CN114382446B - Resource exploitation method and device based on shale reservoir relative permeability - Google Patents
Resource exploitation method and device based on shale reservoir relative permeability Download PDFInfo
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- 238000009736 wetting Methods 0.000 description 7
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- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
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- G01N15/0826—Investigating permeability by forcing a fluid through a sample and measuring fluid flow rate, i.e. permeation rate or pressure change
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
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Abstract
The application discloses a resource exploitation method and device based on shale reservoir relative permeability, and belongs to the technical field of oil and gas field development. According to the application, through respectively establishing flow models of liquid-phase and gas-phase fluids in a single nano pore, correcting the sliding length and the effective viscosity of the fluids related to the flow models based on the actual flowing condition of multiphase fluids in the nano pore, obtaining accurate fluid flow and flowing state characteristics, and obtaining accurate relative permeability by combining with an actual nano pore structure, corresponding working parameters are determined according to different relative permeability during resource exploitation, so that the exploitation efficiency and the exploitation yield of shale reservoir resource exploitation are improved.
Description
Technical Field
The application relates to the technical field of oil and gas field development, in particular to a resource exploitation method and device based on shale reservoir relative permeability.
Background
The relative permeability is used for characterizing the flow characteristics of multiphase fluid and is important basic data for oil and gas reservoir resource exploitation. In actual shale reservoirs, there are typically two or more fluids. Under the condition of multiphase flow, the physical and chemical properties of the fluid in each phase, such as viscosity, density, composition and the like, are different, the saturation of the fluid in each phase is also different, the fluid in each phase in shale is mutually interfered when flowing, and the change of the flowing state of the fluid in each phase has an important influence on the resource exploitation work. Therefore, in the resource exploitation, how to accurately know the flow state of each phase of fluid in the reservoir, and determine the relative permeability, so that determining the corresponding working parameters of resource exploitation based on the relative permeability is an important research direction.
Disclosure of Invention
The embodiment of the application provides a resource exploitation method and device based on shale reservoir relative permeability, which can improve the accuracy of the acquired relative permeability, thereby improving the accuracy of the working parameters of resource exploitation. The technical scheme is as follows:
in one aspect, a method for exploiting resources based on the relative permeability of shale reservoirs is provided, the method comprising:
acquiring the flow of gas-phase fluid and the flow of liquid-phase fluid in the nano-pores of the shale reservoir;
Determining a reference slip length and a reference viscosity corresponding to the gas-phase fluid and the liquid-phase fluid based on contact information between the liquid-phase fluid and the nanopore, wherein the reference slip length and the reference viscosity are used for indicating the flow state characteristics of the fluid in the nanopore;
determining structural information of nanopores of the shale reservoir;
determining a relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
And determining the resource exploitation working parameters of the shale reservoir based on the relative permeability, and carrying out resource exploitation based on the resource exploitation working parameters.
In one possible implementation, the obtaining the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid within the nanopores of the shale reservoir comprises:
Respectively obtaining the flow speeds of gas-phase fluid and liquid-phase fluid;
Based on the flow velocity, a flow rate of the gas phase fluid and a flow rate of the liquid phase fluid in the single nanopore are determined.
In one possible implementation, after determining the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the single nanopore based on the flow rate, the method further includes:
And determining the total flow of the gas-phase fluid and the total flow of the liquid-phase fluid in the unit area based on the flow of the gas-phase fluid and the flow of the liquid-phase fluid in the single nano-pore and the structural information of the nano-pore.
In one possible implementation, the reference slip length and the reference viscosity are determined based on the following formulas (1) and (2):
Wherein μ d represents a reference viscosity, pa.s;
l se represents a reference slip length, m;
L sa represents apparent slip length, m;
L s is expressed as the wall fluid true slip length, nm;
Mu ∞ represents the free fluid viscosity, pa.s;
Mu i represents the interfacial region fluid viscosity, pa.s;
A id, take on the value of Represents the interfacial area, m 2;
a td, take on the value of Represents the total cross-sectional area, m 2;
d c represents the critical thickness of the confining fluid, nm;
d represents pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the parting porous medium, a fractal characteristic of a tortuous flow line of the nanopore, and a tortuosity of the nanopore.
In one possible implementation, the determining the relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores includes:
Determining wet phase saturation and non-wet phase saturation based on the flow rate of the respective phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopore, a wet phase relative permeability and a non-wet phase relative permeability are determined.
In one possible implementation, the wet phase relative permeability and the non-wet phase relative permeability are determined based on the wet phase saturation, the non-wet phase saturation, the structural characteristics of the nanopores, and the following formulas (3) and (4):
wherein K rw represents the relative permeability of the wet phase and has no dimension;
K mw represents the relative permeability of the non-wet phase, dimensionless;
s w represents wet phase saturation,%;
s wc represents the saturation of the fixed wet phase,%;
S nw represents non-wet phase saturation,%;
Mu w represents the wet phase fluid viscosity, pa.s;
mu nw represents the viscosity of the non-wet phase fluid, pa.s;
Wherein m= (D 1-4δD2+6δ2D3-4δ3D4+δ4D5);
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the thickness of the liquid film, nm;
L s is expressed as the wall fluid true slip length, nm;
r max represents the maximum pore radius, nm;
r min represents the minimum pore radius, nm;
d T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane;
D f represents the fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
In one aspect, there is provided a resource recovery device based on shale reservoir relative permeability, the device comprising:
the acquisition module is used for acquiring the flow of gas-phase fluid and the flow of liquid-phase fluid in the nano pores of the shale reservoir;
A first determining module, configured to determine a reference slip length and a reference viscosity corresponding to the gas-phase fluid and the liquid-phase fluid based on contact information between the liquid-phase fluid and the nanopore, where the reference slip length and the reference viscosity are used to indicate a flow state characteristic of the fluid in the nanopore;
a second determining module for determining structural information of the nanopores of the shale reservoir;
A third determination module for determining a relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
and a fourth determining module, configured to determine a resource exploitation operating parameter of the shale reservoir based on the relative permeability, and conduct resource exploitation based on the resource exploitation operating parameter.
In one possible implementation, the obtaining module is configured to:
Respectively obtaining the flow speeds of gas-phase fluid and liquid-phase fluid;
Based on the flow velocity, a flow rate of the gas phase fluid and a flow rate of the liquid phase fluid in the single nanopore are determined.
In one possible implementation, the apparatus further includes:
And a fifth determining module, configured to determine a total flow rate of the gas phase fluid and a total flow rate of the liquid phase fluid in a unit area based on the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the single nanopore and the structural information of the nanopore.
In one possible implementation, the reference slip length and the reference viscosity are determined based on the following formulas (1) and (2):
Wherein μ d represents a reference viscosity, pa.s;
l se represents a reference slip length, m;
L sa represents apparent slip length, m;
L s is expressed as the wall fluid true slip length, nm;
Mu ∞ represents the free fluid viscosity, pa.s;
Mu i represents the interfacial region fluid viscosity, pa.s;
A id, take on the value of Represents the interfacial area, m 2;
a td, take on the value of Represents the total cross-sectional area, m 2;
d c represents the critical thickness of the confining fluid, nm;
d represents pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the parting porous medium, a fractal characteristic of a tortuous flow line of the nanopore, and a tortuosity of the nanopore.
In one possible implementation, the third determining module is configured to:
Determining wet phase saturation and non-wet phase saturation based on the flow rate of the respective phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopore, a wet phase relative permeability and a non-wet phase relative permeability are determined.
In one possible implementation, the wet phase relative permeability and the non-wet phase relative permeability are based on the wet phase saturation, non-wet phase saturation, structural characteristics of the nanopores, and the following formulas (3) and (3)
Equation (4) determines:
wherein K rw represents the relative permeability of the wet phase and has no dimension;
K rnw represents the relative permeability of the non-wet phase, dimensionless;
s w represents wet phase saturation,%;
s wc represents the saturation of the fixed wet phase,%;
S nw represents non-wet phase saturation,%;
Mu w represents the wet phase fluid viscosity, pa.s;
mu nw represents the viscosity of the non-wet phase fluid, pa.s;
Wherein m= (D 1-4δD2+6δ2D3-4δ3D4+δ4D5);
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the thickness of the liquid film, nm;
L s is expressed as the wall fluid true slip length, nm;
r max represents the maximum pore radius, nm;
r min represents the minimum pore radius, nm;
d T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane;
D f represents the fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
In one aspect, a computer device is provided that includes one or more processors and one or more memories having stored therein at least one program code loaded and executed by the one or more processors to perform operations performed by the shale reservoir relative permeability-based resource recovery method.
In one aspect, a computer readable storage medium having at least one program code stored therein is provided, the at least one program code loaded and executed by a processor to perform operations performed by the shale reservoir relative permeability-based resource recovery method.
According to the technical scheme provided by the embodiment of the application, through respectively establishing the flow models of the liquid phase fluid and the gas phase fluid in the single nano-pore, and then correcting the sliding length and the effective viscosity of the fluid related to the flow models based on the actual flowing condition of the multiphase fluid in the nano-pore, accurate fluid flow and flowing state characteristics are obtained, and then the accurate relative permeability is obtained by combining with the actual nano-pore structure, so that when resources are exploited, corresponding working parameters are determined according to different relative permeabilities, and the exploitation efficiency and the output of shale reservoir resource exploitation are improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a resource recovery method based on shale reservoir relative permeability provided by an embodiment of the application;
FIG. 2 is a flow chart of a method for resource recovery based on shale reservoir relative permeability provided by an embodiment of the application;
FIG. 3 is a schematic diagram of a two-phase flow model according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a boundary slip provided by an embodiment of the present application;
FIG. 5 is a graph showing the relative permeability of wet/non-wet phases as a function of wet phase saturation according to an embodiment of the present application;
FIG. 6 is a graphical representation of wet phase/non-wet phase relative permeability as a function of wetting angle provided by an embodiment of the present application;
FIG. 7 is a graph showing the relative permeability of wet/non-wet phases as a function of pore fractal dimension according to an embodiment of the present application;
FIG. 8 is a graph showing the relative permeability of wet phase/non-wet phase as a function of fractal dimension of tortuosity according to an embodiment of the present application;
FIG. 9 is a graph showing the relative permeability of wet/non-wet phases as a function of the thickness of a liquid film according to an embodiment of the present application;
FIG. 10 is a graph showing the relative permeability of wet/non-wet phases as a function of minimum radius according to an embodiment of the present application;
FIG. 11 is a graph showing the relative permeability of wet/non-wet phases as a function of maximum radius according to an embodiment of the present application;
FIG. 12 is a schematic structural view of a resource recovery device based on shale reservoir relative permeability provided by an embodiment of the application;
fig. 13 is a schematic structural diagram of a computer device according to an embodiment of the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present application more apparent, the embodiments of the present application will be described in further detail with reference to the accompanying drawings.
Fig. 1 is a flowchart of a resource exploitation method based on shale reservoir relative permeability according to an embodiment of the present application, and referring to fig. 1, the method may be applied to a computer device, and the method includes:
101. And obtaining the flow of the gas-phase fluid and the flow of the liquid-phase fluid in the nano pores of the shale reservoir.
102. And determining the reference slip length and the reference viscosity corresponding to the gas-phase fluid and the liquid-phase fluid based on the contact information between the liquid-phase fluid and the nano-pores.
Wherein the reference slip length and the reference viscosity are used to indicate a flow state characteristic of a fluid within the nanopore.
103. Structural information of the nanopores of the shale reservoir is determined.
104. Based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores, a relative permeability between the gas phase fluid and the liquid phase fluid is determined.
105. And determining the resource exploitation working parameters of the shale reservoir based on the relative permeability, and carrying out resource exploitation based on the resource exploitation working parameters.
According to the technical scheme provided by the embodiment of the application, through respectively establishing the flow models of the liquid phase fluid and the gas phase fluid in the single nano-pore, and then correcting the sliding length and the effective viscosity of the fluid related to the flow models based on the actual flowing condition of the multiphase fluid in the nano-pore, accurate fluid flow and flowing state characteristics are obtained, and then the accurate relative permeability is obtained by combining with the actual nano-pore structure, so that when resources are exploited, corresponding working parameters are determined according to different relative permeabilities, and the exploitation efficiency and the output of shale reservoir resource exploitation are improved.
In one possible implementation, the obtaining the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid within the nanopores of the shale reservoir comprises:
Respectively obtaining the flow speeds of gas-phase fluid and liquid-phase fluid;
Based on the flow velocity, a flow rate of the gas phase fluid and a flow rate of the liquid phase fluid in the single nanopore are determined.
In one possible implementation, after determining the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the single nanopore based on the flow rate, the method further includes:
And determining the total flow of the gas-phase fluid and the total flow of the liquid-phase fluid in the unit area based on the flow of the gas-phase fluid and the flow of the liquid-phase fluid in the single nano-pore and the structural information of the nano-pore.
In one possible implementation, the reference slip length and the reference viscosity are determined based on the following formulas (1) and (2):
Wherein μ d represents a reference viscosity, pa.s;
l se represents a reference slip length, m;
L sa represents apparent slip length, m;
L s is expressed as the wall fluid true slip length, nm;
Mu ∞ represents the free fluid viscosity, pa.s;
Mu i represents the interfacial region fluid viscosity, pa.s;
A id, take on the value of Represents the interfacial area, m 2;
atd, take the value of Represents the total cross-sectional area, m 2;
d c represents the critical thickness of the confining fluid, nm;
d represents pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the parting porous medium, a fractal characteristic of a tortuous flow line of the nanopore, and a tortuosity of the nanopore.
In one possible implementation, the determining the relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores includes:
Determining wet phase saturation and non-wet phase saturation based on the flow rate of the respective phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopore, a wet phase relative permeability and a non-wet phase relative permeability are determined.
In one possible implementation, the wet phase relative permeability and the non-wet phase relative permeability are based on the wet phase saturation, non-wet phase saturation, structural characteristics of the nanopores, and the following formulas (3) and (3)
Equation (4) determines:
wherein K rw represents the relative permeability of the wet phase and has no dimension;
K mw represents the relative permeability of the non-wet phase, dimensionless;
s w represents wet phase saturation,%;
s wc represents the saturation of the fixed wet phase,%;
S nw represents non-wet phase saturation,%;
Mu w represents the wet phase fluid viscosity, pa.s;
mu nw represents the viscosity of the non-wet phase fluid, pa.s;
Wherein m= (D 1-4δD2+6δ2D3-4δ3D4+δ4D5);
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the thickness of the liquid film, nm;
L s is expressed as the wall fluid true slip length, nm;
r max represents the maximum pore radius, nm;
r min represents the minimum pore radius, nm;
d T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane;
D f represents the fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
Fig. 2 is a flow chart of a resource exploitation method based on shale reservoir relative permeability according to an embodiment of the application. The method may be applied to a computer device, see fig. 2, and the embodiment may specifically comprise the steps of:
201. And obtaining the flow of the gas-phase fluid and the flow of the liquid-phase fluid in the nano pores of the shale reservoir.
The shale reservoir is a dark shale or high-carbon shale which is rich in organic matters and is mature, and cracks and matrix pores exist in the shale or the rock due to the adsorption of the organic matters, so that gas phase and liquid phase resources such as shale gas, shale oil and the like are stored and preserved. The flow rate of the fluid refers to the amount of fluid flowing through the effective cross section of the pipe per unit time.
FIG. 3 is a schematic diagram of a two-phase flow model provided in an embodiment of the present application, where the graph (a) in FIG. 3 is used to represent the distribution of fluids in the nanopores of a shale reservoir, and the distribution positions of the fluids in each phase in the nanopores are different, and the graph (a) in FIG. 3 is used to represent the inner radius, i.e. the radius of the gas phase fluid, in a single nanopore, as r 1, and the radius of the interface of the two-phase fluids as r 0; the graph (b) in fig. 3 is used to represent the flow structure of fluids within the nanopores of a shale reservoir, where the flow velocity and viscosity of each phase of fluid distributed at different locations in the nanopores are different. For example, the velocity of the bound water of the outermost layer, i.e. the stationary wet phase fluid, is denoted v rw, its viscosity is denoted μ rw, the velocity of the wet phase fluid of the middle layer is denoted v w, its viscosity is denoted μ w, the velocity of the gas phase fluid of the inner layer is denoted v g, its viscosity is denoted μ g. Because the flow rate of the fluid is related to the radius of the nanopore and the flow rate of the fluid, in one possible implementation, the flow rates of the gas phase fluid and the liquid phase fluid can be obtained first; and determining the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the single nano-pore based on the flow rate.
In one possible implementation, the driving force on the fluid layer is denoted pi r 2(p1-p2), and the viscous force is denoted 2 pi rL chi. Considering that the fluid has no acceleration, the viscous force is equal to the driving force, the following equation (5) can be obtained:
-2πrLχ+πr2(p1-p2)＝0 (5)
wherein r represents the radius of any position of the nano-pore, and m;
L represents the capillary, i.e. the nanopore length, m;
X represents a shear stress, N/m 2;
p 1 represents the inlet pressure, pa;
p 2 denotes the outlet pressure, pa.
The above formula (5) is rewritten into the following formula (6):
In the embodiment of the present application, the above formula (5) and formula (6) may be applied to both wet phase fluid and non-wet phase fluid. Combining the above equation (6) with newton's law of viscosity, i.e., taking the following equation (7) into the above equation (6), the following equations (8) and (9) can be obtained:
Wherein F represents internal friction between adjacent fluid layers and N;
a represents the contact area between fluids, m 2;
Mu represents dynamic viscosity, pa.s;
du/dy represents the fluid velocity gradient, s -1;
Mu w represents the wet phase fluid viscosity, pa.s;
mu nw represents the viscosity of the non-wet phase fluid, pa.s;
v w represents wet phase fluid velocity, m/s;
v nw denotes the non-wet phase fluid velocity, m/s.
In the above formulas (8) and (9), the minus sign indicates that the speed is inversely proportional to the radius. In one possible implementation, the following equations (10) and (11) are obtained by rewriting the equation (8) and the equation (9), respectively:
Integrating the above-described equation (10) and equation (11) respectively can obtain the following equation (12) and equation (13):
In the embodiment of the present application, the velocity v rw (m/s) of the stationary wet phase fluid is expressed as the following formula (14):
υrw＝0;r0-δ≤r≤r0 (14)
In the above formula, delta represents the fixed liquid film thickness, m;
C w and C nw each represent an integration constant, dimensionless;
r 1 represents the radius of the gas phase fluid, m;
r 0 denotes the two-phase interface radius, m.
In one possible implementation, a boundary slip phenomenon occurs when fluid flows, referring to fig. 4, fig. 4 is a schematic boundary slip diagram provided by an embodiment of the present application, where (a) in fig. 4 illustrates a boundary non-slip model, and (b) in fig. 4 illustrates a boundary slip model, where L s is represented as a wall fluid true slip length. In the embodiment of the present application, considering that the boundary slip and the velocity at the interface of the wet phase and the non-wet phase are equal, the boundary condition may be expressed as the following equation (15) and equation (16):
In one possible implementation, formula (15) and formula (16) are substituted into formula (12) and formula (14), respectively, to obtain the following formula (17) and formula (18), respectively:
In one possible implementation manner, the flow rate of the liquid phase fluid and the flow rate of the gas phase fluid in the single nanopore can be obtained by integrating the two sides of the above formula (17) and the formula (18), and the flow rates of the liquid phase fluid and the gas phase fluid are respectively expressed as a formula (19) and a formula (20):
/>
Wherein q w represents the flow rate of free liquid in the single nanopore, m 3/s;
q nw represents the flow rate of gas in a single nanopore, m 3/s;
r 0 represents the radius of a single nanopore, m;
r 1 represents the radius of the gas phase fluid flow region in the single nanopore, m;
delta represents the fixed liquid film thickness, m.
202. And correcting the slip length of the fluid in the nano-pore to obtain a reference slip length.
In one possible implementation, the liquid-wall interactions in the closed channel are affected by the morphology, physicochemical characteristics of the solid surface, where boundary wall wettability affects particularly well at low shear rates. In order to improve the accuracy of subsequent determination of the relative permeability, in the embodiment of the present application, the slip length of the fluid in the nanopore needs to be corrected in consideration of the fact that the slip length will vary with the pore. Typically, boundary slip occurs at the molecular level, as determined by the contact angle of a reference liquid under reference conditions, where both the reference conditions and the reference liquid can be set by a developer, and the unmodified slip length is expressed as the following equation (21):
Ls＝C/(cosθ+1)2 (21)
wherein, L s is expressed as the true slip length of the wall fluid, nm;
C represents a constant, and in the embodiment of the application, the value of C is 0.41 obtained by experiments and MD simulation;
θ represents the wetting contact angle in degrees.
In one possible implementation, significant slippage of the water/water interface occurs due to the significant difference in the near-wall confining fluid viscosity and the free fluid viscosity. In practical applications, the constraint fluid slip length considering the true slip and apparent slip effects should be replaced by an effective slip length parameter, that is, a reference slip length obtained by correcting the L s, and the reference slip length parameter of the fluid is expressed as the following formula (1), and in the embodiment of the present application, the effective slip length, that is, the reference slip length depends not only on the wall wettability but also on the fluid viscosity and the size of the nano-pores.
Wherein L se denotes an effective slip length, i.e., a reference slip length, m;
L sa represents apparent slip length, m;
L se represents the true slip length of the wall fluid, m;
Mu ∞ represents the free fluid viscosity, pa.s;
Mu d represents the effective viscosity of the confining fluid, pa.s.
203. And correcting the viscosity of the fluid in the nano-pore to obtain the reference viscosity.
Typically, when constraining fluid flow to the nanopore, the fluid viscosity near the pore wall will no longer be accurately described by the core fluid viscosity, the effective viscosity of the fluid being dependent on the core fluid viscosity and the interfacial region. In the embodiment of the present application, considering that the viscosity of the fluid may vary with the pores, in order to obtain the effective viscosity of the limited fluid, that is, the reference viscosity, the weighted average of the volume area and the interfacial nanopore viscosity is used to represent the reference viscosity, which may be specifically expressed as the following formula (2):
/>
Wherein μ d represents the effective viscosity of the volumetric region fluid, pa.s;
Mu i represents the interfacial region fluid viscosity, pa.s;
A id, take on the value of Represents the interfacial area, m 2;
a td, take on the value of Represents the total cross-sectional area, m 2;
d c represents the critical thickness of the confining fluid, nm.
In one possible implementation, the viscosity of the fluid in the interface region is greatly affected by the wall interaction, and may be expressed by the contact angle obtained through experiments and MD simulation, specifically expressed by the following formula (22):
In connection with equation (22), the interfacial region fluid viscosity varies greatly with contact angle as compared to the free fluid. In one possible implementation, for programming calculation and writing convenience, the reference slip length L se and the reference viscosity μ d may be assigned, in one possible implementation, by Let/>The corrected reference slip length and the reference viscosity can be expressed as the following formula (23) and formula (24):
μd＝μ∞[(x-1)y+1] (24)
it should be noted that, the above steps 202 and 203 are steps for determining a reference slip length and a reference viscosity corresponding to the gas-phase fluid and the liquid-phase fluid based on the contact information between the liquid-phase fluid and the nanopore, where the reference slip length and the reference viscosity are used to indicate the flow state characteristics of the fluid in the nanopore, and the execution sequence of the above steps 202 and 203 is not limited in the embodiment of the present application. In the embodiment of the application, the viscosity and the sliding length of the fluid are corrected based on the actual flowing condition of the multiphase fluid in the nano-pores, and the accuracy of the acquired relative permeability can be improved when the relative permeability is determined based on the flowing state characteristics of the fluid.
204. Determining the statistical characteristics of the parting porous medium of the shale reservoir.
The statistical characteristics of the parting porous medium are used for describing the structural characteristics of shale, and can comprise distribution information of the number of pores in the shale, average diameters of the pores, total area of the pores and the like.
In one possible implementation, the pore number and pore diameter of a tight reservoir such as a shale reservoir satisfy the following fractal power law relationship, specifically expressed as the following equation (25):
Wherein d represents the unit diameter, m;
N (d) represents the number of unit models contained in the whole model, and N t total;
D f represents the fractal dimension of the pore, and is typically 1-2 in value in a two-dimensional plane.
In one possible implementation, the relationship between the number of all pores with a diameter greater than or equal to d and the pore size in the nanopores of the shale reservoir is as follows equation (26):
/>
In one possible implementation, if the pore minimum pore diameter is d min, the total pore number N t is represented by the following formula (27):
in one possible implementation, the two sides of the above formula (27) are simultaneously derived to obtain the pore numbers of the intervals d to d+dd, expressed as the following formula (28):
wherein-dN >0 indicates that the number of pores is inversely proportional to the pore diameter size.
In one possible implementation, dividing equation (28) by equation (27) yields the percentage of the number of pores in the range from d to d+dd to the total number of pores, expressed as equation (29) below:
In connection with the above formula (29), the probability density function f (d) of the pore number with respect to the pore size distribution is expressed as the following formula (30):
The above formula (30) needs to satisfy the normalization condition, expressed as the following formula (31):
in one possible implementation, the above formula (31) holds that the data relationship (32) shown in the following formula (32) needs to be satisfied:
In one possible implementation, the tight reservoir pores satisfy d min/dmax<10-2, i.e., the above equation (32) holds approximately, so the fractal theory can be used to describe shale porous media. The average diameter d av of the tight reservoir pores is expressed as the following equation (33):
In one possible implementation, in a fractal porous medium, the total area of shale pores, a p, is represented by the following equation (34):
wherein d max represents the maximum pore radius, nm;
d min represents the minimum pore radius, nm;
Phi represents porosity.
205. Fractal characteristics of tortuosity flow lines when fluid flows in pores of shale reservoirs are determined.
In one possible implementation, when the fluid flows through a spatially structured complex porous medium, the non-uniform pore tortuosity flow line is represented by the following formula (35):
Wherein ε represents the measured dimension, m;
l t represents the actual streamline length, m;
L represents a linear distance, m;
D T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
In one possible implementation, replacing the measurement scale in equation (35) with a nanopore diameter can result in equation (36) below:
Differentiating the two sides of the formula (32) to obtain a formula (37):
Wherein v t＝dLt/dt, represents the curved pore fluid velocity, m/s;
v 0 = dL/dt, representing the fluid velocity of the straight pores, m/s.
Integrating equation (33) over f (d) to obtain the actual average flow rate, specifically expressed as the following equation (38):
In an embodiment of the present application, the data relationship between D T, τ, and D av satisfies the following equation (39):
Wherein L/d av can be determined based on the following formula (40):
206. And determining the average tortuosity of the pores of the shale reservoir.
Since the flow of fluid in the porous medium does not proceed in a straight line but proceeds in a meandering manner, the degree of meandering is used to reflect the degree of such meandering. Wherein, the tortuosity tau is the ratio of the distance L t of the fluid flowing through the curved flow passage to the distance L of the fluid flowing through the straight flow passage, and is expressed as the following formula (41):
The model of average tortuosity as a function of porosity is expressed as the following equation (42):
It should be noted that the above model is suitable for describing the case that the pore space of the tight reservoir is a uniform cube, and the actual situation of the pore distribution of the tight reservoir is not considered. In the embodiment of the present application, the above expression is modified in conjunction with the absolute permeability of the fluid. Wherein the absolute permeability is expressed as the following formula (43):
From the above formula (43), it is clear that only the tight reservoir permeability, porosity, pore radius need be obtained if an average tortuosity is desired. Since the model (43) is derived on the assumption that the tight reservoir space structure satisfies the uniform capillary bundle model, it cannot be directly used for fractal porous media, in which case, taking into account the limitations of the uniform pore bundle model represented by the formula (43), the average tortuosity of the porous media after introducing the pore size distribution probability density function is expressed as the following formula (44):
In one possible implementation, substituting the fractal power law relationship of pore size distribution, i.e., equation (30), into equation (44) can result in an average tortuosity calculation model suitable for a parting porous medium, expressed as the following equation (45):
It should be noted that, the steps 204 to 206 are steps for determining structural information of the nanopores of the shale reservoir. The structural information of the nanopores includes the steps of the statistical characteristics of the parting porous medium, the fractal characteristics of the tortuosity lines of the nanopores and the tortuosity of the nanopores, and the specific execution sequence of the steps 204 to 206 is not limited in the embodiment of the application.
207. The relative permeability between the gas phase fluid and the liquid phase fluid is determined based on the flow rate, flow state characteristics, and structural characteristics of the nanopores of each phase fluid.
Wherein the relative permeability is used to indicate the permeation of each phase of fluid when the multiphase fluids coexist. The flow state characteristics of the respective phase fluid include a reference viscosity of the fluid, a reference slip length, and the like.
In one possible implementation, the total flow rate of the gas phase fluid and the total flow rate of the liquid phase fluid per unit area may be determined based on the flow rates of the gas phase fluid and the liquid phase fluid in the single nanopore, and the structural information of the nanopore. In one possible implementation, the total flow of all nanopores in a single unit area is known to be equal to the sum of the flow of each nanopore after introduction of fractal theory, expressed as the following formulas (46) and (47):
Wherein Q w represents the total flow rate of free liquid in unit area, m 3/s;
q nw represents the total flow rate of gas per unit area, m 3/s;
N represents the total number of pores from the minimum radius r min to the maximum radius r max, one;
q w represents the flow rate of free liquid in a single nanopore, m 3/s;
q nw represents the flow rate of the gas in the single nanopore, m 3/s;
f represents the probability density function of the distribution of nanopores in the medium.
Since the pressure can be expressed as the following equation (48) and equation (49):
Δpw＝(p1-p2)/(Sw-Swc) (48)
Δpnw＝(p1-p2)/Snw (49)
Wherein Δp w represents the pressure, pa, of the liquid phase fluid in the single nanopore;
Δp nw represents the pressure, pa, of the gas phase fluid in the single nanopore;
Combined with darcy's law The following formula (50) and formula (51) can be obtained, where K is the absolute permeability and Kr is the relative permeability.
Wherein K rw represents the relative permeability of the wet phase and has no dimension;
K rnw represents the relative permeability of the non-wet phase, dimensionless;
s w represents wet phase saturation,%;
s wc represents the saturation of the fixed wet phase,%;
s nw represents the non-wet phase saturation,%.
The radius of the non-wetting fluid may be expressed as the following equation (52):
In one possible implementation, wet phase saturation and non-wet phase saturation are determined based on the flow rate of the respective phase fluid, the flow state characteristics, and the structural characteristics of the nanopores. For fractal porous media, the fixed wet phase saturation can be written as the following equation (53):
Simplifying the above equation, the fixed wet phase saturation can be expressed as the following equation (54):
Wherein,
Delta in the above formula represents the thickness of the liquid film, nm;
r max represents the maximum pore radius, nm;
r min represents the minimum pore radius, nm;
d T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane;
D f represents the fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
The absolute permeability of the medium can be written as the following equation (55):
Where N represents the number of capillaries per unit area, dimensionless.
In one possible implementation, the wet phase relative permeability and the non-wet phase relative permeability are determined based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopore. That is, the relative permeabilities of the respective phase fluids obtained by the above-mentioned formulas (19), (20) and formulas (46) to (55) are combined, and expressed as the following formulas (3) and (4):
Wherein m= (D 1-4δD2+6δ2D3-4δ3D4+δ4D5);
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Mu w represents the wet phase fluid viscosity, pa.s;
mu nw represents the viscosity of the non-wet phase fluid, pa.s;
Delta represents the thickness of the liquid film, nm;
L s is expressed as the wall fluid true slip length, nm;
R max represents the maximum pore radius, nm;
r min represents the minimum pore radius, nm;
d T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane;
D f represents the fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
In the embodiment of the present application, the values of the parameters in the above formula (3) and formula (4) are shown in table 1.
Table 1 parameter values for two-phase permeability model analysis of porous media
| Saturation of wet phase S w | 0.9 | Minimum pore radius r min (nm) | 5 |
| Maximum pore radius r max (nm) | 1000 | Tortuosity fractal dimension D T | 1.614 |
| Pore fractal dimension D f | 1.02 | Wet phase viscosity μ w (mPa.s) | 1 |
| Non-wet phase viscosity mu nw (mPa.s) | 0.0184 | Liquid film thickness delta (nm) | 0.1 |
| Wetting contact angle θ (°) | 30 | Porosity phi | 0.0483 |
Based on equation (3) and equation (4), the relative permeability of the fluid is correlated with the multi-dimensional data. FIG. 5 is a schematic diagram showing the variation of wet phase/non-wet phase relative permeability with wet phase saturation according to the embodiment of the present application, wherein as shown in FIG. 5, K rw increases from 0 to 1 because the process of increasing the wet phase saturation from 0 to 1 means that the wet phase fluid gradually replaces the non-wet phase, and the wet phase relative permeability K rw increases with the increase of the wet phase saturation S w; whereas the non-wet phase relative permeability K rnw decreases with increasing wet phase saturation S w, K rnw decreases from 1 to 0.
Fig. 6 is a schematic diagram showing the change of relative permeability of wet phase/non-wet phase with the wetting angle, referring to fig. 6, in the micro-nano pore, the increase of the wetting angle causes the increase of the sliding length, namely the increase of the flow velocity at the interface of the wet phase and the non-flowing fluid, due to the boundary sliding effect, so that the flow quantity in the pore is increased and the flow property is enhanced. Thus as the wetting angle increases, both K rw and K rnw increase.
Fig. 7 is a graph showing the relative permeability of wet/non-wet phases as a function of the fractal dimension of the pores, as shown in fig. 7, for an example of the present application, which means that the percentage of smaller pores increases and thus the average radius of the porous medium decreases. Combining the conclusion that the previous increase in single nanopore radius resulted in a decrease in K rw and K rnw, an increase in D f resulted in a decrease in average radius, and thus an increase in K rw、Krnw. Thus, as the pore fractal dimension D f increases, both K rw and K rnw increase, with a significant increase in K rw and a slow increase in K rnw in the 0.9631% to 0.9632% range.
Fig. 8 is a schematic diagram showing the change of the relative permeability of the wet phase/the non-wet phase along with the fractal dimension of tortuosity, and the increase of the fractal dimension of tortuosity corresponds to a capillary channel with higher tortuosity, so that the flow resistance is improved, and the non-wet phase which is difficult to flow originally is more difficult to flow. That is, equivalently, an increase in wet phase saturation S w results in an increase in K rw and a decrease in S nw results in a decrease in K rnw. Thus as shown in fig. 8, as the tortuosity fractal dimension increases, K rw increases and K rnw decreases.
Fig. 9 is a schematic diagram showing the change of relative permeability of wet phase/non-wet phase with the thickness of the liquid film according to the embodiment of the present application, since when the pore radius r 0 and the two-phase interface radius r 1 are unchanged, the increase of the thickness δ of the liquid film will result in the decrease of the cross-sectional area of the flowing fluid (the sum of wet phase and non-wet phase) in the pores of the circular tube, and the decrease of the cross-sectional area of the wet phase is not changed. The non-wet phase saturation S nw increases and thus K rnw increases; wet phase saturation S w decreases and thus K rw decreases. Thus, as shown in fig. 8, as the liquid film thickness δ increases, K rw decreases and K rnw increases.
FIG. 10 is a graph showing the relative permeability of wet/non-wet phases as a function of minimum radius provided by the examples of the present application, see FIG. 10, wherein K rw increases from 74% to 95% as the minimum pore diameter r min increases; k rnw slowly decreases in the range 0.96309% to 0.96305% with very little variation. As can be seen from fig. 10, the effect of the increase in pore radius on the relative permeability of the wet phase is much greater than the effect on the relative permeability of the non-wet phase.
FIG. 11 is a graph showing the variation of wet phase/non-wet phase relative permeability with maximum radius provided by the present application, see FIG. 11, since the rate of flow increase with pore radius is less than the rate of absolute permeability increase with pore radius, and the effect of pore radius on wet phase relative permeability is much greater than on non-wet phase relative permeability. Thus, as the pore radius increases, K rw decreases from approximately 90.8% to 76.8%; k rnw was reduced from 0.965% to 0.962% with very little variation.
208. And determining the resource exploitation working parameters of the shale reservoir based on the relative permeability, and carrying out resource exploitation based on the resource exploitation working parameters.
In one possible implementation, various operating parameters during resource recovery may be determined based on the relative permeability of the various phases of fluid, e.g., fracture design based on the relative permeability, prediction of shale reservoir productivity, etc. In the embodiment of the present application, a specific method for resource exploitation based on the relative permeability is not limited.
According to the technical scheme provided by the embodiment of the application, through respectively establishing the flow models of the liquid phase fluid and the gas phase fluid in the single nano-pore, and based on the actual flowing condition of the multiphase fluid in the nano-pore, the sliding length and the effective viscosity of the fluid related to the flow models are corrected to obtain accurate fluid flow and flow state characteristics, and then the accurate relative permeability is obtained by combining with the actual nano-pore structure, so that the accurate working parameters are determined during resource exploitation, and the exploitation efficiency and the output of shale reservoir resource exploitation are improved.
In the embodiment of the application, when the relative permeability is determined, the fractal characteristics of the sliding length, the pore tortuosity and the pore diameter distribution of the fluid in the pore of the shale reservoir are fully considered, a two-phase flow model with circular pore gas and water distributed in a ring shape is introduced, and a differential equation of gas and water two-phase velocity distribution is obtained by combining the Newton second law and the Newton viscosity law, so that a velocity equation and a flow equation of gas and water two-phase in a single nano pore are obtained; and then, by combining the relation of the Darcy formula, the absolute permeability expression, the pore radius and the irreducible water saturation, the expression of the gas-water two-phase relative permeability is established. In the process, boundary conditions of a two-phase flow velocity equation are corrected, porous medium characteristics of pore distribution of a tight reservoir are considered, and the fractal theory is applied on the basis of a single-nano-pore model, so that accuracy of relative permeability prediction is effectively improved.
Any combination of the above optional solutions may be adopted to form an optional embodiment of the present application, which is not described herein.
Fig. 12 is a schematic structural diagram of a resource exploiting device based on shale reservoir relative permeability according to an embodiment of the present application, and referring to fig. 12, the device includes:
An acquisition module 1201, configured to acquire a flow rate of a gas phase fluid and a flow rate of a liquid phase fluid in a nanopore of a shale reservoir;
A first determining module 1201, configured to determine a reference slip length and a reference viscosity corresponding to the gas-phase fluid and the liquid-phase fluid based on contact information between the liquid-phase fluid and the nanopore, where the reference slip length and the reference viscosity are used to indicate a flow state characteristic of the fluid in the nanopore;
a second determining module 1203 for determining structural information of nanopores of the shale reservoir;
A third determining module 1204 for determining a relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
a fourth determining module 1205 is configured to determine a resource recovery operating parameter for the shale reservoir based on the relative permeability, and perform resource recovery based on the resource recovery operating parameter.
In one possible implementation, the obtaining module 1201 is configured to:
Respectively obtaining the flow speeds of gas-phase fluid and liquid-phase fluid;
Based on the flow velocity, a flow rate of the gas phase fluid and a flow rate of the liquid phase fluid in the single nanopore are determined.
In one possible implementation, the apparatus further includes:
And a fifth determining module, configured to determine a total flow rate of the gas phase fluid and a total flow rate of the liquid phase fluid in a unit area based on the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the single nanopore and the structural information of the nanopore.
In one possible implementation, the reference slip length and the reference viscosity are determined based on the following formulas (1) and (2):
/>
Wherein μ d represents a reference viscosity, pa.s;
l se represents a reference slip length, m;
L sa represents apparent slip length, m;
L s is expressed as the wall fluid true slip length, nm;
Mu ∞ represents the free fluid viscosity, pa.s;
Mu i represents the interfacial region fluid viscosity, pa.s;
A id, take on the value of Represents the interfacial area, m 2;
a td, take on the value of Represents the total cross-sectional area, m 2;
d c represents the critical thickness of the confining fluid, nm;
d represents pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the parting porous medium, a fractal characteristic of a tortuous flow line of the nanopore, and a tortuosity of the nanopore.
In one possible implementation, the third determining module 1204 is configured to:
Determining wet phase saturation and non-wet phase saturation based on the flow rate of the respective phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopore, a wet phase relative permeability and a non-wet phase relative permeability are determined.
In one possible implementation, the wet phase relative permeability and the non-wet phase relative permeability are determined based on the wet phase saturation, the non-wet phase saturation, the structural characteristics of the nanopores, and the following formulas (3) and (4):
wherein K rw represents the relative permeability of the wet phase and has no dimension;
K rnw represents the relative permeability of the non-wet phase, dimensionless;
s w represents wet phase saturation,%;
s wc represents the saturation of the fixed wet phase,%;
S nw represents non-wet phase saturation,%;
Mu w represents the wet phase fluid viscosity, pa.s;
mu nw represents the viscosity of the non-wet phase fluid, pa.s;
Wherein m= (D 1-4δD2+6δ2D3-4δ3D4+δ4D5);
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
/>
Delta represents the thickness of the liquid film, nm;
L s is expressed as the wall fluid true slip length, nm;
r max represents the maximum pore radius, nm;
r min represents the minimum pore radius, nm;
d T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane;
D f represents the fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
According to the device provided by the embodiment of the application, through respectively establishing the flow models of liquid-phase and gas-phase fluids in a single nano pore, correcting the sliding length and the effective viscosity of the fluids related to the flow models based on the actual flowing condition of the multiphase fluids in the nano pore to obtain accurate fluid flow and flowing state characteristics, and acquiring accurate relative permeability by combining with an actual nano pore structure, the accurate working parameters are determined during resource exploitation, so that the exploitation efficiency and the output of shale reservoir resource exploitation are improved, and further, the working parameters of the resource exploitation can be accurately determined during the oil and gas reservoir exploitation, for example, the accurate reservoir seepage parameters are obtained, the energy production is predicted according to the relative permeability, and the fracturing design is performed.
It should be noted that: the resource exploitation device based on the shale reservoir relative permeability provided in the above embodiment is only exemplified by the division of the above functional modules when the resource is exploited, and in practical application, the above functional allocation may be completed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. In addition, the resource exploitation device based on the shale reservoir relative permeability provided in the above embodiment and the resource exploitation method embodiment based on the shale reservoir relative permeability belong to the same concept, and the specific implementation process is detailed in the method embodiment, which is not described herein again.
Fig. 13 is a schematic structural diagram of a computer device according to an embodiment of the present application, where the computer device 1400 may have a relatively large difference due to different configurations or performances, and may include one or more processors (Central Processing Units, CPU) 1301 and one or more memories 1302, where the one or more memories 1302 store at least one program code, and the at least one program code is loaded and executed by the one or more processors 1301 to implement the methods provided in the foregoing method embodiments. Of course, the computer device 1300 may also have a wired or wireless network interface, a keyboard, an input/output interface, and other components for implementing the functions of the device, which are not described herein.
In an exemplary embodiment, a computer readable storage medium, such as a memory, comprising at least one program code executable by a processor to perform the shale reservoir relative permeability-based resource recovery method of the above-described embodiments is also provided. For example, the computer readable storage medium may be Read-Only Memory (ROM), random-access Memory (Random Access Memory, RAM), compact disc Read-Only Memory (CD-ROM), magnetic tape, floppy disk, optical data storage device, and the like.
It will be appreciated by those of ordinary skill in the art that all or part of the steps of implementing the above-described embodiments may be implemented by hardware, or may be implemented by at least one piece of hardware associated with a program, where the program may be stored in a computer readable storage medium, where the storage medium may be a read-only memory, a magnetic disk or optical disk, etc.
The foregoing description of the preferred embodiments of the present application is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements within the spirit and principles of the present application.
Claims (8)
1. A method of resource exploitation based on shale reservoir relative permeability, the method comprising:
acquiring the flow of gas-phase fluid and the flow of liquid-phase fluid in the nano-pores of the shale reservoir;
Determining a reference slip length and a reference viscosity corresponding to the gas-phase fluid and the liquid-phase fluid based on contact information between the liquid-phase fluid and the nano-pores, wherein the reference slip length and the reference viscosity are used for indicating flow state characteristics of the corresponding fluid in the nano-pores; wherein the reference slip length and the reference viscosity are determined based on the following formula (1) and formula (2):
Wherein μ d represents a reference viscosity, pa.s; l se represents a reference slip length, m; l sa represents apparent slip length, m; l s is expressed as the wall fluid true slip length, nm; mu ∞ represents the free fluid viscosity, pa.s; mu i represents the interfacial region fluid viscosity, pa.s; d c represents the critical thickness of the confining fluid, nm; d represents pore diameter, nm;
A id, take on the value of Represents the interfacial area, m 2;
a td, take on the value of Represents the total cross-sectional area, m 2;
Determining structural information of nanopores of the shale reservoir;
determining a relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores; wherein said determining the relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores comprises: determining wet phase saturation and non-wet phase saturation based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores; determining a wet phase relative permeability and a non-wet phase relative permeability based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopores;
and determining the resource exploitation working parameters of the shale reservoir based on the relative permeability, and carrying out resource exploitation based on the resource exploitation working parameters.
2. The method of claim 1, wherein the obtaining the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid within the nanopores of the shale reservoir comprises:
Respectively obtaining the flow speeds of gas-phase fluid and liquid-phase fluid;
Based on the flow velocity, a flow rate of the gas phase fluid and a flow rate of the liquid phase fluid in the single nanopore are determined.
3. The method of claim 2, wherein after determining the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the single nanopore based on the flow rate, the method further comprises:
And determining the total flow of the gas-phase fluid and the total flow of the liquid-phase fluid in a unit area based on the flow of the gas-phase fluid in the single nano-pore, the flow of the liquid-phase fluid and the structural information of the nano-pore.
4. The method of claim 1, wherein the structural information characterization of the nanopores comprises a parting porous media statistic, a fractal characteristic of a nanopore tortuosity line, and a tortuosity of the nanopores.
5. The method of claim 1, wherein the wet phase relative permeability and the non-wet phase relative permeability are determined based on the wet phase saturation, non-wet phase saturation, structural characteristics of the nanopores, and the following formulas (3) and (4):
wherein K rw represents the relative permeability of the wet phase and has no dimension;
K rnw represents the relative permeability of the non-wet phase, dimensionless;
s w represents wet phase saturation,%;
s wc represents the saturation of the fixed wet phase,%;
S nw represents non-wet phase saturation,%;
Mu w represents the wet phase fluid viscosity, pa.s;
mu nw represents the viscosity of the non-wet phase fluid, pa.s;
Wherein m= (D 1-4δD2+6δ2D3-4δ3D4+δ4D5);
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the thickness of the liquid film, nm;
L s is expressed as the wall fluid true slip length, nm;
r max represents the maximum pore radius, nm;
r min represents the minimum pore radius, nm;
d T represents the tortuosity fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane;
D f represents the fractal dimension of the pore, and the value of the fractal dimension is 1-2 on a two-dimensional plane.
6. A shale reservoir relative permeability-based resource recovery apparatus, the apparatus comprising:
the acquisition module is used for acquiring the flow of gas-phase fluid and the flow of liquid-phase fluid in the nano pores of the shale reservoir;
the device comprises a first determining module, a second determining module and a third determining module, wherein the first determining module is used for determining a reference slip length and a reference viscosity corresponding to a gas-phase fluid and the liquid-phase fluid based on contact information between the liquid-phase fluid and the nano-pores, and the reference slip length and the reference viscosity are used for indicating flow state characteristics of the corresponding fluid in the nano-pores; wherein the reference slip length and the reference viscosity are determined based on the following formula (1) and formula (2):
Wherein μ d represents a reference viscosity, pa.s; l se represents a reference slip length, m; l sa represents apparent slip length, m; l s is expressed as the wall fluid true slip length, nm; mu ∞ represents the free fluid viscosity, pa.s; mu i represents the interfacial region fluid viscosity, pa.s; d c represents the critical thickness of the confining fluid, nm; d represents pore diameter, nm;
A id, take on the value of Represents the interfacial area, m 2;
a td, take on the value of Represents the total cross-sectional area, m 2;
a second determination module for determining structural information of nanopores of the shale reservoir;
A third determination module for determining a relative permeability between the gas phase fluid and the liquid phase fluid based on the flow rate of each phase fluid, the flow state characteristics, and the structural characteristics of the nanopores;
The third determining module is configured to determine wet phase saturation and non-wet phase saturation based on the flow rate of each phase of fluid, the flow state characteristic, and the structural characteristic of the nanopore; determining a wet phase relative permeability and a non-wet phase relative permeability based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopores;
And the fourth determining module is used for determining the resource exploitation working parameters of the shale reservoir based on the relative permeability and carrying out resource exploitation based on the resource exploitation working parameters.
7. The apparatus of claim 6, wherein the acquisition module is to:
Respectively obtaining the flow speeds of gas-phase fluid and liquid-phase fluid;
Based on the flow velocity, a flow rate of the gas phase fluid and a flow rate of the liquid phase fluid in the single nanopore are determined.
8. The apparatus of claim 7, wherein the apparatus further comprises:
And a fifth determining module, configured to determine a total flow rate of the gas phase fluid and a total flow rate of the liquid phase fluid in a unit area based on the flow rates of the gas phase fluid and the liquid phase fluid in the single nanopore and the structural information of the nanopore.
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| CN109100278A (en) * | 2018-07-18 | 2018-12-28 | 西南石油大学 | A kind of apparent permeability calculation method considering shale pore-size distribution feature |
| CN110567858A (en) * | 2019-10-17 | 2019-12-13 | 西南石油大学 | method for predicting shale nano-pore permeability based on fractal theory |
| CN111425191A (en) * | 2020-03-25 | 2020-07-17 | 西南石油大学 | Method and device for calculating gas-water relative permeability of tight reservoir |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109100278A (en) * | 2018-07-18 | 2018-12-28 | 西南石油大学 | A kind of apparent permeability calculation method considering shale pore-size distribution feature |
| CN110567858A (en) * | 2019-10-17 | 2019-12-13 | 西南石油大学 | method for predicting shale nano-pore permeability based on fractal theory |
| CN111425191A (en) * | 2020-03-25 | 2020-07-17 | 西南石油大学 | Method and device for calculating gas-water relative permeability of tight reservoir |
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| Title |
|---|
| 致密砂岩气水相对渗透率模型;张涛;李相方;王香增;胡开银;孙逢瑞;韩松;;中国科学:技术科学(10);第106-114页 * |
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