CN112329240B - Shale gas reservoir apparent permeability calculation method based on fuzzy theory - Google Patents
Shale gas reservoir apparent permeability calculation method based on fuzzy theory Download PDFInfo
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Abstract
The invention discloses a shale gas reservoir apparent permeability calculation method based on a fuzzy theory, which comprises the following steps: establishing a concentration cloud model of free gas and adsorbed gas according to the shale reservoir occurrence mechanism by combining a fuzzy theory; establishing a flux model of the shale gas reservoir considering viscous flow, Knudsen diffusion and surface diffusion of a gas molecule slippage effect; preferably selecting a ridge-shaped distribution membership calculation function considering molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion according to the pore throat structure characteristics of the shale reservoir; calculating the membership degree of the concentration cloud model; and obtaining the apparent permeability of the shale gas reservoir based on the transmission flux relation in the nano pores according to the flux model. According to the shale gas surface permeability analysis method, a gas concentration cloud model is established based on a fuzzy theory according to the adsorption and desorption characteristics of the shale reservoir and considering migration mechanisms such as molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion, and the shale gas surface permeability influenced by molecules is reasonably described.
Description
Technical Field
The invention belongs to the technical field of oil and gas field development, and particularly relates to a shale gas reservoir apparent permeability calculation method based on a fuzzy theory.
Background
Compared with the conventional gas reservoir, the shale gas has great differences in the aspects of reservoir physical properties, reservoir characteristics, migration, seepage mechanism and the like, and the complex formation mode of self-generation and self-storage makes the pore structure of the shale gas very complex, the reservoir rock compactness is extremely strong, and nano-scale pores are developed, so that the permeability of the shale reservoir is extremely low, the characteristic of low permeability seriously influences the micro gas seepage, and the migration and output mechanism is more complex.
At present, many scholars at home and abroad study the adsorption-desorption effect of shale gas aiming at nano-scale pores, consider the migration mechanisms such as gas molecule surface diffusion, viscous flow and Knudsen diffusion, establish a shale gas flow mathematical model and develop corresponding simulation study. The method comprises the following steps of (1) establishing an adsorption model considering the excessive adsorption capacity and a shale apparent permeability model considering the gas transmission influence by the aid of plum wave waves (2020) and the like, and verifying the rationality of the adsorption model and the shale apparent permeability model through test data; the Ledongdong (2018) and the like consider viscous flow, Knudsen diffusion and a surface diffusion mechanism, derive a shale gas apparent permeability model, and verify the accuracy of the established model through an actual test data system; the shale gas reservoir apparent permeability model is established by considering multiple migration mechanisms such as the blazing glow (2017); and for nanoscale pores, considering shale gas adsorption and desorption phase surface diffusion, viscous flow of free gas, slippage effect, Knudsen diffusion and other transport mechanisms, and establishing a page gas single-phase flow mathematical model by using segment permanent steel (2015) and the like.
Although many scholars consider nanoscale pores and various migration mechanisms to research and analyze the shale gas reservoir apparent permeability, the interaction between gas molecules is not negligible due to the fact that a model reaches the molecular scale, and the contribution of each migration mechanism to the permeability in shale gas flow is different due to different conditions generated by the migration mechanism, so that the influence between different migrations needs to be established and considered, and the shale gas reservoir apparent permeability under the actual reservoir conditions is accurately described.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a shale gas reservoir apparent permeability calculation method based on a fuzzy theory for solving the influence of the interaction between molecules in a shale gas permeability migration mechanism on the shale gas reservoir gas flow apparent permeability.
The technical scheme provided by the invention for solving the technical problems is as follows: a shale gas reservoir apparent permeability calculation method based on a fuzzy theory comprises the following steps:
establishing a concentration cloud model of free gas and adsorbed gas according to the shale reservoir occurrence mechanism by combining a fuzzy theory;
establishing a flux model of the shale gas reservoir considering viscous flow, Knudsen diffusion and surface diffusion of a gas molecule slippage effect;
preferably selecting a ridge-shaped distribution membership calculation function considering molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion according to the pore throat structure characteristics of the shale reservoir; performing membership calculation on the established concentration cloud model;
and obtaining the apparent permeability of the shale gas reservoir based on the relationship of the transmission flux in the nano pores according to the calculated slippage effect viscous flow, Knudsen diffusion and surface diffusion membership and the flux model.
The further technical scheme is that the establishment of the concentration cloud model of the free gas and the adsorbed gas according to the shale reservoir occurrence mechanism and by combining the fuzzy theory comprises the following steps:
considering the shale gas adsorption and desorption phenomenon, and establishing a pore throat molecule migration concentration cloud model in the presence of surface diffusion, molecule slippage effect viscous flow and Knudsen diffusion;
dividing the molecular migration concentration cloud model in the pore throat into a surface diffusion area, a Knudsen diffusion area and a slip viscosity considered flow area from the rock wall surface to the center of the pore throat in sequence;
and (3) introducing a membership concept in a fuzzy theory to quantitatively depict a concentration cloud area, and establishing a concentration cloud model of free gas and adsorbed gas.
The further technical scheme is that the establishment of the flux model of the shale gas reservoir considering gas molecule slippage effect viscous flow, Knudsen diffusion and surface diffusion comprises the following steps:
establishing a diffusion gas flux model by combining Fick law and Langmuir adsorption equation;
considering real gas compression, establishing a Knudsen diffusion flux model;
establishing a pore Darcy flow flux model according to the Hagen-Poiseuille law;
and establishing a flux model of the shale gas reservoir according to the concentration cloud model based on the molecular flow relationship.
According to the pore throat structure characteristics of the shale reservoir, the preferred ridge-shaped distribution membership calculation function considering molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion comprises the following steps:
considering that the pore throats are symmetrically distributed from the axis to the rock wall surfaces on two sides, and the membership degree changes nonlinearly, the closer the membership degree changes, the larger the membership degree changes, the fuzzy distribution ridge-shaped distribution function which accords with the concentration cloud model, namely the ridge-shaped distribution membership degree calculation function, is preferably selected.
The further technical scheme is that the membership calculation of the established concentration cloud model comprises the following steps:
substituting the molecular flow form distribution position into a ridge-shaped distribution membership degree calculation function to calculate the slippage effect viscosity flow membership degree A1Knudsen diffusion membership A2Surface diffusion membership A3。
The further technical scheme is that the step of calculating the apparent permeability of the shale gas reservoir based on the nano-pore internal transmission flux relation according to the calculated slip effect viscous flow, Knudsen diffusion and surface diffusion membership and the flux model comprises the following steps:
subjecting the slip effect viscous flow to degree of membership A1Knudsen diffusion membership A2Surface diffusion membership A3Carrying the flux model into a shale gas reservoir flux model;
and obtaining the apparent permeability of the shale gas reservoir according to a shale gas volumetric flow formula, a unit length Darcy formula and a flux model of the shale gas reservoir.
The further technical scheme is that the method further comprises the following steps:
and verifying the accuracy of the obtained apparent permeability by changing the parameters of the concentration cloud model.
The invention has the beneficial effects that: according to the shale gas surface permeability analysis method, a gas concentration cloud model is established based on a fuzzy theory according to the adsorption and desorption characteristics of the shale reservoir and considering migration mechanisms such as molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion, and the shale gas surface permeability influenced by molecules is reasonably described.
Drawings
FIG. 1 is a flow chart of a method provided by the present invention;
FIG. 2 illustrates a gas concentration cloud model provided by the present invention;
FIG. 3 is a fuzzy distribution graph of membership provided by the present invention.
Detailed Description
The present invention will be further described with reference to the following examples and the accompanying drawings.
As shown in fig. 1, the shale gas reservoir apparent permeability calculation method based on the fuzzy theory of the present invention includes:
a. establishing a concentration cloud model of free gas and adsorbed gas according to the shale reservoir occurrence mechanism by combining a fuzzy theory;
considering the shale gas adsorption and desorption phenomenon, surface diffusion, viscous flow of molecular slippage effect and Knudsen diffusion exist; because molecules have various migration forms, different concentrations of each diffusion molecule, different displacement space regions and different mutual influences among the molecules are involved, a pore throat molecule migration concentration cloud model is established, as shown in figure 2, the pore throat molecule migration concentration cloud model is sequentially divided into a surface diffusion region, a Knudsen diffusion region and a slipping viscosity flow region from the rock wall surface to the pore throat center, the three molecular motion modes are mutually mixed and permeated, and the molecular motion is not distinguished by an interface; interaction exists among molecules, gas flow permeability is influenced, the region to which the gas flow permeability belongs is difficult to describe quantitatively, a membership degree concept in a fuzzy theory is introduced to quantitatively describe a concentration cloud region, and the contribution degree of the molecule migration process to the permeability in each mode is described;
b. establishing a flux model of the shale gas reservoir considering viscous flow, Knudsen diffusion and surface diffusion of a gas molecule slippage effect;
the diffusion flow relations of gas molecule slip effect viscous flow, Knudsen diffusion and surface diffusion are as follows:
(1) surface diffusion
When the external conditions change and concentration difference exists, the adsorbed gas adsorbed on the surface of the rock is desorbed and transported to carry out surface diffusion, and the Fick law and the Langmuir adsorption equation are combined to obtain the following formula:
in the formula: j. the design is a squaresFor the mass flow of the diffusion gas, kg/(m)2S); m is gas molar mass, kg/mol; dsIs the surface diffusion coefficient, m2/s；CsmaxFor maximum concentration of adsorbed gas, mol/m3；PLLangmuir pressure, Pa;
(2) when the pore throat size in the shale matrix is close to the average free path of gas molecules, the moving gas molecules collide with the rock wall:
considering true gas compression, Knudsen diffusion flux:
JD＝ρavgDKcg▽P (3)
in the formula: dkKnudsen diffusion coefficient, m2S; z is a gas deviation factor and has no dimension; c. CgIs a gas compression coefficient, Pa-1；JDKnudsen diffusion mass flux, kg/(m)2·s)；reffIs the effective radius; r is a gas constant; t is reservoir temperature, K;
(3) viscous flow of slip effect
According to Hagen-Poiseuille's law, the pore Darcy flow mass flux is:
introducing a correction factor F to correct the influence of the gas slipping on the flow at the tube wall:
mass flux of gas flow under slip effect:
in the formula: j. the design is a squareVMass flux for slip effect, kg/(m)2·s)；ρavgIs the average density of gas in pores, Kg/m3(ii) a Mu is gas viscosity, Pa · s; l is the pore length, m; f is a gas slippage correction coefficient without dimension; alpha is a tangent vector supply coefficient at the pore wall surface and has no dimension; p is the pore pressure difference, pa;
based on the molecular flow relationship and according to a molecular concentration cloud model, the membership degree of surface diffusion to apparent permeability is A1Knudsen diffusion membership of A2Viscosity flow membership of A3Establishing a flux model:
J＝A1JS+A2JD+A3JV (7)
c. preferably selecting a ridge-shaped distribution membership calculation function considering molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion according to the pore throat structure characteristics of the shale reservoir, and performing membership calculation on the established concentration cloud model;
the fuzzy distribution is normal distribution, Cauchy distribution, trapezoidal distribution, gamma distribution, ridge-shaped distribution and the like, so that the fuzzy distribution ridge-shaped distribution conforming to the concentration cloud model is preferably selected by considering that the pore throats are symmetrically distributed from the axial line to rock wall surfaces on two sides and the membership degree is nonlinearly changed, and the closer to the axial line, the larger the membership degree is, and the like, as shown in FIG. 3;
d. obtaining the apparent permeability of the shale gas reservoir based on the relationship of the transmission flux in the nano pores according to the calculated slippage effect viscous flow, Knudsen diffusion and surface diffusion membership and the flux model;
shale gas volumetric flow rate:
substituting the flux model (7) in step (b) into formula (9) in step (d):
darcy formula for unit length:
the apparent permeability relationship is given by:
e. verifying the accuracy of the obtained apparent permeability by changing the parameters of the concentration cloud model; namely, the molecular flow area in the concentration cloud model is changed, and the apparent permeability model is verified.
By changing the position parameters in the established concentration cloud model molecular migration mechanism, the membership value of each migration contribution to permeability flow is calculated and shown in tables 1 and 2.
It can be seen that the effect between the molecules is not negligible when the gas flows, and there is some effect on shale gas seepage, which contributes to the flow to a degree related to the region in which the gas is located in the pore throat.
TABLE 1 membership values for molecular migration in different regions
TABLE 2 membership values for molecular migration in different regions
Although the present invention has been described with reference to the above embodiments, it should be understood that the present invention is not limited to the above embodiments, and those skilled in the art can make various changes and modifications without departing from the scope of the present invention.
Claims (4)
1. A shale gas reservoir apparent permeability calculation method based on a fuzzy theory is characterized by comprising the following steps:
establishing a concentration cloud model of free gas and adsorbed gas according to the shale reservoir occurrence mechanism by combining a fuzzy theory;
the method specifically comprises the following steps: considering the shale gas adsorption and desorption phenomenon, and establishing a pore throat molecule migration concentration cloud model in the presence of surface diffusion, molecule slippage effect viscous flow and Knudsen diffusion;
dividing the molecular migration concentration cloud model in the pore throat into a surface diffusion area, a Knudsen diffusion area and a slip viscosity considered flow area from the rock wall surface to the center of the pore throat in sequence;
introducing a membership concept in a fuzzy theory to quantitatively depict a concentration cloud area, and establishing a concentration cloud model of free gas and adsorbed gas;
establishing a flux model of the shale gas reservoir considering viscous flow, Knudsen diffusion and surface diffusion of a gas molecule slippage effect;
selecting a ridge-shaped distribution membership calculation function considering molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion according to the pore throat structure characteristics of the shale reservoir; performing membership calculation on the established concentration cloud model;
the method specifically comprises the following steps: substituting the molecular flow form distribution position into a ridge-shaped distribution membership degree calculation function to calculate the slippage effect viscosity flow membership degree A1Knudsen diffusion membership A2Surface diffusion membership A3；
Obtaining the apparent permeability of the shale gas reservoir based on the relationship of the transmission flux in the nano pores according to the calculated slippage effect viscous flow, Knudsen diffusion and surface diffusion membership and the flux model;
the method specifically comprises the following steps: subjecting the slip effect viscous flow to degree of membership A1Knudsen diffusion membership A2Surface diffusion membership A3Carrying the flux model into a shale gas reservoir flux model;
J＝A1JS+A2JD+A3JV
in the formula: j. the design is a squareVMass flux for slip effect, kg/(m)2·s)；JsFor the mass flow of the diffusion gas, kg/(m)2·s)；JDKnudsen diffusion flux, kg/(m)2·s)；A1Viscosity flow membership for slip effect; a. the2As Knudsen diffusion membership; a. the3Is the surface diffusion membership;
and obtaining the apparent permeability of the shale gas reservoir according to a shale gas volumetric flow formula, a unit length Darcy formula and a flux model of the shale gas reservoir.
2. The shale gas reservoir apparent permeability calculation method based on the fuzzy theory as claimed in claim 1, wherein the establishing of the flux model of the shale gas reservoir considering gas molecule slippage effect viscous flow, Knudsen diffusion and surface diffusion comprises:
establishing a diffusion gas flux model by combining Fick law and Langmuir adsorption equation;
considering real gas compression, establishing a Knudsen diffusion flux model;
establishing a pore Darcy flow flux model according to the Hagen-Poiseuille law;
and establishing a flux model of the shale gas reservoir according to the concentration cloud model based on the molecular flow relationship.
3. The shale gas reservoir apparent permeability calculation method based on the fuzzy theory as claimed in claim 2, wherein the selecting the ridge-shaped distribution membership degree calculation function considering molecular slippage effect viscous flow, Knudsen diffusion and surface diffusion according to the pore-throat structure characteristics of the shale reservoir comprises:
considering that the pore throats are symmetrically distributed from the axial direction to the rock wall surfaces on two sides, the membership degree changes nonlinearly, the closer to the axial direction, the larger the membership degree change is, and the fuzzy distribution ridge-shaped distribution function, namely a ridge-shaped distribution membership degree calculation function, which accords with the concentration cloud model is selected.
4. The shale gas reservoir apparent permeability calculation method based on the fuzzy theory as claimed in claim 1, further comprising:
and verifying the accuracy of the obtained apparent permeability by changing the parameters of the concentration cloud model.
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