CN103412323A - Method for predicting longitudinal wave velocity of rock rich in solid organic matters - Google Patents

Abstract

The invention provides a method for predicting the longitudinal wave velocity of a rock rich in solid organic matters, which comprises the following steps: extracting rock skeleton parameters, solid organic matter parameters and fluid parameters; based on a three-layer plaque saturation model, respectively calculating potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matter by using the rock skeleton parameters, the solid organic matter parameters and the fluid parameters; according to the Hamilton principle and the Lagrange equation, establishing a dual-pore dual-fluid rock wave equation by utilizing potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matters; and predicting the velocity dispersion and attenuation of the longitudinal wave according to the plane wave analysis solution and the dual-pore dual-fluid rock wave equation. The method can truly reflect and accurately predict the dispersion and attenuation of the seismic waves in the reservoir, can process the condition of the dual fluid containing any fluid, and particularly improves the prediction precision of the longitudinal wave velocity of the oil-water saturated rock.

Description

Method for predicting longitudinal wave velocity of rock rich in solid organic matters

Technical Field

The invention relates to the field of seismic rock physics, in particular to a method for predicting longitudinal wave velocity of a rock rich in solid organic matters.

Background

With the increasing price of petroleum and the concern of safety in strategic resource supply, people are turning their attention to the development of unconventional oil and gas resources, wherein rocks (such as shale) rich in solid organic matters become a representative of unconventional resources and have great potential. Shale rich in organic matter is complex in composition, mainly composed of an inorganic mineral framework and organic matter dispersed therein, and has strong heterogeneous characteristics. When animal and plant plants are buried at the time of deposition, the organic molecules produce two primary solid organic substances under diagenesis: kerogen and bitumen. Kerogen is a major source and carrier of shale oil and gas resources, however, the fundamental relationship between abundance of organic constituents and petrophysical properties is still poorly understood. Particularly, a method for predicting the longitudinal wave velocity of the rock rich in solid organic matters is important, and the method can help us to establish an exploration and development means for developing complex rock environments.

Rock skeletons are media filled with pores and fractures in which oil and gas resources can be generated, stored and transported. In the rock rich in solid organic matters, the primary organic matters such as kerogen have solid-like forms and are filled in the rock framework in the form of non-uniform adulterants. The kerogen and other solid organic matters have micro-pores and cracks, and gaseous and liquid organic matters such as natural gas and micro-oil drops are adsorbed in the kerogen and other solid organic matters, so that the kerogen and other solid organic matters are a source for generating potential oil and gas resources. Both in the inorganic mineral framework and inside the kerogen, a large number of microporosities of different dimensions, shapes and numbers are found, which constitute sites for the generation and storage of hydrocarbons.

The rock skeleton and the solid organic matter are pore media, but the rock physical parameters such as porosity, density, permeability, elastic modulus and the like are greatly different, and the rock skeleton and the solid organic matter must be regarded as a rock system with double pores. Gas and liquid substances (such as natural gas, oil and the like) exist in pore systems of the kerogen and the rock skeleton at the same time, and the gas and the liquid substances can migrate along the crack pore systems under the conditions of external water pressure and the like, so that oil and gas resources which can be developed and utilized are formed. The fluids have different physical properties of density, viscosity, elastic modulus and the like, the saturation degree of the fluids has important influence on the propagation speed of longitudinal waves, and the coexistence of the fluids makes the rock become a pore medium system containing dual fluids. Thus, rocks rich in solid organic matter have dual porosity and dual fluid characteristics. The method is used for establishing the relationship between two types of pores/two types of fluids and the rock longitudinal wave velocity, and providing a method for predicting the rock longitudinal wave velocity under different porosities and different fluid contents, and has a remarkable meaning for developing shale oil and gas resources through seismic wave exploration.

Reservoir rock compressional velocity prediction rich in solid organic matters is one of hot spots in the field of seismic petrophysics, and is still under development. Currently, the existing compressional velocity prediction methods are mainly based on plaque models of unsaturated pore systems (see White J.E. computed differential velocities and orientations in Rocks with Partial Gas conservation. Geophysics, 1975). In the rock skeleton containing pores, double fluids (gas and liquid) are uniformly distributed in a space slice mode, the plaque size of the gas and the liquid is far larger than that of mineral crystal particles, and meanwhile, the plaque size of the gas and the liquid is far smaller than the wavelength of longitudinal waves and is in a mesoscopic scale. The gas and liquid patches are equivalent to an inner spherical core and an outer spherical shell having the same spherical center. When the longitudinal wave passes through the double fluid plaque, the movement of the fluid in the pore space relative to the rock skeleton is caused, and the propagation speed of the longitudinal wave is changed. The change of the speed of the longitudinal wave along with the frequency is called frequency dispersion, and the change of the amplitude of the longitudinal wave along with the frequency is called attenuation. Meanwhile, the speed can also change regularly along with the difference of gas and liquid contents. The external pressure can cause the inner and outer layers of media (respectively containing gas and fluid) to deform in different degrees, and the plaque model can well predict the longitudinal wave velocity of the dual-fluid pore medium based on the influence of the content of the gas and the fluid and the influence of physical properties on the pore deformation and the pressure. However, the plaque model of White does not take into account the dual porosity effect caused by the difference in porosity between the inner and outer media. Meanwhile, the White model simplifies and neglects the physical parameters of the internal gas, and cannot process the longitudinal wave velocity of the rocks containing non-gas organic matters (such as oil-water saturation) in the plaque. Johnson proposed a branch function-based method for predicting dispersion/attenuation of longitudinal wave velocity in 2001 (see Johnson D.L. theory of Frequency Dependent Acoustics in Patch-structured Porous media. J Acoust SocAm, 2001.) this method was very stable to the calculation of longitudinal wave velocity in unsaturated pore media, but it only considered the case of one type of skeleton, two fluids.

A biological-Rayleigh method for predicting longitudinal Wave velocity of a Double-pore medium of a fluid and two frameworks is provided based on Hamilton principle of Wave Propagation of a pore medium and a Rayleigh method, Bajing and the like of kinetic energy calculation of a fluid containing bubbles (see the documents of Ba J, Carcinone J.M., Nie J.X.Biot-Rayleigh Theory of Wave Propagation in Double-pore-porous media. journal of geographic Research, 2011). According to the method, double pore media with different porosities, elastic moduli and permeabilities are considered, a longitudinal wave propagation equation is established through a Lagrange equation from the potential energy, the kinetic energy and the dissipated energy of the pore media, and the relation between the speed change and the frequency of the longitudinal wave is obtained. The method can be expanded to the condition that a rock framework and two types of pore fluid (gas and liquid) permeate, wherein the rock is internally provided with one type of air holes and one type of water holes, and the gas and water unsaturated rock is approximately regarded as another type of dual pore medium model. However, the method can only process the conditions of one type of fluid, two types of skeletons or one rock skeleton and two types of pore fluids, and cannot predict the longitudinal wave velocity of the rock containing double pores and double fluids. Since Rayleigh theory can only calculate the kinetic energy of the fluid containing bubbles, the method cannot predict the longitudinal wave velocity of the rock containing non-gas organic matters (such as oil-water saturation) in the plaque.

Therefore, for predicting the longitudinal wave velocity of the rock rich in the solid organic matters, the existing plaque saturation model faces the following difficulties: the longitudinal wave velocity of the rock containing two pores and two fluids at the same time cannot be predicted; when the interior of the plaque contains non-gaseous organic matters such as oil and water (such as oil-water saturation), the longitudinal wave velocity of the rock cannot be predicted.

Disclosure of Invention

The main purpose of the embodiments of the present invention is to provide a method for predicting a longitudinal wave velocity of a rock rich in solid organic matter, so as to solve the problems that the prior art cannot predict a longitudinal wave velocity of a rock simultaneously containing two pores and two fluids, and cannot predict a longitudinal wave velocity of a rock when a plaque contains non-gas organic matter such as oil and water (e.g., oil-water saturation).

In order to achieve the above object, an embodiment of the present invention provides a method for predicting a longitudinal wave velocity of a rock rich in solid organic matter, including:

extracting rock skeleton parameters, solid organic matter parameters and fluid parameters;

based on a three-layer plaque saturation model, respectively calculating potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matter by using the rock skeleton parameters, the solid organic matter parameters and the fluid parameters; the three-layer plaque saturation model is a physical model established according to the characteristics of double pores and double fluids of a rock system rich in solid organic matters;

according to the Hamilton principle and the Lagrange equation, establishing a dual-pore dual-fluid rock wave equation by utilizing potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matters;

and predicting the velocity dispersion and attenuation of the longitudinal wave according to the plane wave analysis solution and the dual-pore dual-fluid rock wave equation.

By means of the technical scheme, according to the characteristics that rocks rich in solid organic matters have double pores and double fluids, a three-layer plaque saturation model is established, potential energy, kinetic energy and dissipation energy of a rock system are calculated respectively based on the three-layer plaque saturation model, then a double-pore double-fluid rock wave equation is established according to the Hamilton principle and the Lagrange equation, and further longitudinal wave velocity dispersion and attenuation prediction are achieved; compared with the prior art, the method simultaneously considers the influences of two pores and two types of fluids on the longitudinal wave velocity, can truly reflect and accurately predict the dispersion and attenuation of seismic waves in a reservoir, can process the condition of double fluids containing any fluid, and particularly improves the prediction precision of the longitudinal wave velocity of the oil-water saturated rock.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without inventive labor.

FIG. 1 is a schematic flow chart of a method for predicting longitudinal wave velocity of a rock rich in solid organic matter according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a three-layer plaque saturation model according to an embodiment of the present invention;

FIG. 3 is a comparison graph of the prediction results of longitudinal wave velocity provided by the second embodiment of the present invention;

FIG. 4 is a comparison graph of the prediction results of longitudinal wave velocity provided by the third embodiment of the present invention;

FIG. 5 is a graph of logging parameters provided by a fourth embodiment of the present invention;

fig. 6 is a graph of the predicted longitudinal wave velocity according to the fourth embodiment of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Example one

The embodiment provides a method for predicting the longitudinal wave velocity of a rock rich in solid organic matters, which comprises the following steps of:

step S11, extracting rock skeleton parameters, solid organic matter parameters and fluid parameters;

step S12, based on the three-layer plaque saturation model, respectively calculating potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matter by using the rock skeleton parameters, the solid organic matter parameters and the fluid parameters; the three-layer plaque saturation model is a physical model established according to the characteristics of double pores and double fluids of a rock system rich in solid organic matters;

step S13, according to the Hamilton principle and the Lagrange equation, establishing a dual-pore dual-fluid rock wave equation by utilizing potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matter;

and step S14, predicting velocity dispersion and attenuation of the longitudinal wave according to a plane wave analysis solution and the dual-pore dual-fluid rock wave equation.

Aiming at the step S11, the method has the function of obtaining accurate and credible petrophysical parameters, provides experimental data for predicting the longitudinal wave velocity of the double-hole double-fluid rock, and is the basis of the subsequent technology.

Specifically, step S11 is to obtain parameters such as porosity, density, permeability, and dry skeleton elastic modulus of a rock skeleton composed of mineral particles based on a core experiment; based on a scanning electron microscope and a nanoindentation technology, parameters such as the elastic modulus, the porosity and the density of the solid organic matter are obtained through rock physical experiments; in specific implementation, the method for acquiring the parameters of the rock skeleton, the solid organic matter and the fluid, which is commonly used in the prior art, can be adopted, for example:

obtaining parameters such as rock mineral components, mineral volume ratio, permeability, porosity, shale content and the like according to geological reports, logging information, core slices, electron microscope analysis and the like of a target area; calculating to obtain equivalent elastic modulus of the mineral particle framework and the solid organic matter based on a Voigt-Reuss-Hill model; according to the information of temperature, pressure, mineralization degree and the like of the stratum of the target area, the characteristics of the fluid are analyzed, and parameters such as density, viscosity, elastic modulus and the like of the fluid are determined.

Step S11 requires the collection of appropriate core samples and laboratory petrophysical experimental conditions. Given the various mineral components in the rock and their elastic moduli, and the unknown way of combining the minerals, the Voigt and reus limits give the upper and lower limits of the rock elastic modulus.

The Voigt limit, also known as the Isostrain average, is calculated as follows, equation 1:

$M_V=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{f}_i{M}_i$ (A)Formula 1)

The reus limit, also known as equal stress averaging, is calculated as follows, equation 2:

$\frac{1}{M_R}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{f_i}{M_i}$ (formula 2)

In equations 1 and 2, N represents the number of constituent components, f_iVolume fraction of i-th medium, M_iIs the modulus of elasticity, M, of the i-th medium_VDenotes the upper limit of Voigt, M_RRepresents the lower reus limit. M_iAny one of the moduli may be represented: bulk modulus K, shear modulus μ, Young's modulus E, and the like.

The Voigt-reus-Hill mean model is the arithmetic mean of both the Voigt upper bound and the reus lower bound, expressed as follows:

$M_{\mathrm{VRH}}=\frac{M_V+M_R}{2}$ (formula 3)

In formula 3, M_VRHNamely the Voigt-reus-Hill average modulus, the modulus of any one of the elastic modulus and the matrix modulus of the rock skeleton required when the dry skeleton modulus of the rock is calculated later can be expressed.

Aiming at the step S12, the core is to establish a three-layer plaque saturation model capable of better reflecting the characteristics of a rock system rich in solid organic matters according to the characteristics of double pores and double fluids of the rock system; as shown in fig. 2, a schematic diagram of a three-layer plaque saturation model is shown, and the technical points of the three-layer plaque saturation model include:

(1) the method is characterized in that rock frameworks, non-uniformity of solid organic matters and non-uniformity of two types of fluids are combined into a whole, a double-pore double-fluid rock system rich in the solid organic matters is equivalent to a three-layer spherical shell with the same spherical center position, each layer of spherical shell is a shell type area with a certain thickness, the three layers of spherical shells are defined as an outer spherical shell, a middle spherical shell and an inner spherical shell, and the shell type area where the outer spherical shell is located is an outer pore area omega₃The shell type area where the middle spherical shell is located is a middle layer pore area omega₂The shell area where the inner spherical shell is located is an inner layer pore area omega₁(ii) a Different pore regions allow for different pore characteristics and different fluid characteristics; the surface of the outer spherical shell is ltf-3 (hereinafter referred to as outer interface ltf-3), the interface of the outer spherical shell and the middle spherical shell is ltf-2 (hereinafter referred to as middle interface ltf-2), the interface of the middle spherical shell and the inner spherical shell is ltf-1 (hereinafter referred to as inner interface ltf-1), and the region between the ltf-3 of the outer interface and the ltf-2 of the middle interface is an outer-layer pore region omega₃The region between the middle interface ltf-2 and the inner interface ltf-1 is a middle layer pore region omega₂The area within the ltf-1 of the inner interface is an inner-layer pore area omega₁；

(2) When the first fluid space saturation region is positioned in the solid organic matter, the middle interface ltf-2 represents the boundary between the solid organic matter and the mineral framework, and the middle layer pore region omega₂And inner pore region omega₁Representing the spatial area occupied by solid organic matter; the inner interface ltf-1 represents the boundary between the first and second fluids, the inner pore region omega₁Representing a region of space occupied by a first type of fluid; in this case, the outer pore region Ω₃Middle layer pore region omega₂And inner pore region omega₁Has a porosity ofThe characteristic parameter of the fluid satisfies f₂＝f₃≠f₁；

(3) When the first fluid spatial saturation region exceeds the solid organic matter, the middle interface ltf-2 represents the boundary between the first fluid and the second fluid, the middle layer pore region omega₂And inner pore region omega₁Representing a region of space occupied by a fluid representing a first type; inner interface ltf-1 represents the boundary between solid organic matter and mineral framework, inner pore region omega₁Representing the spatial area occupied by solid organic matter; in this case, the outer pore region Ω₃Middle layer pore region omega₂And inner pore region omega₁Has a porosity of

The characteristic parameter of the fluid satisfies f₁＝f₂≠f₃；

Wherein,

respectively an inner layer pore region omega₁Middle layer pore region omega₂Outer pore region omega₃Porosity of (c); f. of₁、f₂、f₃Respectively an inner layer pore region omega₁Middle layer pore region omega₂Outer pore region omega₃The characteristic parameter of the fluid.

Further, the step of calculating potential energy, kinetic energy and dissipation energy of the dual-pore dual-fluid rock system in step S12 includes the following steps:

step S121, calculating potential energy W of the dual-pore dual-fluid rock system:

(formula 4)

In formula 4, m is 1,2, 3; i is 1,2, 3; j is 1,2, 3;

represents the porosity in the pore region of the mth layer; zeta_mRepresenting the volume content change of the fluid caused by the fluid flowing between the boundaries of different pore areas; n is the rock skeleton shear modulus; a is the solid modulus of elasticity; q_mIs a solid, fluid-coupled elastic modulus; r_mIs the fluid modulus of elasticity.

I₁、I₂Respectively, the first and second strain invariants of the rock skeleton are as follows:

I₁＝e₁₁+e₂₂+e₃₃(formula 5)

$I_2=\left|\begin{array}{cc}{e}_{11}& e_{12}\\ e_{21}& e_{22}\end{array}\right|+\left|\begin{array}{cc}{e}_{22}& e_{23}\\ e_{32}& e_{33}\end{array}\right|+\left|\begin{array}{cc}{e}_{33}& e_{31}\\ e_{13}& e_{11}\end{array}\right|$ (formula 6)

Component e of strain tensor_ijIs defined as:

$e_{\mathrm{ij}}=\frac{1}{2}(u_{i\′j}+u_{j\′i})$ (formula 7)

U in formula 7 represents a spatial displacement component of the rock skeleton; xi_mA first strain invariant representing a fluid; the subscript i' j denotes the spatial derivative along the j coordinate for component i; the subscript j' i represents the spatial derivative along the i coordinate of component j;

ξ_m＝ε₁₁+ε₂₂+ε₃₃(formula 8)

The fluid strain is defined as:

${\mathrm{\ϵ}}_{\mathrm{ij}}^{\left(m\right)}=\frac{1}{2}(U_{i\′j}^{\left(m\right)}+U_{j\′i}^{\left(m\right)})$ (formula 9)

U in equation 9^(m)Representing the spatial displacement component of the fluid in the pore region of the mth layer.

Step S122, calculating the kinetic energy T of the rock system rich in the solid organic matters:

$T=\frac{1}{2}\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{00}{\stackrel{\·}{u}}_i^2+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\underset{m=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{0m}\stackrel{\·}{u_i}{\stackrel{\·}{U}}_i^{\left(m\right)}+\frac{1}{2}\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\underset{m=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{\mathrm{mm}}{\stackrel{\·}{U}}_i^{\left(m\right)2}+T_L$ (formula 10)

In equation 10, the intermediate parameters are defined as follows:

(formula 11)

In formula 11,. rho₀Is the density of the rock skeleton,

is the m-th layer mineral crystal particle density;representing the fluid density of the mth layer of pore area in the three-layer plaque model; a is a parameter of the pore geometry; t is_LIs the local flow kinetic energy caused by the difference between the dual pores.

By r₁、r₂、r₃Respectively representing the radiuses of an inner interface ltf-1, a middle interface ltf-2 and an outer interface ltf-3 in the three-layer plaque saturation model; for T_LThe calculation of (a) is realized by the following method:

local flow kinetic energy T of three-layer plaque saturation model_LIs shown as

Wherein N is₀The number of plaques within a unit volume is expressed,

the local flow kinetic energy of each plaque is expressed and calculated by the following formula:

(formula 12)

Equation 12, equation right first termIs the inner pore region omega₁The kinetic energy of the internal fluid (hereinafter referred to as internal fluid kinetic energy) is calculated according to the sphere harmonic vibration theory in this embodiment₁The specific calculation process of the kinetic energy of the internal fluid is as follows:

considering the fluid incompressible condition, the fluid displacement in the sphere area is obtained:

(formula 13)

In the formula 13, r₀Representing the displacement of the fluid at rest; r is_lhIs the displacement coefficient;

coordinates representing angular directions of the space spherical coordinate system;

the spherical harmonic vibration is expressed as:

${Y_l}^h({\mathrm{\θ}}_0,{\mathrm{\φ}}_0)={(-1)}^{\max (h,0)}\sqrt{\frac{(2l+1)(l-|h|!)}{4\mathrm{\π}(l+|h\left|\right)!}}{P_l}^{\left|h\right|}\left(\cos {\mathrm{\θ}}_0\right)e^{\mathrm{ih}{\mathrm{\φ}}_0}$ (formula 14)

In equation 14

Representing a first class Legendre function;

considering the quadrature nature of harmonic vibrations within a sphere, the internal fluid kinetic energy is expressed as:

(formula)15）

When the order h of the Legendre function is 1, and l of the Legendre function is 1, the local flow kinetic energy T of the three-layer plaque saturation model is considered in consideration of the conservation condition that the fluid flows on the inner spherical shell boundary ltf-1_LFinally, it is expressed as:

(formula 16)

In the formula 16, the first and second phases,

represents the porosity of the m-th layer of pore region;

satisfy

Wherein v is_mThe volume ratio of the m-th layer of pore area to the total volume of the plaque; r is_m0Representing the initial radius of the spherical shell of the mth layer; ${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00003468896300012.png,HDA00003468896300031.png"\; state="\{\{state\}\}">k</figure-callout>}}_1=1+\frac{v_1}{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2},$

the existing dual-fluid plaque model only considers the gas condition, and neglects the kinetic energy of the internal gas. The invention provides a method for calculating an inner-layer pore region omega according to a sphere harmonic vibration theory₁The calculation method of the kinetic energy of the internal fluid realizes the plaqueThe prediction of the longitudinal wave velocity of the pore system containing the non-gas organic matters inside can be used for processing the conditions of various types of double fluids, particularly the prediction precision of the longitudinal wave velocity of oil-water saturated rocks is improved, and the application range of the plaque model in seismic rock physics is expanded.

Step S123, calculating the dissipation energy D of the rock system rich in the solid organic matters:

the movement of the fluid relative to the rock skeleton generates friction, causing energy losses, which are expressed as dissipated energy

$D=\frac{1}{2}\underset{m=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_m\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{({\stackrel{\&CenterDot;}{U}}_i^{\left(m\right)}-\stackrel{\&CenterDot;}{u_i})}^2$ (formula 17)

In the formula 17, b_mIs a dissipation coefficient, and

η_m、κ_m、v_mrespectively the m-th layer of poresThe fluid viscosity of the region, the permeability of the rock skeleton and the volume ratio of the m-th layer of pore region to the total volume of the plaque.

The local flow dissipation energy due to the dual pore difference is expressed as:

$D_L={\mathrm{\&beta;}}_1\frac{{\mathrm{\&phi;}}_1{\mathrm{\&phi;}}_2^2}{6}{r}_{10}^2{\stackrel{\&CenterDot;}{\mathrm{\&zeta;}}}_1^2+{\mathrm{\&beta;}}_2\frac{{\mathrm{\&phi;}}_2{\mathrm{\&phi;}}_3^2}{6}{\mathrm{<figure-callout\; id="20"\; label="r"\; filenames="HDA00003468896300021.png"\; state="\{\{state\}\}">r</figure-callout>}}_{20}^2{\stackrel{\&CenterDot;}{\mathrm{\&zeta;}}}_2^2$ (formula 18)

In the formula 18, the process is described,

aiming at the step S13, which is to establish an accurate physical relationship between the longitudinal wave velocity and the pore characteristics and the fluid characteristics, the present embodiment obtains a wave equation of the dual-pore dual-fluid rock system by using the potential energy, the kinetic energy and the dissipation energy of the dual-pore dual-fluid rock system according to the classical mechanics hamilton principle and the lagrange equation:

(formula 19)

Wherein U is a rock skeleton displacement vector and U is a fluid displacement vector.

For step S14, which is to carry the plane wave analytic solution into the dual-pore dual-fluid rock wave equation established in step S13, an equation with respect to wave number k is obtained using the condition that the equation determinant is zero:

$\left|\begin{array}{cccc}{a}_{11}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{11}& a_{12}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{12}& a_{13}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{13}& a_{14}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{14}\\ a_{21}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{21}& a_{22}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{22}& a_{23}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{23}& a_{24}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{24}\\ a_{31}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{31}& a_{32}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{32}& a_{33}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{33}& a_{34}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{34}\\ a_{41}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{41}& a_{42}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{42}& a_{43}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{43}& a_{44}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003468896300012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+b_{44}\end{array}\right|=0$ (formula 20)

Equation 20 relates to k²Higher order equation of (c), k²There are four solutions, representing one fast P-wave and three slow P-waves, respectively. Wherein, a_ij、b_ijIs a coefficient of_ij、b_ijAnd bulk modulus A, N, R₁、R₂、R₃，Q₁、Q₂、Q₃Porosity of

Plaque radius r₁₀、r₂₀Density ρ₀₀、ρ₀₁、ρ₀₂、ρ₀₃、ρ₁₁、ρ₂₂、ρ₃₃Coefficient of dissipation b₁、b₂、b₃The following functional relationship exists between the frequencies ω:

1）

in the formula 21 $\mathrm{\&iota;}=\sqrt{-1}.$

According to the above equations 20 and 21, the functional relationship k (ω) between the frequency ω and the wave number k can be obtained, and further the prediction equation of the velocity of the longitudinal wave can be utilizedAnd attenuation prediction formulaAnd predicting longitudinal wave velocity, wherein im (k) and Re (k) are respectively an imaginary part and a real part of k.

The method for predicting the longitudinal wave velocity of the rock rich in the solid organic matter has the characteristics of accuracy and strong applicability, is particularly advantageous for predicting the longitudinal wave velocity dispersion and attenuation of two types of partially saturated rock of fluid under the conditions of two types of different pores containing mineral frameworks and organic matter doping, can estimate the velocity change curve of the solid organic matter under different contents, and can estimate the velocity change condition of the longitudinal wave under different gas and water contents.

After the predicted value of the longitudinal wave velocity of the dual-pore dual-fluid rock is obtained, the conditions of the abundance of solid organic matters and the saturation of different fluids in the underground target region can be guided to be explored through seismic exploration according to the sensitive change conditions of the wave velocity on pore difference and fluid difference.

In this embodiment, if two types of pores of the dual pores in the three-layer plaque saturation model are the same, the model is equivalent to a common single-pore two-fluid model, and at this time, the longitudinal wave velocity prediction method degrades into a common single-pore two-fluid model. Therefore, the compressional wave velocity prediction method provided by the embodiment has more general characteristics.

Example two

Based on the method provided by the first embodiment, two types of pores of the dual pores in the three-layer plaque saturation model are set to be the same, and then the longitudinal wave velocity prediction method is degraded into a single-pore two-fluid mode (hereinafter referred to as a single-pore two-fluid longitudinal wave velocity prediction method).

In this example, French Vosgian sandstone (Bacri J. -C., salt D.Sound with Oil and Brine at Different concentrations, 1986) is used, and the rock parameters are: the matrix bulk modulus is 37GPa, the matrix longitudinal wave velocity is 2050m/s, the matrix transverse wave velocity is 1240m/s, the matrix average density is 2.65g/cm3, the water longitudinal wave velocity is 1550m/s, the oil longitudinal wave velocity is 1275m/s, the water viscosity is 0.001Pa s, the oil viscosity is 0.076Pa s, the water density is 1.015g/cm3, the oil density is 0.775g/cm3, the porosity is 0.21, the permeability is 0.11D, and the plaque size is 1 mm.

In the embodiment, the single-pore double-fluid longitudinal wave velocity prediction method and the Biot-Rayleigh method are used for predicting the longitudinal wave velocity of the French Vosgian sandstone, wherein the prediction by using the single-pore double-fluid longitudinal wave velocity prediction method is divided into two situations of ignoring the internal fluid kinetic energy and calculating the internal fluid kinetic energy. FIG. 3 shows a comparison of three predictions; wherein BR stands for the Biot-Rayleigh method;

a longitudinal wave velocity prediction method which represents the single-pore double-fluid longitudinal wave velocity prediction method and ignores the kinetic energy of the internal fluid;

representing the single-pore double-fluid longitudinal wave velocity prediction method and a longitudinal wave velocity prediction method of internal fluid kinetic energy; the abscissa represents the water saturation; the ordinate represents the longitudinal wave velocity at 350KHz in meters per second (m/s). The comparative analysis of the prediction results shows that the speed of the inventionThe prediction is closer to the experimental value.

EXAMPLE III

This example uses Fort Union sandstone, which is a river miscellaneous sandstone, with a relatively low porosity (0.085). The example is a core at 3223 meters from a well located in the green river basin, penne anticline, wyoming, usa. The rock parameters are: the matrix bulk modulus is 35GPa, the matrix bulk modulus is 7.14Gpa, the framework shear modulus is 9.06Gpa, the water bulk modulus is 2.25GPa, the air bulk modulus is 0.8MPa, the water viscosity is 0.001Pa s, the air viscosity is 0.00001Pa s, the average matrix density is 2.65g/cm3, the water density is 0.997g/cm3, the air density is 0.1g/cm3, the porosity is 0.085, and the permeability is 0.5 mD.

Heterosandstones have a dark sedimentary rock with a low mud content and often a high carbonate content, and contain from 65 to 95% of the available quartz. These rocks have the characteristics of (1) containing over 25% of unstable materials (i.e. feldspar and rock fragments); (2) the gravel content is higher than that of feldspar; (3) there are more voids (open pore spaces) or mineral macadam (usually carbonate) than clay or argillaceous backbones. Based on the observation of mineral grains and pores in rock slices, the Fort Union sandstone grain diameter is between 0.125 and 0.15 millimeters.

This example uses the wave velocity observation data of low frequency low porosity unsaturated sandstone (Murphy, academic measurements of Partial Gas preservation in Tight sandtons, JOURNAL OFGEOPHYSICAL RESEARCH,1984) published in 1984 by Murphy, and compared with the results predicted by the present invention.

The method provided by the first embodiment, the method proposed in Johnson2001, the Whtie method after correction and the Biot-Rayleigh method are respectively adopted for predicting the compressional wave velocity of the Fort Union sandstone; in the prediction using the method provided in example one, we selected the average size of the plaque radius of 0.15mm, where the low-void doping volume fraction is 80%, the porosity of the internal low-void doping is 50% of the average porosity (0.085), and the internal permeability is 1% of the average permeability (0.5 mD).

FIG. 4 shows a comparison of the predicted results, wherein BR stands for the Biot-Rayleigh method; johnson stands for the method proposed in Johnson2001, White for the modified Whtie method; TLP represents the method proposed by the invention (method provided in the first embodiment). In fig. 4, the abscissa represents the water saturation; the ordinate represents the velocity in meters per second (m/s) at the longitudinal wave. It is found from fig. 4 that the velocity prediction results of longitudinal waves provided by the first embodiment are more consistent with experimental observation, especially the velocity prediction with water saturation higher than 50% is more close to the experimental observation data. The three-layer plaque saturation model provided by the invention can accurately depict the uneven characteristics of the pore rock and has obvious advantages compared with other methods.

Example four

In this embodiment, the method provided in the first embodiment is used to predict the velocity of the longitudinal wave in the depth segment of 920-960 using the data of porosity, water saturation and mud-to-mass ratio obtained by logging. Figure 5 shows a log parameter profile for this well. The rock stratum in the well is in an oil-water saturated state, and the rock skeleton minerals adopt quartz and clay parameters. In FIG. 5, the porosity, water saturation and shale fraction at depth 920-960 meters are plotted on the abscissa, and the formation depth is plotted on the ordinate.

The rock parameters are as follows: the bulk modulus of the matrix is 36.6GPa, the bulk modulus of the framework and the shear modulus are calculated from the porosity and the bulk modulus of the matrix (Pride formula), the bulk modulus of water is 2.25GPa, the bulk modulus of oil is 1.23GPa, the viscosity of water is 0.001 pas, the viscosity of oil is 7.6e-5 pas, the average density of the matrix is calculated according to the density of quartz (2.65g/cm3), the density of clay (1.58g/cm3) and the content of mud, the density of water is 1.0g/cm3, the density of oil is 0.755g/cm3, and the permeability is 100 mD.

In the embodiment, when the method provided by the first embodiment is adopted for prediction, the average size of the radius of the plaque is selected to be 10mm, wherein the volume ratio of low-porosity doping is estimated according to the content of the mud ratio. The porosity of the internal low-pore doping is 70% of the average porosity, the density is 1.2 times the average density, and the permeability is 1% of the average permeability. For the well acoustic wave experimental data, the frequency of 20kHz is adopted for calculation, and the velocity prediction can be well matched with the acoustic logging experimental data through the graph 5, which shows that under the condition that the longitudinal wave velocity is unknown, the method provided by the invention can well predict the longitudinal wave velocity curve only by depending on the formation porosity, the water saturation and the mud-mass ratio.

This example further substituted the kerogen rock parameters into the above model, replacing the clay position, with a kerogen bulk modulus of 2.9GPa, a shear modulus of 2.7GPa, and a density of 1.3g/cm3, resulting in a predicted longitudinal wave velocity curve as shown in fig. 6. In FIG. 6, the abscissa represents a curve in which Vp_TLPVplog is a longitudinal wave velocity prediction curve and an acoustic logging curve of a depth section of 920-.

Comparing fig. 5, it can be found that: kerogen-containing formations having higher longitudinal wave velocities than clay-containing formations; the longitudinal wave velocity of the kerogen-containing rock stratum has small fluctuation along with the depth. According to the method, different speed characteristics of the stratum containing the organic matters and the stratum containing the clay can be analyzed and compared, and the organic matter distribution in the stratum can be identified according to the speed change characteristics.

In summary, the method for predicting the longitudinal wave velocity of the rock rich in the solid organic matter provided by the embodiment of the invention has the following beneficial effects:

(1) the influence of two pores and two types of fluid on the longitudinal wave velocity can be considered simultaneously; the conventional longitudinal wave velocity prediction method for the unsaturated pore medium only can consider framework nonuniformity or fluid nonuniformity alone, but cannot combine the framework nonuniformity and the fluid nonuniformity together. For rocks rich in solid organic matters, after considering the influence of the difference between the organic matters and the pores of the mineral framework, the saturation conditions of fluids such as oil, gas and water are difficult to reflect, and the method cannot truly reflect and accurately predict the dispersion and attenuation of seismic waves in a reservoir stratum; by taking shale rich in kerogen as an example, the method provided by the invention can predict the influence of kerogen, oil, gas and water on the longitudinal wave velocity at normal temperature, and can predict the change of the longitudinal wave velocity in the process of converting solid kerogen into fluid oil gas under the condition of high-temperature fracturing;

(2) according to the distribution of pore characteristics and fluid characteristics under the real condition, the method can be degraded into a common single-pore double-fluid or double-pore single-fluid velocity prediction method, so that the method has more general characteristics; for example, in the longitudinal wave velocity prediction of French Vosgian sandstone (single pore double fluid) containing oil and water, the velocity prediction of the invention for internal non-gas saturation (oil-water) is found to be closer to experimental data by comparing with a Biot-Rayleigh method;

(3) the fluid energy calculation is more accurate, and the speed prediction precision is improved. In the past, the plaque saturation model has inaccurate calculation on the double fluid containing non-gas inside, which is caused by neglecting the kinetic energy of the internal fluid; by utilizing the sphere harmonic vibration model, the invention strictly calculates the kinetic energy of the fluid in the plaque, can process the condition of the double fluid containing any fluid, and particularly improves the prediction precision of the longitudinal wave velocity of the oil-water saturated rock, thereby being beneficial to expanding the application range of the current seismic rock physics.

The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A method for predicting longitudinal wave velocity of rock rich in solid organic matters is characterized by comprising the following steps:

extracting rock skeleton parameters, solid organic matter parameters and fluid parameters;

based on a three-layer plaque saturation model, respectively calculating potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matter by using the rock skeleton parameters, the solid organic matter parameters and the fluid parameters; the three-layer plaque saturation model is a physical model established according to the characteristics of double pores and double fluids of a rock system rich in solid organic matters;

according to the Hamilton principle and the Lagrange equation, establishing a dual-pore dual-fluid rock wave equation by utilizing potential energy, kinetic energy and dissipation energy of the rock system rich in the solid organic matters;

and predicting the velocity dispersion and attenuation of the longitudinal wave according to the plane wave analysis solution and the dual-pore dual-fluid rock wave equation.

2. The method of claim 1, wherein the three-layer plaque saturation model is:

the rock system rich in the solid organic matters is equivalent to three layers of spherical shells with the same spherical center position, wherein the three layers of spherical shells are respectively an outer spherical shell, a middle spherical shell and an inner spherical shell; the shell type area where the outer spherical shell is located is an outer layer pore area, the shell type area where the middle spherical shell is located is a middle layer pore area, and the shell type area where the inner spherical shell is located is an inner layer pore area; the surface of the outer spherical shell is an outer boundary surface, the interface of the outer spherical shell and the middle spherical shell is a middle interface, and the interface of the middle spherical shell and the inner spherical shell is an inner interface;

when the first type of fluid space saturation area is positioned in the solid organic matter, the middle interface represents the boundary between the solid organic matter and the mineral framework, and the middle layer pore area and the inner layer pore area represent the space area occupied by the solid organic matter; the inner interface represents a boundary between the first fluid type and the second fluid type, and the inner pore region represents a spatial region occupied by the first fluid type; in this case, the porosity of the inner layer pore region, the middle layer pore region and the outer layer pore region is satisfiedThe characteristic parameter of the fluid satisfies f₂＝f₃≠f₁；

When the first fluid type space saturation area exceeds the solid organic matter, the middle interface represents the boundary between the first fluid type and the second fluid type, and the middle layer pore area and the inner layer pore areaRepresenting a region of space occupied by a fluid representing a first type; the inner interface represents the boundary between the solid organic matter and the mineral framework, and the inner pore area represents the spatial area occupied by the solid organic matter; in this case, the porosity of the inner layer pore region, the middle layer pore region and the outer layer pore region is satisfied

The characteristic parameter of the fluid satisfies f₁＝f₂≠f₃；

Wherein,the porosity of the inner layer pore area, the middle layer pore area and the outer layer pore area respectively; f. of₁、f₂、f₃The fluid characteristic parameters of the inner layer pore area, the middle layer pore area and the outer layer pore area are respectively.

3. The method of claim 2, wherein the potential energy of the rock system rich in solid organic matter is calculated using the following formula:

wherein W is the potential energy of the rock system rich in solid organic matter; m is 1,2, 3; i is 1,2, 3; j is 1,2, 3;

the porosity in the pore region of the mth layer in the three-layer plaque saturation model is obtained; zeta_mThe volume content change of the fluid caused by the fluid flowing between the boundaries of different pore areas; a is the solid modulus of elasticity; n is the shear modulus of the rock skeleton; q_mA solid, fluid-coupled elastic modulus in the pore region of the mth layer; r_mIs the fluid elastic modulus in the pore region of the mth layer; i is₁、I₂Are respectively a rock skeletonA first and a second strain invariant; e.g. of the type_ijIs a component of the strain tensor; u is the spatial displacement component of the rock skeleton; the subscript i' j denotes the spatial derivative along the j coordinate for component i; the subscript j' i represents the spatial derivative along the i coordinate of component j; xi_mA first strain invariant for fluid within the mth layer of pore regions; u shape^(m)Is the spatial displacement component of the fluid in the pore region of the mth layer.

4. The method of claim 3, wherein the kinetic energy of the solid organic matter rich rock system is calculated using the following formula:

wherein T is the kinetic energy of the rock system rich in the solid organic matter; rho₀Is the density of the rock skeleton,is the m-th layer mineral crystal particle density;

the fluid density of the pore area of the mth layer in the three-layer plaque saturation model; a is a parameter of the pore geometry; t is_LLocal flow kinetic energy due to the difference between the dual pores;

represents the porosity of the mth layer of media itself;

satisfy

Wherein v is_mThe volume ratio of the m-th layer of pore area; r is_m0Representing the initial radius of the spherical shell of the mth layer;

local flow kinetic energy T caused by the difference between the dual pores_LCalculated using the following formula:

wherein N is₀Number of plaques per volume;

coordinates representing angular directions of the space spherical coordinate system; omega₁、Ω₂、Ω₃Respectively representing an inner layer pore area, a middle layer pore area and an outer layer pore area in the three-layer plaque saturation model; r is₁、r₂、r₃The radiuses of an inner spherical shell, a middle spherical shell and an outer spherical shell in the three-layer patch saturation model are respectively; r is₀Displacement when the fluid is static; r is_lhIn order to be the coefficient of displacement,

is a Legendre function of the first kind, where P_l(x) Representing legendre orthogonal polynomials.

5. The method of claim 4, wherein the dissipated energy of the solid organic matter rich rock system is calculated using the following formula:

wherein D is the dissipated energy of the rock system rich in solid organic matter; b_mIs the dissipation factor; eta_m,κ_m,v_mRespectively the fluid viscosity and rock bone of the mth layer of pore area in the three-layer plaque saturation modelThe permeability of the scaffold and the volume ratio occupied by the pore region of the mth layer.

6. The method of claim 5, wherein the dual pore dual fluid rock wave equation is:

wherein U is a rock skeleton displacement vector and U is a fluid displacement vector.

7. The method according to claim 6, wherein the longitudinal wave velocity dispersion and attenuation are predicted according to a plane wave analysis solution and the dual-pore dual-fluid rock wave equation, specifically:

and substituting the plane wave analysis solution into the dual-pore dual-fluid rock wave equation, and obtaining an equation about the wave number k by using the condition that the equation determinant is zero:

$\left|\begin{array}{cccc}{a}_{11}{k}^2+b_{11}& a_{12}{k}^2+b_{12}& a_{13}{k}^2+b_{13}& a_{14}{k}^2+b_{14}\\ a_{21}{k}^2+b_{21}& a_{22}{k}^2+b_{22}& a_{23}{k}^2+b_{23}& a_{24}{k}^2+b_{24}\\ a_{31}{k}^2+b_{31}& a_{32}{k}^2+b_{32}& a_{33}{k}^2+b_{33}& a_{34}{k}^2+b_{34}\\ a_{41}{k}^2+b_{41}& a_{42}{k}^2+b_{42}& a_{43}{k}^2+b_{43}& a_{44}{k}^2+b_{44}\end{array}\right|=0$

the wave number k is solved using the following formula:

wherein, omega is the longitudinal wave frequency;

prediction formula of velocity of longitudinal wave

And attenuation prediction formula

And predicting longitudinal wave velocity, wherein im (k) and Re (k) are respectively an imaginary part and a real part of k.

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