CN107480316B - Method for calculating gas transmission flow in shale nanopores - Google Patents
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Abstract
The invention belongs to the technical field of shale gas development, and particularly relates to a method for calculating gas transmission flow in shale nanopores, which comprises the following steps: A. collecting reservoir temperature, pore size and gas related parameters; B. judging the gas flow state of the reservoir; C. establishing a corresponding gas mass transmission equation according to the reservoir gas flow state; D. establishing a mass transmission unified equation of reservoir gas in different flow states; E. the ratio of the gas transport flow of the different transport mechanisms in the nanopores in the total transport flow is calculated. The invention fully considers the characteristic that the shale gas mainly exists in a free state and an adsorption state, establishes a gas mass transmission unified equation under a multi-scale and multi-flow state, can calculate the gas transmission flow of the gas in different transmission modes in the nanometer pores, and researches the transmission mechanism of the gas in the nanometer pores according to the proportion of the gas transmission flow in the total gas transmission flow.
Description
Technical Field
The invention relates to a method for calculating gas transmission flow in shale nanopores, and belongs to the technical field of shale gas development.
Background
Compared with a conventional natural gas reservoir, the shale gas has the characteristics of multiple occurrence modes and multiple transmission modes in the shale reservoir, ① has various occurrence modes, because the shale gas reservoir has the characteristic of self-generation and self-storage, besides free gas in pores and cracks, a large amount of adsorbed gas is also generated on the walls of nano-micron pores, and part of the shale gas is dissolved in kerogen and water, ② the shale gas is transmitted in the shale reservoir to show multi-scale property, firstly, the shale gas reservoir and seepage space comprise organic matter nano pores, micro pores, natural micro cracks of the reservoir and a multi-scale complex crack network formed by fracture transformation, the flowing of the shale gas in the reservoir has multi-scale property, and secondly, the shale gas has different flow states in different pore diameters, so that the shale gas has multiple transmission mechanisms such as adsorption-desorption, diffusion, seepage, slip-shedding flow, Knudsen diffusion flow and the like in the flowing process.
In order to accurately describe the overall processes of shale gas adsorption-desorption, diffusion, seepage, slippage, Knudsen diffusion and the like which exist, influence and restrict each other simultaneously and the comprehensive influence of environmental factors such as pore diameter, pressure, temperature and the like on the transmission rule, the currently adopted method is to represent the flow states of the adsorbed shale gas under different pore media and external conditions by introducing dimensionless Knudsen numbers, and then select a related equation to calculate the corresponding gas transmission flow for each flow state. However, because shale gas has multiple transmission modes in micro-nano pores and different transmission modes are mutually transformed, the prior art cannot respectively and conveniently and accurately describe each process and transformation in the multiple transmission modes.
Disclosure of Invention
The invention provides a method for calculating gas transmission flow in shale nanopores and aims to solve the problems in the prior art.
The technical scheme of the invention is as follows:
the invention provides a method for calculating gas transmission flow in shale nanopores, which comprises the following steps:
A. collecting reservoir temperature, reservoir pressure, pore size and gas related parameters;
B. judging the gas flow state of the reservoir;
C. establishing a corresponding gas mass transmission equation according to the reservoir gas flow state;
D. establishing a mass transmission unified equation of reservoir gas in different flow states;
E. and calculating the proportion of the transmission flow of the gas in the total transmission flow of the gas under different transmission mechanisms in the nanometer pores according to the mass transmission unified equation.
In an embodiment of the present invention, in the step a, the gas related parameters include gas type, gas constant, gas molar mass, gas viscosity, tangential momentum adjustment coefficient, gas molecular density, average pressure, surface maximum concentration, langmuir pressure, and surface diffusion coefficient.
In an embodiment of the present invention, in step B, the knudsen coefficient (Kn) is used to determine a gas flow state in the reservoir, and the knudsen coefficient (Kn) is calculated according to the following formula:
in the formula: Kn-Knudsen coefficient, no dimension; kBBoltzmann constant, 1.3805 × 10-23J/K; p-reservoir pressure, MPa; t-reservoir temperature, K; pi-constant, 3.14; δ — gas molecule collision diameter, m; d-pore throat diameter, nm.
In an embodiment of the present invention, in the step C, the gas mass transport equation includes a free gas mass transport equation and an adsorbed gas mass transport equation.
In the embodiment of the present invention, in the step D, the mass transfer unified equation and the calculation formula are as follows:
in the formula: j. the design is a squaretolTotal mass flow, kg/(m)2·s)；JviciousViscous flow mass flow, kg/(m)2·s)；JslipSlip effect mass flow, kg/(m)2·s)；Jknudsen-Knudsen diffusion mass flow, kg/(m)2·s)；JsurfaceSurface diffusion mass flow, kg/(m)2S); rho-gas density, kg/m3(ii) a Mu-gas viscosity, Pa · s; k is a radical ofDShale intrinsic permeability, m2；dm-gas molecular diameter, m; r-croup radius, m; p-reservoir pressure, MPa; p is a radical ofL-Langmuir pressure, MPa; f is the slippage coefficient and is dimensionless; dk-Knudsen diffusion coefficient, m2/s；M—Gas molar mass, g/mol; ds-surface diffusion coefficient, m2/s；CsmaxMaximum adsorption concentration of adsorbed gas, mol/m3(ii) a ε -contribution coefficient, dimensionless.
In an embodiment of the present invention, in the step E, the nanopores include micropores (pore diameter less than or equal to 2nm), mesopores (pore diameter less than or equal to 50nm), and macropores (pore diameter less than 50 nm).
The invention has the beneficial effects that: the method for calculating the gas transmission flow in the shale nanopores fully considers the characteristic that the shale gas mainly exists in a free state and an adsorption state, adopts a method combining continuous medium mechanics and molecular kinematics, comprehensively considers multiple transmission mechanisms of viscous flow, Knudsen diffusion, slippage effect, desorption effect of the adsorption shale gas and surface diffusion of the adsorption shale gas, establishes a gas mass transmission unified equation under a multi-scale and multi-flow state, can calculate the gas transmission flow of the gas in different transmission modes in the nanopores, and researches the transmission mechanism of the gas in the nanopores according to the proportion of the gas transmission flow in the total gas transmission flow.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained based on these drawings without inventive efforts.
FIG. 1 is a graph showing the change of gas transport ratio with pressure under a micropore (pore diameter of 1nm) condition provided by the present invention;
FIG. 2 is a graph showing the change of gas transport ratio with pressure under the condition of micropores (pore diameter of 2nm) provided by the present invention;
FIG. 3 is a graph showing the change of gas transport ratio with pressure under a mesoporous (pore diameter of 5nm) condition provided by the present invention;
FIG. 4 is a graph showing the change of gas transport ratio with pressure under a mesoporous (pore diameter of 10nm) condition provided by the present invention;
FIG. 5 is a graph showing the change of gas transport ratio with pressure under a mesoporous (pore diameter of 25nm) condition provided by the present invention;
FIG. 6 is a graph showing the change of gas transport ratio with pressure under a mesoporous (pore diameter of 50nm) condition provided by the present invention;
FIG. 7 is a graph showing the change of gas transmission ratio with pressure under a condition of macropores (pore diameter of 100nm) provided by the present invention;
FIG. 8 is a graph showing the change of gas transport ratio with pressure under a condition of large pores (pore diameter of 500nm) provided by the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings of the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The invention provides a method for calculating gas transmission flow in shale nanopores and aims to solve the problems in the prior art.
The invention provides a method for calculating gas transmission flow in shale nanopores, which comprises the following steps:
A. collecting reservoir temperature, reservoir pressure, pore size and gas related parameters;
B. judging the gas flow state of the reservoir;
C. establishing a corresponding gas mass transmission equation according to the reservoir gas flow state;
D. establishing a mass transmission unified equation of reservoir gas in different flow states;
E. and calculating the proportion of the transmission flow of the gas in the total transmission flow of the gas under different transmission mechanisms in the nanometer pores according to the mass transmission unified equation.
In an embodiment of the present invention, in the step a, the gas related parameters include a gas type, a gas constant, a gas molar mass, a gas viscosity, a tangential momentum adjusting coefficient, a gas molecular density, a mean pressure, a surface maximum concentration, a langmuir pressure, and a surface diffusion coefficient.
In an embodiment of the present invention, in step B, the knudsen coefficient (Kn) is used to determine the gas flow state in the reservoir, and the calculation formula of the knudsen coefficient (Kn) is as follows:
in the formula: λ -mean molecular free path, nm; d-pore throat diameter, nm; wherein, the expression of the gas average molecular free path lambda is as follows:
substituting the formula (2) into the formula (1) to obtain the detailed gas KnThe expression of the number:
in the formula: kn-knudsen coefficient, dimensionless; kBBoltzmann constant, 1.3805 × 10-23J/K; p-reservoir pressure, MPa; t-reservoir temperature, K; pi-constant, 3.14; δ — gas molecule collision diameter, m; d-pore throat diameter, nm.
According to Knudsen number (K)n) The gas flow state is divided into continuous flow, slip-off flow and transitionFlow and free molecular flow, as shown in table 1:
table 1 gas flow staging table
In an embodiment of the present invention, in the step C, the gas mass transport equation includes a free gas mass transport equation and an adsorbed gas mass transport equation.
(1) Free shale gas mass transfer equation
Free shale gas (free gas) is present in matrix pores and cracks, and mainly generates viscous flow, slippage and Knudsen diffusion.
① viscous flow mass transfer equation
The shale develops a large number of nano-scale pores, the nano-pores can be regarded as a capillary model, and the shale can be regarded as composed of capillaries and a matrix. When the Knudsen number of the shale gas is far less than 1, the movement of gas molecules is mainly governed by intermolecular collision, the collision between the molecules and the wall surface is less, the interaction between the gas molecules is more frequent than the collision between the gas molecules and the pore surface (pore wall), the gas mainly flows continuously, and the gas can be described by a viscous flow mass transfer equation. When the influence of the existence of adsorbed gas on the capillary radius is not considered, the natural permeability of a single capillary with a bore radius r is calculated according to the following formula:
in the formula: k is a radical ofDShale intrinsic permeability, m2(ii) a r-radius of croup, m, r ═ d/2.
Viscous flow caused by the presence of a pressure gradient between the single component gases can be expressed by darcy's law as a mass transfer equation describing viscous flow, as follows:
in the formula: j. the design is a squareviciousViscous flow mass flow, kg/(m)2S); rho-gas density, kg/m3(ii) a Mu-gas viscosity, Pa · s; p-reservoir pressure, Pa;
-pressure gradient, MPa.
For gas transport in a nanotube, the nanopore roar effective radius decreases when considering the effect of the presence of adsorbed gas on the nanopore radius, and thus the effective radius of nanopore roar when considering the effect of adsorbed gas can be expressed as:
in the formula: r ise-nanopore effective radius, m; dm-gas molecular diameter, m; p is a radical ofLLangmuir pressure, MPa.
By substituting formula (6) for formula (5), it is possible to obtain:
② slip effect mass transfer equation
When the size of the shale pore is reduced, or the gas pressure is reduced, the gas molecular free path is increased, the gas molecular free path has comparability with the size of the bore diameter, and the collision of the gas molecules with the wall surface of the pore is not negligible. At 0.001 < KnWhen the gas molecular velocity of the shale on the wall surface is less than 0.1, because the gas molecular velocity of the shale on the wall surface is not zero any more, a slip phenomenon exists at the moment, and a calculation formula of the permeability of the shale reservoir layer considering the slip effect is as follows:
in the formula: k is a radical ofslipPermeability taking slip effect into account, m2；paverThe average pressure of an inlet and an outlet is Pa when the permeability of the rock core is tested through experiments; bkSlip factor, Pa.
In order to embody the slippage effect in the seepage equation, a slippage factor is introduced to correct the nanopore slippage effect, and the slippage factor is substituted by the formula (8):
wherein R is a gas constant, J/(mol. K); m-gas molar mass, kg/mol; p is a radical ofavgAverage pressure (average pressure of an inlet and an outlet in a circular single pipe), Pa, α, a tangential momentum adjusting coefficient, no dimension and a value of 0-1.
The mass transfer equation when considering the slip effect can therefore be written as:
in the formula: j. the design is a squareslipSlip flow mass flow, kg/(m)2·s)。
③ Knudsen diffusion mass transport equation
K when the croup diameter decreases or the molecular mean free path increases (at low pressure)nAt > 10, gas molecules collide more easily with the pore walls than with other gas molecules, which means that the gas molecules reach a point that can be nearly independent of each other, called Knudsen diffusion.
Jknudsen＝ανρ (12)
Wherein α -dimensionless probability coefficient and dimensionless, v-average molecular speed, m/s, rho-gas molecular density, kg/m3。
When both ends of the tube have gas, the net flow transmitted by the tube is directly proportional to the gas density at both ends of the tube, and equation (12) can be written as:
Jknudsen＝αν(ρin-ρout) (13)
in the formula: rhoinGas density at the inlet of the pipe, kg/m3；ρoutGas density at the outlet of the pipe, kg/m3。
According to the gas dynamics theory, the average molecular motion velocity of a gas is:
for a circular long straight tube (L > > d) having a diameter d and a length L, α is d/3L, and formula (14) is substituted into formula (13), and the following can be obtained:
writing equation (15) as a partial differential form can be written as:
equation (16) can also be written in the form of gas concentration C, i.e.:
and Knudsen diffusion coefficient in nanopores DkThe expression is as follows:
in the formula: dk-Knudsen diffusion coefficient, m2/s。
And the gas density expression can be written as:
by substituting formula (18) for formula (17), it is possible to obtain:
therefore, in combination with equations (19), (20), Knudsen diffusion mass transfer equation can be expressed as:
in the formula: j. the design is a squareknudsen-Knudsen diffusion mass flow, kg/(m)2·s)。
(2) Adsorption state shale gas mass transfer equation
The adsorption state shale gas (adsorption gas) is generated on the wall surface of the pore and the surface of the solid shale particles, and mainly performs desorption and surface diffusion.
① desorption mass transfer equation
The Langmuir isothermal adsorption model assumes that wall surface adsorbed gas and free gas are in instantaneous dynamic equilibrium under certain temperature and pressure conditions, adopts the Langmuir isothermal adsorption model, and has the expression form of adsorption mass:
in the formula: q. q.sadsAdsorption capacity per unit volume of shale, kg/m3；VstdMolar volume, m, of shale gas under standard conditions3/mol；
During development, the formation pressure gradually decreases, if t1At time of formation pressure p1，t2At time of formation pressure p2Then the formation pressure p can be calculated1Is decreased to p2Desorption amount of normal adsorption shale gas:
in the formula: Δ q ofadsDesorption of shale gas in the adsorbed state, kg/m, due to pressure drop3；VLLangmuir volume, m3/kg。
② surface diffusion mass transfer equation
The shale gas has not only desorption effect on the micro-nano pore surface, but also transmission along the adsorption wall surface, namely surface diffusion effect. Different from other transmission modes of pressure gradient or concentration gradient action, the shale gas surface diffusion is transmitted under the action of the adsorption potential field, and factors influencing the shale gas surface diffusion are many, including pressure, temperature, nano-pore wall surface property, shale gas molecule property, interaction of shale gas molecules and the nano-pore wall surface and the like.
When the surface diffusion gas transport equation is expressed in the form of a concentration gradient, which is equal to the product of the surface diffusion coefficient and the concentration gradient, the surface diffusion mass flow calculation formula is as follows:
in the formula: j. the design is a squaresurfaceSurface diffusion mass flow, kg/(m)2·s)；CsConcentration of adsorbed gas on the wall surface of pores, mol/m3；DsSurface diffusion coefficient, m2S; l-pore wall length, m.
The adsorbed gas coverage θ can be expressed as:
in the formula: theta-adsorbed gas coverage without dimension; csmaxMaximum adsorption concentration of adsorbed gas, mol/m3(ii) a V-actual adsorbed gas volume per unit mass of shale, m3/kg；CsmaxMaximum adsorbed concentration of adsorbed gas, mol/m.
Formula (25) can be further rewritten as:
by substituting formula (26) into formula (24), the shale gas surface diffusion mass transfer equation satisfying the Langmuir isothermal adsorption equation can be obtained:
in the embodiment provided by the present invention, in the step D, the viscous flow of the free-state shale gas, the slip flow, the Knudsen diffusion, and the desorption and surface diffusion effects of the adsorbed-state shale gas are considered, and the total transmission quality thereof is the sum of the transmission qualities caused by the several transmission modes. And (3) superposing the equations (7), (11), (21) and (23) and (27), and introducing the contribution coefficient epsilon to establish a mass transfer equation which can describe the full-scale multi-flow state, wherein the expression is as follows:
wherein:
in the formula: j. the design is a squaretolTotal mass flow, kg/(m)2·s)；JviciousViscous flow mass flow, kg/(m)2·s)；JslipSlip effect mass flow, kg/(m)2·s)；Jknudsen-Knudsen diffusion mass flow, kg/(m)2·s)；JsurfaceSurface diffusion mass flow, kg/(m)2S); rho-gas density, kg/m3(ii) a Mu-gas viscosity, Pa · s; k is a radical ofDShale intrinsic permeability, m2；dm-gas molecular diameter, m; r-croup radius, m; p-reservoir pressure, MPa; p is a radical ofL-Langmuir pressure, MPa; f is the slippage coefficient and is dimensionless; dk-Knudsen diffusion coefficient, m2S; m-gas molar mass, kg/mol; dsSurface diffusion coefficient, m2/s；CsmaxMaximum adsorption concentration of adsorbed gas, mol/m3(ii) a ε -contribution coefficient, dimensionless.
Specifically, in this embodiment, in the embodiment provided by the present invention, the calculation formula of the contribution coefficient ∈ is as follows:
in the formula: cA-constant, dimensionless, value of 1; kn-knudsen coefficient, dimensionless; knviscous-the number Knudsen of the transition from continuous flow to quasi-diffusive flow, which takes 0.3; s-constant, value 1.
In the formula: rvicious-viscous flow mass transfer ratio,%; rslip-slip effect mass transfer ratio,%; rknudsen-knudsen diffusion mass transport ratio,%; rsurface-surface diffusion mass transport ratio,%; specifically, in the present invention, the delivery ratio defined by the equations (31) to (34) is the ratio of the various delivery flows of the gas in different flow states to the total delivery flow.
Example (b):
in the first step, reservoir temperature, reservoir pressure, pore size and gas related parameters were collected, with the results shown in the following table:
TABLE 1 reservoir and Experimental gas related parameters Table
Note: calculating the data required for calculating surface diffusion termCoefficient of contribution epsilon, taking CA＝0，Knviscous＝0.3，S＝1。
In the second step, as shown in fig. 1 and 2, the relevant parameters in table 1 are substituted into equations (31) to (34), and the gas transport ratio in each transport mode when the gas flows in the micropores is calculated.
As can be seen from fig. 1 and 2: under the micropore condition, the diameter of the nanometer pore is smaller, the specific surface area is larger, the content of the adsorbed gas is higher, and the adsorbed gas transmission mechanism is stronger; and the free gas has smaller transmission flow because the pore diameter is smaller. In different gas transmission modes, the proportion occupied by surface diffusion transmission under the micropore condition is the largest, and then the slippage effect, Knudsen diffusion and viscous flow are adopted, along with the increase of pressure, the content of adsorbed gas is increased, the transmission proportion occupied by the surface diffusion effect is further increased, the movement among gas molecules is gradually weakened along with the increase of pressure, and therefore the transmission proportion occupied by the viscous flow, the slippage flow and the Knudsen diffusion is gradually reduced.
Third, as shown in fig. 3 to 6, the relevant parameters in table 1 are substituted into equations (31) to (34), and the gas transport ratio in each transport mode when the gas flows in the mesopores is calculated.
As can be seen from fig. 3 to 6: under the condition of mesopores, as the diameter of pores is increased, the specific surface area begins to be reduced, the content of adsorbed gas is reduced, so that the proportion occupied by surface diffusion and transmission is gradually reduced, and the proportion occupied by viscous flow, slip effect and Knudsen diffusion is gradually increased. With the increase of the pressure, the movement activity of gas molecules is reduced, the transmission ratio of surface diffusion and viscous flow is increased, and the transmission ratio of the slip effect and Knudsen diffusion is reduced.
In the fourth step, as shown in fig. 7 and 8, the relevant parameters in table 1 are substituted into equations (31) to (34), and the gas transport ratio in each transport mode when the gas flows through the large pores is calculated.
As can be seen from fig. 7 and 8: under the condition of macropores, as the diameter of pores is increased, viscous flow action is dominant, the transmission ratio is highest, and the transmission ratios of non-linear flows such as slip effect, Knudsen diffusion and surface diffusion are sequentially decreased.
The calculation method for the gas transmission flow in the shale nano-scale pores has the advantages that: the method for calculating the gas transmission flow in the shale nanopores fully considers the characteristic that the shale gas mainly exists in a free state and an adsorption state, adopts a method combining continuous medium mechanics and molecular kinematics, comprehensively considers multiple transmission mechanisms of viscous flow, Knudsen diffusion, slippage effect, desorption effect of the adsorption state shale gas and surface diffusion of the adsorption state shale gas, establishes a gas mass transmission unified equation under a multi-scale and multi-flow state, can calculate the gas transmission flow of the gas in the nanopores in different transmission modes by utilizing the mass transmission unified equation, and researches the transmission mechanism of the gas in the nanopores according to the proportion of the gas transmission flow in the total gas transmission flow.
Although the present invention has been described with reference to the above embodiments, it should be understood that the invention is not limited to the above embodiments, and various changes and modifications may be made by those skilled in the art without departing from the scope of the invention.
Claims (4)
1. The method for calculating the gas transmission flow in the shale nanopores is characterized by comprising the following steps of:
A. collecting reservoir temperature, reservoir pressure, pore size and gas related parameters;
B. judging the gas flow state of the reservoir;
using the Knudsen coefficient (K)n) Judging the gas flow state in the reservoir, the Knudsen coefficient (K)n) The calculation formula is as follows:
in the formula: kn-knudsen coefficient, dimensionless; kBBoltzmann constant, 1.3805 × 10-23J/K; p-reservoir pressure, MPa; t-reservoir temperature, K; pi-constant, 3.14; δ — gas molecule collision diameter, m; d-pore throat diameter, nm;
C. establishing a corresponding gas mass transmission equation according to the reservoir gas flow state;
D. establishing a mass transmission unified equation of reservoir gas in different flow states;
E. and calculating the proportion of the transmission flow of the gas in the total transmission flow of the gas under different transmission mechanisms in the nanometer pores according to the mass transmission unified equation.
2. The method according to claim 1, wherein in step a, the gas related parameters comprise gas type, gas constant, gas molar mass, gas viscosity, gas molecular density, surface maximum concentration, langmuir pressure and surface diffusion coefficient.
3. The method of claim 1, wherein in step C, the mass transport equations include a free gas mass transport equation and an adsorbed gas mass transport equation.
4. The method according to claim 1, wherein in step D, the unified equation and calculation formula for quality transmission are as follows:
in the formula: j. the design is a squaretolTotal mass flow, kg/(m)2·s)；JviciousViscous flow mass flow, kg/(m)2·s)；JslipSlip effect mass flow, kg/(m)2·s)；JknudsenKnudsen diffusion mass flow, kg-(m2·s)；JsurfaceSurface diffusion mass flow, kg/(m)2S); rho-gas density, kg/m3(ii) a Mu-gas viscosity, Pa · s; k is a radical ofDShale intrinsic permeability, m2；dm-gas molecular diameter, m; r-croup radius, m; p-reservoir pressure, MPa; p is a radical ofL-Langmuir pressure, MPa; f is the slippage coefficient and is dimensionless; dk-Knudsen diffusion coefficient, m2S; m-gas molar mass, kg/mol; ds-surface diffusion coefficient, m2/s；CsmaxMaximum adsorption concentration of adsorbed gas, mol/m3(ii) a ε -contribution coefficient, dimensionless.
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