory Download PDF

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CN113176614A
CN113176614A CN202110479626.5A CN202110479626A CN113176614A CN 113176614 A CN113176614 A CN 113176614A CN 202110479626 A CN202110479626 A CN 202110479626A CN 113176614 A CN113176614 A CN 113176614A
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宗兆云
姜曼
印兴耀
李坤
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China University of Petroleum East China
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    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/40—Seismology; Seismic or acoustic prospecting or detecting specially adapted for well-logging
    • G01V1/44—Seismology; Seismic or acoustic prospecting or detecting specially adapted for well-logging using generators and receivers in the same well
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    • G01V2210/6169—Data from specific type of measurement using well-logging
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Abstract

The invention discloses a rock physics theory-based reservoir effective pressure prestack inversion prediction method, which belongs to the field of geophysical inversion research and comprises the following steps: s01, firstly, establishing a rock physical model; s02 modulus of saturation rocksAnd musThe expression (c) is used for solving the natural logarithm, and then a reference point m is selected0Performing Taylor expansion to obtain a multivariate function expression, and then expressing the multivariate function by using a Jacobian matrix; s03, calculating corresponding partial derivatives in the Jacobian matrix in S02, and substituting the partial derivatives into the reflection coefficient RppThe approximate equation of the pressure sensor is simplified to obtain a reflection coefficient equation, the influence of the effective pressure on the elastic parameters of the reservoir and the seismic reflection characteristics is explained from a rock physics mechanism, sampling and experimental testing are not needed to be carried out on all work areas, the implementation is convenient, the prediction result is more accurate, and the effective pressure prediction of deep and deep reservoirs is realized.

Description

Reservoir effective pressure prestack inversion prediction method based on rock physics theory
Technical Field
The invention relates to the field of geophysical inversion research, in particular to a reservoir effective pressure prestack inversion prediction method based on a rock physics theory.
Background
At present, the conventional oil and gas exploration and development technology is basically mature, and exploration and development of deep land, deep sea and unconventional reservoirs become new research hotspots. The pressure conditions of deep layers, deep water and unconventional reservoirs are different from those of conventional reservoirs, particularly the deep layers of a hydrocarbon-bearing basin, and are influenced by the structure movement, and overpressure oil and gas reservoirs are often developed relatively, so that the research on the influence of pressure on the physical properties of reservoir rocks and the analysis of microscopic main control factors of the reservoir rocks have important significance on the geological understanding of deep hydrocarbon reservoirs, particularly compact reservoirs and the exploration and development of deep reservoirs.
Previous studies on pressure effects have focused on the formation pressure, pore pressure (formation pressure) and the differential effective pressure between them. The existing reservoir pressure prediction method mainly comprises the following steps:
(1) empirical formula method. Preparing a rock sample, obtaining elastic parameters of the rock under different effective pressures under laboratory conditions, obtaining a corresponding empirical formula through data fitting, and applying the empirical formula to the whole work area; many scholars perform a large number of experimental simulations, and provide empirical relations on the basis of experimental results to describe the relation between different types of pressure and the longitudinal and transverse wave velocities, and the existence of corresponding abnormal pressure is judged according to the abnormal longitudinal and transverse wave velocities. However, the empirical relationship is lack of theoretical basis, the same set of parameters cannot be applied to all the work areas, and it is very inconvenient to sample and experimentally test all the work areas.
(2) Normal compaction trend method. The method comprises the steps of firstly predicting the normal compaction trend of reservoir parameters changing along with the depth under the normal pressure condition according to logging or geological data, predicting the formation pore pressure through the difference between observation parameters and the parameters under normal compaction, further calculating the effective pressure of the reservoir, deducing the effective pressure change condition of the whole work area by combining methods such as seismic elastic impedance inversion and the like, wherein the method is also an important means for effectively predicting the pressure through logging data at present. The method is also applied to seismic inversion prediction of effective pressure, and elastic impedance seismic prestack inversion work is performed under a Bayes frame by using the difference between reservoir parameters under normal compaction and actually measured reservoir parameters according to the normal compaction trend, so that the prediction of the effective pressure of a work area is completed. However, the normal compaction trend cannot be measured, and can only be inferred through other well logging or geological data, which causes certain difficulties for the implementation of the method.
The method is lack of guidance of a rock physics theory, and influence of effective pressure on reservoir elastic parameters and seismic reflection characteristics cannot be explained from a rock physics mechanism, so that the effective pressure seismic prestack inversion prediction method of the reservoir based on the rock physics theory and considering the influence of the effective pressure on the seismic reflection characteristics is provided, and effective pressure prediction of deep and deep reservoirs is realized based on an approximate equation of seismic reflection coefficients containing the effective pressure influence.
Disclosure of Invention
The invention aims to provide a rock physics theory-based reservoir effective pressure prestack inversion prediction method, which can realize that the rock physics theory is used as a theoretical basis and can accurately obtain a reservoir effective pressure predicted value.
In order to solve the problems, the invention adopts the following technical scheme:
a reservoir effective pressure prestack inversion prediction method based on a rock physics theory comprises the following steps:
s01, firstly, establishing a rock physical model, regarding the rock as a mixture of a sandstone part (representing that the mineral is quartz) and a argillaceous part (representing that the mineral is clay mineral), and calculating the matrix modulus K of the rock by using a V-R-H average according to the content of the logging argillaceousmAnd mumThen through KmAnd mumCalculating the saturated rock modulus KsAnd musAnd by the matrix density ρ of the rockmCalculating the density ρ of saturated rockss；
S02 modulus of saturation rocksAnd musThe expression (c) is used for solving the natural logarithm, and then a reference point m is selected0Performing Taylor expansion to obtain a multivariate function expression, and then expressing the multivariate function by using a Jacobian matrix;
s03, calculating corresponding partial derivatives in the Jacobian matrix in S02, and substituting the partial derivatives into the reflection coefficient RppThe approximate equation of (2) is simplified to obtainA reflection coefficient equation;
s04, substituting the seismic wavelet into a reflection coefficient equation to synthesize a seismic record;
s05, comparing the actual seismic record with the synthetic seismic record in S04, and calculating posterior probability by using a Bayesian formula according to the difference of reservoir parameters under the actual seismic record and reservoir parameters of the synthetic seismic record;
s06, obtaining a target function according to the posterior probability result in the S05;
s07, repeating the steps S04-S06 on the target function in the S06, performing iterative inversion, and deducing a reflection coefficient approximation equation reflecting the influence of effective pressure on the seismic reflection characteristics of the reservoir;
and S08, performing inversion prediction by using the reflection coefficient approximation equation obtained in the S07 to obtain an effective pressure value curve of the reservoir.
As a preferable scheme of the invention, the rock matrix modulus K in S01mAnd mumThe calculation formula of (2) is as follows:
Km＝(1-Vsh)Kquartz+VshKsh
μm＝(1-Vsh)μquartz+Vshμsh。
as a preferable scheme of the invention, the saturation rock modulus K in S01sP for introducing effective pressure in the calculating stepeInfluence, according to a linear approximation, the pore space stiffness K is calculated from the effective pressureφAnd bulk modulus K of matrixmWherein the values of the parameters a and B are related to the lithology characteristics of the work area:
Figure BDA0003048132400000031
after introduction of the influence of effective pressure KsThe calculation formula of (2) is as follows:
Figure BDA0003048132400000032
Figure BDA0003048132400000041
as a preferable embodiment of the present invention, the μsThe calculation formula of (2) is as follows:
μs＝μd＝μm(1-φ)q≈μm(1-q·φ)
in the formula: q is a constant related to the pore aspect ratio, KfIs the bulk modulus of the pore fluid,. phi.s,μdThe shear modulus of saturated rock and dry rock skeletons, respectively.
As a preferable scheme of the invention, the matrix density rho of the rock in S01mThe calculation formula of (2) is as follows:
ρm＝ρquartz(1-Vsh)+ρshVsh
in the formula: density of quartz ρquartzAnd density of the sludge rhoshTaking an empirical value;
p in the S01sThe calculation formula of (2) is as follows:
ρs＝φρf+(1-φ)ρm
in the formula: rhofAnd ρmThe density of the pore fluid and the rock matrix, respectively.
In a preferred embodiment of the present invention, the saturated rock modulus K in S02 issAnd musThe expression of (2) finds the expression of natural logarithm as:
f(m)＝ln(Ks),g(m)＝ln(μs),h(m)＝ln(ρs)
in the formula: the index m denotes the matrix parameter, s denotes the saturation rock parameter, f denotes the fluid parameter, m denotes the fluid volume modulus K, the rock porosity φfShale content eta and effective pressure PeThe vectors of the components.
As a preferred embodiment of the present invention, the reference point m is selected in S020Obtaining a multivariate function expression after Taylor expansionThe formula is as follows:
Figure BDA0003048132400000051
as a preferred embodiment of the present invention, the jacobian matrix in S02 is represented as:
Figure BDA0003048132400000052
in a preferred embodiment of the present invention, the reflection coefficient R is substituted in S03ppThe approximate equation of (a) is:
Figure BDA0003048132400000053
wherein m is a model parameter vector, theta is an incident angle, t is a corresponding partial derivative parameter, J represents a Jacobian matrix, and the method is simplified to obtain:
Figure BDA0003048132400000054
wherein Kf,PePhi, eta and rho respectively represent the bulk modulus, effective pressure, porosity, shale content and density of the fluid, A, B is an empirical parameter obtained according to the characteristics of a work area, and gamma is the ratio of transverse wave velocity and longitudinal wave velocity. A. the1,A2,A3,A4The reflectance coefficients, respectively, fluid bulk modulus, effective pressure, porosity, shale content, density, are related to the angle of incidence.
In a preferred embodiment of the present invention, the verification of the effective pressure value curve of the reservoir obtained in S08 can be detected by the well curve measured values near the well profile.
Compared with the prior art, the invention has the advantages that:
according to the method, the rock physics theory considering the influence of the effective pressure is used for deducing the reflection coefficient approximate equation, the earthquake pre-stack inversion prediction of the effective pressure of the reservoir is completed, the influence of the effective pressure on the elastic parameters and the earthquake reflection characteristics of the reservoir is explained from a rock physics mechanism, sampling and experimental testing are not needed to be carried out on all work areas, the implementation is convenient, the prediction result is more accurate, and the effective pressure prediction of deep and deep water reservoirs is realized.
Drawings
FIG. 1 is a flow chart of inversion prediction according to the present invention;
FIG. 2 is a comparison of the effective borehole inversion results of a test well with actual measurement data when the present invention is applied to a deep shale gas work area;
FIG. 3 is a cross-sectional view of a well traversed by the inversion results of effective pressure when the present invention is applied to a deep shale gas work area.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and all other embodiments obtained by those skilled in the art without any inventive work are within the scope of the present invention.
In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "top/bottom", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
To facilitate an understanding of the invention, the invention will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete. It will be understood that when an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
Example (b):
referring to fig. 1, a method for predicting effective pressure prestack inversion of a reservoir based on petrophysical theory includes the following steps:
s01, firstly, establishing a rock physical model, regarding the rock as a mixture of a sandstone part (representing that the mineral is quartz) and a argillaceous part (representing that the mineral is clay mineral), and calculating the matrix modulus K of the rock by using a V-R-H average according to the content of the logging argillaceousmAnd mumThen through KmAnd mumCalculating the saturated rock modulus KsAnd musAnd by the matrix density ρ of the rockmCalculating the density ρ of saturated rockss；
S02 modulus of saturation rocksAnd musThe expression (c) is used for solving the natural logarithm, and then a reference point m is selected0Performing Taylor expansion to obtain a multivariate function expression, and then expressing the multivariate function by using a Jacobian matrix;
s03, calculating corresponding partial derivatives in the Jacobian matrix in S02, and substituting the partial derivatives into the reflection coefficient RppThe approximation equation of (2) is simplified to obtain a reflection coefficient equation;
s04, substituting the seismic wavelet into a reflection coefficient equation to synthesize a seismic record;
s05, comparing the actual seismic record with the synthetic seismic record in S04, and calculating posterior probability by using a Bayesian formula according to the difference of reservoir parameters under the actual seismic record and reservoir parameters of the synthetic seismic record;
s06, obtaining a target function according to the posterior probability result in the S05;
s07, repeating the steps S04-S06 on the target function in the S06, performing iterative inversion, and deducing a reflection coefficient approximation equation reflecting the influence of effective pressure on the seismic reflection characteristics of the reservoir;
and S08, performing inversion prediction by using the reflection coefficient approximation equation obtained in the S07 to obtain an effective pressure value curve of the reservoir.
In particular, the rock matrix modulus K in S01mAnd mumThe calculation formula of (2) is as follows:
Km＝(1-Vsh)Kquartz+VshKsh
μm＝(1-Vsh)μquartz+Vshμsh。
in particular, the saturated rock modulus K in S01sP for introducing effective pressure in the calculating stepeInfluence, according to a linear approximation, the pore space stiffness K is calculated from the effective pressureφAnd bulk modulus K of matrixmWherein the values of the parameters a and B are related to the lithology characteristics of the work area:
Figure BDA0003048132400000081
after introduction of the influence of effective pressure KsThe calculation formula of (2) is as follows:
Figure BDA0003048132400000082
Figure BDA0003048132400000083
in particular, the musThe calculation formula of (2) is as follows:
μs＝μd＝μm(1-φ)q≈μm(1-q·φ)
in the formula: q is a constant related to the pore aspect ratio, KfIs the bulk modulus of the pore fluid,. phi.s,μdThe shear modulus of saturated rock and dry rock skeletons, respectively.
Specifically, the matrix density ρ of the rock in S01mThe calculation formula of (2) is as follows:
ρm＝ρquartz(1-Vsh)+ρshVsh
in the formula: density of quartz ρquartzAnd density of the sludge rhoshTaking an empirical value;
p in the S01sThe calculation formula of (2) is as follows:
ρs＝φρf+(1-φ)ρm
in the formula: rhofAnd ρmThe density of the pore fluid and the rock matrix, respectively.
Specifically, the saturated rock modulus K in S02sAnd musThe expression of (2) finds the expression of natural logarithm as:
f(m)＝ln(Ks),g(m)＝ln(μs),h(m)＝ln(ρs)
in the formula: the index m denotes the matrix parameter, s denotes the saturation rock parameter, f denotes the fluid parameter, m denotes the fluid volume modulus K, the rock porosity φfShale content eta and effective pressure PeThe vectors of the components.
Specifically, the reference point m is selected in S020Obtaining a multivariate function expression after Taylor expansion as follows:
Figure BDA0003048132400000091
Figure BDA0003048132400000092
Figure BDA0003048132400000093
specifically, the jacobian matrix in S02 is represented as:
Figure BDA0003048132400000094
specifically, the reflection coefficient R is substituted in S03ppThe approximate equation of (a) is:
Figure BDA0003048132400000101
wherein m is a model parameter vector, theta is an incident angle, t is a corresponding partial derivative parameter, J represents a Jacobian matrix, and the method is simplified to obtain:
Figure BDA0003048132400000102
wherein Kf,PePhi, eta and rho respectively represent the bulk modulus, effective pressure, porosity, shale content and density of the fluid, A, B is an empirical parameter obtained according to the characteristics of a work area, and gamma is the ratio of transverse wave velocity and longitudinal wave velocity. A. the1,A2,A3,A4The reflectance coefficients, respectively, fluid bulk modulus, effective pressure, porosity, shale content, density, are related to the angle of incidence.
Referring to fig. 2 and fig. 3, the examination of the effective pressure value curve of the reservoir obtained in S08 can be detected by the measured well curve value near the well-crossing profile, and it can be seen that the inversion result of a single well is consistent with the variation trend of the measured data, and the value is very similar, and the effective pressure value obtained through inversion prediction is better matched with the measured well curve value near the target layer of the well-crossing profile, thus proving the effectiveness of the method.
The working principle is as follows: synthesizing seismic records by matching seismic wavelets with a reflection coefficient equation, calculating posterior probability by using a Bayesian formula according to reservoir parameters under actual seismic records and differences of reservoir parameters of the synthesized seismic records, calculating a target function by the posterior probability, performing iterative inversion on the target function, and deriving a reflection coefficient approximation equation reflecting the influence of effective pressure on reservoir seismic reflection characteristics from the influence of the effective pressure on reservoir elastic parameters based on a related rock physics theory so as to complete the prediction of effective pressure.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the equivalent replacement or change according to the technical solution and the modified concept of the present invention should be covered by the scope of the present invention.

Claims (10)

1. A reservoir effective pressure prestack inversion prediction method based on a rock physics theory is characterized by comprising the following steps:
s01, firstly, establishing a rock physical model, regarding the rock as a mixture of a sandstone part (representing that the mineral is quartz) and a argillaceous part (representing that the mineral is clay mineral), and calculating the matrix modulus K of the rock by using a V-R-H average according to the content of the logging argillaceousmAnd mumThen through KmAnd mumCalculating the saturated rock modulus KsAnd musAnd by the matrix density ρ of the rockmCalculating the density ρ of saturated rockss；
S02 modulus of saturation rocksAnd musThe expression (c) is used for solving the natural logarithm, and then a reference point m is selected0Performing Taylor expansion to obtain a multivariate function expression, and then expressing the multivariate function by using a Jacobian matrix;
s03, calculating corresponding partial derivatives in the Jacobian matrix in S02, and substituting the partial derivatives into the reflection coefficient RppThe approximation equation of (2) is simplified to obtain a reflection coefficient equation;
s04, substituting the seismic wavelet into a reflection coefficient equation to synthesize a seismic record;
s05, comparing the actual seismic record with the synthetic seismic record in S04, and calculating posterior probability by using a Bayesian formula according to the difference of reservoir parameters under the actual seismic record and reservoir parameters of the synthetic seismic record;
s06, obtaining a target function according to the posterior probability result in the S05;
s07, repeating the steps S04-S06 on the target function in the S06, performing iterative inversion, and deducing a reflection coefficient approximation equation reflecting the influence of effective pressure on the seismic reflection characteristics of the reservoir;
and S08, performing inversion prediction by using the reflection coefficient approximation equation obtained in the S07 to obtain an effective pressure value curve of the reservoir.
2. The method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: the rock matrix modulus K in S01mAnd mumThe calculation formula of (2) is as follows:
Km＝(1-Vsh)Kquartz+VshKsh
μm＝(1-Vsh)μquartz+Vshμsh。
3. the method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: saturated rock modulus K in S01sP for introducing effective pressure in the calculating stepeInfluence, according to a linear approximation, the pore space stiffness K is calculated from the effective pressureφAnd bulk modulus K of matrixmWherein the values of the parameters a and B are related to the lithology characteristics of the work area:
Figure FDA0003048132390000021
after introduction of the influence of effective pressure KsThe calculation formula of (2) is as follows:
Figure FDA0003048132390000022
Figure FDA0003048132390000023
4. the method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: the musThe calculation formula of (2) is as follows:
μs＝μd＝μm(1-φ)q≈μm(1-q·φ)
in the formula: q is a constant related to the pore aspect ratio, KfIs the bulk modulus of the pore fluid,. phi.s,μdThe shear modulus of saturated rock and dry rock skeletons, respectively.
5. The method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: the matrix density ρ of the rock in S01mThe calculation formula of (2) is as follows:
ρm＝ρquartz(1-Vsh)+ρshVsh
in the formula: density of quartz ρquartzAnd density of the sludge rhoshTaking an empirical value;
p in the S01sThe calculation formula of (2) is as follows:
ρs＝φρf+(1-φ)ρm
in the formula: rhofAnd ρmThe density of the pore fluid and the rock matrix, respectively.
6. The method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: saturated rock modulus K in S02sAnd musThe expression of (2) finds the expression of natural logarithm as:
f(m)＝ln(Ks),g(m)＝ln(μs),h(m)＝ln(ρs)
in the formula: the index m denotes the matrix parameter, s denotes the saturation rock parameter, f denotes the fluid parameter, m denotes the fluid volume modulus K, the rock porosity φfShale content eta and effective pressure PeThe vectors of the components.
7. The method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: selecting a reference point m in the S020Obtaining a multivariate function expression after Taylor expansion as follows:
Figure FDA0003048132390000031
Figure FDA0003048132390000032
Figure FDA0003048132390000033
8. the method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: the jacobian matrix in S02 is represented as:
Figure FDA0003048132390000034
9. the method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: substituting the reflection coefficient R into the S03ppThe approximate equation of (a) is:
Figure FDA0003048132390000041
wherein m is a model parameter vector, theta is an incident angle, t is a corresponding partial derivative parameter, J represents a Jacobian matrix, and the method is simplified to obtain:
Figure FDA0003048132390000042
wherein Kf,PePhi, eta and rho respectively represent the bulk modulus, effective pressure, porosity, shale content and density of the fluid, A, B is an empirical parameter obtained according to the characteristics of a work area, and gamma is the ratio of transverse wave velocity and longitudinal wave velocity. A. the1,A2,A3,A4The reflectance coefficients, respectively, fluid bulk modulus, effective pressure, porosity, shale content, density, are related to the angle of incidence.
10. The method for predicting the effective pressure prestack inversion of the reservoir based on the petrophysical theory according to claim 1, wherein the method comprises the following steps: the verification of the effective pressure value curve of the reservoir obtained in S08 can be detected by the well curve measured values near the well profile.
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