CN108952695B - Method for predicting fluid activity of oil and gas reservoir - Google Patents

Abstract

The invention relates to the technical field of exploration and development, and particularly discloses a method for predicting the fluid activity of an oil and gas reservoir, which comprises the following steps: firstly, obtaining a linear approximate expression of a reflection coefficient; secondly, frequency division processing is carried out; thirdly, obtaining a recombined forward operator; fourthly, constructing an objective function under a Bayes framework: and adding a sparse regularization term and a low-frequency model constraint term introduced by prior probability distribution to finally obtain a target functional, solving the gradient of a model parameter F of the target functional, setting the gradient to be 0 to obtain a final nonlinear inversion equation of the model parameter, and solving the value of F by using a least square method to obtain a fluid activity value. The invention relates to a frequency-dependent inversion prediction method of fluid activity under a Bayesian theory framework, which can improve the reliability of reservoir prediction and fluid identification, so that the physical significance of fluid activity calculation is more definite, and the result is more reliable.

Description

Method for predicting fluid activity of oil and gas reservoir

Technical Field

The invention relates to the technical field of oil and gas exploration and development, in particular to a method for calculating the fluid activity of an oil and gas reservoir.

Background

The fluid activity of the oil and gas reservoir is defined as the ratio of the permeability of the reservoir to the fluid viscosity coefficient, and reflects the combined action of the permeability (or connectivity) of a pore structure in a rock framework of the reservoir and the type and viscosity of pore fluid, so that the fluid activity of the reservoir has important significance for determining the elastic parameters, the internal structure, the fluid-containing property and the like of the reservoir rock. The domestic and foreign application examples show that compared with the conventional seismic data and inversion profiles, the method can only predict the static parameters of the reservoir, the fluid activity can better reflect the quality of the reservoir, and the productivity of high-quality reservoirs in the reservoir and fluids in the reservoir can be effectively predicted. Fluid activity can predict premium reservoir development zones in areas where reservoir heterogeneity is strong; the characteristics of the fluid in a reservoir are studied in areas where the reservoir is homogeneous or relatively homogeneous. Especially fluid mobility, has shown great potential in the description and evaluation of thin-thickness sandstone reservoirs with strong lateral heterogeneity. A new method is developed to guide inversion of reservoir fluid activity parameters in actual exploration, and more reliable technical support can be provided for oil-gas seismic exploration.

The existing method for calculating the fluid activity is based on a low-frequency-domain fluid saturated pore medium seismic signal reflection simplified asymptotic representation theory, a time-frequency analysis method is adopted to calculate the fluid activity attribute, the rock physical meaning of the method is not clear, and the inversion accuracy is low.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: a frequency-dependent inversion prediction method of fluid activity under a Bayesian theory framework is provided, and reliability of reservoir prediction and fluid identification is improved.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a method of hydrocarbon reservoir fluid activity prediction comprising the steps of:

first, a linear approximation expression of the reflection coefficient is obtained:

is provided with a formula (1-1),

in the formula (1-1), R is a reflection coefficient, and F is fluid mobility; rho_fIs the fluid density; omega is seismic wave angular frequency; r₀、R₁Respectively, a zeroth order term and a first order term of the asymptotic representation of the reflection coefficient, which are functions related to the properties of reservoir rocks and fluids;

a first order Taylor expansion on the fluid activity F is made for equation (1-1) to obtain a linear approximation of the reflection coefficient R:

rearranging formula (2), writing formula (2) as:

R(F,ω)＝A₀(F₀,ω)+B₀(F₀,ω)·F (3)，

in the formula (3), F₀Is a fluid activity characteristic value of a fluid contained in the reservoir, and A₀、B₀The specific expression is as follows:

and secondly, performing frequency division treatment: expressing the reflection coefficient as R_ω＝[R_ω1 R_ω2 … R_ωM]^TAnd M represents the number of frequencies, and the value of the reflection coefficient at an arbitrary frequency is calculated using equation (3):

note A_ωi＝[A_0ωi A_0ωi L A_0ωi]^T，F＝[F(t₁) F(t₂) L F(t_n)]^T，

Equation (5) can be rewritten as:

R_ωi＝A_ωi+B_ωi·F (6)；

thirdly, obtaining a recombined forward operator: substituting equation (6) into the unstable seismic convolution model S (omega)_i)＝W_i·R_ωiAnd the item shifting arrangement is carried out to obtain:

S(ω_i)-S'(ω_i)＝W_i·B_ωi·F (7)，

s (omega) in formula (7)_i)＝W_i·R_ωi，S'(ω_i)＝W_i·A_ωiFinally, the recombined positive operator is obtained as follows:

fourthly, constructing an objective function under a Bayes framework: adding a sparse regularization term and a low-frequency model constraint term introduced by prior probability distribution to finally obtain a target functional as follows:

in formula (9), σ_n ²And σ_F ²Respectively, noise distribution and covariance of inversion model parameters; xi and D are low frequency prior and regularization matrices, respectively; lambda [ alpha ]_lIs a model constraint coefficient;

and (3) solving the gradient of the model parameter F in the formula (9), setting the gradient to be 0, obtaining a final nonlinear inversion equation of the model parameter, and solving the value of F by using a least square method to obtain the fluid activity value.

The technical scheme of the invention has the following beneficial effects: the invention relates to a frequency-dependent inversion prediction method of fluid activity under a Bayesian theory framework, which can improve the reliability of reservoir prediction and fluid identification, so that the physical significance of fluid activity calculation is more definite, and the result is more reliable.

Drawings

FIG. 1 is a schematic cross-sectional view of two-dimensional seismic data for a work area.

Fig. 2 is a schematic view of a fluid activity profile obtained by inversion calculation using the method of the present invention.

Detailed Description

The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.

The existing fluid activity calculation method is as follows:

wherein R is the reflection coefficient and F is the fluid activity; rho_fIs the fluid density; omega is seismic wave angular frequency; r₀、R₁Respectively, a zeroth order term and a first order term of the asymptotic representation of the reflection coefficient, which are functions related to the properties of reservoir rocks and fluids;

c is a defined complex function. As can be seen from the above equation, reservoir fluid activity is proportional to the first derivative of the reflection coefficient at frequency ω. After time-frequency decomposition is carried out on the seismic signals, a single-frequency instantaneous amplitude spectrum a (omega) is used for replacing a reflection coefficient R at a corresponding frequency, so that a fluid activity attribute F (see an expression (1-6)) can be obtained, and the fluid activity attribute F is approximate calculation. However, the physical significance of this method is not clear, and the accuracy of the fluid activity found is low. In order to solve the problems, the invention provides a new calculation method, and the feasibility of the new method in calculating the fluid activity is verified through example analysis.

The invention relates to a method for predicting the fluid activity of an oil and gas reservoir, which is based on the low-frequency asymptotic representation theory of normal reflection coefficients at the interface of pore media containing saturated fluid and is used for carrying out frequency-dependent inversion prediction on the fluid activity under a Bayes framework, wherein the calculation process comprises the following steps:

the first step is as follows: a first order Taylor expansion on the fluid activity F is made for equation (1-1) to obtain a linear approximation of the reflection coefficient

For the sake of convenience, the formula (2) is rearranged and written as

R(F,ω)＝A₀(F₀,ω)+B₀(F₀,ω)·F (3)

In the formula (3), F₀Is a value of a certain fluid activity of the fluids contained in the reservoir, we call the fluid activity characteristic value, and A₀、B₀The specific expression is as follows:

the second step is that: because the reflection coefficient is related to the frequency, when the forward operator is constructed, the frequency division processing is firstly carried out, and the reflection coefficient is expressed as R_ω＝[R_ω1 R_ω2 … R_ωM]^TAnd M represents the number of frequencies. Calculating the value of the reflection coefficient at an arbitrary frequency using the formula (3)

Note A_ωi＝[A_0ωi A_0ωi L A_0ωi]^T，F＝[F(t₁) F(t₂) L F(t_n)]^T，

The formula (5) can be rewritten as

R_ωi＝A_ωi+B_ωi·F (6)

The third step: substituting equation (6) into the unstable seismic convolution model S (omega)_i)＝W_i·R_ωiIs obtained by item shifting

S(ω_i)-S'(ω_i)＝W_i·B_ωi·F (7)

Wherein S (ω)_i)＝W_i·R_ωi，S'(ω_i)＝W_i·A_ωi. Finally obtaining the recombinedThe positive calculus is as follows

The fourth step: in order to improve the stability of frequency-dependent inversion, a sparse regularization term and a low-frequency model constraint term introduced by prior probability distribution are added when a target function is constructed under a Bayes framework, and a target functional is finally obtained

In formula (9): sigma_n ²And σ_F ²Respectively, noise distribution and covariance of inversion model parameters; xi and D are low frequency prior and regularization matrices, respectively; lambda [ alpha ]_lAre model constraint coefficients. The idea of Bayesian estimation is to minimize the target functional J (F), and the gradient of the model parameter F is solved by the formula (9) and is set to 0, so as to obtain the final nonlinear inversion equation of the model parameter, and the value of F is solved by using the least square method, so as to obtain the value of the fluid activity.

FIG. 1 is two-dimensional seismic data for a work area. Fig. 2 is a fluid activity profile of the two-dimensional data shown in fig. 1 obtained by inversion calculation using the method of the present invention, and the higher the fluid activity value, the better the reservoir oil-gas content. The high value region of fig. 2 is consistent with the actual hydrocarbon reservoir, so it can be seen that the calculation method proposed by the present invention has good results for hydrocarbon reservoir prediction.

The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (1)

1. A method for predicting the fluid activity of a hydrocarbon reservoir is characterized by comprising the following steps:

first, a linear approximation expression of the reflection coefficient is obtained:

is provided with a formula (1-1),

in the formula (1-1), R is a reflection coefficient, and F is fluid mobility; rho_fIs the fluid density; omega is seismic wave angular frequency; r₀、R₁Respectively, a zeroth order term and a first order term of the asymptotic representation of the reflection coefficient, which are functions related to the properties of reservoir rocks and fluids;

a first order Taylor expansion on the fluid activity F is made for equation (1-1) to obtain a linear approximation of the reflection coefficient R:

rearranging formula (2), writing formula (2) as:

R(F,ω)＝A₀(F₀,ω)+B₀(F₀,ω)·F (3)，

in the formula (3), F₀Is a fluid activity characteristic value of a fluid contained in the reservoir, and A₀、B₀The specific expression is as follows:

and secondly, performing frequency division treatment: expressing the value of the reflection coefficient at an arbitrary frequency as R_ωi＝[R_ωi(t₁)R_ωi(t₂)..R_ωi(t_n)]^TWherein, t₁,t₂,...,t_nRepresenting different time depths, from 1 to n, and calculating a reflection coefficient at an arbitrary frequency using equation (3)Numerical values:

note A_ωi＝[A_0ωi A_0ωi L A_0ωi]^T，F＝[F(t₁) F(t₂)L F(t_n)]^T，

Equation (5) is written as:

R_ωi＝A_ωi+B_ωi·F (6)；

thirdly, obtaining a recombined forward operator: substituting equation (6) into the unstable seismic convolution model S (omega)_i)＝W_i·R_ωiAnd the item shifting arrangement is carried out to obtain:

S(ω_i)-S'(ω_i)＝W_i·B_ωi·F (7)，

s (omega) in formula (7)_i)＝W_i·R_ωi，S'(ω_i)＝W_i·A_ωiFinally, the recombined positive operator is obtained as follows:

fourthly, constructing an objective function under a Bayes framework: adding a sparse regularization term and a low-frequency model constraint term introduced by prior probability distribution to finally obtain a target functional as follows:

in formula (9), σ_n ²And σ_F ²Respectively, noise distribution and covariance of inversion model parameters; xi and D are low frequency prior and regularization matrices, respectively; lambda [ alpha ]_lIs a model constraint coefficient;

and (3) solving the gradient of the model parameter F in the formula (9), setting the gradient to be 0, obtaining a final nonlinear inversion equation of the model parameter, and solving the value of F by using a least square method to obtain the fluid activity value.

Images