CN104570084A - Cross-scale seismic rock physical attenuation model and method for predicating attenuation and dispersion - Google Patents

Abstract

The invention discloses a cross-scale seismic rock physical attenuation model and a method for predicating attenuation and dispersion. The model simulates characteristics of underground oil-gas-bearing double-phase medium, and adopts the construction structure that the influence of a jet flow of a micro-scale fracture in a BISQ elastic wave prorogation theory is introduced under the framework of a macro-scale Biot double-phase medium wave prorogation theory; a periodic stratification White module under mesoscale is introduced, so as to ensure that water-bearing stratums and gas-bearing stratums are alternatively and periodically overlaid; the horizontal direction of each stratum is infinitely extended; each stratum adopts isotropic medium; the thickness of each stratum is far less than seismic wavelength and is greater than the particle size; the control equation of each stratum adopts a BISQ elastic wave prorogation equation, so that the cross-scale seismic rock physical attenuation model is constructed. The model comprises three scale attenuation mechanisms, namely a micro-scale Biot flow, a mesoscale local flow and the micro-scale jet flow. The invention further discloses a method for predicating the longitudinal wave attenuation and dispersion of the model. A predicated attenuation value is very consistent with an attenuation value measured by experiments.

Description

Across yardstick earthquake rock physics attenuation model and the method predicting decay and frequency dispersion

Technical field

The present invention relates to exploration physical earth field, be specifically related to the method across yardstick earthquake rock physics attenuation model and prediction decay and frequency dispersion.

Background technology

Underground oil and gas oily medium shows obvious two-phase media feature in elasticity, and in research two-phase media, the propagation law of seismic event is significant for the precision improving oil-gas exploration.Fluid can be caused during the propagation of seismic event in two-phase media to flow (WIFF), and then produce seismic wave attenuation and frequency dispersion (M ü ller, 2010).When seismic event through time, due to rock skeleton or pore fluid skewness, produce pressure gradient, thus cause fluid flow cause decay and frequency dispersion.Can be divided three classes from yardstick with the earthquake rock physics theory of fluid about seismic event attenuation by absorption: macro-scale attenuating mechanism, meso-scale (be less than earthquake wavelength and much larger than particle size) attenuating mechanism and micro-scale attenuating mechanism.Because geological data dominant frequency is at tens hertz, frequency span is limited, and the sight attenuating mechanism that is situated between is most important.The representative of macro-scale attenuation theory is Biot(1956) elastic wave prorogation theory propagated in two-phase media of the seismic event of deriving, it is the classical theory framework of research two-phase media, but the decling phase of the decay of this theoretical prediction and actual measurement is smaller, the permeability of trying to achieve and the coefficient of viscosity are not inconsistent the affecting laws of decay and frequency dispersion and experiment.Difform hole at seismic event through out-of-date, different deformation can be produced, cause the flowing of hole inner fluid, thus produce decay, Mavko and Nur(1975) this mechanism is called injection stream, the decay of micro-scale is mainly acted on by " injection stream " in crack and causing, its representational theory is Dvorkin(1993) set up " BISQ " elastic wave prorogation theory, the BISQ that Yang Dinghui (2000) have studied pore space anisotropy is theoretical, expand the range of application of BISQ theory, He Qiao to step on etc. (2000, 2001, 2003) based on Biot theory and injection stream theory, to derive the Seismic Wave Propagation Equations of oil-containing water two-phase fluid pore media, and carry out forward simulation.Nie Jianxin (2004), based on EFFECTIVE MEDIUM THEORY, proposes BISQ model in fractional saturation poroelasticity medium, and analyzes wave propagation rule.Tang Xiaoming (2011) considers the interaction in hole and crack, theoretical and BISQ is theoretical promotes to Biot, and analyzes the impact of crack on decay and Dispersion Characteristics.But its unpredictable seismic event is in the decay of seismic band.The attenuating mechanism of meso-scale mainly contains: the cycle stratification patch that White etc. (1975) set up saturated and spherical patchy saturation, subsequently Dutta and Ode(1979) with more rigorous pore media mechanics, the spherical patchy saturation that White proposes is revised.Vogelaar(2007) and Liu Jiong (2009,2010) solve the attenuation of P-wave and frequency dispersion that analyze two kinds of White patchy saturations by the method for direct decoupling.Pride and Berryman(2003) and Ba Jing (2011) dual porosity model of deriving, use pseudo-spectrometry numerical simulation to dissipate containing Biot and see with middle the seismic wave field flowed in porous medium, analyze middle sight fluid and to flow the seismic wave attenuation caused.Although these models can portray the decay of seismic event at seismic band, do not consider that micro-scale crack is on the impact of seismic event at seismic band.

Summary of the invention

For the deficiencies in the prior art, the object of the invention is to: provide across yardstick earthquake rock physics attenuation model, institute's established model approaches complicated underground medium more, can portray crack on the impact of seismic event and can predictably seismic wave in the decay of seismic band.Another object of the present invention is to provide and utilizes the decay of above-mentioned model prediction seismic event at seismic band and the method for frequency dispersion.

The technical solution used in the present invention is: across yardstick earthquake rock physics attenuation model, this model is the model of simulate formation oily two-phase media characteristic, it is characterized in that:

The method building this model is:

Under macro-scale Biot two-phase media elastic wave prorogation theory framework, introduce the impact of " injection stream " in micro-scale crack in " BISQ " elastic wave prorogation theory, on this basis, introduce the cycle stratification White model under meso-scale, make water-bearing zone and gas-bearing horizon interaction cycle stacked, every layer laterally unlimited extends, and is isotropic medium, and the thickness of every layer will be greater than particle size much smaller than earthquake wavelength; The governing equation of every layer is " BISQ " Time Migration of Elastic Wave Equation, builds the earthquake rock physics attenuation model across yardstick.

Further, the impact introducing " injection stream " in micro-scale crack in " BISQ " elastic wave prorogation theory refers to: this parameter of feature spray penetration is introduced " BISQ " Time Migration of Elastic Wave Equation, portrays micro-scale crack " injection stream " and act on size.

Further, the concrete steps building this model are:

Step 1: by elastic constitutive relation and nonlinear New-tonian law, set up Biot model;

Step 2: take into full account the injection stream mass conservation of micro-crack, the law of conservation of mass of pipeline stream on the basis of Biot model, set up BISQ model;

Step 3: the meso-scale boundary condition taking into full account feature unit on the basis of BISQ model, builds across yardstick earthquake petrophysical model and every layer of " BISQ " Time Migration of Elastic Wave Equation thereof.

Further, in step 3, described feature unit refers to,

From this model each levels interphase, get the half of upper and lower two-layer height and as cylindrical height, cylinder diameter is got infinitely small, and such right cylinder is called feature unit;

Described feature unit is not only full of longitudinal macroscopic view " Biot stream ", also there is the microcosmic " injection stream " due to Effect of Fissure, and Jie that Gas-Water Contant hydrodynamic pressure difference causes sees " local stream "; It is stacked that numerous feature unit composition gas-bearing horizon and water-bearing zone obtain the cycle, the laterally unlimited extension of every layer;

Described meso-scale refers to the difference yardstick of Jie's sight " local stream " that energy reaction gas water layer hydrodynamic pressure difference causes.

Further, described every layer " BISQ " Time Migration of Elastic Wave Equation is:

ρ ₁₁u _tt+ρ ₁₂U _tt+b(u _t-U _t)＝P ₁u _xx+Q ₁U _xx

ρ ₁₂u _tt+ρ ₂₂U _tt-b(u _t-U _t)＝Q ₁u _xx+R ₁U _xx(1)；

In formula, ρ ₁₁+ ρ ₁₂=(1-φ) ρ ₂, ρ ₁₂+ ρ ₂₂=φ ρ _f, ρ ₁₂=(1-ζ) φ ρ _f, $b=\frac{\mathrm{\η}}{\mathrm{\κ}}{\mathrm{\φ}}^2\sqrt{1+i\frac{w}{{2w}_B}},w_B=\frac{\mathrm{\φ\η}}{\mathrm{k\ζ}{\mathrm{\ρ}}_f},P_1=K_d+\frac{4}{3}\mathrm{\μ}+\frac{{(\mathrm{\α}-\mathrm{\φ})}^2}{\mathrm{\φ}}{F}_1,$ Q ₁＝(α－φ)Ｆ _１，R ₁＝φF ₁，

Wherein, u, U are respectively solid and displacement of fluid, and subscript t, x representative is to its seeking time and directional derivative; Subscript s, f, d represent solid, fluid and rock skeleton respectively; φ is factor of porosity, and ρ is density, and ζ is the structure factor of pore media, and for spherical solid particles r=0.5, η, κ are respectively the coefficient of viscosity and the permeability of fluid; W is circular frequency, w _bfor Biot characteristic frequency; K is bulk modulus, and α is Biot coefficient, j ₁, for single order and zero Bessel function, R _bfor feature jet flow length, μ is the modulus of shearing of skeleton.

Further, the described model parameter across yardstick earthquake rock physics attenuation model is explained by existing geologic information and is obtained.

Predict the attenuation of P-wave of above-mentioned model and the method for frequency dispersion, it is characterized in that:

The method comprises: with the solid displacement of the upper and lower interface of feature unit in the method solving model of the bilingual coupling of Dutta, and then try to achieve the plane wave modulus of feature unit, finally obtain the decay across yardstick earthquake rock physics attenuation model and frequency dispersion.

Further, the solid displacement of the upper and lower interface of feature unit in described solving model, and then the concrete grammar of the plane wave modulus of trying to achieve feature unit is:

Each feature unit in this model, when the external world applies a simple harmonic quantity power time (simulation longitudinal wave propagation), feature unit can produce uniaxial strain θ e ^iwt, thus can the equivalent plane mode amount of this model:

Uniaxial strain in formula is:

${\mathrm{\θe}}^{\mathrm{net}}=\frac{u_b{e}^{\mathrm{net}}-u_a{e}^{\mathrm{net}}}{d_a+d_b}---\left(3\right);$

Wherein, u _a, u _bfor the solid displacement of the upper and lower interface of feature unit.

The frequency dispersion speed of feature unit can obtain:

$V_p=\mathrm{real}(w/\sqrt{P^{*}/{\mathrm{\ρ}}_e})---\left(4\right);$

Wherein, ρ _efor equivalent density,

${\mathrm{\ρ}}_e=d_a({\mathrm{\φ}}_a{\mathrm{\ρ}}_f^a+(1-{\mathrm{\φ}}_a){\mathrm{\ρ}}_s^a)/(d_a+d_b)+d_b({\mathrm{\φ}}_b{\mathrm{\ρ}}_f^b+(1-{\mathrm{\φ}}_b){\mathrm{\ρ}}_s^b)/(d_a+d_b),$

Subscript a, b represent the earthquake petrophysical parameter of levels respectively.

The quality factor of feature unit:

$Q=\frac{\mathrm{real}\left(P^{*}\right)}{\mathrm{imag}\left(P^{*}\right)}---\left(5\right).$

Utilize Dutta to solve the Time Migration of Elastic Wave Equation shown in formula (1) the method for the bilingual coupling of two-phase media Time Migration of Elastic Wave Equation of spherical White model, first write Time Migration of Elastic Wave Equation as following form:

$\begin{array}{c}{\mathrm{\ρ}}_b{u}_{\mathrm{tt}}+{\mathrm{\ρ}}_f{W}_{\mathrm{tt}}=H{u}_{\mathrm{xx}}+\frac{Q_1+R_1}{\mathrm{\φ}}{W}_{\mathrm{xx}}\\ {\mathrm{\ρ}}_f{u}_{\mathrm{tt}}+m{W}_{\mathrm{tt}}=\frac{Q_1+R_1}{\mathrm{\φ}}{u}_{\mathrm{xx}}+\frac{R_1}{{\mathrm{\φ}}^2}{W}_{\mathrm{xx}}-\frac{b}{{\mathrm{\φ}}^2}{W}_t\end{array}---\left(6\right);$

In formula, W=φ (U-u), ρ _b=[(1-φ) ρ _e+ φ ρ _f], H=P ₁+ 2Q ₁+ R ₁, m=ρ ₂₂/ φ.

The form of the quasi-static solution of the equation shown in formula (6) is made to be:

u=u(x)e ^iwtW＝W(x)e ^net(7)。

Then solid and fluid structurecoupling displacement are carried out decoupling zero, are write as following form:

W＝W _e+W _du＝u _e+u _d(8)。

Wherein: u _d=σ _dw _d, u _e=σ _ew _e, bring into together with formula (11) in the equation shown in formula (6) and following two Time Migration of Elastic Wave Equations can be obtained:

$\begin{array}{c}(\frac{{\∂}^2}{{\∂x}^2}+k_c^2)W_c\left(x\right)=0\\ (\frac{{\∂}^2}{{\∂x}^2}+k_d^2)W_d\left(x\right)=0\end{array}---\left(9\right).$

Wherein, the displacement coefficient σ of Concerning With Fast-slow Waves _c, σ _dmeet following quadratic equation with one unknown:

$(\frac{Q_1+R_1}{\mathrm{\φ}}{\mathrm{\ρ}}_b-H{\mathrm{\ρ}}_f){\mathrm{\σ}}^1+(\frac{{\mathrm{\ρ}}_b{R}_1}{{\mathrm{\φ}}^2}-\mathrm{mH}+\frac{\mathrm{ibH}}{{\mathrm{\φ}}^{2}w})\mathrm{\σ}+(\frac{{\mathrm{\ρ}}_f{R}_1}{{\mathrm{\φ}}^2}-\frac{m{(Q_1+R)}_1}{\mathrm{\φ}}+\frac{\mathrm{ib}(Q_1+R)}{{\mathrm{w\φ}}^1})=0---\left(10\right);$

Speed wave number k _c, k _dfor:

In formula, σ ₁₁=ρ _bσ _c+ ρ _f, σ ₁₂=ρ _bσ _d+ ρ _f, σ ₂₁=ρ _fσ _c+ m, σ ₂₂=ρ _fσ _d+ m, c ₁=H σ _c+ (Q _i+ R _i)/φ, c ₂=H σ _d+ (Q _i+ R _i)/φ, c ₃=(Q _i+ R _i) σ _e/ φ+R _i/ φ ², c ₄=(Q _i+ R _i) σ _d/ φ+R _i/ φ ².

Fluid structurecoupling displacement can be obtained and solid displacement is by solving formula (8):

W=Blcos(k _cx)+B2sin(k _cx)+B3cos(k _dx)+B4sin(k _dx)

u=σ _cBlcos(k _cx)+σ _cB2sin(k _cx)+σ _dB3cos(k _dx)+σ _dB4sin(k _dx) (12)；

Wherein, B ₁, B ₂, B ₃, B ₄it is undetermined coefficient.

According to the total stress of feature unit upper and lower interface and the phase shift of stream maintenance etc., the total stress in bed interface place is continuous, pore pressure continuously, solid displacement is continuous and fluid flow is equal, set up as downstream condition:

$\begin{array}{ccc}1)& {\mathrm{\τ}}_a=-P_e{e}^{\mathrm{iwt}}& x=-d_a\\ 2)& u_a=U_a& x=-d_a\\ 3)& {\mathrm{\τ}}_b=-P_e{e}^{\mathrm{iwt}}& x=d_b\\ 4)& u_b=U_b& x=d_b\\ 5)& {\mathrm{\τ}}_a={\mathrm{\τ}}_b& x=0\\ 6)& P_f^a=P_f^b& x=0\\ 7)& u_a=u_b& x=0\\ 8)& W_a=W_b& x=0\end{array}---\left(13\right).$

By solving above eight absorbing boundary equations, eight undetermined coefficients of levels solid displacement can be tried to achieve, and then solid displacement can be obtained.

By solving above eight absorbing boundary equations, eight undetermined coefficients of levels solid displacement can be tried to achieve, and then solid displacement can be obtained, calculate attenuation of P-wave across yardstick earthquake petrophysical model and frequency dispersion finally by formula (2)-formula (5).

In order to make, established model approaches complicated underground medium more, can portray crack on the impact of seismic event and can predictably seismic wave in the decay of seismic band, model of the present invention provides across yardstick earthquake rock physics attenuation model, both introduced the impact in micro-scale crack, and seismic event can have been portrayed again in the decay of seismic band and frequency dispersion.This beneficial effect across yardstick earthquake rock physics attenuation model is, consider macro-scale " Biot stream ", the attenuating mechanism of meso-scale " local stream " and micro-scale " injection stream " three yardsticks affected, because the saturated fluid of underground medium flows the seismic event caused in the decay of seismic band and frequency dispersion when predicting seismic wave propagation.Earthquake petrophysical model not only considers harder circular hole gap, also contemplates soft hole-crack, makes model more closely descend Complicated Geologic Condition.The pad value doped and the pad value of laboratory measurement more identical.

Accompanying drawing explanation

Fig. 1 is the schematic diagram across yardstick earthquake rock physics attenuation model.

Fig. 2 builds the technical scheme process flow diagram across yardstick earthquake rock physics attenuation model.

Fig. 3 a is using the formula of White1975, Biot equation as cycle stratification White model cootrol equation and the attenuation of P-wave figure shaking petrophysical model across band.

Fig. 3 b is that the formula of White1975, Biot equation are as cycle stratification White model cootrol equation and the compressional wave frequency dispersion figure shaking petrophysical model across band.

Fig. 4 a is the attenuation of P-wave figure of this attenuation model under different permeability condition.

Fig. 4 b is the compressional wave frequency dispersion figure of this attenuation model under different permeability condition.

The attenuation of P-wave figure of this attenuation model under the different gas saturation condition of Fig. 5 a.

The compressional wave frequency dispersion figure of this attenuation model under the different gas saturation condition of Fig. 5 b.

The attenuation of P-wave figure of this attenuation model under the different gas saturation condition of Fig. 5 c.

The compressional wave frequency dispersion figure of this attenuation model under the different gas saturation condition of Fig. 5 d.

Fig. 6 a is the attenuation of P-wave figure of this attenuation model under different FRACTURE CHARACTERISTICS spray penetration condition.

Fig. 6 b is the compressional wave frequency dispersion figure of this attenuation model under different FRACTURE CHARACTERISTICS spray penetration condition.

Embodiment

Below in conjunction with drawings and Examples, the present invention will be further described.

Embodiment 1.Across yardstick earthquake rock physics attenuation model, it is characterized in that: this model is the model of simulate formation oily two-phase media characteristic, consider the attenuating mechanism of macro-scale, meso-scale, micro-scale, under given physical property and fluid parameter condition, can predictably seismic wave in the decay of seismic band and frequency dispersion.

The method building this model is:

Under macro-scale Biot two-phase media elastic wave prorogation theory framework, introduce the impact of " injection stream " in micro-scale crack in " BISQ " elastic wave prorogation theory, on this basis, introduce the cycle stratification White model under meso-scale, make water-bearing zone and gas-bearing horizon interaction cycle stacked, every layer laterally unlimited extends, and is isotropic medium, and the thickness of every layer will be greater than particle size much smaller than earthquake wavelength; The governing equation of every layer is " BISQ " Time Migration of Elastic Wave Equation, builds the earthquake rock physics attenuation model across yardstick.

The concrete steps building this model, as shown in the technical scheme process flow diagram of Fig. 2, comprising:

Step 1: by elastic constitutive relation and nonlinear New-tonian law, set up Biot model; Biot model considers the effect of macroscopic view " Biot stream ".

Step 2: take into full account the injection stream mass conservation of micro-crack, the law of conservation of mass of pipeline stream on the basis of Biot model, set up BISQ model.The impact introducing " injection stream " in micro-scale crack in " BISQ " elastic wave prorogation theory refers to: this parameter of feature spray penetration is introduced " BISQ " Time Migration of Elastic Wave Equation, portrays micro-scale crack " injection stream " and act on size.BISQ model considers " injection stream " effect.

Step 3: the meso-scale boundary condition taking into full account feature unit on the basis of BISQ model, builds the math equation across yardstick earthquake petrophysical model.Meso-scale just refers to the yardstick between both macro and micro; It is generally acknowledged that its yardstick is between nanometer and millimeter.Meso-scale of the present invention refers to the difference yardstick of Jie's sight " local stream " that energy reaction gas water layer hydrodynamic pressure difference causes.

Described feature unit refers to, from this model each levels interphase, get the half of upper and lower two-layer height and as cylindrical height, cylinder diameter is got infinitely small, and such right cylinder is called feature unit; Described feature unit is not only full of longitudinal macroscopic view " Biot stream ", also there is the microcosmic " injection stream " due to Effect of Fissure, and Jie that Gas-Water Contant hydrodynamic pressure difference causes sees " local stream ".Fig. 1 illustrates the schematic diagram across yardstick earthquake rock physics attenuation model.Gas-bearing horizon in figure and the water-bearing zone cycle stacked, laterally infinitely extend, be made up of numerous right cylinder feature unit.

Described every layer " BISQ " Time Migration of Elastic Wave Equation is:

ρ ₁₁u _tt+ρ ₁₂U _tt+b(u _t-U _t)＝P ₁u _xx+Q ₁U _xx

ρ ₁₂u _tt+ρ ₂₂U _tt-b(u _t-U _t)＝Q ₁u _xx+R ₁U _xx(1)；

In formula, ρ ₁₁+ ρ ₁₂=(1-φ) ρ ₂, ρ ₁₂+ ρ ₂₂=φ ρ _f, ρ ₁₂=(1-ζ) φ ρ _f, $b=\frac{\mathrm{\η}}{\mathrm{\κ}}{\mathrm{\φ}}^2\sqrt{1+i\frac{w}{{2w}_B}},w_B=\frac{\mathrm{\φ\η}}{\mathrm{k\ζ}{\mathrm{\ρ}}_f},P_1=K_d+\frac{4}{3}\mathrm{\μ}+\frac{{(\mathrm{\α}-\mathrm{\φ})}^2}{\mathrm{\φ}}{F}_1,$ Q ₁＝(α-φ)F ₁，R ₁＝φF ₁，

Wherein, u, U are respectively solid and displacement of fluid, and subscript t, x representative is to its seeking time and directional derivative; In each coefficient expressions,

Subscript s, f, d represent solid, fluid and rock skeleton respectively; φ is factor of porosity, and ρ is density, and ζ is the structure factor of pore media, and for spherical solid particles r=0.5, η, κ are respectively the coefficient of viscosity and the permeability of fluid; W is circular frequency, w _bfor Biot characteristic frequency; K is bulk modulus, and α is Biot coefficient, , J ₁, for single order and zero Bessel function, R _bfor feature jet flow length, μ is the modulus of shearing of skeleton.

The described model parameter across yardstick earthquake rock physics attenuation model can be explained by existing geologic information and obtain.

This is across yardstick earthquake rock physics attenuation model.It comprises " Biot " stream of macro-scale, " injection stream " three kinds of yardstick attenuating mechanisms of " the local stream " of meso-scale and the yardstick of microcosmic, can predict that physical parameter (permeability, feature spray penetration), fluid parameter (gas saturation) are decayed under seismic band on seismic event and the impact of frequency dispersion.Described gas saturation S _gthickness for gas-bearing horizon accounts for the ratio of feature unit gross thickness.Concrete formula is: S _g=d _a/ (d _a+ d _b), wherein, d _afor the interfacial distance of feature unit top interface distance, d _bfor the feature unit ground interfacial distance of cross-sectional distance (consulting Fig. 1).

Embodiment 2.Predict above-mentioned across the attenuation of P-wave of yardstick earthquake rock physics attenuation model and the method for frequency dispersion, comprise: with the solid displacement of the upper and lower interface of feature unit in the method solving model of the bilingual coupling of Dutta, and then try to achieve the plane wave modulus of feature unit, finally obtain the decay across yardstick earthquake rock physics attenuation model and frequency dispersion.

The solid displacement of the upper and lower interface of feature unit in described solving model, and then the concrete grammar of the plane wave modulus of trying to achieve feature unit is:

Each feature unit in this model, when the external world applies a simple harmonic quantity power time (simulation longitudinal wave propagation), feature unit can produce uniaxial strain θ e ^net, thus can the equivalent plane mode amount of this model:

Uniaxial strain in formula is:

${\mathrm{\θe}}^{\mathrm{net}}=\frac{u_b{e}^{\mathrm{net}}-u_a{e}^{\mathrm{net}}}{d_a+d_b}---\left(3\right);$

Wherein, u _a, u _bfor the solid displacement of the upper and lower interface of feature unit.

The frequency dispersion speed of feature unit can obtain:

$V_p=\mathrm{real}(w/\sqrt{P^{*}/{\mathrm{\ρ}}_e})---\left(4\right);$

Wherein, ρ _efor equivalent density,

${\mathrm{\ρ}}_e=d_a({\mathrm{\φ}}_a{\mathrm{\ρ}}_f^a+(1-{\mathrm{\φ}}_a){\mathrm{\ρ}}_s^a)/(d_a+d_b)+d_b({\mathrm{\φ}}_b{\mathrm{\ρ}}_f^b+(1-{\mathrm{\φ}}_b){\mathrm{\ρ}}_s^b)/(d_a+d_b),$

Subscript a, b represent the earthquake petrophysical parameter of levels respectively.

The quality factor of feature unit:

$Q=\frac{\mathrm{real}\left(P^{*}\right)}{\mathrm{imag}\left(P^{*}\right)}---\left(5\right).$

Utilize Dutta to solve Time Migration of Elastic Wave Equation formula (1) Suo Shi the method for the bilingual coupling of two-phase media Time Migration of Elastic Wave Equation of spherical White model, first write Time Migration of Elastic Wave Equation as following form:

$\begin{array}{c}{\mathrm{\ρ}}_b{u}_{\mathrm{tt}}+{\mathrm{\ρ}}_f{W}_{\mathrm{tt}}=H{u}_{\mathrm{xx}}+\frac{Q_1+R_1}{\mathrm{\φ}}{W}_{\mathrm{xx}}\\ {\mathrm{\ρ}}_f{u}_{\mathrm{tt}}+m{W}_{\mathrm{tt}}=\frac{Q_1+R_1}{\mathrm{\φ}}{u}_{\mathrm{xx}}+\frac{R_1}{{\mathrm{\φ}}^2}{W}_{\mathrm{xx}}-\frac{b}{{\mathrm{\φ}}^2}{W}_t\end{array}---\left(6\right);$

In formula, W=φ (U-u), ρ _b=[(1-φ) ρ _e+ φ ρ _f], H=P ₁+ 2Q ₁+ R ₁, m=ρ ₂₂/ φ.

The form of the quasi-static solution of equation shown in formula (6) is made to be:

u＝u(x)e ^iwtW＝W(x)e ^net(7)。

Then solid and fluid structurecoupling displacement are carried out decoupling zero, are write as following form:

W＝W _e+W _du＝u _e+u _d(8)；

Wherein: u _d=σ _dw _d, u _e=σ _ew _e; Bring into together with formula (11) in equation (6) and following two Time Migration of Elastic Wave Equations can be obtained:

$\begin{array}{c}(\frac{{\∂}^2}{{\∂x}^2}+k_c^2)W_c\left(x\right)=0\\ (\frac{{\∂}^2}{{\∂x}^2}+k_d^2)W_d\left(x\right)=0\end{array}---\left(9\right);$

Wherein, the displacement coefficient σ of Concerning With Fast-slow Waves _c, σ _dmeet following quadratic equation with one unknown:

$(\frac{Q_1+R_1}{\mathrm{\φ}}{\mathrm{\ρ}}_b-H{\mathrm{\ρ}}_f){\mathrm{\σ}}^1+(\frac{{\mathrm{\ρ}}_b{R}_1}{{\mathrm{\φ}}^2}-\mathrm{mH}+\frac{\mathrm{ibH}}{{\mathrm{\φ}}^{2}w})\mathrm{\σ}+(\frac{{\mathrm{\ρ}}_f{R}_1}{{\mathrm{\φ}}^2}-\frac{m{(Q_1+R)}_1}{\mathrm{\φ}}+\frac{\mathrm{ib}(Q_1+R)}{{\mathrm{w\φ}}^1})=0---\left(10\right).$

Speed wave number k _c, k _dfor:

In formula, σ ₁₁=ρ _bσ _c+ ρ _f, σ ₁₂=ρ _bσ _d+ ρ _f, σ ₂₁=ρ _fσ _c+ m, σ ₂₂=ρ _fσ _d+ m, c ₁=H σ _c+ (Q _i+ R _i)/φ, c ₂=H σ _d+ (Q _i+ R _i)/φ, c ₃=(Q _i+ R _i) σ _e/ φ+R _i/ φ ², c ₄=(Q _i+ R _i) σ _d/ φ+R _i/ φ ².

Fluid structurecoupling displacement can be obtained and solid displacement is by solving formula (8):

W=Blcos(k _cx)+B2sin(k _cx)+B3cos(k _dx)+B4sin(k _dx)

u=σ _cBlcos(k _cx)+σ _cB2sin(k _cx)+σ _dB3cos(k _dx)+σ _dB4sin(k _dx) (12)；

Wherein, B ₁, B ₂, B ₃, B ₄it is undetermined coefficient.

According to the total stress of feature unit upper and lower interface and the phase shift of stream maintenance etc., the total stress in bed interface place is continuous, pore pressure continuously, solid displacement is continuous and fluid flow is equal, set up as downstream condition:

$\begin{array}{ccc}1)& {\mathrm{\τ}}_a=-P_e{e}^{\mathrm{iwt}}& x=-d_a\\ 2)& u_a=U_a& x=-d_a\\ 3)& {\mathrm{\τ}}_b=-P_e{e}^{\mathrm{iwt}}& x=d_b\\ 4)& u_b=U_b& x=d_b\\ 5)& {\mathrm{\τ}}_a={\mathrm{\τ}}_b& x=0\\ 6)& P_f^a=P_f^b& x=0\\ 7)& u_a=u_b& x=0\\ 8)& W_a=W_b& x=0\end{array}---\left(13\right).$

By solving above eight absorbing boundary equations, eight undetermined coefficients of levels solid displacement can be tried to achieve, and then solid displacement can be obtained, calculate attenuation of P-wave across yardstick earthquake petrophysical model and frequency dispersion finally by formula 2-5.

By the method, can also predict that physical parameter (as permeability, feature spray penetration), fluid parameter (as gas saturation) are decayed under seismic band on seismic event and the impact of frequency dispersion.

The present invention's design across yardstick earthquake rock physics attenuation model and prediction effect thereof, compare and adopt classic method modeling, the pad value doped and the pad value of experiment measuring more identical.

Fig. 3 a is using the formula of White1975, Biot equation as cycle stratification White model cootrol equation and the attenuation of P-wave figure shaking petrophysical model across band.Fig. 3 b is that the formula of White1975, Biot equation are as cycle stratification White model cootrol equation and the compressional wave frequency dispersion figure shaking petrophysical model across band.Visible, after adding " injection stream " impact in crack, can there is corresponding change in the decay of seismic band and frequency dispersion in seismic event.

Fig. 4 a is the attenuation of P-wave figure of this attenuation model under different permeability condition.Fig. 4 b is the compressional wave frequency dispersion figure of this attenuation model under different permeability condition.Visible, along with the rising of permeability, decay dominant frequency is to high-frequency mobile, and damping peak is constant.

Fig. 5 a-Fig. 5 d is attenuation of P-wave and the frequency dispersion of this attenuation model under different gas saturation condition.Visible, along with the increase of gas saturation, the decay of compressional wave and frequency dispersion first increase and then reduce.When gas saturation 0.1, the attenuation of P-wave of this attenuation model is maximum, with Gautam(2003) experimental result consistent.

Fig. 6 a is the attenuation of P-wave figure of this attenuation model under different FRACTURE CHARACTERISTICS spray penetration condition.Fig. 6 b is the compressional wave frequency dispersion figure of this attenuation model under different FRACTURE CHARACTERISTICS spray penetration condition.Curve 1 represents vertical frequency decay (a) and frequency dispersion (b) that calculate as this attenuation model every layer governing equation with " Biot " equation, curve 2,3,4,5,6,7,8,9 represent respectively injection characteristics length be 1,0.4,0.01,0.05,0.02,0.01,0.001,0.0001m.Visible, when feature spray penetration increases gradually, attenuation of P-wave and the frequency dispersion of this attenuation model increase gradually, the effect of " injection stream " in crack reduces, when feature spray penetration is reduced to a certain degree, attenuation of P-wave and the frequency dispersion of this attenuation model are constant, and " injection stream " impact on this attenuation model in crack remains unchanged.

Above embodiment is to illustrate the invention and not to limit the present invention.

Claims (8)

1., across yardstick earthquake rock physics attenuation model, this model is the model of simulate formation oily two-phase media characteristic, it is characterized in that:

The method building this model is:

Under macro-scale Biot two-phase media elastic wave prorogation theory framework, introduce the impact of " injection stream " in micro-scale crack in " BISQ " elastic wave prorogation theory, on this basis, introduce the cycle stratification White model under meso-scale, make water-bearing zone and gas-bearing horizon interaction cycle stacked, every layer laterally unlimited extends, and is isotropic medium, and the thickness of every layer will be greater than particle size much smaller than earthquake wavelength; The governing equation of every layer is " BISQ " Time Migration of Elastic Wave Equation, builds the earthquake rock physics attenuation model across yardstick.

2. as claimed in claim 1 across yardstick earthquake rock physics attenuation model, it is characterized in that:

The impact introducing " injection stream " in micro-scale crack in " BISQ " elastic wave prorogation theory refers to: this parameter of feature spray penetration is introduced " BISQ " Time Migration of Elastic Wave Equation, portrays micro-scale crack " injection stream " and act on size.

3. as claimed in claim 2 across yardstick earthquake rock physics attenuation model, it is characterized in that: the concrete steps building this model are:

Step 1: by elastic constitutive relation and nonlinear New-tonian law, set up Biot model;

Step 2: take into full account the injection stream mass conservation of micro-crack, the law of conservation of mass of pipeline stream on the basis of Biot model, set up BISQ model;

Step 3: the meso-scale boundary condition taking into full account feature unit on the basis of BISQ model, builds across yardstick earthquake petrophysical model and every layer of " BISQ " Time Migration of Elastic Wave Equation thereof.

It is 4. as claimed in claim 3 that across yardstick earthquake rock physics attenuation model, it is characterized in that: in step 3, described feature unit refers to,

From this model each levels interphase, get the half of upper and lower two-layer height and as cylindrical height, cylinder diameter is got infinitely small, and such right cylinder is called feature unit;

Described feature unit is not only full of longitudinal macroscopic view " Biot stream ", also there is the microcosmic " injection stream " due to Effect of Fissure, and Jie that Gas-Water Contant hydrodynamic pressure difference causes sees " local stream "; It is stacked that numerous feature unit composition gas-bearing horizon and water-bearing zone obtain the cycle, the laterally unlimited extension of every layer;

Described meso-scale refers to the difference yardstick of Jie's sight " local stream " that energy reaction gas water layer hydrodynamic pressure difference causes.

5. as described in a claim as any in claim 1 to 4 across yardstick earthquake rock physics attenuation model, it is characterized in that: described every layer " BISQ " Time Migration of Elastic Wave Equation is:

ρ ₁₁u _tt+ρ ₁₂U _tt+b(u _t-U _t)＝P ₁u _xx+Q ₁U _xx

ρ ₁₂u _tt+ρ ₂₂U _tt-b(u _t-U _t)＝Q ₁u _xx+R ₁U _xx(1)；

In formula, ρ ₁₁+ ρ ₁₂=(1-φ) ρ ₂, ρ ₁₂+ ρ ₂₂=φ ρ _f, ρ ₁₂=(1-ζ) φ ρ _f, $b=\frac{\mathrm{\η}}{\mathrm{\κ}}{\mathrm{\φ}}^2\sqrt{1+i\frac{w}{{2w}_B}},w_B=\frac{\mathrm{\φ\η}}{\mathrm{k\ζ}{\mathrm{\ρ}}_f},P_1=K_d+\frac{4}{3}\mathrm{\μ}+\frac{{(\mathrm{\α}-\mathrm{\φ})}^2}{\mathrm{\φ}}{F}_1,$ Q ₁=(α-φ)F ₁，R ₁=φF ₁，

Wherein, u, U are respectively solid and displacement of fluid, and subscript t, x representative is to its seeking time and directional derivative; Subscript s, f, d represent solid, fluid and rock skeleton respectively; φ is factor of porosity, and ρ is density, and ζ is the structure factor of pore media, and for spherical solid particles r=0.5, η, κ are respectively the coefficient of viscosity and the permeability of fluid; W is circular frequency, w _bfor Biot characteristic frequency; K is bulk modulus, and α is Biot coefficient, j ₁, for single order and zero Bessel function, R _bfor feature jet flow length, μ is the modulus of shearing of skeleton.

6. as claimed in claim 5 across yardstick earthquake rock physics attenuation model, it is characterized in that: the described model parameter across yardstick earthquake rock physics attenuation model is explained by existing geologic information and obtained.

7. predict described in claim 1 to 6 any claim across the attenuation of P-wave of yardstick earthquake rock physics attenuation model and the method for frequency dispersion, it is characterized in that:

The method comprises: with the solid displacement of the upper and lower interface of feature unit in the method solving model of the bilingual coupling of Dutta, and then try to achieve the plane wave modulus of feature unit, finally obtain the decay across yardstick earthquake rock physics attenuation model and frequency dispersion.

8. the attenuation of P-wave predicted as claimed in claim 7 and the method for frequency dispersion, it is characterized in that: the solid displacement of the upper and lower interface of feature unit in described solving model, and then the concrete grammar of the plane wave modulus of trying to achieve feature unit is:

Each feature unit in this model, when the external world applies a simple harmonic quantity power time, feature unit can produce uniaxial strain θ e ^iwt, thus can the equivalent plane mode amount of this model:

Uniaxial strain in formula is:

${\mathrm{\θe}}^{\mathrm{net}}=\frac{u_b{e}^{\mathrm{net}}-u_a{e}^{\mathrm{net}}}{d_a+d_b}---\left(3\right);$

Wherein, u _a, u _bfor the solid displacement of the upper and lower interface of feature unit;

The frequency dispersion speed of feature unit can obtain:

$V_p=\mathrm{real}(w/\sqrt{P^{*}/{\mathrm{\ρ}}_e})---\left(4\right);$

Wherein, ρ _efor equivalent density,

${\mathrm{\ρ}}_e=d_a({\mathrm{\φ}}_a{\mathrm{\ρ}}_f^a+(1-{\mathrm{\φ}}_a){\mathrm{\ρ}}_s^a)/(d_a+d_b)+d_b({\mathrm{\φ}}_b{\mathrm{\ρ}}_f^b+(1-{\mathrm{\φ}}_b){\mathrm{\ρ}}_s^b)/(d_a+d_b),$

Subscript a, b represent the earthquake petrophysical parameter of levels respectively;

The quality factor of feature unit:

$Q=\frac{\mathrm{real}\left(P^{*}\right)}{\mathrm{imag}\left(P^{*}\right)}---\left(5\right);$

Utilize the method for Dutta to the bilingual coupling of two-phase media Time Migration of Elastic Wave Equation of spherical White model to solve the Time Migration of Elastic Wave Equation shown in formula 1, first write Time Migration of Elastic Wave Equation as following form:

$\begin{array}{c}{\mathrm{\ρ}}_b{u}_{\mathrm{tt}}+{\mathrm{\ρ}}_f{W}_{\mathrm{tt}}=H{u}_{\mathrm{xx}}+\frac{Q_1+R_1}{\mathrm{\φ}}{W}_{\mathrm{xx}}\\ {\mathrm{\ρ}}_f{u}_{\mathrm{tt}}+m{W}_{\mathrm{tt}}=\frac{Q_1+R_1}{\mathrm{\φ}}{u}_{\mathrm{xx}}+\frac{R_1}{{\mathrm{\φ}}^2}{W}_{\mathrm{xx}}-\frac{b}{{\mathrm{\φ}}^2}{W}_t\end{array}---\left(6\right);$

In formula, W=φ (U-u), ρ _b=[(1-φ) ρ _a+ φ ρ _f], H=P ₁+ 2Q ₁+ R ₁, m=ρ ₂₂/ φ;

The form of the quasi-static solution of the equation shown in formula 6 is made to be:

u＝u(x)e ^iwtW＝W(x)e ^iwt(7)；

Then solid and fluid structurecoupling displacement are carried out decoupling zero, are write as following form:

W＝W _e+W _du＝u _e+u _d(8)；

Wherein: u _d=σ _dw _d, u _e=σ _ew _e, bring into together with formula (11) in the equation shown in formula (6) and following two Time Migration of Elastic Wave Equations can be obtained:

$\begin{array}{c}(\frac{{\∂}^2}{{\∂x}^2}+k_c^2)W_c\left(x\right)=0\\ (\frac{{\∂}^2}{{\∂x}^2}+k_d^2)W_d\left(x\right)=0\end{array}---\left(9\right);$

Wherein, the displacement coefficient σ of Concerning With Fast-slow Waves _c, σ _dmeet following quadratic equation with one unknown:

$(\frac{Q_1+R_1}{\mathrm{\φ}}{\mathrm{\ρ}}_b-H{\mathrm{\ρ}}_f){\mathrm{\σ}}^1+(\frac{{\mathrm{\ρ}}_b{R}_1}{{\mathrm{\φ}}^2}-\mathrm{mH}+\frac{\mathrm{ibH}}{{\mathrm{\φ}}^{2}w})\mathrm{\σ}+(\frac{{\mathrm{\ρ}}_f{R}_1}{{\mathrm{\φ}}^2}-\frac{m{(Q_1+R)}_1}{\mathrm{\φ}}+\frac{\mathrm{ib}(Q_1+R)}{{\mathrm{w\φ}}^1})=0---\left(10\right);$

Speed wave number k _c, k _dfor:

In formula, σ ₁₁=ρ _bσ _c+ ρ _f, σ ₁₂=ρ _bσ _d+ ρ _f, σ ₂₁=ρ _fσ _c+ m, σ ₂₂=ρ _fσ _d+ m, c ₁=H σ _c+ (Q _i+ R _i)/φ, c ₂=H σ _d+ (Q _i+ R _i)/φ, c ₃=(Q _i+ R _i) σ _e/ φ+R _i/ φ ², c ₄=(Q _i+ R _i) σ _d/ φ+R _i/ φ ²;

Fluid structurecoupling displacement can be obtained and solid displacement is by solving formula 8:

W＝Blcos(k _cx)+B2sin(k _cx)+B3cos(k _dx)+B4sin(k _dx)

u＝σ _cBlcos(k _cx)+σ _cB2sin(k _cx)+σ _dB3cos(k _dx)+σ _dB4sin(k _dx) (12)；

Wherein, B1, B2, B3, B4 are undetermined coefficients;

According to the total stress of feature unit upper and lower interface and the phase shift of stream maintenance etc., the total stress in bed interface place is continuous, pore pressure continuously, solid displacement is continuous and fluid flow is equal, set up as downstream condition:

$\begin{array}{ccc}1)& {\mathrm{\τ}}_a=-P_e{e}^{\mathrm{iwt}}& x=-d_a\\ 2)& u_a=U_a& x=-d_a\\ 3)& {\mathrm{\τ}}_b=-P_e{e}^{\mathrm{iwt}}& x=d_b\\ 4)& u_b=U_b& x=d_b\\ 5)& {\mathrm{\τ}}_a={\mathrm{\τ}}_b& x=0\\ 6)& P_f^a=P_f^b& x=0\\ 7)& u_a=u_b& x=0\\ 8)& W_a=W_b& x=0\end{array}---\left(13\right);$

By solving above eight absorbing boundary equations, eight undetermined coefficients of levels solid displacement can be tried to achieve, and then solid displacement can be obtained;

By solving above eight absorbing boundary equations, eight undetermined coefficients of levels solid displacement can be tried to achieve, and then solid displacement can be obtained, calculate attenuation of P-wave across yardstick earthquake petrophysical model and frequency dispersion finally by formula (2)-formula (5).