Anisotropy characterization method based on improved Christoffel equation

Abstract

The invention provides an anisotropy characterization method based on an improved Christoffel equation, and belongs to the technical field of oil and gas field development. The method comprises the following steps: establishing a Zoeppritz equation precision analysis model under a complex anisotropy theory suitable for a compact conglomerate oil reservoir in a to-be-researched area; establishing an influence model of anisotropy on elastic parameters and an influence model of the elastic parameters and rock density on reflection coefficients; establishing an anisotropic medium phase velocity equation according to a Christoffel equation; based on the shear modulus and density change, converting an anisotropic medium phase velocity equation from a disturbance coefficient form into a reflectivity term form, and characterizing the anisotropy of the anisotropic medium by using the anisotropic medium phase velocity equation in the reflectivity term form. The method is high in prediction precision, and is higher in prediction precision especially under the condition of a small incident angle.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field development, and in particular to an anisotropy characterization method based on an improved Christoffel equation. Background Art

[0002] A large amount of practical experience and theoretical research have shown that the existence of anisotropy in underground media in conglomerate reservoir development is relatively widespread. The real underground medium is not uniform and isotropic, but inhomogeneous and anisotropic. Entering the 21st century, the demand for energy is increasing, the exploration situation is becoming more and more complicated, the difficulty of oil and gas exploration is becoming more and more difficult, and the accuracy requirements for seismic wave transmission data are becoming higher. This makes the description of the earth's medium closer to the real situation, and also makes the study of anisotropy more forward-looking and challenging.

[0003] In the past AVO (Amplitude variation with offset) analysis, the assumption was that the medium was isotropic. However, in reality, the earth's medium is widely anisotropic. The anisotropy of the medium refers to the differences in the physical properties of the medium in all directions. During the propagation of seismic waves in anisotropic media, the propagation velocity is affected by the propagation direction, and the phase velocity is inconsistent with the group velocity. Shear waves will also split. In this case, if it is still assumed that the underground medium is isotropic, it will lead to errors in velocity analysis, resulting in larger errors in time-to-depth conversion. Therefore, how to evaluate the seismic imaging effects of each production well under different exploration methods, find problems, take targeted adjustment methods and countermeasures, and then improve the imaging of reflection interfaces such as fault planes is crucial to the current development of oil and gas fields. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides an anisotropy characterization method based on the improved Christoffel equation, establishes a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area; establishes a model of the influence of anisotropy on elastic parameters and elastic parameters and rock density on reflection coefficient; establishes an anisotropic medium phase velocity equation according to the Christoffel equation; based on the shear modulus and density changes, the anisotropic medium phase velocity equation is converted from the perturbation coefficient form to the reflectivity term form, and the anisotropic medium phase velocity equation in the reflectivity term form is used to characterize the anisotropy of the anisotropic medium. The present invention has high prediction accuracy, especially for the case of small incident angles, the prediction accuracy is higher.

[0005] The present invention provides an anisotropy characterization method based on an improved Christoffel equation, comprising the following steps:

[0006] Step 1: Establish a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area;

[0007] Step 2: Establish the model of the influence of anisotropy on elastic parameters and the influence of elastic parameters and rock density on reflection coefficient;

[0008] Step 3, establishing the anisotropic medium phase velocity equation according to the improved Christoffel equation expressed by the perturbation coefficient;

[0009] Step 4: Based on the shear modulus and density changes, the anisotropic medium phase velocity equation is converted from the perturbation coefficient form to the reflectivity form, and the anisotropy of the anisotropic medium is characterized by the anisotropic medium phase velocity equation in the reflectivity form;

[0010] Among them, in step 4, the phase velocity equation of anisotropic medium in the form of reflectivity is defined as: relative change of shear modulus Relative density change and the relative change of bulk modulus or relative change of Lamé coefficient Function of

[0011] The approximate formula of the phase velocity equation of anisotropic media in the reflectivity form is:

[0012]

[0013]

[0014] in,

[0015] V P , V s , ρ are the average values ​​of longitudinal wave velocity, shear wave velocity and density on both sides of the interface respectively;

[0016] λ, μ, K, are the average values ​​of the Lame coefficient, the average value of the shear modulus, and the average value of the bulk modulus on both sides of the interface, respectively;

[0017] Δλ, Δμ, ΔK, and Δρ are the difference in Lame coefficient, shear modulus, bulk modulus, and density on both sides of the interface, respectively;

[0018] R pp is the reflectivity term;

[0019] λ is the average of the incident and transmission angles.

[0020] Preferably, in step 1, a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, as follows:

[0021] The ideal porous rock is composed of four parts: rock matrix, pore fluid, rock skeleton and saturated rock itself. For porous media, rock matrix refers to the mineral components that constitute the rock, rock skeleton refers to the framework of the rock, and pore fluid refers to gas, oil or water. The essence of studying the porous medium theory is to study the influence of each component of the rock on the rock as a whole. Combined with the work area data of the study area, literature research and evaluation standards are combined to establish the standardization of theoretical parameters and disturbance terms, and establish the precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area.

[0022] Preferably, in step 1, a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, specifically including: based on a uniform isotropic medium, the longitudinal wave velocity V is established using the density ρ, bulk modulus K, shear modulus μ or Lame coefficient λ p and the shear wave velocity V s The Zoeppritz equation representation system is as follows:

[0023]

[0024]

[0025] When the rock is saturated with fluid, due to the influence of the fluid, based on the Biot and Gassmann theory, we get:

[0026] λ sat =λ dry +β 2 M

[0027] K sat =K dry +β 2 M

[0028] μ sat =μ dry

[0029] The fluid term f is added to the above formula as a result of the fluid effect, and the fluid term f = β 2 M;

[0030] The longitudinal wave velocity of the saturated fluid medium is obtained as:

[0031]

[0032] The parameters of the Zoeppritz equation are changed from the longitudinal wave velocity V P , shear wave velocity V S and density ρ are transformed into the fluid term f. By transforming the above equation, the fluid term is expressed in terms of elastic parameters as follows:

[0033]

[0034] Establish a series of standard judgment items to determine the standard Zoeppritz equation representation system;

[0035] in,

[0036]

[0037] K dry , K m and K fl represent the bulk moduli of matrix skeleton, minerals, and fluid, respectively;

[0038] φ is the porosity;

[0039] λ sat is the Lame coefficient of saturated medium;

[0040] λ dry is the Lame coefficient of the drying medium;

[0041] K sat is the bulk modulus of the saturated medium;

[0042] K dry is the bulk modulus of the drying medium;

[0043] K m is the mineral bulk modulus;

[0044] μ sat is the shear modulus of the saturated medium;

[0045] μ dry is the shear modulus of the drying medium;

[0046] It is the longitudinal wave of saturated medium;

[0047] is the ratio of the P-wave velocity to the S-wave velocity of dry rock;

[0048] is the shear modulus of shear waves of saturated medium;

[0049] is the longitudinal wave shear modulus of the saturated medium.

[0050] Preferably, in step three, the matrix elements in the Christoffel matrix are used to represent the longitudinal wave incident on the poroelastic medium in the form of perturbation coefficients, the representation of the Zoeppritz equation is improved to obtain an improved Christoffel equation, and then the anisotropic medium phase velocity equation is established through the improved Christoffel equation.

[0051] Preferably, the anisotropic medium phase velocity equation is established according to the improved Christoffel equation, which specifically includes:

[0052] Assume the Christoffel equation is as follows:

[0053]

[0054] in,

[0055] Γ 12 =Γ 21 , Γ 13 =Γ 31 , Γ 23 =Γ 32 , are symmetric values ​​of the propagation direction vector;

[0056] ρ is the density;

[0057] v is the speed;

[0058] make:

[0059] x=ρV 2

[0060] a=-(Γ 11 +Γ 22 +Γ 33 )

[0061]

[0062]

[0063] Substituting (2) into (1), we obtain:

[0064] x 3 +ax 2 +bx+c=0 (3)

[0065] Among them, a, b, c are intermediate variables;

[0066] Assume there is a set of intermediate variables y, d and q, where x = ya / 3, Substituting the intermediate variables y, d and q into equation (3), we obtain the following equation:

[0067] y 3+dy+q=0 (4); Since d<0, only when When this condition is met, equation (4) obtains real roots, and the real roots of equation (4) are expressed as:

[0068]

[0069] in,

[0070]

[0071] The phase velocity formula of anisotropic media is derived as follows:

[0072] ρv 2 =ya / 3.

[0073] Preferably, in step 4, based on the shear modulus and density change, the anisotropic medium phase velocity equation is converted from a perturbation coefficient form to a reflectivity term form, specifically including:

[0074] The fluid reflectivity term is expressed as a perturbation coefficient in the form of:

[0075]

[0076] Define a series:

[0077] According to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of fluid term, the perturbation coefficient form expression of fluid term is obtained:

[0078]

[0079] Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of shear modulus, the expression of shear modulus perturbation coefficient form is obtained:

[0080]

[0081] Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the density change, the density perturbation coefficient form expression is obtained:

[0082]

[0083]

[0084] The disturbance coefficient is used to represent the ratio of different media such as shear waves and longitudinal waves. The specific expression is as follows:

[0085]

[0086]

[0087]

[0088]

[0089] Substituting the above four proportional equations into the coefficient matrix P, we can obtain the coefficient matrix of each element represented by the perturbation coefficient and the ratio of the longitudinal and transverse wave velocities:

[0090]

[0091] The matrix P is a 4×4 matrix containing 16 elements, each of which can be represented by the elastic parameter V P , V S , ρ and incident angle θ0 are represented;

[0092] in,

[0093] a f is the perturbation coefficient of the fluid term;

[0094] a μ is the perturbation coefficient of the shear modulus;

[0095] a ρ is the perturbation coefficient of density;

[0096] μ1 is the shear modulus of layer 1;

[0097] μ0 is the shear modulus of layer 0;

[0098] ρ1 is the density of layer 1;

[0099] ρ0 is the density of the 0 layer

[0100] Δf is the difference in fluid terms;

[0101] f is the fluid term;

[0102] f1 is the 1st layer fluid term;

[0103] f0 is the 0-layer fluid term;

[0104] Δμ is the difference in shear modulus;

[0105] μ is the shear modulus;

[0106] μ1 is the shear modulus of layer 1;

[0107] μ0 is the shear modulus of layer 0;

[0108] Δρ is the density difference;

[0109] ρ is the density;

[0110] ρ1 is the density of layer 1;

[0111] ρ0 is the 0-layer density;

[0112] is the average value of the shear wave velocity ratio;

[0113] is the average value of the longitudinal wave velocity ratio;

[0114] s0 is medium 0 shear wave;

[0115] s1 is the shear wave of medium 1;

[0116] γ0 is the average value of the ratio of longitudinal and transverse wave velocities;

[0117] (γ0) sat is the average value of the ratio of longitudinal and transverse wave velocities in the saturated medium;

[0118] (γ0) dry is the average value of the ratio of longitudinal and transverse wave velocities of the dry medium;

[0119] α f is the perturbation coefficient of the fluid term;

[0120] is the perturbation coefficient of the 1-layer fluid term;

[0121] is the perturbation coefficient of the 2-layer fluid term.

[0122] Preferably, the perturbation coefficient of the fluid term is represented by the reflectivity of the fluid according to the reflectivity to the anisotropic medium reflection coefficient.

[0123] Preferably, the matrix P is expressed as

[0124]

[0125] Each element in the first row is represented by

[0126] A 11 = -sinθ0,

[0127]

[0128]

[0129]

[0130] Each element in the second row is represented by

[0131] A 21 =[1-sin 2 θ0] 1 / 2 ,

[0132]

[0133]

[0134]

[0135] Each element in the third row is represented by

[0136]

[0137]

[0138]

[0139]

[0140] Each element in the fourth row is represented by

[0141]

[0142]

[0143]

[0144]

[0145] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0146] (1) The present invention adopts the perturbation form of the Christoffel equation, which increases the parameter difference compared with the theoretical equation before the improvement, highlighting the influence of fluid, shear modulus and density on the AVO curve. The error between the first-order approximation formula used in the prior art and the precise expression is increasing, while the second-order and third-order nonlinear approximation formula curves of the present invention can still be well predicted at small angles, which is close to the precise expression. Compared with the prior art, the present invention has a higher accuracy in predicting the elastic parameters of the medium.

[0147] (2) The present invention improves the Christoffel equation through Zoeppritz. The improved Christoffel equation can effectively describe the influence of fluid term, shear modulus and density on it, and effectively distinguish the main influencing variable parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0148] Figure 1 A comparison diagram of the reflection curves of the partial approximate equation and the exact Zoeppritz equation when the difference in parameters on both sides of the interface of an embodiment of the present invention is small (the perturbation coefficient is 0.2);

[0149] Figure 2A comparison diagram of the reflection curves of the partial approximate equation and the exact Zoeppritz equation when the difference in parameters on both sides of the interface of an embodiment of the present invention is small (the perturbation coefficient is 0.4);

[0150] Figure 3 The difference of reflection wave curves under different density media in one embodiment of the present invention;

[0151] Figure 4 (a) in is a μ = 0.2 when the difference in Δρ / ρ value affects the change of reflection coefficient with incident angle, (b) is a μ = 0.4 when the difference in Δρ / ρ value affects the change of reflection coefficient with incident angle, (c) is a μ = 0.6 when the difference in Δρ / ρ value affects the change of reflection coefficient with incident angle, (d) is a μ =0.8 when the difference in Δρ / ρ value affects the change of the reflection coefficient with the incident angle; in the figure, the mark 1 represents the first-order approximation, 2 represents the second-order approximation, 3 represents the third-order approximation, and 4 represents the exact approximation;

[0152] Figure 5 (a) in is a ρ = 0.2 when the difference in Δf / f value affects the change of reflection coefficient with incident angle, (b) is a ρ =0.4 when the difference in Δρ / ρ value affects the change of reflection coefficient with incident angle, (c) is a ρ = 0.6 when the difference in Δρ / ρ value affects the change of reflection coefficient with incident angle, (d) is a ρ =0.6 when the difference in Δρ / ρ value affects the change of reflection coefficient with incident angle; in the figure, mark 1 represents the first-order approximation, 2 represents the second-order approximation, 3 represents the third-order approximation, and 4 represents the exact approximation;

[0153] Figure 6 (a) in is a f = 0.2 when the difference in Δμ / μ value affects the change of reflection coefficient with incident angle, (b) is a f = 0.4 when the difference in Δμ / μ value affects the change of reflection coefficient with incident angle, (c) is a f = 0.6 when the difference in Δμ / μ value affects the change of reflection coefficient with incident angle, (d) is a f =0.8 when the difference in Δμ / μ value affects the change of the reflection coefficient with the incident angle; in the figure, the mark 1 represents the first-order approximation, 2 represents the second-order approximation, 3 represents the third-order approximation, and 4 represents the exact approximation;

[0154] Figure 7The flowchart of the anisotropy characterization method based on the improved Christoffel equation according to one embodiment of the present invention. DETAILED DESCRIPTION

[0155] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings.

[0156] The present invention provides an anisotropy characterization method based on an improved Christoffel equation, comprising the following steps:

[0157] Step 1: Establish a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area;

[0158] Step 2: Establish the model of the influence of anisotropy on elastic parameters and the influence of elastic parameters and rock density on reflection coefficient;

[0159] Step 3, establishing the anisotropic medium phase velocity equation according to the improved Christoffel equation expressed by the perturbation coefficient;

[0160] Step 4: Based on the shear modulus and density changes, the anisotropic medium phase velocity equation is converted from the perturbation coefficient form to the reflectivity form, and the anisotropy of the anisotropic medium is characterized by the anisotropic medium phase velocity equation in the reflectivity form;

[0161] Among them, in step 4, the phase velocity equation of anisotropic medium in the form of reflectivity is defined as: relative change of shear modulus Relative density change and the relative change of bulk modulus or relative change of Lamé coefficient Function of

[0162] The approximate formula of the phase velocity equation of anisotropic media in the reflectivity form is:

[0163]

[0164]

[0165] in,

[0166] V P , V s , ρ are the average values ​​of longitudinal wave velocity, shear wave velocity and density on both sides of the interface respectively;

[0167] λ, μ, K, are the average values ​​of the Lame coefficient, the average value of the shear modulus, and the average value of the bulk modulus on both sides of the interface, respectively;

[0168] Δλ, Δμ, ΔK, and Δρ are the difference in Lame coefficient, shear modulus, bulk modulus, and density on both sides of the interface, respectively;

[0169] R pp is the reflectivity term;

[0170] θ is the average of the incident and transmitted angles.

[0171] According to a specific implementation scheme of the present invention, in step 1, a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, as follows:

[0172] The ideal porous rock is composed of four parts: rock matrix, pore fluid, rock skeleton and saturated rock itself. For porous media, rock matrix refers to the mineral components that constitute the rock, rock skeleton refers to the framework of the rock, and pore fluid refers to gas, oil or water. The essence of studying the porous medium theory is to study the influence of each component of the rock on the rock as a whole. Combined with the work area data of the study area, literature research and evaluation standards are combined to establish the standardization of theoretical parameters and disturbance terms, and establish the precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area.

[0173] According to a specific implementation scheme of the present invention, in step 1, a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, specifically including: based on a uniform isotropic medium, using density ρ, bulk modulus K, shear modulus μ or Lame coefficient λ to establish the longitudinal wave velocity V p and the shear wave velocity V s The Zoeppritz equation representation system is as follows:

[0174]

[0175]

[0176] When the rock is saturated with fluid, due to the influence of the fluid, based on the Biot and Gassmann theory, we get:

[0177] λ sat =λ dry +β 2 M

[0178] K sat =K dry +β 2 M

[0179] μ sat =μ dry

[0180] The fluid term f is added to the above formula as a result of the fluid effect, and the fluid term f = β 2 M;

[0181] The longitudinal wave velocity of the saturated fluid medium is obtained as:

[0182]

[0183] The parameters of the Zoeppritz equation are changed from the longitudinal wave velocity V P , shear wave velocity V S and density ρ are transformed into the fluid term f. By transforming the above equation, the fluid term is expressed in terms of elastic parameters as follows:

[0184]

[0185] Establish a series of standard judgment items to determine the standard Zoeppritz equation representation system;

[0186] in,

[0187]

[0188] K dry , K m and K fl represent the bulk moduli of matrix skeleton, minerals, and fluid, respectively;

[0189] φ is the porosity;

[0190] λ sat is the Lame coefficient of saturated medium;

[0191] λ dry is the Lame coefficient of the drying medium;

[0192] K sat is the bulk modulus of the saturated medium;

[0193] K dry is the bulk modulus of the drying medium;

[0194] K m is the mineral bulk modulus;

[0195] μ sat is the shear modulus of the saturated medium;

[0196] μ dry is the shear modulus of the drying medium;

[0197] It is the longitudinal wave of saturated medium;

[0198] is the ratio of the P-wave velocity to the S-wave velocity of dry rock;

[0199] is the shear modulus of shear waves of saturated medium;

[0200] is the longitudinal wave shear modulus of the saturated medium.

[0201] According to a specific embodiment of the present invention, in step three, the matrix elements in the Christoffel matrix are used to represent the longitudinal wave incident on the poroelastic medium in the form of perturbation coefficients, the representation of the Zoeppritz equation is improved to obtain an improved Christoffel equation, and then the anisotropic medium phase velocity equation is established through the improved Christoffel equation.

[0202] According to a specific embodiment of the present invention, the anisotropic medium phase velocity equation is established according to the improved Christoffel equation, which specifically includes:

[0203] Assume the Christoffel equation is as follows:

[0204]

[0205] in,

[0206] Γ 12 =Γ 21 , Γ 13 =Γ 31 , Γ 23 =Γ 32 , are symmetric values ​​of the propagation direction vector;

[0207] ρ is the density;

[0208] v is the speed;

[0209] make:

[0210] x=ρV 2

[0211] a=-(Γ 11 +Γ 22 +Γ 33 )

[0212]

[0213]

[0214] Substituting (2) into (1), we obtain:

[0215] x 3 +ax 2 +bx+c=0 (3)

[0216] Among them, a, b, c are intermediate variables;

[0217] Assume there is a set of intermediate variables y, d and q, where x = ya / 3, Substituting the intermediate variables y, d and q into equation (3), we obtain the following equation:

[0218] y 3 +dy+q=0 (4);

[0219] Since d < 0, only when When this condition is met, equation (4) obtains real roots, and the real roots of equation (4) are expressed as:

[0220]

[0221] in,

[0222]

[0223] The phase velocity formula of anisotropic media is derived as follows:

[0224] ρv 2 =ya / 3.

[0225] According to a specific embodiment of the present invention, in step 4, based on the shear modulus and density changes, the anisotropic medium phase velocity equation is converted from the perturbation coefficient form to the reflectivity term form, specifically including:

[0226] The fluid reflectivity term is expressed as a perturbation coefficient in the form of:

[0227]

[0228] Define a series:

[0229] According to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of fluid term, the perturbation coefficient form expression of fluid term is obtained:

[0230]

[0231] Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of shear modulus, the expression of shear modulus perturbation coefficient form is obtained:

[0232]

[0233] Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the density change, the density perturbation coefficient form expression is obtained:

[0234]

[0235]

[0236] The disturbance coefficient is used to represent the ratio of different media such as transverse waves and longitudinal waves. The specific expression is as follows:

[0237]

[0238]

[0239]

[0240]

[0241] Substituting the above four proportional equations into the coefficient matrix P, we can obtain the coefficient matrix of each element represented by the perturbation coefficient and the ratio of the longitudinal and transverse wave velocities:

[0242]

[0243] The matrix P is a 4×4 matrix containing 16 elements, each of which can be represented by the elastic parameter V P , V S , ρ and incident angle θ0 are represented;

[0244] in,

[0245] a f is the perturbation coefficient of the fluid term;

[0246] a μ is the perturbation coefficient of the shear modulus;

[0247] a ρ is the perturbation coefficient of density;

[0248] μ1 is the shear modulus of layer 1;

[0249] μ0 is the shear modulus of layer 0;

[0250] ρ1 is the density of layer 1;

[0251] ρ0 is the density of the 0 layer

[0252] Δf is the difference in fluid terms;

[0253] f is the fluid term;

[0254] f1 is the 1st layer fluid term;

[0255] f0 is the 0-layer fluid term;

[0256] Δμ is the difference in shear modulus;

[0257] μ is the shear modulus;

[0258] μ1 is the shear modulus of layer 1;

[0259] μ0 is the shear modulus of layer 0;

[0260] Δρ is the density difference;

[0261] ρ is the density;

[0262] ρ1 is the density of layer 1;

[0263] ρ0 is the 0-layer density;

[0264] is the average value of the shear wave velocity ratio;

[0265] is the average value of the longitudinal wave velocity ratio;

[0266] s0 is medium 0 shear wave;

[0267] s1 is the shear wave of medium 1;

[0268] γ0 is the average value of the ratio of longitudinal and transverse wave velocities;

[0269] (γ0) sat is the average value of the ratio of longitudinal and transverse wave velocities in the saturated medium;

[0270] (γ0) dry is the average value of the ratio of longitudinal and transverse wave velocities of the dry medium;

[0271] a f is the perturbation coefficient of the fluid term;

[0272] is the perturbation coefficient of the 1-layer fluid term;

[0273] is the perturbation coefficient of the 2-layer fluid term.

[0274] According to a specific embodiment of the present invention, the perturbation coefficient of the fluid term is represented by the reflectivity of the fluid according to the reflectivity to the anisotropic medium reflection coefficient.

[0275] According to a specific embodiment of the present invention, the matrix P is expressed as

[0276]

[0277] Each element in the first row is represented by

[0278] A 11 = -sinθ0,

[0279]

[0280]

[0281]

[0282] Each element in the second row is represented by

[0283] A 21 =[1-sin 2 θ0] 1 / 2 ,

[0284]

[0285]

[0286]

[0287] Each element in the third row is represented by

[0288]

[0289]

[0290]

[0291]

[0292] Each element in the fourth row is represented by

[0293]

[0294]

[0295]

[0296]

[0297] Example 1

[0298] According to a specific embodiment of the present invention, the anisotropy characterization method based on the improved Christoffel equation of the present invention is described in detail below.

[0299] The present invention provides an anisotropy characterization method based on an improved Christoffel equation, comprising the following steps:

[0300] Step 1: Establish a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area;

[0301] Step 2: Establish the model of the influence of anisotropy on elastic parameters and the influence of elastic parameters and rock density on reflection coefficient;

[0302] Step 3, establishing the anisotropic medium phase velocity equation according to the improved Christoffel equation expressed by the perturbation coefficient;

[0303] Step 4: Based on the shear modulus and density changes, the anisotropic medium phase velocity equation is converted from the perturbation coefficient form to the reflectivity form, and the anisotropy of the anisotropic medium is characterized by the anisotropic medium phase velocity equation in the reflectivity form;

[0304] Among them, in step 4, the phase velocity equation of anisotropic medium in the form of reflectivity is defined as: relative change of shear modulus Relative density change and the relative change of bulk modulus or relative change of Lamé coefficient Function of

[0305] The approximate formula of the phase velocity equation of anisotropic media in the reflectivity form is:

[0306]

[0307]

[0308] in,

[0309] V P , V s , ρ are the average values ​​of longitudinal wave velocity, shear wave velocity and density on both sides of the interface respectively;

[0310] λ, μ, K, are the average values ​​of the Lame coefficient, the average value of the shear modulus, and the average value of the bulk modulus on both sides of the interface, respectively;

[0311] Δλ, Δμ, ΔK, and Δρ are the difference in Lame coefficient, shear modulus, bulk modulus, and density on both sides of the interface, respectively;

[0312] R pp is the reflectivity term;

[0313] θ is the average of the incident and transmitted angles.

[0314] Among them, in step 1, the accuracy analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, as follows:

[0315] The ideal porous rock is composed of four parts: rock matrix, pore fluid, rock skeleton and saturated rock itself. For porous media, rock matrix refers to the mineral components that constitute the rock, rock skeleton refers to the framework of the rock, and pore fluid refers to gas, oil or water. The essence of studying the porous medium theory is to study the influence of each component of the rock on the rock as a whole. Combined with the work area data of the study area, literature research and evaluation standards are combined to establish the standardization of theoretical parameters and disturbance terms, and establish the precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area.

[0316] Among them, in step 1, the precision analysis model of Zoeppritz equation under complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, which specifically includes: based on uniform isotropic medium, the density ρ, bulk modulus K, shear modulus μ or Lame coefficient λ is used to establish the longitudinal wave velocity V p and the shear wave velocity V s The Zoeppritz equation representation system is as follows:

[0317]

[0318]

[0319] When the rock is saturated with fluid, due to the influence of the fluid, based on the Biot and Gassmann theory, we get:

[0320] λ sat =λ dry +β 2 M

[0321] K sat =K dry +β 2 M

[0322] μ sat =μ dry

[0323] The fluid term f is added to the above formula as a result of the fluid effect, and the fluid term f = β 2 M;

[0324] The longitudinal wave velocity of the saturated fluid medium is obtained as:

[0325]

[0326] The parameters of the Zoeppritz equation are changed from the longitudinal wave velocity V P , shear wave velocity V S and density ρ are transformed into the fluid term f. By transforming the above equation, the fluid term is expressed in terms of elastic parameters as follows:

[0327]

[0328] Establish a series of standard judgment items to determine the standard Zoeppritz equation representation system;

[0329] in,

[0330]

[0331] K dry , K m and K fl represent the bulk moduli of matrix skeleton, minerals, and fluid, respectively;

[0332] φ is the porosity;

[0333] λ sat is the Lame coefficient of saturated medium;

[0334] λ dry is the Lame coefficient of the drying medium;

[0335] K sat is the bulk modulus of the saturated medium;

[0336] K dry is the bulk modulus of the drying medium;

[0337] K m is the mineral bulk modulus;

[0338] μ sat is the shear modulus of the saturated medium;

[0339] μ dry is the shear modulus of the drying medium;

[0340] It is the longitudinal wave of saturated medium;

[0341] is the ratio of the P-wave velocity to the S-wave velocity of dry rock;

[0342] is the shear modulus of shear waves of saturated medium;

[0343] is the longitudinal wave shear modulus of the saturated medium.

[0344] Among them, in step three, the matrix elements in the Christoffel matrix are used to represent the longitudinal wave incident on the poroelastic medium in the form of perturbation coefficients, the representation of the Zoeppritz equation is improved, and the improved Christoffel equation is obtained. Then, the anisotropic medium phase velocity equation is established through the improved Christoffel equation.

[0345] Among them, the anisotropic medium phase velocity equation is established according to the improved Christoffel equation, which specifically includes:

[0346] Assume the Christoffel equation is as follows:

[0347]

[0348] in,

[0349] Γ 12 =Γ 21 , Γ 13 =Γ 31 , Γ 23 =Γ 32 , are symmetric values ​​of the propagation direction vector;

[0350] ρ is the density;

[0351] v is the speed;

[0352] make:

[0353] x=ρV 2

[0354] a=-(Γ 11 +Γ 22 +Γ 33 )

[0355]

[0356]

[0357] Substituting (2) into (1), we obtain:

[0358] x 3 +ax 2 +bx+c=0 (3)

[0359] Among them, a, b, c are intermediate variables;

[0360] Assume there is a set of intermediate variables y, d and q, where x = ya / 3, Substituting the intermediate variables y, d and q into equation (3), we obtain the following equation:

[0361] y 3 +dy+q=0 (4);

[0362] Since d < 0, only when When this condition is met, equation (4) obtains real roots, and the real roots of equation (4) are expressed as:

[0363]

[0364] in,

[0365]

[0366] The phase velocity formula of anisotropic media is derived as follows:

[0367] ρv 2 =ya / 3.

[0368] Among them, in step 4, based on the shear modulus and density changes, the phase velocity equation of the anisotropic medium is converted from the perturbation coefficient form to the reflectivity term form, specifically including:

[0369] The fluid reflectivity term is expressed as a perturbation coefficient in the form of:

[0370]

[0371] Define a series:

[0372] According to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of fluid term, the perturbation coefficient form expression of fluid term is obtained:

[0373]

[0374] Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of shear modulus, the expression of shear modulus perturbation coefficient form is obtained:

[0375]

[0376] Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the density change, the density perturbation coefficient form expression is obtained:

[0377]

[0378]

[0379] The disturbance coefficient is used to represent the ratio of different media such as shear waves and longitudinal waves. The specific expression is as follows:

[0380]

[0381]

[0382]

[0383]

[0384] Substituting the above four proportional equations into the coefficient matrix P, we can obtain the coefficient matrix of each element represented by the perturbation coefficient and the ratio of the longitudinal and transverse wave velocities:

[0385]

[0386] The matrix P is a 4×4 matrix containing 16 elements, each of which can be represented by the elastic parameter V P , V S , ρ and incident angle θ0 are represented;

[0387] in,

[0388] a f is the perturbation coefficient of the fluid term;

[0389] a μ is the perturbation coefficient of the shear modulus;

[0390] a ρ is the perturbation coefficient of density;

[0391] μ1 is the shear modulus of layer 1;

[0392] μ0 is the shear modulus of layer 0;

[0393] ρ1 is the density of layer 1;

[0394] ρ0 is the density of the 0 layer

[0395] Δf is the difference in fluid terms;

[0396] f is the fluid term;

[0397] f1 is the 1st layer fluid term;

[0398] f0 is the 0-layer fluid term;

[0399] Δμ is the difference in shear modulus;

[0400] μ is the shear modulus;

[0401] μ1 is the shear modulus of layer 1;

[0402] μ0 is the shear modulus of layer 0;

[0403] Δρ is the density difference;

[0404] ρ is the density;

[0405] ρ1 is the density of layer 1;

[0406] ρ0 is the 0-layer density;

[0407] is the average value of the shear wave velocity ratio;

[0408] is the average value of the longitudinal wave velocity ratio;

[0409] s0 is medium 0 shear wave;

[0410] s1 is the shear wave of medium 1;

[0411] γ0 is the average value of the ratio of longitudinal and transverse wave velocities;

[0412] (γ0) sat is the average value of the ratio of longitudinal and transverse wave velocities in the saturated medium;

[0413] (γ0) dry is the average value of the ratio of longitudinal and transverse wave velocities of the dry medium;

[0414] α f is the perturbation coefficient of the fluid term;

[0415] is the perturbation coefficient of the 1-layer fluid term;

[0416] is the perturbation coefficient of the 2-layer fluid term.

[0417] Among them, according to the reflectivity to the anisotropic medium reflection coefficient, the perturbation coefficient of the fluid term is expressed by the reflectivity of the fluid.

[0418] Among them, the matrix P is expressed as

[0419]

[0420] Each element in the first row is represented by

[0421] A 11 = -sinθ0,

[0422]

[0423]

[0424]

[0425] Each element in the second row is represented by

[0426] A 21 =[1-sin 2 θ0] 1 / 2 ,

[0427]

[0428]

[0429]

[0430] Each element in the third row is represented by

[0431]

[0432]

[0433]

[0434]

[0435] Each element in the fourth row is represented by

[0436]

[0437]

[0438]

[0439]

[0440] The influence of the difference of disturbance terms on the Zoeppritz equation and its Shuey approximation, the model parameters are designed as shown in Table 1, where the model parameters refer to the upper medium and the lower layer Poisson's ratio has 5 cases, 4 of which are smaller than the lower layer Poisson's ratio. Model parameters, use Zoeppritz equation and Shuey approximation to calculate the longitudinal wave reflection coefficient curve respectively.

[0441] Table 1. Model parameters

[0442]

[0443] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for characterizing anisotropy based on the improved Christoffel equation, characterized in that: The steps include: Step 1: Establish a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area; Step 2: Establish the model of the influence of anisotropy on elastic parameters and the influence of elastic parameters and rock density on reflection coefficient; Step 3, establishing the anisotropic medium phase velocity equation according to the improved Christoffel equation expressed by the perturbation coefficient; Step 4: Based on the shear modulus and density changes, the anisotropic medium phase velocity equation is converted from the perturbation coefficient form to the reflectivity form, and the anisotropy of the anisotropic medium is characterized by the anisotropic medium phase velocity equation in the reflectivity form; Among them, in step 4, the phase velocity equation of anisotropic medium in the form of reflectivity is defined as: relative change of shear modulus Relative density change and the relative change of bulk modulus or relative change of Lamé coefficient Function of The approximate formula of the phase velocity equation of anisotropic media in the reflectivity form is: in, V P , V s , ρ are the average values ​​of longitudinal wave velocity, shear wave velocity and density on both sides of the interface respectively; λ, μ, K, are the average values ​​of the Lame coefficient, the average value of the shear modulus, and the average value of the bulk modulus on both sides of the interface, respectively; Δλ, Δμ, ΔK, and Δρ are the difference in Lame coefficient, shear modulus, bulk modulus, and density on both sides of the interface, respectively; R pp is the reflectivity term; θ is the average of the incident and transmitted angles.

2. The anisotropy characterization method based on the improved Christoffel equation according to claim 1, characterized in that: In step 1, a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, as follows: The ideal porous rock is composed of four parts: rock matrix, pore fluid, rock skeleton and saturated rock itself. For porous media, rock matrix refers to the mineral components that constitute the rock, rock skeleton refers to the framework of the rock, and pore fluid refers to gas, oil or water. The essence of studying the porous medium theory is to study the influence of each component of the rock on the rock as a whole. Combined with the work area data of the study area, literature research and evaluation standards are combined to establish the standardization of theoretical parameters and disturbance terms, and establish the precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area.

3. The anisotropy characterization method based on the improved Christoffel equation according to claim 2, characterized in that: In step 1, a precision analysis model of the Zoeppritz equation under the complex anisotropy theory applicable to the tight conglomerate reservoir in the study area is established, which specifically includes: based on a uniform isotropic medium, the density ρ, bulk modulus K, shear modulus μ or Lame coefficient λ is used to establish the longitudinal wave velocity V p and the shear wave velocity V s The Zoeppritz equation representation system is as follows: When the rock is saturated with fluid, due to the influence of the fluid, based on the Biot and Gassmann theory, we get: l sat =λ dry +b 2 M K sat =K dry +b 2 M m sat =μ dry The fluid term f is added to the above formula as a result of the fluid effect, and the fluid term f = β 2 M; The longitudinal wave velocity of the saturated fluid medium is obtained as: The parameters of the Zoeppritz equation are changed from the longitudinal wave velocity V P , shear wave velocity V S and density ρ are transformed into the fluid term f. By transforming the above equation, the fluid term is expressed in terms of elastic parameters as follows: Establish a series of standard judgment items to determine the standard Zoeppritz equation representation system; in, K dry , K m and K fl represent the bulk moduli of matrix skeleton, minerals, and fluid, respectively; φ is the porosity; λ sat is the Lame coefficient of saturated medium; K dry is the Lame coefficient of the drying medium; K sat is the bulk modulus of the saturated medium; K dry is the bulk modulus of the drying medium; K m is the mineral bulk modulus; μ sat is the shear modulus of the saturated medium; μ dry is the shear modulus of the drying medium; It is the longitudinal wave of saturated medium; is the ratio of the P-wave velocity to the S-wave velocity of dry rock; is the shear modulus of shear waves of saturated medium; is the longitudinal wave shear modulus of the saturated medium.

4. The anisotropy characterization method based on the improved Christoffel equation according to claim 1, characterized in that: In step three, the matrix elements in the Christoffel matrix are used to represent the longitudinal wave incident on the poroelastic medium in the form of perturbation coefficients, and the representation of the Zoeppritz equation is improved to obtain the improved Christoffel equation. The anisotropic medium phase velocity equation is then established through the improved Christoffel equation.

5. The anisotropy characterization method based on the improved Christoffel equation according to claim 4, characterized in that: The phase velocity equation of anisotropic media is established based on the improved Christoffel equation, which includes: Assume that the Christoffel equation is as follows: in, Γ 12 =Γ 21 , Γ 13 =Γ 31 , Γ 23 =Γ 32 , are symmetric values ​​of the propagation direction vector; ρ is the density; v is the speed; make: x=ρv 2 α=-(Γ 11 +C 22 +C 33 ) Substituting (2) into (1), we obtain: x 3 +ax 2 +bx+c=0 (3) Among them, a, b, c are intermediate variables; Assume there is a set of intermediate variables y, d and q, where x = ya / 3, Substituting the intermediate variables y, d and q into equation (3), we obtain the following equation: the 3 +dy+q=0 (4)? Since d < 0, only when When this condition is met, equation (4) obtains real roots, and the real roots of equation (4) are expressed as: in, The phase velocity formula of anisotropic media is derived as follows: pv 2 =ya / 3.

6. The anisotropy characterization method based on the improved Christoffel equation according to claim 1, characterized in that: In step 4, based on the shear modulus and density changes, the phase velocity equation of the anisotropic medium is converted from the perturbation coefficient form to the reflectivity term form, specifically including: The fluid reflectivity term is expressed as a perturbation coefficient in the form of: Define a series: According to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of fluid term, the perturbation coefficient form expression of fluid term is obtained: Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the change of shear modulus, the expression of shear modulus perturbation coefficient form is obtained: Similarly, according to the definition of reflectivity form and the conversion method from reflectivity form to perturbation coefficient form, based on the density change, the density perturbation coefficient form expression is obtained: The disturbance coefficient is used to represent the ratio of different media such as shear waves and longitudinal waves. The specific expression is as follows: Substituting the above four proportional equations into the coefficient matrix P, we can obtain the coefficient matrix of each element represented by the perturbation coefficient and the ratio of the longitudinal and transverse wave velocities: The matrix P is a 4×4 matrix containing 16 elements, each of which can be represented by the elastic parameter V P , V S , ρ and incident angle θ0 are represented; in, a f is the perturbation coefficient of the fluid term; a μ is the perturbation coefficient of the shear modulus; a ρ is the perturbation coefficient of density; μ1 is the shear modulus of layer 1; μ0 is the shear modulus of layer 0; ρ1 is the density of layer 1; ρ0 is the density of the 0 layer Δf is the difference in fluid terms; f is the fluid term; f1 is the 1st layer fluid term; f0 is the 0-layer fluid term; Δμ is the difference in shear modulus; μ is the shear modulus; μ1 is the shear modulus of layer 1; μ0 is the shear modulus of layer 0; Δρ is the density difference; ρ is the density; ρ1 is the density of layer 1; ρ0 is the 0-layer density; is the average value of the shear wave velocity ratio; is the average value of the longitudinal wave velocity ratio; s0 is medium 0 shear wave; s1 is the shear wave of medium 1; γ0 is the average value of the ratio of longitudinal and transverse wave velocities; (γ0) sat is the average value of the ratio of longitudinal and transverse wave velocities in the saturated medium; (γ0) dry is the average value of the ratio of longitudinal and transverse wave velocities of the dry medium; a f is the perturbation coefficient of the fluid term; is the perturbation coefficient of the 1-layer fluid term; is the perturbation coefficient of the 2-layer fluid term.

7. The anisotropy characterization method based on the improved Christoffel equation according to claim 6, characterized in that: According to the reflectivity to anisotropic medium reflection coefficient, the perturbation coefficient of the fluid term is expressed by the reflectivity of the fluid.

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