CN114936534A - Method for calculating apparent permeability of oil phase of nanoscale porous medium of tight reservoir - Google Patents
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Abstract
The invention provides a method for calculating the apparent permeability of a nano-scale porous medium oil phase of a compact reservoir, belonging to the technical field of unconventional oil exploitation; the theoretical problem of the existing compact reservoir crude oil nonlinear seepage theory is solved; the method comprises the following steps: determining a hypothesis condition; determining a fluid-solid interaction mechanism; determining a spatial non-uniform distribution function of the viscosity of crude oil in the nanoscale pore throat according to a mathematical expression of the viscosity of fluid in statistical mechanics and by combining an influence mechanism of fluid viscosity in the nanoscale pore throat due to interaction forces between flow and solid molecules; constructing a section velocity distribution function; determining a computation model of the oil phase apparent permeability of the nanoscale porous medium of the compact reservoir based on flow-solid interaction according to the permeability definition and combining Darcy's law and a flow function of the nanoscale pore throat crude oil; the invention is applied to unconventional oil and gas resource exploitation.
Description
Technical Field
The invention provides a method for calculating the apparent permeability of a nano-scale porous medium oil phase of a compact reservoir, belonging to the technical field of unconventional oil and gas resource development.
Background
The efficient development of unconventional petroleum resources such as compact oil, shale oil and the like is vital to relieving the energy crisis, however, the characteristic feature of the unconventional petroleum resource occurrence reservoir is porous medium nanoscale pore throat enrichment, and the effective development of the conventional oil and gas exploitation technical means is difficult to realize. Currently unconventional reservoirs enable efficient development of developments benefiting from fracture reformation techniques. The problems of low reservoir utilization degree, quick yield reduction and the like exist in the implementation process of the fracturing modification technology, and the reason is that the fracturing modification technology mainly uses crude oil in artificial fractures and micro fractures, but the crude oil in a matrix is difficult to use. The nanometer pore throat in the reservoir matrix is enriched, the oil gas is difficult to flow in the matrix, and the output difficulty is high. Therefore, the method accurately recognizes the flow characteristics of the crude oil in the nano-scale pore throat and has important significance for the efficient development of unconventional oil and gas.
The fluid within the nanoscale pore throat will exhibit unconventional hydrodynamic properties under the fluid confinement effect: under a certain external pressure driving condition, the flow of the fluid in the nano-scale pore throat is 4-5 orders of magnitude higher than the predicted value of the traditional fluid mechanics theory. Therefore, the classical oil and gas reservoir development seepage theory is difficult to be applied to the unconventional oil resource development process, so that the unconventional oil resource development process analysis and the process technology optimization cannot be carried out. Therefore, accurate understanding of the nonlinear seepage characteristics of crude oil in the nanoscale pore throat is an urgent problem to be solved in unconventional petroleum resource development.
Disclosure of Invention
Aiming at the theoretical problems existing in the existing compact reservoir crude oil nonlinear seepage theory, the invention aims to provide a compact reservoir nanoscale porous medium oil phase apparent permeability calculation method based on a flow-solid interaction mechanism.
The method can more accurately calculate the crude oil apparent permeability of unconventional petroleum resource reservoirs such as compact oil, shale oil and the like, and on the basis, a typical compact oil reservoir is taken as an example to simulate and optimize the development mode of the compact oil reservoir so as to realize the high-efficiency development of the compact oil reservoir.
The method is based on certain assumed conditions, combines Newton's internal friction law and Darcy's law, and derives a crude oil fluid dynamics model in the nanoscale pore throat and a nanoscale porous medium crude oil nonlinear permeability model.
The crude oil apparent permeability model can be combined with reservoir development simulation software such as CMG (China Mobile gateway group) and the like to simulate and optimize unconventional reservoir development processes such as compact oil, shale oil and the like.
The detailed technical scheme of the invention is as follows:
a method for calculating the oil phase apparent permeability of a compact reservoir nanoscale porous medium based on a flow-solid interaction mechanism is characterized in that an oil phase apparent permeability calculation model considering the flow-solid interaction is established:
1) determining hypothetical conditions
In a tight reservoir, the flow process of crude oil in the nanoscale pore throat is significantly affected by the solid surface, so the flow characteristics are more complex, and a nonlinear seepage process is caused. The following assumptions are made here:
ignoring the electrostatic forces seen among crude oil molecules, crude oil molecules and pore throat solid phase molecules;
neglecting the influence of water, namely neglecting the intermolecular hydration force action;
the pore throat size is larger than 2nm, and the fluid conforms to the assumption of a continuous medium;
neglecting the influence of the crude oil and the solid phase composition on the fluid-solid interaction;
the chemical reaction process is omitted.
2) Nanopore throat flow solid phase interaction
On the solid surface of the pore throat, fluid molecules are influenced by the solid surface molecules to present an ordered arrangement state, an ordered arrangement self-layering is formed, and the fluid molecules far away from the wall surface are still in a random arrangement state. According to the molecular thermodynamic theory, the intermolecular interaction energy of the near-wall fluid comprises cohesive energy, surface energy and solvation energy, and the mathematical expressions are respectively as follows:
in the formula, E coh Denotes the fluid cohesive energy, C VDW Represents the van der waals force parameter, σ represents the effective diameter of the fluid molecule, in m; e surf Represents surface energy in J.m -2 (ii) a A represents the Hamaker parameter, J; d 0 Represents the fluid-solid interface distance, m, equal to about sigma/2.5; e solv Representing the solvation energy, and d represents the distance of the fluid molecules from the solid surface.
3) Non-uniform distribution function of fluid viscosity
According to statistical mechanics theory, fluid viscosity can be viewed as a form of chemical reaction, the thermodynamic expression of which can be written as:
in the formula, h p Representing Planck constant, 6.62607015 × 10 -34 J·s；v m Represents the fluid molecular volume in m 3 (ii) a E represents the free energy of the fluid per unit area, in J.m -2 (ii) a n represents the number of fluid molecules per unit area, and the unit is m -2 ；k B Denotes the Boltzmann constant, 1.380649X 10 -23 J·K -1 (ii) a T represents the system temperature in K. In bulk fluid systems, the viscosity of the fluid is determined by the intermolecular interactions of the fluid, i.e., flowThe free energy in the body is only cohesive energy, so the viscosity of the bulk fluid is μ 0 The expression is as follows:
in the nano-scale pore throat, the viscosity of the fluid is determined by interaction forces between flow-flow and flow-solid molecules, namely the free energy in the fluid is cohesive energy and solvation energy, so that the expression of the viscosity mu of the fluid in the nano-scale porous medium is as follows:
to simplify the formula for engineering applications, the characterization flow-solid phase interaction parameter α is defined here:
combining the formulas (1) to (7), and considering the fluid viscosity as a positive value, obtaining the expression of the viscosity of the crude oil in the nano-scale pore throat:
where R represents the pore throat radius and R represents the distance of the flow cell from the pore throat centerline in m.
For ease of engineering analysis, the effective viscosity μ is defined herein eff And viscosity change ratio:
4) boundary slip velocity function
5) Cross sectional velocity distribution function
The integral function of the cross-sectional velocity can be expressed as:
in the formula (I), the compound is shown in the specification,
the external pressure driving pressure gradient is expressed in Pa/m.
Introducing a variable x ═ R)/sigma, and correcting the formula by adopting an element conversion method:
in order to conveniently solve the above-mentioned transcendental integral, the integrand is processed by adopting a function fitting mode. Assuming a fluid molecular diameter of
The size of the nanochannel ranges from 1nm to 1000nm, and the value of the corresponding parameter x ranges from 0 to 2000. In [0,2000 ]]Within the value range of (2), the corresponding exp (-x) function value can be directly obtained. And fitting the function value by adopting a least square method, wherein the fitting result shows that: function 1/(x +1) 2 The fitting effect of (2) is good, and the correlation coefficient reaches 0.9863. Thus, the integral part of the cross-sectional velocity function can be written as:
solving the integral can yield:
inverse transformation is carried out on the integral to obtain a section speed distribution function:
where Ei represents an exponential integration function, erfi represents an error function, and C is an integration constant.
Through functional analysis and model simplification, the cross-sectional velocity distribution function can be simplified as:
combining boundary slip conditions (namely a slip velocity function), the velocity distribution function of the crude oil section in the nanopore throat is as follows:
in the formula, σ s olid Represents the effective diameter of the solid molecule, and the unit is m; tau is eff Representing the effective stress of the fluid to create boundary slip velocity.
6) Cross sectional flow function
And (3) performing area integration on the section velocity distribution function on the section of the nanopore throat to obtain a flow function of the crude oil of the nanopore throat:
7) apparent permeability of oil phase of nano-scale porous medium
According to the permeability definition, combining Darcy's law and the flow function of the nanopore throat crude oil (equation (19)), the apparent permeability of the oil phase of the dense reservoir nanoscale porous medium considering the flow-solid phase interaction can be expressed as follows:
preferably, the step 4) of the slip speed function includes the following specific steps:
according to the molecular thermodynamic theory as well as the tribological theory, the surface force caused by the surface energy is an important parameter leading to the phenomenon of velocity boundary slip: the speed slip phenomenon occurs at the fluid-solid interface if and only if the applied pressure is greater than the surface force. The stress value caused by surface force is defined as the critical stress value tau c The expression is as follows:
wherein ε represents a solid surface friction coefficient; sigma solid Represents the effective diameter of the solid molecule in m. According to the chemical thermodynamic theory, slip velocity u surf Can be expressed as:
defining effective stress tau eff The mathematical expression is as follows:
in the above formula, τ represents the shear stress of the fluid flow under external pressure.
Compared with the prior art, the invention has the beneficial effects that: according to the invention, through the analysis of the flow-solid molecular interaction energy, the distribution function of the crude oil viscosity in the nano-scale pore throat on the space is obtained. By combining Newton's internal friction law and boundary slip conditions, the cross-section velocity distribution function and cross-section flow function of the flowing nano-scale pore throat crude oil under a certain external pressure driving condition are obtained through deduction. And further, according to the permeability definition, a nanoscale porous medium oil phase apparent permeability calculation model based on a flow-solid interaction mechanism is provided, and the geological characteristics of the permeability of the compact reservoir are more accurately evaluated. The model realizes the explicit treatment of the fluid-solid interaction in the nanoscale nonlinear flow model and the compact reservoir nonlinear seepage model, provides a more accurate permeability characterization method for the development and evaluation of the unconventional oil reservoir, and provides convenience for the efficient development theory development and the technical optimization of the unconventional oil reservoir.
Drawings
The invention is further described below with reference to the accompanying drawings:
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a reservoir geological model built according to tight reservoir conditions in an embodiment of the present disclosure.
Detailed Description
As shown in fig. 1-2, the invention provides a method for calculating apparent permeability of a dense reservoir nanoscale porous medium oil phase based on a flow-solid phase interaction mechanism, which comprises the following steps: determining a hypothesis condition; clear flow-solid phase interaction mechanism; establishing a crude oil viscosity non-uniform distribution function; constructing a section velocity distribution function; and (3) providing a nano-scale porous medium oil phase apparent permeability model. According to the invention, a spatial non-uniform distribution function of the crude oil viscosity in the nanoscale pore throat is obtained by analyzing a flow-solid phase interaction mechanism on the surface of the solid in the nanoscale pore throat. The Newton's internal friction law and the boundary slip condition are combined, and the cross-section velocity distribution function and the flow function of the flowing of the nano-scale pore throat crude oil under a certain external pressure driving condition are obtained through deduction. According to the porous medium permeability definition, a nanoscale porous medium oil phase apparent permeability model based on a flow-solid phase interaction mechanism is provided. The model realizes the explicit treatment of the fluid-solid interaction in the nanoscale nonlinear flow model and the compact reservoir nonlinear seepage model, and provides a more accurate permeability characterization method for the development and evaluation of unconventional oil reservoirs.
The present invention is further illustrated by, but is not limited to, the following specific examples.
Examples 1,
A method for calculating the apparent permeability of a dense reservoir nanoscale porous medium oil phase based on a flow-solid phase interaction mechanism comprises a nanoscale porous medium oil phase permeability calculation model:
1) explicitly assuming conditions
In an unconventional oil reservoir enriched by nanoscale pore throats, the flow process of crude oil is complex, and the following assumptions are made in order to facilitate analysis and research of nonlinear seepage characteristics of the crude oil:
ignoring the electrostatic forces seen among crude oil molecules, crude oil molecules and pore throat solid phase molecules;
neglecting the influence of water, namely neglecting the intermolecular hydration force action;
the pore throat size is larger than 2nm, and the fluid conforms to the assumption of a continuous medium;
neglecting the influence of the crude oil and the solid phase composition on the fluid-solid interaction;
the chemical reaction process is omitted.
2) Nanopore throat flow solid phase interaction
According to the molecular thermodynamic theory, the intermolecular interaction energy of the near-wall fluid comprises cohesive energy, surface energy and solvation energy, and the mathematical expressions are as follows:
in the formula, E coh Denotes the fluid cohesive energy, C VDW Represents the van der waals force parameter, and σ represents the effective diameter of the fluid molecule; e surf Represents the surface energy; a represents a Hamaker parameter; d 0 Represents the fluid-solid interface distance, which is equal to sigma/2.5; e solv Representing the solvation energy, d represents the distance of the fluid molecules from the solid surface.
And analyzing according to the properties of the components of the crude oil and the properties of the rock components of the reservoir to obtain the average size of the molecules of the crude oil, the average size of solid-phase molecules on the surface of the pore throat, Van der Waals force parameters of interaction between flow and solid molecules and Hamaker parameters.
3) Non-uniform distribution function of fluid viscosity
Calculating a flow-solid phase interaction characterization parameter alpha:
wherein n represents the number of fluid molecules per unit area; k is a radical of B Is Boltzmann constant, 1.380649 × 10 -23 J·K -1 (ii) a T represents the system temperature. The effective diameter sigma of the fluid molecules and the Hamaker parameter A can be obtained through the step 2), and then the flow-solid interaction characterization parameter alpha can be obtained through the calculation of the formula.
Expression of the non-uniform distribution function μ (r) of crude oil viscosity in the nanoscale pore throat:
and the distribution rule of the fluid viscosity in the nanoscale pore throat on the space can be obtained by combining the flow-solid phase interaction characterization parameter value and the viscosity non-uniform distribution function. Calculated by the viscosity change ratio:
obtaining the change rule of the viscosity of the crude oil in the nano-scale pore throat.
4) Boundary slip velocity function
Critical stress value tau for producing slip boundary c The expression is as follows:
wherein ε represents a solid surface friction coefficient; σ s olid Representing the effective diameter of the solid molecule. According to the chemical thermodynamic theory, slip velocity u surf Can be expressed as:
defining effective stress tau eff The mathematical expression is as follows:
according to the analysis of the flow-solid phase interaction mechanism in the step 2), the critical stress value tau is referred to c Expression to obtain effective stress value tau of boundary fluid under a certain external pressure driving condition eff Further obtaining the fluid slip velocity u on the surface of the solid surf 。
5) Cross sectional velocity distribution function
The integral function of the cross-sectional velocity can be expressed as:
in the formula (I), the compound is shown in the specification,
indicating an external pressure driven pressure gradient.
By solving the above formula transcendental integral, combining step 3) and step 4), the velocity distribution function of the crude oil section in the nanopore throat is:
in the formula, σ solid Representing the effective diameter of the solid molecule.
6) Cross sectional flow function
Performing area integration on the cross section velocity distribution function (step 5)) on the cross section of the nanopore throat to obtain a flow function of the nanopore throat crude oil:
7) apparent permeability of nano-scale porous medium oil phase
According to the permeability definition, combining Darcy's law with step 6), the apparent permeability of the oil phase of the dense reservoir nanoscale porous medium considering the flow-solid phase interaction can be expressed as:
the permeability of the tight reservoir enriched by the nano-scale pore throat can be accurately given by completing the steps 1) to 7).
Examples 2,
A method of use in a tight oil reservoir gas injection development simulation using the simulation method of example 1, comprising:
combining the calculation results of the oil phase apparent permeability models of the nanoscale porous media of the tight reservoir established in the steps 1) to 7) with a CMG oil reservoir numerical simulator to simulate the development process of the tight reservoir.
And in the simulation tight reservoir development process, the model calculation result is combined with a CMG oil reservoir numerical simulator, the oil phase permeability value of the tight reservoir obtained by calculation is led into a reservoir physical property module, and the elastic development process after the tight reservoir is fractured is simulated.
Application example:
taking a tight oil reservoir block of a certain oil field as an example, the pore throat size data and the inherent permeability value of the reservoir are measured. According to the oil phase apparent permeability calculation model provided by the invention, the inherent permeability and the apparent permeability of the porous medium under different pore throat sizes are calculated and obtained according to the geological conditions of the reservoir matrix with the porosity of 7% and the pore throat tortuosity of 1.4, as shown in table 1.
| Average pore throat radius/nm | Intrinsic permeability/(10) -3 μm 2 ) | Apparent permeability/(10) -3 μm 2 ) |
| 10 | 0.000625 | 0.00057 |
| 20 | 0.00250 | 0.00234 |
| 50 | 0.01562 | 0.01488 |
| 100 | 0.0625 | 0.0609 |
| 200 | 0.2500 | 0.2475 |
Table 1 tight reservoir intrinsic permeability and apparent permeability
A reservoir geological model is built based on tight reservoir conditions as shown in figure 2. Wherein the abscissa is the transverse length of the reservoir geological model, and the ordinate is the longitudinal length of the model. The physical meaning of the contrasting color bars is to indicate the oil saturation within the reservoir. Setting the initial oil reservoir pressure to be 50MPa and the oil reservoir temperature to be 115 ℃. Setting reservoir fractures by adopting a grid encryption method: the crack length was 128m, the width was 24m, and the crack permeability was 50 mD.
The reservoir matrix permeability parameter values were calculated using simulations (see table 1). And the matrix permeability adopts inherent permeability and apparent permeability respectively, the elastic development process after the fracturing of the compact reservoir is simulated, and the crude oil extraction degree is compared. Simulation results show that the flow-solid interaction in the nano pore throat has a non-negligible influence on the crude oil production of the compact reservoir.
It should be noted that, regarding the specific structure of the present invention, the connection relationship between the modules adopted in the present invention is determined and can be realized, except for the specific description in the embodiment, the specific connection relationship can bring the corresponding technical effect, and the technical problem proposed by the present invention is solved on the premise of not depending on the execution of the corresponding software program.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (7)
1. A method for calculating the apparent permeability of a dense reservoir nanoscale porous medium oil phase is based on a flow-solid interaction mechanism and is characterized in that: the method for establishing the nano-scale porous medium oil phase apparent permeability calculation model comprises the following steps:
s1: determining the hypothetical conditions: neglecting the electrostatic force among crude oil molecules and between crude oil molecules and pore throat solid phase molecules; neglecting the influence of water, namely neglecting the action of intermolecular hydration force; the pore throat size is larger than 2nm, and the fluid conforms to the assumption of a continuous medium; neglecting the influence of the crude oil and the solid phase composition on the fluid-solid interaction; ignoring the chemical reaction process;
s2: determining the fluid-solid interaction mechanism: on the solid surface of the pore throat, fluid molecules are influenced by the solid surface molecules to present an ordered arrangement state, an ordered arrangement self-layering is formed, and the fluid molecules far away from the wall surface are still in a random arrangement state;
s3: establishing a crude oil viscosity non-uniform distribution function: determining a spatial non-uniform distribution function of the viscosity of the crude oil in the nanoscale pore throat according to the flow-solid interaction mechanism determined in the step S2 and a mathematical expression of the viscosity of the fluid in statistical mechanics, wherein the viscosity of the fluid is influenced by interaction forces between flow-flow molecules and flow-solid molecules;
s4: constructing a section velocity distribution function: determining a cross-section velocity distribution function, a boundary slip velocity function and a flow function of flowing of the nano-scale pore throat crude oil under a certain external pressure driving condition by combining a Newton internal friction law and a boundary slip condition;
s5: and determining a calculation model of the oil phase apparent permeability of the nanoscale porous medium of the compact reservoir layer based on the fluid-solid interaction according to the permeability definition and by combining Darcy's law and the flow function of the nanoscale pore throat crude oil.
2. The method for calculating the apparent permeability of the oil phase of the tight reservoir nanoscale porous medium according to claim 1, wherein the method comprises the following steps: the step S2 is specifically calculated as follows:
according to the molecular thermodynamic theory, the intermolecular interaction energy of the near-wall fluid comprises cohesive energy, surface energy and solvation energy, and the mathematical expressions are as follows:
in the above formula: e coh Denotes the cohesive energy of the fluid, C VDW Represents the van der waals force parameter, and σ represents the effective diameter of the fluid molecule, and has the unit of m; e surf Represents surface energy in J.m -2 (ii) a A represents a Hamaker parameter with the unit of J; d 0 Represents the fluid-solid interface spacing, and the unit is m; e solv Representing the solvation energy, d represents the distance of the fluid molecules from the solid surface.
3. The method for calculating the apparent permeability of the oil phase of the tight reservoir nanoscale porous medium according to claim 2, characterized in that: the step S3 specifically includes:
according to the theory of statistical mechanics, the thermodynamic expression of fluid viscosity is:
in the above formula, h p Representing the Planck constant, is 6.62607015 multiplied by 10 -34 J·s；v m Represents the fluid molecular volume in m 3 (ii) a E represents the free energy of the fluid per unit area, in J.m -2 (ii) a n represents the number of fluid molecules per unit area, and the unit is m -2 ；k B Representing a boltzmann constant of 1.380649 × 10 -23 J·K -1 (ii) a T represents the system temperature in K;
in bulk fluid systems, the viscosity of the fluid is determined by the intermolecular interactions of the fluid, i.e.The free energy in the fluid is only cohesive energy, so that the viscosity mu of the bulk fluid 0 The expression is as follows:
in the nano-scale pore throat, the viscosity of the fluid is determined by interaction forces between flow-flow and flow-solid molecules, namely the free energy in the fluid is cohesive energy and solvation energy, so that the expression of the viscosity mu of the fluid in the nano-scale porous medium is as follows:
to simplify the formula for engineering applications, a parameter α characterizing the flow-solid phase interaction is defined:
taking the fluid viscosity as a positive value, obtaining an expression of the viscosity of the crude oil in the nanoscale pore throat:
in the above formula, R represents the pore throat radius, and R represents the distance between the flow cell and the pore throat centerline, and is expressed in m.
4. The method for calculating the apparent permeability of the oil phase of the compact reservoir nanoscale porous medium according to claim 3, characterized by comprising the following steps: the step S4 cross-sectional velocity distribution function is calculated as follows:
the calculation is carried out by combining Newton's law of internal friction and crude oil viscosity expression, and the integral function of the section velocity is expressed as:
in the above formula, the first and second carbon atoms are,
expressing the gradient of external pressure driving pressure, and the unit is Pa/m;
introducing a variable x ═ R)/sigma, and correcting the formula by adopting an element conversion method:
through function analysis and model simplification, the cross-sectional velocity distribution function is simplified as follows:
in the above formula, C is an integration constant;
combining boundary slip conditions, namely a slip velocity function, the velocity distribution function of the section of the crude oil in the nanopore throat is as follows:
in the above formula, σ solid Represents the effective diameter of the solid molecule, and the unit is m; tau is eff Representing the effective stress at which the fluid produces boundary slip velocity.
5. The method for calculating the apparent permeability of the oil phase of the compact reservoir nanoscale porous medium according to claim 4, wherein the method comprises the following steps: the flow function calculation formula of the nano-scale pore throat crude oil in the step S4 is as follows:
and (3) performing area integration on the section velocity distribution function on the section of the nanopore throat to obtain a flow function of the crude oil of the nanopore throat:
in the above equation, Ei represents an exponential integration function, and erfi represents an error function.
6. The method for calculating the apparent permeability of the oil phase of the compact reservoir nanoscale porous medium according to claim 5, characterized by comprising the following steps: in the step S5, according to the permeability definition, combining the darcy' S law and the nanopore throat crude oil flow function, the apparent permeability of the oil phase of the dense reservoir nanoscale porous medium considering the flow-solid interaction is expressed as:
7. the method for calculating the apparent permeability of the oil phase of the compact reservoir nanoscale porous medium according to claim 6, wherein the method comprises the following steps: the calculation of the boundary slip speed function in step S4 is as follows:
according to the molecular thermodynamic theory as well as the tribological theory, the surface force caused by surface energy is an important parameter leading to the phenomenon of velocity boundary slip: the speed slip phenomenon occurs at the fluid-solid interface if and only if the applied pressure is greater than the surface force, the stress value caused by the surface force being defined as the critical stress value tau c The expression is:
wherein ε represents a solid surface friction coefficient; sigma solid Represents the effective diameter of the solid molecule, and the unit is m;
according to the chemical thermodynamic theory, slip velocity u surf Expressed as:
defining effective stress tau eff The mathematical expression is:
in the above formula, τ represents the shear stress of the fluid flow under external pressure.
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