CN112525803A - Sandstone porosity effective stress coefficient calculation method based on clay shell model - Google Patents
Sandstone porosity effective stress coefficient calculation method based on clay shell model Download PDFInfo
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Abstract
The invention relates to a clay shell model-based sandstone porosity effective stress coefficient calculation method, belonging to the field of rock mechanics effective stress coefficient calculation; the method solves the problems that the existing method for calculating the effective porosity model by using a theoretical model is few, the precision is low and the like; the technical scheme is as follows: providing a clay shell-shaped model, obtaining a clay shell-shaped porosity effective stress coefficient expansion formula by a chain method according to a porosity effective stress coefficient definition formula and in combination with a clay shell-shaped physical model porosity definition formula, and obtaining a clay shell-shaped porosity effective stress coefficient equation; and substituting the porosity, the clay content, the Poisson ratio and the rigidity ratio into a clay shell-shaped porosity effective stress coefficient model, and calculating the porosity effective stress coefficient. Based on the analysis result of the scanning electron microscope, the clay shell model is provided, the clay shell porosity effective stress coefficient model is deduced, the porosity effective stress coefficient is accurately calculated, the calculation effect accuracy is high, and the popularization is strong.
Description
Technical Field
The invention relates to a clay shell model-based sandstone porosity effective stress coefficient calculation method, and belongs to the field of rock mechanics effective stress coefficient calculation.
Background
All oil and gas reservoir rocks belong to porous media, and the most difference of the porous media from general solid materials is that the porous media have pores and the pores contain fluid, and the pore fluid generates pore fluid pressure. Therefore, the concept of the effective stress law is often used in the research of the mechanical properties of the oil and gas reservoir rock and the physical properties related to the mechanical properties such as stress sensitivity. The research of the effective stress law is the basis for understanding the sensitivity degree of the reservoir stress from the mechanism, and a series of models representing the relationship between the porosity and the permeability and the effective stress are built by many scholars based on the effective stress law. The research on the effective stress rule is essentially the research on the effective stress coefficient, and is very important for determining the effective stress coefficient of porosity.
However, the existing research on the effective stress coefficient of porosity has few documents, and the patent number is CN201710403114.4, namely a method for determining the effective stress coefficient of rock, the method comprises the steps of drawing a relation curve of unloading bias voltage increment and axial/circumferential strain increment under different confining pressures, and performing data fitting on the curve to obtain the effective elastic modulus and Poisson ratio related to the bias voltage level; the axial effective stress coefficient and the annular effective stress coefficient of the rock sample are calculated through a formula, the effective stress coefficient obtained by the method is relatively reliable, but the test is required to be completed, and the cost is high. CN201410320028.3 'a method for determining effective stress coefficient of rock based on pore compression experiment' fits a fitting function of effective stress and pore compression coefficient, measures a pore pressure constant value of a saturated rock core and a pore pressure value after increasing confining pressure, determines the reduction of the pore volume of the rock core, and finally determines the effective stress coefficient value of the rock according to a calculation formula of the effective stress born by a rock framework and the pore compression coefficient of the rock. In 2017, panke in the thesis of master graduate, "research on porosity stress sensitivity of clay-containing tight sandstone", imagines the distribution forms of four kinds of clay, and supposes that not only the clay exists in the pores, but also a part of the clay exists outside the pores, and is directly acted by confining pressure, so that a porosity effective stress calculation model is deduced, but the model is not very consistent with the actual situation, the calculated result is greatly different from the actual real result, and the accuracy of the calculation result is in doubt.
Generally, most of the existing methods for calculating and analyzing the effective stress coefficient of porosity use physical experiments to calculate and measure, and few methods for calculating by using theoretical models have questionable calculation accuracy, so that more accurate calculation methods are needed.
Disclosure of Invention
The invention aims to: in order to solve the problems of few methods for calculating the effective porosity model by using a theoretical model, low precision and the like, the invention provides a clay shell model based on the analysis result of a scanning electron microscope, deduces the clay shell porosity effective stress coefficient model, accurately calculates the effective porosity stress coefficient, has high calculation effect accuracy and strong popularization.
In order to achieve the purpose, the invention provides a clay shell model-based sandstone porosity effective stress coefficient calculation method, which comprises the following steps:
s100, adhering chlorite and illite to the inner wall of a pore in a shell form based on a scanning electron microscope analysis result, providing a clay shell model, and determining the porosity, the clay content, the Poisson ratio and the rigidity ratio of a rock sample containing clay minerals;
s200, obtaining the clay shell porosity effective stress coefficient expansion by a chain method according to the porosity effective stress coefficient definition formula and combining the clay shell physical model porosity definition formula, the main steps are,
s201, determining a porosity effective stress coefficient definition formula and a clay shell physical model porosity definition formula, wherein the porosity effective stress coefficient definition formula is
In the formula
Is a porosity effective stress coefficient, and has no dimensional quantity;φporosity, dimensionless;P pis pore pressure in MPa;P cis confining pressure in MPa; the porosity of the clay shell-shaped physical model is defined as
In the formula:
is the pore inner radius, and the unit is mum; b is the outer radius of the pores in μm;
s202, obtaining a clay shell porosity effective stress coefficient expansion form by a chain method, wherein the clay shell porosity effective stress coefficient expansion form is
；
S300, solving a partial derivative relational expression of the displacement of the inner wall surface and the outer wall surface of the pore to the pore pressure and the confining pressure and a partial derivative relational expression of the porosity to the inner wall surface and the outer wall surface of the pore, mainly comprising the following steps,
s301, calculating a partial derivative relational expression of the displacement of the inner wall surface of the pore to the pore pressure, wherein the partial derivative relational expression of the displacement of the inner wall surface of the pore to the pore pressure is
In the formula
Is the partial derivative of the displacement of the inner wall surface of the pore to the pore pressure;v cis the Poisson ratio of clay minerals without dimension;μ cthe Lame coefficient of clay mineral is dimensionless;A 1p、B 1pis a transition coefficient;
s302, calculating a partial derivative relation formula of the displacement of the inner wall surface of the pore to the confining pressure, wherein the partial derivative relation formula of the displacement of the inner wall surface of the pore to the confining pressure is
In the formula
The partial derivative of the displacement of the inner wall surface of the pore to the confining pressure;A 1c、B 1cis a transition coefficient;
s303, solving a partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure, wherein the partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure is
In the formula
The partial derivative of the displacement of the outer wall surface of the pore to the pore pressure is obtained; b is the outer radius of the pores in μm;v rthe Poisson ratio of the rock skeleton is a dimensionless quantity;A 2p、B 2pis a transition coefficient;
s304, solving a partial derivative relational expression of the displacement of the outer wall surface of the pore to the confining pressure, wherein the partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure is
In the formula
The partial derivative of the displacement of the outer wall surface of the pore to the confining pressure is obtained;μ rthe Lame coefficient of the rock skeleton is free of dimensional quantity;A 2c、B 2cis a transition coefficient;
s305, calculating partial derivative relational expressions of the porosity on the inner wall surface and the outer wall surface of the pore, wherein the partial derivative relational expressions of the porosity on the inner wall surface and the outer wall surface of the pore are respectively
；
S400, defining a shell-shaped clay mineral content relational expression and a rigidity ratio of a rock framework to clay to obtain an effective stress coefficient equation of the clay shell-shaped porosity;
s401, defining the relation of the content of the shell-shaped clay minerals as
Defining the rigidity ratio of the rock skeleton to the clay as in the formulaF cThe content of the shell-shaped clay minerals is zero dimensional quantity; c is the radius of the inner wall surface of the rock framework, and the unit is mum; the rigidity ratio of the stone framework to the clay is free of dimensional quantity;
s402, substituting the 5 partial derivative relational expressions obtained in the step S300 into an effective stress coefficient expansion of clay shell porosity to obtain
；
S403, substituting the rigidity ratio of the stone skeleton to the clay and the shell-shaped clay mineral content relational expression into the step S402 formula to obtain the effective stress coefficient model of the clay shell-shaped porosity, wherein the effective stress coefficient model of the clay shell-shaped porosity is
In the formula
，ωIs a constant;
s500, substituting the porosity, the clay content, the Poisson ratio and the rigidity ratio into a clay shell-shaped porosity effective stress coefficient model, and calculating the porosity effective stress coefficient.
In the method for calculating the effective stress coefficient of sandstone porosity based on the clay shell model, when the clay mineral content value of the rock sample is 0 and the rigidity ratio value is 1, the effective stress coefficient of porosity calculated by using the clay shell porosity effective stress coefficient model of the step S403 is equal to 1.
Compared with the prior art, the invention has the following beneficial effects: (1) the effective stress coefficient of the porosity is calculated by using the model, so that the complicated process of physical experiment testing is reduced; (2) the model is consistent with the reality, and the calculation result is more accurate; (3) the popularization is strong.
Drawings
In the drawings:
FIG. 1 is a technical scheme of the method.
Fig. 2 is a schematic diagram of a clay shell model.
Detailed Description
The present invention will be further described with reference to the following embodiments and drawings.
The invention provides a clay shell model-based sandstone porosity effective stress coefficient calculation method, and FIG. 1 is a technical route diagram of the method, and the method comprises the following steps:
s100, based on the analysis result of a scanning electron microscope, adhering chlorite and illite to the inner wall of a pore in a shell form, and providing a clay shell model, wherein the clay shell model is as shown in figure 2, the porosity of a rock sample containing clay minerals is measured by a pore infiltration instrument, the Poisson ratio is measured by Katahara in 1949, the Poisson ratios of the kaolinite, the illite and the chlorite are respectively 0.26, 0.25 and 0.27, and the shear modulus of the clay minerals is uniformly 0.25 multiplied by 104 MPa; the comprehensive elastic modulus and Poisson's ratio of the rock sample are measured by a longitudinal and transverse wave experiment;
s200, obtaining the clay shell porosity effective stress coefficient expansion by a chain method according to the porosity effective stress coefficient definition formula and combining the clay shell physical model porosity definition formula, the main steps are,
s201, determining a porosity effective stress coefficient definition formula and a clay shell physical model porosity definition formula, wherein the porosity effective stress coefficient definition formula is
In the formula
Is a porosity effective stress coefficient, and has no dimensional quantity;φporosity, dimensionless;P pis pore pressure in MPa;P cis confining pressure in MPa; the above-mentionedThe porosity of the clay shell-like physical model is defined as
In the formula:
is the pore inner radius, and the unit is mum; b is the outer radius of the pores in μm;
s202, obtaining a clay shell porosity effective stress coefficient expansion form by a chain method, wherein the clay shell porosity effective stress coefficient expansion form is
；
S300, solving a partial derivative relational expression of the displacement of the inner wall surface and the outer wall surface of the pore to the pore pressure and the confining pressure and a partial derivative relational expression of the porosity to the inner wall surface and the outer wall surface of the pore, mainly comprising the following steps,
s301, calculating a partial derivative relational expression of the displacement of the inner wall surface of the pore to the pore pressure, wherein the partial derivative relational expression of the displacement of the inner wall surface of the pore to the pore pressure is
In the formula
Is the partial derivative of the displacement of the inner wall surface of the pore to the pore pressure;v cis the Poisson ratio of clay minerals without dimension;μ cthe Lame coefficient of clay mineral is dimensionless;A 1p、B 1pis a transition coefficient;
s302, calculating a partial derivative relation formula of the displacement of the inner wall surface of the pore to the confining pressure, wherein the partial derivative relation formula of the displacement of the inner wall surface of the pore to the confining pressure is
In the formula
The partial derivative of the displacement of the inner wall surface of the pore to the confining pressure;A 1c、B 1cis a transition coefficient;
s303, solving a partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure, wherein the partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure is
In the formula
The partial derivative of the displacement of the outer wall surface of the pore to the pore pressure is obtained; b is the outer radius of the pores in μm;v rthe Poisson ratio of the rock skeleton is a dimensionless quantity;A 2p、B 2pis a transition coefficient;
s304, solving a partial derivative relational expression of the displacement of the outer wall surface of the pore to the confining pressure, wherein the partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure is
In the formula
The partial derivative of the displacement of the outer wall surface of the pore to the confining pressure is obtained;μ rthe Lame coefficient of the rock skeleton is free of dimensional quantity;A 2c、B 2cis a transition coefficient;
s305, calculating partial derivative relational expressions of the porosity on the inner wall surface and the outer wall surface of the pore, wherein the partial derivative relational expressions of the porosity on the inner wall surface and the outer wall surface of the pore are respectively
；
S400, defining a shell-shaped clay mineral content relational expression and a rigidity ratio of a rock framework to clay to obtain an effective stress coefficient equation of the clay shell-shaped porosity;
s401, defining the relation of the content of the shell-shaped clay minerals as
Defining the rigidity ratio of the rock skeleton to the clay as in the formulaF cThe content of the shell-shaped clay minerals is zero dimensional quantity; c is the radius of the inner wall surface of the rock framework, and the unit is mum; the rigidity ratio of the stone framework to the clay is free of dimensional quantity;
s402, substituting the 5 partial derivative relational expressions obtained in the step S300 into an effective stress coefficient expansion of clay shell porosity to obtain
；
S403, substituting the rigidity ratio of the stone skeleton to the clay and the shell-shaped clay mineral content relational expression into the step S402 formula to obtain the effective stress coefficient model of the clay shell-shaped porosity, wherein the effective stress coefficient model of the clay shell-shaped porosity is
In the formula
，ωIs a constant;
s500, substituting the porosity, the clay content, the Poisson ratio and the rigidity ratio into a clay shell-shaped porosity effective stress coefficient model, and calculating the porosity effective stress coefficient.
Further, when the clay mineral content of the rock sample is taken as 0 and the rigidity ratio is taken as 1, the effective stress coefficient of porosity calculated by using the clay shell-shaped porosity effective stress coefficient model of the step S403 is equal to 1.
The method comprises the following steps:
the first verification method comprises the following steps: for homogeneous single-component rock samples, the effective stress coefficient of porosity is 1, and the degree of influence of internal pressure and confining pressure on the porosity is the same. One of the methods for verifying whether the theoretical model is reasonable is to take an extreme value for the parameter and analyze whether the calculation result under the extreme condition is correct. For conventional sandstone samples, the main source of the effective stress coefficient of porosity not equal to 1 is the presence of clay minerals, in other words, the effective stress coefficient of porosity of a one-component homogeneous rock sample should be equal to 1. To change the model to a single component model, there are two approaches: (1) taking the clay mineral content as 0; (2) the stiffness ratio was taken to be 1. Both of them are satisfied to explain the reliability of the theoretical model.
By respectively adopting the methods researched by the invention and the research on the porosity stress sensitivity of clay-containing tight sandstone, extreme values are taken to calculate the effective stress coefficient of porosity, and the calculation results are shown in table 1. None of the results of the calculation of the velcade papers satisfies this phenomenon, and the gap is large.
TABLE 1 theoretical verification of effective stress coefficient of porosity for shell model
And a second verification method:
filling modes of chlorite and illite in clay minerals conform to distribution characteristics of a shell model, a porosity effective stress coefficient determination experiment is designed and developed, porosity values under different confining pressure and pore fluid pressure combinations are determined, regression fitting is carried out on confining pressure, internal pressure and porosity data obtained by the experiment by adopting a binary linear regression method, and the relation formula is
Wherein:a 0、a 1、a 2-fitting coefficients, dimensionless; -confining pressure, MPa; internal pressure, MPa.
Combining the definition of the effective stress coefficient of the porosity, obtaining the effective stress coefficient expression of the porosity as follows:
according to the above method, three blocks can be calculated by experimentThe effective stress coefficient of the porosity of the rock sample is compared with the calculation result of a theoretical model, such as the result shown in table 2.
TABLE 2 Shell model porosity effective stress coefficient calculation
The comparison result shows that the absolute error between the theoretical calculation result and the measured value is small, the absolute error is less than 1 percent, and the precision is high, so that the reliability of the theoretical model is demonstrated.
Compared with the prior art, the invention has the following beneficial effects: (1) the effective stress coefficient of the porosity is calculated by using the model, so that the complicated process of physical experiment testing is reduced; (2) the model is consistent with the reality, and the calculation result is more accurate; (3) the popularization is strong.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that: modifications and equivalents may be made thereto without departing from the spirit and scope of the invention and it is intended to cover in the claims the invention as defined in the appended claims.
Claims (2)
1. The sandstone porosity effective stress coefficient calculation method based on the clay shell model is characterized by comprising the following steps of:
s100, determining the porosity, the clay content, the Poisson ratio and the rigidity ratio of a clay mineral-containing rock sample;
s200, obtaining the clay shell porosity effective stress coefficient expansion by a chain method according to the porosity effective stress coefficient definition formula and combining the clay shell physical model porosity definition formula, the main steps are,
s201, determining a porosity effective stress coefficient definition formula and a clay shell physical model porosity definition formula, wherein the porosity effective stress coefficient definition formula is
In the formula
Is a porosity effective stress coefficient, and has no dimensional quantity;φporosity, dimensionless;P pis pore pressure in MPa;P cis confining pressure in MPa; the porosity of the clay shell-shaped physical model is defined as
In the formula:
is the pore inner radius, and the unit is mum; b is the outer radius of the pores in μm;
s202, obtaining a clay shell porosity effective stress coefficient expansion form by a chain method, wherein the clay shell porosity effective stress coefficient expansion form is
；
S300, solving a partial derivative relational expression of the displacement of the inner wall surface and the outer wall surface of the pore to the pore pressure and the confining pressure and a partial derivative relational expression of the porosity to the inner wall surface and the outer wall surface of the pore, mainly comprising the following steps,
s301, calculating a partial derivative relational expression of the displacement of the inner wall surface of the pore to the pore pressure, wherein the partial derivative relational expression of the displacement of the inner wall surface of the pore to the pore pressure is
In the formula
Is the partial derivative of the displacement of the inner wall surface of the pore to the pore pressure;v cis the Poisson ratio of clay minerals without dimension;μ cis the Lame coefficient of clay mineral and has no dimensionAn amount;A 1p、B 1pis a transition coefficient;
s302, calculating a partial derivative relation formula of the displacement of the inner wall surface of the pore to the confining pressure, wherein the partial derivative relation formula of the displacement of the inner wall surface of the pore to the confining pressure is
In the formula
The partial derivative of the displacement of the inner wall surface of the pore to the confining pressure;A 1c、B 1cis a transition coefficient;
s303, solving a partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure, wherein the partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure is
In the formula
The partial derivative of the displacement of the outer wall surface of the pore to the pore pressure is obtained; b is the outer radius of the pores in μm;v rthe Poisson ratio of the rock skeleton is a dimensionless quantity;A 2p、B 2pis a transition coefficient;
s304, solving a partial derivative relational expression of the displacement of the outer wall surface of the pore to the confining pressure, wherein the partial derivative relational expression of the displacement of the outer wall surface of the pore to the pore pressure is
In the formula
The partial derivative of the displacement of the outer wall surface of the pore to the confining pressure is obtained;μ rthe Lame coefficient of the rock skeleton is free of dimensional quantity;A 2c、B 2cis a transition coefficient;
s305, calculating the porosity to the inner wall of the poreThe partial derivative relation between the surface and the outer wall surface of the pore, and the partial derivative relation between the porosity and the inner wall surface of the pore and the outer wall surface of the pore are respectively
；
S400, defining a shell-shaped clay mineral content relation and a rigidity ratio of a rock framework to clay to obtain a clay shell-shaped porosity effective stress coefficient model;
s401, defining the relation of the content of the shell-shaped clay minerals as
Defining the rigidity ratio of the rock skeleton to the clay as in the formulaF cThe content of the shell-shaped clay minerals is zero dimensional quantity; c is the radius of the inner wall surface of the rock framework, and the unit is mum; the rigidity ratio of the stone framework to the clay is free of dimensional quantity;
s402, substituting the 5 partial derivative relational expressions obtained in the step S300 into an effective stress coefficient expansion of clay shell porosity to obtain
；
S403, substituting the rigidity ratio of the stone skeleton to the clay and the shell-shaped clay mineral content relational expression into the step S402 formula to obtain the effective stress coefficient model of the clay shell-shaped porosity, wherein the effective stress coefficient model of the clay shell-shaped porosity is
In the formula
，ωIs a constant;
s500, substituting the porosity, the clay content, the Poisson ratio and the rigidity ratio into a clay shell-shaped porosity effective stress coefficient model, and calculating the porosity effective stress coefficient.
2. The clay shell model-based sandstone porosity effective stress coefficient calculation method according to claim 1, wherein the method comprises the following steps: and when the clay mineral content of the rock sample is taken as 0 and the rigidity ratio is taken as 1, calculating by using the clay shell-shaped porosity effective stress coefficient model obtained in the step S403 to obtain the porosity effective stress coefficient equal to 1.
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