CN114382446A - Resource exploitation method and device based on shale reservoir relative permeability - Google Patents
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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 method, the flow models of liquid-phase fluid and gas-phase fluid in a single nanopore are respectively established, the slippage length and the effective viscosity of the fluid related to the flow models are corrected based on the actual flow condition of the multiphase fluid in the nanopore, accurate fluid flow and flow state characteristics are obtained, and the accurate relative permeability is obtained by combining the actual nanopore structure, so that corresponding working parameters are determined according to different relative permeabilities during resource exploitation, and the exploitation efficiency and the output 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 representing the flow characteristics of the multiphase fluid and is important basic data for the exploitation of resources of oil and gas reservoirs. In actual shale reservoirs, there are typically two or more fluids present. Under the condition of multi-phase flow, the physicochemical properties, such as viscosity, density, composition and the like, of each phase fluid are different, and the saturation degrees of each phase fluid are different, so that the flow of each phase fluid in the shale can interfere with each other, and the change of the flow state of each phase fluid has important influence on resource exploitation work. Therefore, in resource exploitation, how to accurately know the flow state of each phase fluid in a reservoir and determine the relative permeability is an important research direction, so that the corresponding resource exploitation working parameter is determined based on the relative permeability.
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 obtained relative permeability, and thus improve the accuracy of resource exploitation working parameters. The technical scheme is as follows:
in one aspect, a resource exploitation method based on shale reservoir relative permeability is provided, and the method includes:
acquiring the flow of gas-phase fluid and the flow of liquid-phase fluid in the nanopores 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, the reference slip length and the reference viscosity being indicative of a flow regime characteristic of the fluid within 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 regime characteristics, and the structural characteristics of the nanopores;
and determining a resource exploitation working parameter of the shale reservoir based on the relative permeability, and performing resource exploitation based on the resource exploitation working parameter.
In one possible implementation, the obtaining of the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the nanopores of the shale reservoir comprises:
respectively acquiring the flow velocities of a gas phase fluid and a liquid phase fluid;
based on the flow velocity, the flow rate of the gas phase fluid in the single nanopore and the flow rate of the liquid phase fluid 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 velocity, the method further comprises:
and determining the total flow rate of the gas phase fluid and the total flow rate of the liquid phase fluid in the 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 equations (1) and (2):
wherein, mudDenotes the reference viscosity, pa.s;
Lserepresents a reference slip length, m;
Lsarepresents the apparent slip length, m;
Lsexpressed as wall fluid true slip length, nm;
μ∞represents the free fluid viscosity, pa.s;
μirepresents interfacial region fluid viscosity, pa.s;
Aidis valued as
Denotes the interfacial area, m2；
AtdIs valued as
Denotes the total cross-sectional area, m2；
dcRepresents the critical thickness of the confining fluid, nm;
d represents the pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the typed porous medium, a fractal characteristic of a nanopore tortuosity streamline, 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 regime characteristics, and the structural characteristics of the nanopores includes:
determining the wet phase saturation and the non-wet phase saturation based on the flow rate of each phase fluid, the flow state characteristics and the structural characteristics of the nanopores;
the relative wet phase permeability and the relative non-wet phase permeability are determined based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopores.
In one possible implementation, the wet phase relative permeability and the non-wet phase relative permeability are determined based on the wet phase saturation based, the non-wet phase saturation based, the structural characteristics of the nanopores, and the following equations (3) and (4):
wherein, KrwRepresents the relative permeability of the wet phase and is dimensionless;
Kmwrepresents the relative permeability of the non-wet phase and is dimensionless;
Swwet phase saturation,%;
Swcrepresents the fixed wet phase saturation,%;
Snwrepresents non-wet phase saturation,%;
μwrepresents the wet phase fluid viscosity, pa.s;
μnwrepresents the viscosity of the non-wet phase fluid, pa.s;
wherein M ═ D1-4δD2+6δ2D3-4δ3D4+δ4D5)；
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the liquid film thickness, nm;
Lsexpressed as wall flowTrue slip length, nm;
rmaxrepresents the maximum pore radius, nm;
rminrepresents the minimum pore radius, nm;
DTthe tortuosity fractal dimension of the pore is expressed, and the value of the tortuosity fractal dimension on a two-dimensional plane is 1-2;
Dfand (3) expressing the fractal dimension of the pores, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane.
In one aspect, a resource exploitation device based on relative permeability of a shale reservoir is provided, and the device comprises:
the acquisition module is used for acquiring the flow of gas phase fluid and the flow of liquid phase fluid in the nanopores of the shale reservoir;
a first determination module for 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, the reference slip length and the reference viscosity being indicative of a flow state characteristic of the fluid within the nanopore;
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 condition characteristics, and the structural characteristics of the nanopores;
and the fourth determination 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.
In one possible implementation, the obtaining module is configured to:
respectively acquiring the flow velocities of a gas phase fluid and a liquid phase fluid;
based on the flow velocity, the flow rate of the gas phase fluid in the single nanopore and the flow rate of the liquid phase fluid are determined.
In one possible implementation, the apparatus further includes:
and the fifth determining module is used for 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 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 equations (1) and (2):
wherein, mudDenotes the reference viscosity, pa.s;
Lserepresents a reference slip length, m;
Lsarepresents the apparent slip length, m;
Lsexpressed as wall fluid true slip length, nm;
μ∞represents the free fluid viscosity, pa.s;
μirepresents interfacial region fluid viscosity, pa.s;
Aidis valued as
Denotes the interfacial area, m2；
AtdIs valued as
Denotes the total cross-sectional area, m2；
dcRepresents the critical thickness of the confining fluid, nm;
d represents the pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the typed porous medium, a fractal characteristic of a nanopore tortuosity streamline, and a tortuosity of the nanopore.
In one possible implementation, the third determining module is configured to:
determining the wet phase saturation and the non-wet phase saturation based on the flow rate of each phase fluid, the flow state characteristics and the structural characteristics of the nanopores;
the relative wet phase permeability and the relative non-wet phase permeability are determined based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopores.
In one possible implementation, the relative wet-phase permeability and the relative non-wet-phase permeability are based on the saturation based on the wet-phase, saturation based on the non-wet-phase, structural characteristics of the nanopores, and the following equations (3) and (b)
Equation (4) determines:
wherein, KrwRepresents the relative permeability of the wet phase and is dimensionless;
Krnwrepresents the relative permeability of the non-wet phase and is dimensionless;
Swwet phase saturation,%;
Swcrepresents the fixed wet phase saturation,%;
Snwrepresents non-wet phase saturation,%;
μwrepresents the wet phase fluid viscosity, pa.s;
μnwrepresents the viscosity of the non-wet phase fluid, pa.s;
wherein M ═ D1-4δD2+6δ2D3-4δ3D4+δ4D5)；
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the liquid film thickness, nm;
Lsexpressed as wall fluid true slip length, nm;
rmaxrepresents the maximum pore radius, nm;
rminrepresents the minimum pore radius, nm;
DTthe tortuosity fractal dimension of the pore is expressed, and the value of the tortuosity fractal dimension on a two-dimensional plane is 1-2;
Dfand (3) expressing the fractal dimension of the pores, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane.
In one aspect, a computer apparatus is provided that includes one or more processors and one or more memories having at least one program code stored therein that is loaded into and executed by the one or more processors to perform the operations performed by the shale reservoir relative permeability based resource production 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 being loaded into and executed by a processor to perform the operations performed by the shale reservoir relative permeability based resource production method.
According to the technical scheme provided by the embodiment of the application, the flow models of the liquid phase fluid and the gas phase fluid in the single nanometer pore are respectively established, the slippage length and the effective viscosity of the fluid related to the flow models are corrected based on the actual flowing condition of the multiphase fluid in the nanometer pore, accurate fluid flow and flowing state characteristics are obtained, the accurate relative permeability is obtained by combining the actual nanometer pore structure, and therefore when resources are mined, corresponding working parameters are determined according to different relative permeabilities, and the mining efficiency and the yield of shale reservoir resource mining are improved.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flow chart of a resource exploitation method based on shale reservoir relative permeability according to an embodiment of the present application;
FIG. 2 is a flow chart of a resource exploitation method based on shale reservoir relative permeability according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a two-phase flow model provided by an embodiment of the present application;
FIG. 4 is a schematic diagram of boundary sliding provided by an embodiment of the present application;
FIG. 5 is a schematic illustration of wet phase/non-wet phase relative permeability as a function of wet phase saturation provided by an embodiment of the present application;
FIG. 6 is a graphical illustration of wet phase/non-wet phase relative permeability as a function of wetting angle as provided by an example of the present application;
FIG. 7 is a schematic representation of wet phase/non-wet phase relative permeability as a function of pore fractal dimension as provided in the examples herein;
FIG. 8 is a schematic illustration of relative wet phase/non-wet phase permeability as a function of fractal dimension of tortuosity according to an embodiment of the present application;
FIG. 9 is a schematic representation of the wet phase/non-wet phase relative permeability as a function of liquid film thickness provided by an example of the present application;
FIG. 10 is a graphical illustration of wet phase/non-wet phase relative permeability as a function of minimum radius provided by an example of the present application;
FIG. 11 is a graphical illustration of wet phase/non-wet phase relative permeability as a function of maximum radius provided by an example of the present application;
FIG. 12 is a schematic structural diagram of a resource exploitation device based on relative permeability of a shale reservoir 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
To make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.
Fig. 1 is a flowchart of a resource exploitation method based on relative permeability of a shale reservoir 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 acquiring the flow of the gas phase fluid and the flow of the liquid phase fluid in the nanopores of the shale reservoir.
102. Based on the contact information between the liquid phase fluid and the nanopores, reference slip lengths and reference viscosities corresponding to the gas phase fluid and the liquid phase fluid are determined.
Wherein the reference slip length and the reference viscosity are indicative of a flow regime characteristic of a fluid within the nanopore.
103. Determining structural information of the nanopores of the shale reservoir.
104. The relative permeability between the gas phase fluid and the liquid phase fluid is determined based on the flow rate of each phase fluid, the flow regime characteristics, and the structural characteristics of the nanopores.
105. And determining a resource exploitation working parameter of the shale reservoir based on the relative permeability, and performing resource exploitation based on the resource exploitation working parameter.
According to the technical scheme provided by the embodiment of the application, the flow models of the liquid phase fluid and the gas phase fluid in the single nanometer pore are respectively established, the slippage length and the effective viscosity of the fluid related to the flow models are corrected based on the actual flowing condition of the multiphase fluid in the nanometer pore, accurate fluid flow and flowing state characteristics are obtained, the accurate relative permeability is obtained by combining the actual nanometer pore structure, and therefore when resources are mined, corresponding working parameters are determined according to different relative permeabilities, and the mining efficiency and the yield of shale reservoir resource mining are improved.
In one possible implementation, the obtaining of the flow rate of the gas phase fluid and the flow rate of the liquid phase fluid in the nanopores of the shale reservoir comprises:
respectively acquiring the flow velocities of a gas phase fluid and a liquid phase fluid;
based on the flow velocity, the flow rate of the gas phase fluid in the single nanopore and the flow rate of the liquid phase fluid 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 velocity, the method further comprises:
and determining the total flow rate of the gas phase fluid and the total flow rate of the liquid phase fluid in the 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 equations (1) and (2):
wherein, mudDenotes the reference viscosity, pa.s;
Lserepresents a reference slip length, m;
Lsarepresents the apparent slip length, m;
Lsexpressed as wall fluid true slip length, nm;
μ∞represents the free fluid viscosity, pa.s;
μirepresents interfacial region fluid viscosity, pa.s;
Aidis valued as
Denotes the interfacial area, m2；
Atd, value is
Denotes the total cross-sectional area, m2；
dcRepresents the critical thickness of the confining fluid, nm;
d represents the pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the typed porous medium, a fractal characteristic of a nanopore tortuosity streamline, 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 regime characteristics, and the structural characteristics of the nanopores includes:
determining the wet phase saturation and the non-wet phase saturation based on the flow rate of each phase fluid, the flow state characteristics and the structural characteristics of the nanopores;
the relative wet phase permeability and the relative non-wet phase permeability are determined based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopores.
In one possible implementation, the relative wet-phase permeability and the relative non-wet-phase permeability are based on the saturation based on the wet-phase, saturation based on the non-wet-phase, structural characteristics of the nanopores, and the following equations (3) and (b)
Equation (4) determines:
wherein, KrwRepresents the relative permeability of the wet phase and is dimensionless;
Kmwrepresents the relative permeability of the non-wet phase and is dimensionless;
Swwet phase saturation,%;
Swcrepresents the fixed wet phase saturation,%;
Snwrepresents non-wet phase saturation,%;
μwrepresents the wet phase fluid viscosity, pa.s;
μnwrepresents the viscosity of the non-wet phase fluid, pa.s;
wherein M ═ D1-4δD2+6δ2D3-4δ3D4+δ4D5)；
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the liquid film thickness, nm;
Lsexpressed as wall fluid true slip length, nm;
rmaxrepresents the maximum pore radius, nm;
rminrepresents the minimum pore radius, nm;
DTthe tortuosity fractal dimension of the pore is expressed, and the value of the tortuosity fractal dimension on a two-dimensional plane is 1-2;
Dfand (3) expressing the fractal dimension of the pores, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane.
Fig. 2 is a flowchart of a resource exploitation method based on the relative permeability of a shale reservoir according to an embodiment of the present application. The method can be applied to a computer device, and referring to fig. 2, the embodiment may specifically include the following steps:
201. and acquiring the flow of the gas phase fluid and the flow of the liquid phase fluid in the nanopores of the shale reservoir.
The shale reservoir refers to mature dark shale or high-carbon shale rich in organic matters, and gas-phase and liquid-phase resources, such as shale gas, shale oil and the like, are stored and preserved due to organic matter adsorption or cracks and matrix pores existing in rocks. The flow rate of the fluid means the amount of fluid flowing through an effective cross section of a pipe per unit time.
FIG. 3 is a schematic diagram of a two-phase flow model provided in an embodiment of the present application, such as (a) in FIG. 3 for illustrating the nanopores in a shale reservoirThe distribution of the fluid is different in the distribution position of each phase fluid in the nanopores, as shown in the diagram (a) in 3, and in a single nanopore, the inner radius, namely the radius of the gas phase fluid, is represented as r1The radius of the two-phase fluid interface is denoted as r0(ii) a Fig. 3 (b) is a graph illustrating the flow structure of the fluid in the nanopores of the shale reservoir, and the flow velocity and viscosity of each phase fluid distributed at different positions in the nanopores are different. For example, the velocity of the outermost bound water, i.e. the immobile wet phase fluid, is denoted vrwThe viscosity is expressed as μrwThe velocity of the wet phase fluid of the intermediate layer is denoted vwThe viscosity is expressed as μwThe velocity of the gas phase fluid of the inner layer is denoted by vgThe viscosity is expressed as μg. Because the flow rate of the fluid is related to the radius of the nanopores and the flow velocity of the fluid, in one possible implementation, the flow velocities 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 nanometer pore according to the flow velocity.
In one possible implementation, the driving force acting on the fluid layer is expressed as π r2(p1-p2) The viscous force is expressed as 2 π rL χ. Considering that the fluid has no acceleration, the viscous force is equal to the driving force, and the following formula (5) can be obtained:
-2πrLχ+πr2(p1-p2)＝0 (5)
wherein r represents the radius of any position of the nanopore, m;
l represents the capillary, i.e. the nanopore length, m;
x represents a shear stress, N/m2；
p1Denotes the inlet pressure, Pa;
p2indicating the outlet pressure, Pa.
The above formula (5) is rewritten as the following formula (6):
in the embodiment of the present application, the above equations (5) and (6) may be applied to both the wet phase fluid and the non-wet phase fluid. Combining the above equation (6) with newton's law of viscosity, i.e., substituting the following equation (7) into the above equation (6), the following equations (8) and (9) can be obtained:
wherein F represents the internal friction between adjacent fluid layers, N;
a represents the contact area between the fluids, m2；
μ represents dynamic viscosity, pa.s;
du/dy denotes the fluid velocity gradient, s-1；
μwRepresents the wet phase fluid viscosity, pa.s;
μnwrepresents the viscosity of the non-wet phase fluid, pa.s;
vwrepresents the wet phase fluid velocity, m/s;
vnwrepresenting the non-wet phase fluid velocity, m/s.
In the above equations (8) and (9), the minus sign indicates that the velocity is inversely proportional to the radius. In one possible implementation, the following equations (10) and (11) are obtained by rewriting equations (8) and (9), respectively:
by integrating the above equations (10) and (11), respectively, the following equations (12) and (13) can be obtained:
in the present example, the stationary wet phase fluid velocity vrw(m/s) represented by the following formula (14):
υrw＝0；r0-δ≤r≤r0 (14)
in the above formula, δ represents the thickness of the stationary liquid film, m;
Cwand CnwAll represent integral constants and are dimensionless;
r1represents the radius of the gas phase fluid, m;
r0denotes the two-phase boundary radius, m.
In a possible implementation manner, a boundary slip phenomenon occurs when a fluid flows, referring to fig. 4, fig. 4 is a schematic diagram of a boundary slip provided by an embodiment of the present application, fig. 4 (a) illustrates a boundary no-slip model, fig. 4 (b) illustrates a boundary slip model, and L in the diagramsExpressed as the wall fluid true slip length. In the embodiment of the present application, the boundary condition may be expressed as the following formula (15) and formula (16) in consideration of boundary slip and equal velocity at the interface between the wet phase and the non-wet phase:
in one possible implementation, substituting equation (15) and equation (16) into equation (12) and equation (14) above, respectively, results in the following equation (17) and equation (18), respectively:
in one possible implementation, the two sides of the above equation (17) and equation (18) are integrated to obtain the flow rate of the liquid phase fluid and the flow rate of the gas phase fluid in the single nanopore, which are respectively expressed as equation (19) and equation (20):
wherein q iswDenotes the flow of free liquid in the individual nanopores, m3/s；
qnwRepresents the flow rate of gas in a single nanopore, m3/s；
r0Represents the radius of a single nanopore, m;
r1represents the radius, m, of the flow region of the gas phase fluid in the single nanopore;
δ represents the stationary liquid film thickness, m.
202. And correcting the slip length of the fluid in the nanopore to obtain the reference slip length.
In one possible implementation, the liquid-wall interaction in the closed channel is influenced by the solid surface morphology, physicochemical characteristics, where the boundary wall wettability influences the effect particularly at low shear rates. In order to improve the accuracy of the 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 varies with the pore. In general, the boundary slip occurs at a molecular level and is determined by a contact angle of a reference liquid under a reference condition, wherein the reference condition and the reference liquid can be set by a developer, and an uncorrected slip length is expressed by the following formula (21):
Ls＝C/(cosθ+1)2 (21)
wherein L issExpressed as wall fluid true slip length, nm;
c represents a constant, and in the embodiment of the present application, the value of C is obtained by experiments and MD simulation to be 0.41;
θ represents the wetting contact angle in units.
In one possible implementation, significant slippage at the water/water interface can occur due to the significant difference in the near-wall constrained fluid viscosity and the free fluid viscosity. In practical application, the constraint fluid slip length considering true slip and apparent slip effects is replaced by an effective slip length parameter, namely LsThe corrected reference slip length, the parameter of the reference slip length of the fluid is expressed as the following formula (1), and in the embodiment of the application, the effective slip length, namely the reference slip length, not only depends on the wettability of the wall surface, but also depends on the viscosity of the fluid and the size of the nano pores.
Wherein L isseRepresents the effective slip length, i.e. the reference slip length, m;
Lsarepresents the apparent slip length, m;
Lserepresenting the true slip length of the wall surface fluid, m;
μ∞represents the free fluid viscosity, pa.s;
μdrepresenting the effective viscosity of the confining fluid, pa.s.
203. The viscosity of the fluid in the nanopore is corrected to obtain a reference viscosity.
Typically, when the confining fluid flows to the nanopores, the fluid viscosity near the walls of the pores 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, in order to obtain the effective viscosity of the confined fluid, i.e. the reference viscosity, considering the case that the viscosity of the fluid varies with the pores, the reference viscosity is expressed by using a weighted average of the viscosity of the volume region and the interfacial nanopores, which can be specifically expressed by the following formula (2):
wherein, mudRepresents the effective viscosity of the fluid in the volume area, pa.s;
μirepresents interfacial region fluid viscosity, pa.s;
Aidis valued as
Denotes the interfacial area, m2；
AtdIs valued as
Denotes the total cross-sectional area, m2；
dcRepresenting the critical thickness, nm, of the confining fluid.
In one possible implementation, the viscosity of the fluid in the interface region is greatly affected by the wall interaction, and can be expressed by the contact angle obtained by experiment and MD simulation, which is specifically expressed by the following formula (22):
in combination with equation (22), the interfacial region fluid viscosity varies more with contact angle than the free fluid. In one possible implementation, the reference slip length L may be calculated for programming, ease of writingseReference viscosity μdIs evaluated, in one possible implementation, by
Order to
The corrected reference slip length and the reference viscosity can be expressed as the following equation (23) and equation (24):
μd＝μ∞[(x-1)y+1] (24)
it should be noted that, the step 202 and the step 203 are steps of 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 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 step 202 and the step 203 is not limited in the embodiment of the present application. In the embodiment of the application, the viscosity and the slip length of the fluid are corrected based on the actual flow condition of the multiphase fluid in the nanopores, and the accuracy of the obtained relative permeability can be improved when the relative permeability is determined based on the flow state characteristics of the fluid in the subsequent process.
204. And determining the statistic characteristics of the typing porous media of the shale reservoir.
The statistical characteristics of the typed porous medium are used for describing the structural characteristics of the shale, and may include distribution information of the number of pores in the shale, average diameter of the pores, total area of the pores, and the like.
In one possible implementation, the number of pores and the diameter of pores in a tight reservoir such as a shale reservoir satisfy the following fractal power law relationship, which is specifically expressed by the following formula (25):
wherein d represents a unit diameter, m;
n (d) represents the number of unit models contained in the whole model, and N is totaltA plurality of;
Dfand (3) representing the fractal dimension of the pore, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane under the common condition.
In one possible implementation, the relationship between the pore size and the number of all pores with a diameter greater than or equal to d in the nanopores of the shale reservoir is as in the following equation (26):
in one possible implementation, if the pores have a minimum pore diameter dminTotal number of pores NtExpressed as the following formula (27):
in one possible implementation, the above equation (27) is simultaneously differentiated on both sides to obtain the number of pores in the interval d to d + dd, which is expressed by the following equation (28):
wherein-dN >0 indicates that the number of wells is inversely proportional to the size of the diameter of the wells.
In one possible implementation, dividing equation (28) by equation (27) yields the percentage of the number of pores in the interval from d to d + dd over the total number of pores, expressed as equation (29) below:
in conjunction with the above equation (29), the probability density function f (d) of the number of pores with respect to the pore size distribution is expressed as the following equation (30):
the above formula (30) satisfies the normalization condition, and is expressed as the following formula (31):
in one possible implementation, the above equation (31) holds to satisfy the data relationship (32) shown in the following equation (32):
in one possible implementation, the tight reservoir pore satisfies dmin/dmax<10-2Namely, the above formula (32) is approximately established, so that the shale porous medium can be described by using a fractal theory. Mean diameter d of tight reservoir poresavExpressed by the following formula (33):
in one possible implementation, in the fractal porous medium, the total area a of the shale porespExpressed as the following formula (34):
wherein d ismaxRepresents the maximum pore radius, nm;
dminrepresents the minimum pore radius, nm;
phi denotes porosity.
205. Fractal characteristics of a tortuous flow line are determined as the fluid flows within the pores of the shale reservoir.
In one possible implementation, when the fluid flows through the spatially structured complex porous media, the non-uniform pore tortuosity streamline is expressed by the following equation (35):
where ε represents the scale of the measurement, m;
Ltrepresents the actual streamline length, m;
l represents a linear distance, m;
DTand (3) expressing the fractal dimension of tortuosity of the pores, wherein 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 the nanopore diameter, the following equation (36) can be derived:
differentiating both sides of the above equation (32) to obtain equation (37):
wherein v ist＝dLt(ii) dt, represents flexural pore fluid velocity, m/s;
v0dL/dt, which represents the fluid velocity of the straight pores, m/s.
Integrating the equation (33) with f (d) to obtain the actual average flow velocity, which is expressed as the following equation (38):
in the examples of the present application, DTτ and davThe data relationship therebetween satisfies the following formula (39):
wherein, L/davMay be determined based on the following equation (40):
206. and determining the average tortuosity of pores of the shale reservoir.
Since the flow of fluid in the porous medium does not follow a straight line but flows forward with a meandering shape, the degree of meandering is used to reflect the degree of meandering. Wherein, the tortuosity tau is the distance L of the fluid flowing on the bending flow passagetThe ratio of the distance L to the straight flow path is expressed by the following equation (41):
the model relating the average tortuosity to the porosity is expressed by the following formula (42):
it should be noted that the above model is suitable for describing the situation 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 present embodiment, the above expression is modified in combination with the absolute permeability of the fluid. Wherein the absolute permeability is expressed as the following formula (43):
from the above equation (43), it can be seen that only the tight reservoir permeability, porosity and pore radius need to be obtained if the average tortuosity is required. Since the model (43) is derived on the assumption that the compact reservoir space structure satisfies the uniform capillary bundle model, the model cannot be directly used for fractal porous media, in this case, the average tortuosity of the porous media after introducing the pore size distribution probability density function is expressed by the following formula (44) in consideration of the limitation of the uniform pore bundle model represented by the formula (43):
in one possible implementation, substituting the fractal power law relationship of pore size distribution, equation (30), into equation (44) can result in a mean tortuosity calculation model for a typed porous medium, expressed as equation (45) below:
it should be noted that the steps 204 to 206 are steps of determining the structural information of the nanopores of the shale reservoir. The structural information characteristics of the nanopores include statistical characteristics of the typing porous medium, fractal characteristics of a nanopore tortuous streamline, and tortuosity of the nanopores, and the specific execution sequence of the steps 204 to 206 is not limited in the embodiment of the present application.
207. The relative permeability between the gas phase fluid and the liquid phase fluid is determined based on the flow rate of each phase fluid, the flow regime characteristics, and the structural characteristics of the nanopores.
Wherein the relative permeability is used for indicating the permeability of each phase fluid when the multiphase fluids coexist. The flow state characteristics of each 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 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 total flow rate per unit area of all nanopores is equal to the sum of the flow rates per nanopore, expressed as the following equation (46) and equation (47), after introducing fractal theory:
wherein Q iswDenotes the total flow of free liquid per unit area, m3/s；
QnwDenotes the total flow of gas per unit area, m3/s；
N represents the minimum radius rminTo the maximum radius rmaxTotal number of pores of (a), number;
qwrepresents the flow of free liquid in a single nanopore, m3/s；
qnwRepresents the flow rate of gas in a single nanopore, m3/s；
f represents the probability density function of the distribution of the nanopores in the medium.
Since the pressure can be expressed as the following formula (48) and formula (49):
Δpw＝(p1-p2)/(Sw-Swc) (48)
Δpnw＝(p1-p2)/Snw (49)
wherein, Δ PwRepresenting liquid phase flow in a single nanoporeThe pressure of the body, Pa;
ΔPnwrepresenting the pressure of gas phase fluid in a single nanopore, Pa;
combined with Darcy's law
The following formula (50) and formula (51) can be obtained, where K is absolute permeability and Kr is relative permeability.
Wherein, KrwRepresents the relative permeability of the wet phase and is dimensionless;
Krnwrepresents the relative permeability of the non-wet phase and is dimensionless;
Swwet phase saturation,%;
Swcrepresents the fixed wet phase saturation,%;
Snwindicates non-wet phase saturation,%.
The radius of the non-wetting fluid can be expressed by the following equation (52):
in one possible implementation, the wet phase saturation and the non-wet phase saturation are determined based on the flow rate of the respective phase fluid, the flow regime 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 the content of the first and second substances,
δ in the above formula represents the liquid film thickness, nm;
rmaxrepresents the maximum pore radius, nm;
rminrepresents the minimum pore radius, nm;
DTthe tortuosity fractal dimension of the pore is expressed, and the value of the tortuosity fractal dimension on a two-dimensional plane is 1-2;
Dfand (3) expressing the fractal dimension of the pores, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane.
The absolute permeability of the media can be written as the following equation (55):
wherein N represents the number of capillaries per unit area, and has no dimension.
In one possible implementation, the relative wet phase permeability and the relative non-wet phase permeability are determined based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopores. That is, the relative permeability of each phase fluid can be obtained by combining the above equations (19) and (20) and equations (46) to (55), and is expressed by the following equations (3) and (4):
wherein M ═ D1-4δD2+6δ2D3-4δ3D4+δ4D5)；
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
μwRepresents the wet phase fluid viscosity, pa.s;
μnwrepresents the viscosity of the non-wet phase fluid, pa.s;
delta represents the liquid film thickness, nm;
Lsexpressed as wall fluid true slip length, nm;
Rmaxrepresents the maximum pore radius, nm;
Rminrepresents the minimum pore radius，nm；
DTThe tortuosity fractal dimension of the pore is expressed, and the value of the tortuosity fractal dimension on a two-dimensional plane is 1-2;
Dfand (3) expressing the fractal dimension of the pores, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane.
In the embodiment of the present application, values of each parameter in the above formulas (3) and (4) are shown in table 1.
TABLE 1 parameter values for porous media two-phase permeability model analysis
| Wet phase saturation Sw | 0.9 | Minimum pore radius rmin(nm) | 5 |
| Maximum pore radius rmax(nm) | 1000 | Fractal dimension of tortuosity DT | 1.614 |
| Fractal dimension of pore Df | 1.02 | Wet phase viscosity muw(mPa.s) | 1 |
| Non-wet phase viscosity munw(mPa.s) | 0.0184 | Liquid film thickness delta (nm) | 0.1 |
| Wetting contact Angle θ (°) | 30 | Porosity phi | 0.0483 |
Based on the above equation (3) and equation (4), the relative permeability of the fluid is associated with the multidimensional data. FIG. 5 is a schematic diagram of relative wet phase/non-wet phase permeability as a function of wet phase saturation provided in an example of the present application, and it can be seen from FIG. 5 that the relative wet phase permeability K is obtained since the process of increasing the wet phase saturation from 0 to 1 means that the wet phase fluid gradually replaces the non-wet phaserwDependent on the wet phase saturation SwIncreased by an increase of KrwIncreasing from 0 to 1; rather than the relative permeability K of the wet phasernwDependent on the wet phase saturation SwIncrease and decrease, KrnwFrom 1 to 0.
Fig. 6 is a schematic diagram of a wet phase/non-wet phase relative permeability varying with a wetting angle according to an embodiment of the present application, and referring to fig. 6, in a micro-nano pore, due to a boundary slip effect, a slip length is increased due to an increase in the wetting angle, that is, a flow velocity at an interface between a wet phase and a non-flowing fluid is increased, so that a flow rate in the pore is increased, and a flow performance is enhanced. Thus as the wetting angle increases, KrwAnd KrnwAre all increasing.
Fig. 7 is a schematic diagram of relative wet phase/non-wet phase permeability as a function of fractal dimension of pores according to the present application, where an increase in fractal dimension of pores means that the percentage of smaller pores increases and thus the average radius of the porous medium decreases, as shown in fig. 7. The increase of the radius of the single nanopore in the binding front leads to KrwAnd KrnwConclusion of decrease, DfIncreasing results in a decrease in the mean radius, and thus Krw、KrnwAnd is increased. Thus, with the pore fractal dimension DfIncrease, KrwAnd KrnwAre all increased, KrwIncrease is significant and KrnwSlowly increasing in the range of 0.9631% to 0.9632%.
Fig. 8 is a schematic diagram of the relative permeability of the wet phase/non-wet phase according to the variation of the fractal dimension of tortuosity, which is provided by the embodiment of the present application, and since the increase of the fractal dimension of tortuosity corresponds to the capillary channel with higher tortuosity, the flow resistance is increased, so that the non-wet phase which originally has difficulty in flowing is more difficult to flow. I.e. equivalent to the wet phase saturation SwIncrease results in KrwIncrease of SnwDecrease results in KrnwAnd decreases. Thus, as shown in FIG. 8, K increases with fractal dimension of tortuosityrwIncrease and KrnwAnd decreases.
FIG. 9 is a schematic representation of the relative wet/non-wet permeability as a function of the thickness of the liquid film as provided by the examples herein, as measured at the pore radius r0And the radius r of the two-phase interface1While constant, an increase in the liquid film thickness δ results in a decrease in the cross-sectional area of the flowing fluid (sum of wet and non-wet phases) within the pores of the barrel, the non-wet phase cross-sectional area is constant and the wet phase cross-sectional area is decreased. Therefore, non-wet phase saturation SnwIs increased, thereby KrnwIncreasing; wet phase saturation SwDecrease, thereby KrwAnd decreases. Thus, as shown in FIG. 8, as the liquid film thickness δ increases, KrwDecrease and KrnwAnd is increased.
FIG. 10 is a schematic diagram of the relative permeability of wet phase/non-wet phase as a function of minimum radius according to an embodiment of the present application, see FIG. 10, as a function of minimum pore size rminIncrease, KrwIncrease from 74% to 95%; krnwThe temperature slowly decreases in the range of 0.96309-0.96305%, and the variation range is extremely small. As can be seen from fig. 10, the increase in pore radius has a much greater effect on the relative permeability of the wet phase than on the relative permeability of the non-wet phase.
Fig. 11 is a schematic diagram of the relative permeability of wet phase/non-wet phase as a function of the maximum radius according to the present embodiment, referring to fig. 11, since the rate of flow increase with the pore radius is less than the rate of absolute permeability increase with the pore radius, and the effect of the pore radius on the relative permeability of wet phase is much greater than the effect on the relative permeability of non-wet phase. Thus, followIncrease in pore radius, KrwDecrease from near 90.8% to 76.8%; krnwThe range of the change is extremely small from 0.965% to 0.962%.
208. And determining a resource exploitation working parameter of the shale reservoir based on the relative permeability, and performing resource exploitation based on the resource exploitation working parameter.
In one possible implementation, various operating parameters in the resource exploitation process may be determined based on the relative permeability of the fluids of the phases, for example, fracturing design based on the relative permeability, predicting the productivity of shale reservoirs, and the like. In the embodiments of the present application, a specific method for resource exploitation based on relative permeability is not limited.
According to the technical scheme provided by the embodiment of the application, the flow models of the liquid phase fluid and the gas phase fluid in the single nanometer pore are respectively established, the slippage length and the effective viscosity of the fluid related to the flow models are corrected based on the actual flowing condition of the multiphase fluid in the nanometer pore, accurate fluid flow and flowing state characteristics are obtained, the accurate relative permeability is obtained by combining the actual nanometer pore structure, and therefore during resource exploitation, accurate working parameters are determined, and exploitation efficiency and yield of shale reservoir resource exploitation are improved.
In the embodiment of the application, when the relative permeability is determined, the slippage length of fluid in the pores of the shale reservoir, the tunnel tortuosity and the fractal characteristics of pore size distribution are fully considered, a two-phase flow model with annular distribution of gas and water in the circular pores is introduced, a differential equation of gas-water two-phase velocity distribution is obtained by combining a Newton's second law and a Newton's viscosity law, and further a velocity equation and a flow equation of gas-water two-phase in a single nanometer pore are obtained; and establishing an expression of relative permeability of gas-water two phases by combining a Darcy formula, an absolute permeability expression, a pore radius and the relation of the saturation of the bound water. In the process, the boundary condition of the two-phase flow velocity equation is corrected, the porous medium characteristics of compact reservoir pore distribution are considered, and the fractal theory is applied on the basis of the single nanopore model, so that the accuracy of the relative permeability prediction is effectively improved.
All the above optional technical solutions may be combined arbitrarily to form optional embodiments of the present application, and are not described herein again.
Fig. 12 is a schematic structural diagram of a resource exploitation device based on relative permeability of a shale reservoir provided in an embodiment of the present application, and referring to fig. 12, the device includes:
an obtaining module 1201, configured to obtain 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, configured to determine 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 regime characteristics, and the structural characteristics of the nanopores;
a fourth determining module 1205, configured to determine a resource exploitation working parameter of the shale reservoir based on the relative permeability, and perform resource exploitation based on the resource exploitation working parameter.
In one possible implementation, the obtaining module 1201 is configured to:
respectively acquiring the flow velocities of a gas phase fluid and a liquid phase fluid;
based on the flow velocity, the flow rate of the gas phase fluid in the single nanopore and the flow rate of the liquid phase fluid are determined.
In one possible implementation, the apparatus further includes:
and the fifth determining module is used for 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 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 equations (1) and (2):
wherein, mudDenotes the reference viscosity, pa.s;
Lserepresents a reference slip length, m;
Lsarepresents the apparent slip length, m;
Lsexpressed as wall fluid true slip length, nm;
μ∞represents the free fluid viscosity, pa.s;
μirepresents interfacial region fluid viscosity, pa.s;
Aidis valued as
Denotes the interfacial area, m2；
AtdIs valued as
Denotes the total cross-sectional area, m2；
dcRepresents the critical thickness of the confining fluid, nm;
d represents the pore diameter, nm.
In one possible implementation, the structural information characteristic of the nanopore includes a statistical characteristic of the typed porous medium, a fractal characteristic of a nanopore tortuosity streamline, and a tortuosity of the nanopore.
In one possible implementation, the third determining module 1204 is configured to:
determining the wet phase saturation and the non-wet phase saturation based on the flow rate of each phase fluid, the flow state characteristics and the structural characteristics of the nanopores;
the relative wet phase permeability and the relative non-wet phase permeability are determined based on the wet phase saturation, the non-wet phase saturation, and the structural characteristics of the nanopores.
In one possible implementation, the wet phase relative permeability and the non-wet phase relative permeability are determined based on the wet phase saturation based, the non-wet phase saturation based, the structural characteristics of the nanopores, and the following equations (3) and (4):
wherein, KrwRepresents the relative permeability of the wet phase and is dimensionless;
Krnwrepresents the relative permeability of the non-wet phase and is dimensionless;
Swwet phase saturation,%;
Swcrepresents the fixed wet phase saturation,%;
Snwrepresents non-wet phase saturation,%;
μwrepresents the wet phase fluid viscosity, pa.s;
μnwrepresents the viscosity of the non-wet phase fluid, pa.s;
wherein M ═ D1-4δD2+6δ2D3-4δ3D4+δ4D5)；
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the liquid film thickness, nm;
Lsexpressed as wall fluid true slip length, nm;
rmaxrepresents the maximum pore radius, nm;
rminrepresents the minimum pore radius, nm;
DTthe tortuosity fractal dimension of the pore is expressed, and the value of the tortuosity fractal dimension on a two-dimensional plane is 1-2;
Dfand (3) expressing the fractal dimension of the pores, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane.
The device provided by the embodiment of the application comprises a flow model, a flow model of liquid phase fluid and gas phase fluid in a single nanometer pore is established respectively, based on the actual flowing condition of multiphase fluid in the nanometer pore, the slippage length and the effective viscosity of the fluid related to the flow model are corrected, accurate fluid flow and flowing state characteristics are obtained, and accurate relative permeability is obtained by combining an actual nanometer pore structure, so that accurate working parameters are determined during resource exploitation, the exploitation efficiency and the yield of shale reservoir resource exploitation are improved, further, in the oil and gas reservoir exploitation process, the working parameters of resource exploitation can be accurately determined, for example, accurate reservoir seepage parameters are obtained, the yield is predicted according to the relative permeability, and fracturing design and the like are carried out.
It should be noted that: in the resource exploitation device based on the relative permeability of the shale reservoir provided by the embodiment, only the division of the functional modules is taken as an example for resource exploitation, and in practical application, the function distribution can be completed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules, so as to complete all or part of the functions described above. In addition, the resource exploitation device based on the shale reservoir relative permeability provided by the embodiment and the resource exploitation method based on the shale reservoir relative permeability provided by the embodiment belong to the same concept, and the specific implementation process is detailed in the method embodiment and is not repeated herein.
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 generate a relatively large difference due to a difference in configuration or performance, and may include one or more processors (CPUs) 1301 and one or more memories 1302, where at least one program code is stored in the one or more memories 1302, and the at least one program code is loaded and executed by the one or more processors 1301 to implement the methods provided by the foregoing method embodiments. Certainly, the computer device 1300 may further have components such as a wired or wireless network interface, a keyboard, and an input/output interface, so as to perform input and output, and the computer device 1300 may further include other components for implementing device functions, which are not described herein again.
In an exemplary embodiment, a computer readable storage medium, such as a memory including at least one program code executable by a processor, is also provided to perform the shale reservoir relative permeability based resource recovery method of the above embodiments. For example, the computer-readable storage medium may be a Read-Only Memory (ROM), a Random Access Memory (RAM), a Compact Disc Read-Only Memory (CD-ROM), a magnetic tape, a floppy disk, an optical data storage device, and the like.
It will be understood by those skilled in the art that all or part of the steps of implementing the above embodiments may be implemented by hardware, or implemented by at least one program code associated with hardware, where the program code is stored in a computer readable storage medium, such as a read only memory, a magnetic or optical disk, etc.
The above description is only exemplary of the present application and should not be taken as limiting, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (10)
1. A method for resource recovery based on the relative permeability of a shale reservoir, the method comprising:
acquiring the flow of gas-phase fluid and the flow of liquid-phase fluid in the nanopores of the shale reservoir;
determining reference slip lengths and reference viscosities corresponding to the gas phase fluid and the liquid phase fluid based on contact information between the liquid phase fluid and the nanopores, the reference slip lengths and the reference viscosities being indicative of flow regime characteristics of the fluids within the nanopores;
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 regime characteristics, and the structural characteristics of the nanopores;
and determining a resource exploitation working parameter of the shale reservoir based on the relative permeability, and carrying out resource exploitation based on the resource exploitation working parameter.
2. The method of claim 1, wherein 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 acquiring the flow velocities of a gas phase fluid and a 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 velocity, the method further comprises:
and determining the total flow rate of the gas phase fluid and the total flow rate of the liquid phase fluid in the 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.
4. The method of claim 1, wherein the reference slip length and the reference viscosity are determined based on the following equations (1) and (2):
wherein, mudDenotes the reference viscosity, pa.s;
Lserepresents a reference slip length, m;
Lsarepresents the apparent slip length, m;
Lsexpressed as wall fluid true slip length, nm;
μ∞represents the free fluid viscosity, pa.s;
μirepresents interfacial region fluid viscosity, pa.s;
Aidis valued as
Denotes the interfacial area, m2；
AtdIs valued as
Denotes the total cross-sectional area, m2；
dcRepresents the critical thickness of the confining fluid, nm;
d represents the pore diameter, nm.
5. The method of claim 1, wherein the structural information characteristic of the nanopores comprises a statistical characteristic of the patterned porous media, a fractal characteristic of the nanopore tortuosity streamlines, and a tortuosity of the nanopores.
6. The method of claim 1, wherein 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 regime characteristics, and the structural characteristics of the nanopores comprises:
determining a wet phase saturation and a non-wet phase saturation based on the flow rate of the phase fluids, the flow regime 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.
7. The method of claim 6, wherein 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 equations (3) and (4):
wherein, KrwRepresents the relative permeability of the wet phase and is dimensionless;
Krnwrepresents the relative permeability of the non-wet phase and is dimensionless;
Swwet phase saturation,%;
Swcrepresents the fixed wet phase saturation,%;
Snwrepresents non-wet phase saturation,%;
μwrepresents the wet phase fluid viscosity, pa.s;
μnwrepresents the viscosity of the non-wet phase fluid, pa.s;
wherein M ═ D1-4δD2+6δ2D3-4δ3D4+δ4D5)；
Y＝D1；
Z＝(1-Snw)D1-2(δ-Ls)D2+δ(δ-2Ls)D3；
Delta represents the liquid film thickness, nm;
Lsexpressed as wall fluid true slip length, nm;
rmaxrepresents the maximum pore radius, nm;
rminrepresents the minimum pore radius, nm;
DTthe tortuosity fractal dimension of the pore is expressed, and the value of the tortuosity fractal dimension on a two-dimensional plane is 1-2;
Dfand (3) expressing the fractal dimension of the pores, wherein the value of the fractal dimension is 1-2 in a two-dimensional plane.
8. A resource extraction 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 nanopores of the shale reservoir;
a first determination module for determining a reference slip length and a reference viscosity corresponding to a gas phase fluid and a liquid phase fluid based on contact information between the liquid phase fluid and the nanopore, the reference slip length and the reference viscosity being indicative of a flow regime characteristic of the fluid within the nanopore;
a second determination module to determine 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 regime characteristics, and the structural characteristics of the nanopores;
and the fourth determination 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.
9. The apparatus of claim 8, wherein the obtaining module is configured to:
respectively acquiring the flow velocities of a gas phase fluid and a 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.
10. The apparatus of claim 9, further comprising:
and the fifth determining module is used for 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 nanopore and the structural information of the nanopore.
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| US20160299117A1 (en) * | 2015-04-08 | 2016-10-13 | King Fahd University Of Petroleum And Minerals | Method for permeability prediction of shale gas |
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