CN111982756A - Two-phase seepage dynamic simulation method and device based on pore network model - Google Patents

Two-phase seepage dynamic simulation method and device based on pore network model Download PDF

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CN111982756A
CN111982756A CN202010794668.3A CN202010794668A CN111982756A CN 111982756 A CN111982756 A CN 111982756A CN 202010794668 A CN202010794668 A CN 202010794668A CN 111982756 A CN111982756 A CN 111982756A
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saturation
throat
wetting phase
capillary force
pore
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CN111982756B (en
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王秀坤
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China University of Petroleum Beijing
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Abstract

The invention provides a two-phase seepage dynamic simulation method and device based on a pore network model. The method comprises the following steps: setting initial capillary force of a pore or a throat on the basis of a pore network model, and acquiring wetting phase saturation corresponding to the initial capillary force; and on the basis of the saturation of the wetting phase corresponding to the initial capillary force, setting the saturation of the inlet end and the outlet end and the boundary conditions of the pressure, and acquiring pressure data and saturation data for each time step on the basis of the changed capillary force and the relative permeability to finish the simulation of the two-phase seepage. The invention also provides a dynamic simulation device. The simulation method and the simulation device can more accurately simulate the dynamic state of the two-phase seepage.

Description

Two-phase seepage dynamic simulation method and device based on pore network model
Technical Field
The invention relates to a two-phase seepage dynamic simulation method and device based on a pore network model, and belongs to the technical field of oil reservoir exploitation.
Background
The multi-phase seepage of the porous medium is a phenomenon widely existing in nature, is closely related to the aspects of oil and gas field development, carbon dioxide sequestration, underground hydraulics, biological seepage and the like, and how to explore the microcosmic seepage rule is a hotspot problem in recent years. The three-dimensional pore structure of the researched material can be obtained through an advanced CT scanning technology, and the pore network of the researched material can be extracted and generated through a reasonable image processing algorithm. Then, the simulation calculation of the multiphase flow can be carried out on the pore network, and the micro mechanism recognition of the multiphase flow can be obtained.
However, the traditional pore network flow simulation method is based on the quasi-steady-state assumption that the viscous force of the fluid is ignored and only the capillary force is considered. The existing dynamic flow simulation method is immature, the mechanism is considered to be insufficient, the simulation accuracy is low, and the method is not in line with the reality.
Disclosure of Invention
In order to solve the above technical problems, an object of the present invention is to provide a dynamic simulation method capable of accurately simulating two-phase seepage.
Another object of the present invention is to provide a dynamic simulation apparatus capable of accurately simulating two-phase seepage.
A two-phase seepage dynamic simulation method based on a pore network model comprises the following steps:
setting initial capillary force of a pore or a throat on the basis of a pore network model, and acquiring wetting phase saturation corresponding to the initial capillary force;
on the basis of the saturation of the wetting phase corresponding to the initial capillary force, the saturation of the inlet end and the outlet end and the boundary conditions of the pressure are set on the basis of the material conservation of the two phases, and pressure data and saturation data are obtained for each time step on the basis of the capillary force and the relative permeability of each pore or throat, so that the simulation of the two-phase seepage is completed.
The established pore network model has no special requirements, and the conventional pore network model in the field can be adopted.
In one embodiment of the present invention, based on two-phase material conservation, the pressure data can be obtained by the following equation:
Figure BDA0002625119300000021
wherein the content of the first and second substances,
Figure BDA0002625119300000022
pc is capillary pressure in Pa, SwIndicates the wetting phase saturation,%;
K＝0.6GA2；
a is the area of the cross section of the aperture or throat in m2；
L is the length of the aperture or throat in m;
p represents pressure in Pa;
k is the conductivity coefficient in m4；
i, j is the number of pores or roars;
r represents relative permeability;
w represents the wetting phase;
n represents a non-wetting phase
Pj wPressure in Pa for the wetting phase;
Pj npressure in Pa for the non-wetting phase.
In one embodiment of the present invention, the saturation data may be obtained by the following formula:
Figure BDA0002625119300000023
wherein S iswIndicating the wetting phase saturation;
l represents the current time step in units of s;
l +1 represents the next time step in units of s;
Δ t represents a time step in units of s;
v denotes the volume of the pore or throat in m3；
K is the conductivity coefficient in m4；
i, j is the number of pores or roars:
r represents relative permeability;
w represents the wetting phase;
p represents pressure in Pa.
In one embodiment of the present invention, the wetting phase saturation corresponding to the initial capillary force is obtained by the following formula:
Figure BDA0002625119300000031
wherein S iswThe saturation of the wetting phase corresponding to the initial capillary force is zero dimension;
r is the radius of the inscribed circle of the aperture or throat, and the unit is m;
sigma is interfacial tension with the unit of N/m;
θ is the contact angle in degrees;
pc is capillary pressure in Pa;
Figure BDA0002625119300000032
where G is the shape factor of the cross-section of the aperture or throat, i.e. the square of the cross-sectional area divided by the cross-sectional perimeter in m2；
θ is the contact angle in °;
beta is a half angle of one angle of the section, and the unit is an angle;
i is the designation for the three corners of the triangular cross-section of the aperture or throat.
In one embodiment of the present invention,
Figure BDA0002625119300000033
the wetting phase saturation is 1 and,
Figure BDA0002625119300000034
wherein θ is the contact angle in °;
sigma is interfacial tension with the unit of N/m;
Swthe wetting phase saturation corresponding to the initial capillary force;
r is the radius of the inscribed circle of the aperture or throat, and the unit is m;
PCcapillary pressure in Pa;
β1and beta2Denotes the half angle of the triangular cross-section of the aperture or throat, respectively, in units of°。
In a specific embodiment of the invention, for each pore or throat, a varying capillary force is obtained:
saturation S for pore or throat wetting phasewThe increased process, i.e. the sucking process:
Figure BDA0002625119300000035
Figure BDA0002625119300000036
when the capillary force is
Figure BDA0002625119300000037
Sw<Sw1The capillary force is
Figure BDA0002625119300000038
For wetting phase saturation SwThe reduction process, i.e. the expulsion process:
Figure BDA0002625119300000041
a capillary force of
Figure BDA0002625119300000042
Wherein
Figure BDA0002625119300000043
Figure BDA0002625119300000044
Sw<Sw2Capillary forces of
Figure BDA0002625119300000045
Wherein θ is the contact angle in °;
sigma is interfacial tension with the unit of N/m;
Swthe wetting phase saturation,%, corresponding to the initial capillary force;
pc is capillary pressure in Pa;
r is the radius of the inscribed circle of the aperture or throat in m.
In a particular embodiment of the invention, for each pore or throat, a varying relative permeability is obtained:
for wetting phase saturation SwThe added process is as follows:
when S isw<Sw1Then, then
Figure BDA0002625119300000046
Wherein
Figure BDA0002625119300000047
Figure BDA0002625119300000048
When the saturation of the wetting phase Sw>Sw1Then Krw＝1，Krn＝0；
For wetting phase saturation SwReduced process if Sw>Sw2Then, then
Figure BDA0002625119300000049
Figure BDA00026251193000000410
Wherein
Figure BDA00026251193000000411
When S isw>Sw2Then Krw＝1，Krn＝0；
Where G is the shape factor of the cross-section of the aperture or throat, i.e. the square of the cross-sectional area divided by the cross-sectional perimeter in m2；
KrwRelative permeability of a wetting phase without dimension;
Krnrelative permeability of non-wetting phase, no dimension;
βithe half angle of the sectional area, in radians;
Gia shape factor of a single half angle, no dimension;
Gi *shape factor of the region occupied by the non-wetting phase, dimensionless;
Gcithe shape factor of the region occupied by the wetting phase, dimensionless;
θ is the contact angle in °;
Snindicating non-wetting phase saturation.
The invention also provides a two-phase seepage dynamic simulation device based on the pore network model, which comprises:
the initial acquisition module is used for setting initial capillary force of a pore or a throat on the basis of the pore network model and acquiring wetting phase saturation corresponding to the initial capillary force;
and the dynamic simulation module is used for acquiring pressure data and saturation data on the basis of initialization to complete the simulation of the two-phase seepage.
In one embodiment of the present invention, in the dynamic simulation module, based on the two-phase material conservation, the pressure data can be obtained by the following formula:
Figure BDA0002625119300000051
wherein Pc is capillary pressure in Pa, SwIndicating the wetting phase saturation;
K＝0.6GA2；
a is the area of the cross section of the aperture or throat in m2；
L is the length of the aperture or throat in m;
p represents pressure in Pa;
g is a form factor, dimensionless;
k is the conductivity coefficient in m4；
i, j is the number of pores or roars;
r represents relative permeability;
w represents the wetting phase;
n represents a non-wetting phase.
In one embodiment of the present invention, in the dynamic simulation module, the saturation data can be obtained by the following formula:
Figure BDA0002625119300000052
wherein S iswIndicating the wetting phase saturation;
l represents the current time step in units of s;
l +1 represents the next time step in units of s;
Δ t represents a time step in units of s;
v denotes the volume of the pore or throat in m3；
i, j is the number of pores or roars:
r represents relative permeability;
w represents the wetting phase;
p represents pressure in Pa.
In an embodiment of the present invention, in the initial obtaining module, the saturation of the wetting phase corresponding to the initial capillary force is obtained by the following formula:
Figure BDA0002625119300000061
wherein S iswThe saturation of the wetting phase corresponding to the initial capillary force is zero dimension;
r is the radius of the inscribed circle of the aperture or throat, and the unit is m;
sigma is interfacial tension with the unit of N/m;
θ is the contact angle in degrees;
pc is capillary pressure in Pa;
Figure BDA0002625119300000062
g is the shape factor of the cross section of the aperture or throat, i.e. the square of the cross-sectional area divided by the cross-sectional perimeter in m2；
θ is the contact angle in °;
beta is a half angle of one angle of the section, and the unit is an angle;
i is the designation for the three corners of the triangular cross-section of the aperture or throat.
In one embodiment of the present invention, in the dynamic simulation module,
Figure BDA0002625119300000063
the wetting phase saturation is 1 and,
Figure BDA0002625119300000064
Figure BDA0002625119300000065
wherein θ is the contact angle in degrees;
sigma is interfacial tension with the unit of N/m;
Swthe wetting phase saturation corresponding to the initial capillary force;
r is the radius of the inscribed circle of the aperture or throat, and the unit is m;
PCcapillary pressure in Pa;
β1and beta2The half angle of the triangular cross section of the aperture or throat, respectively, is expressed in degrees.
In one embodiment of the invention, in the dynamic simulation module, for each pore and throat, a varying capillary force is obtained:
saturation S for pore or throat wetting phasewThe process of the addition is that the process,
Figure BDA0002625119300000071
when the capillary force is
Figure BDA0002625119300000072
Sw<Sw1The capillary force is
Figure BDA0002625119300000073
For wetting phase saturation SwThe process of the reduction is carried out in such a way that,
Figure BDA0002625119300000074
a capillary force of
Figure BDA0002625119300000075
Wherein
Figure BDA0002625119300000076
Sw<Sw2Capillary forces of
Figure BDA0002625119300000077
Wherein θ is the contact angle in °;
sigma is interfacial tension with the unit of N/m;
Swthe wetting phase saturation,%, corresponding to the initial capillary force;
pc is capillary pressure in Pa;
r is the radius of the inscribed circle of the aperture or throat in m.
In one embodiment of the invention, in the dynamic simulation module, for each pore and throat, a varying relative permeability is obtained:
for wetting phase saturation SwAn increasing process when Sw<Sw1Then, then
Figure BDA0002625119300000078
Figure BDA0002625119300000079
Wherein
Figure BDA00026251193000000710
When the saturation of the wetting phase Sw>Sw1Then Krw＝1，K rn0. For wetting phase saturation SwThe process of reduction, also called expulsion, if Sw>Sw2Then, then
Figure BDA00026251193000000711
Wherein
Figure BDA00026251193000000712
When the saturation of the wetting phase Sw>Sw2Then Krw＝1，Krn＝0；
G is the shape factor of the cross section of the aperture or throat, i.e. the square of the cross-sectional area divided by the cross-sectional perimeter in m2；
KrwRelative permeability of a wetting phase without dimension;
Krnrelative permeability of non-wetting phase, no dimension;
βithe half angle of the sectional area, in radians;
Gia shape factor of a single half angle, no dimension;
Gi *shape factor of the region occupied by the non-wetting phase, dimensionless;
Gcithe shape factor of the region occupied by the wetting phase, dimensionless;
θ is the contact angle in °;
Snindicating non-wetting phase saturation.
The invention also provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the computer program to realize the steps of the above two-phase seepage flow dynamic simulation method based on the pore network model.
The present invention further provides a computer-readable storage medium, on which a computer program is stored, wherein the computer program, when being executed by a processor, implements the steps of the above-mentioned two-phase percolation flow dynamic simulation method based on a pore network model according to the present invention.
The two-phase seepage dynamic simulation method and device based on the pore network model realize dynamic representation of the porous medium pore-scale oil-water movement law, can explore and reveal the multi-phase seepage law of the porous medium in microcosmic essence, and define the movement law of oil and water in the pore throat three-dimensional pore distribution, thereby having important scientific value and having a plurality of applications in engineering.
Drawings
Fig. 1 is a schematic diagram of a two-phase seepage dynamic simulation apparatus based on a pore network model according to an embodiment of the present invention.
Fig. 2 is a schematic flow chart of a two-phase seepage dynamic simulation method based on a pore network model according to an embodiment of the present invention.
FIG. 3 is a graph of the pore size probability density of an embodiment of the present invention.
Figure 4 is a cross section of an aperture or throat according to one embodiment of the present invention.
FIG. 5 is a graph illustrating relative permeability curves of pores or throats according to an embodiment of the present invention.
FIG. 6 is a schematic diagram of the distribution of non-zero entries in the coefficient matrix in the pressure equation according to an embodiment of the present invention.
Fig. 7 is a graph showing the saturation distribution (Sw is increased as the color is brighter) during spontaneous imbibition according to an embodiment of the present invention.
Fig. 8 is a graph of the effect of different wetting angles on imbibition recovery levels for one embodiment of the invention.
Detailed Description
The technical solutions of the present invention will be described in detail below in order to clearly understand the technical features, objects, and advantages of the present invention, but the present invention is not limited to the practical scope of the present invention.
Example 1
The embodiment first provides a two-phase seepage dynamic simulation device based on a pore network model, as shown in fig. 1, the device includes:
the initial acquisition module is used for setting initial capillary force of a pore or a throat on the basis of the established pore network model and acquiring the saturation of a wetting phase corresponding to the initial capillary force;
and the dynamic simulation module is used for setting the saturation of the inlet end and the outlet end and the boundary conditions of the pressure on the basis of initialization, acquiring pressure data and saturation data for each time step on the basis of the changed capillary force and the relative permeability, and completing the simulation of the two-phase seepage.
The embodiment further provides a two-phase seepage dynamic simulation method based on a pore network model, as shown in fig. 2, the method includes:
setting initial capillary force of a pore or a throat on the basis of the established pore network model, and acquiring wetting phase saturation corresponding to the initial capillary force;
on the basis of initialization, the saturation of the inlet end and the outlet end and the boundary conditions of the pressure are set, pressure data and saturation data are obtained for each time step on the basis of the variable capillary force and the relative permeability, and the simulation of the two-phase seepage is completed.
In particular, the amount of the solvent to be used,
1. taking the Barnett shale spontaneous imbibition process as a research object, determining the conductivity coefficient K of each pore and throat according to the established two-dimensional 20 × 60 pore network (the pore size distribution is shown in fig. 3), the saturation distribution condition of the initial wetting phase and the non-wetting phase, the pore size and shape of the pore or throat (the cross-sectional schematic diagram is shown in fig. 4), and the shape factor G ═ 0.035; and the effective conductivity of each phase was determined based on the relative permeabilities of the wetting and non-wetting phases (as shown in fig. 5).
2. Taking each pore or throat as a research object, and acquiring pressure equations of a wetting phase and a non-wetting phase of the pore or throat based on material conservation
Figure BDA0002625119300000091
On the basis, based on the connection relation of the pore and the throat and combining with boundary conditions, pressure is establishedThe sparse matrix of the force equation has a matrix shape as shown in fig. 6, which has 120 pores, a matrix size of 1200 × 1200, and 6040 non-zero terms in the corresponding three-diagonal matrix in addition to the boundary condition. From this sparse matrix, the pressure distribution at the next time step can be found.
3. Based on the obtained pressure distribution, the flow rate of the wetting phase and the non-wetting phase between each pore and the throat is calculated, the material exchange amount between each pore and the throat is determined, and then the saturation equation is utilized
Figure BDA0002625119300000092
Figure BDA0002625119300000101
The saturation of each pore or throat is updated.
4. On the basis of obtaining the saturation of the wetting phase and the non-wetting phase, the capillary force of each pore or throat is updated according to the capillary force function of each pore or throat, and for the sucking process,
Figure BDA0002625119300000102
when the capillary force is
Figure BDA0002625119300000103
Sw<Sw1The capillary force is
Figure BDA0002625119300000104
5. And returning to the step 2, repeating the steps 2-4, calculating the pressure and the saturation of the wetting phase and the non-wetting phase under each time step, and recording the pressure, the flow and the saturation distribution result of each time step.
6. According to the calculation method provided above, the Barnett shale spontaneous imbibition process can be simulated, fig. 7 is a plane development diagram when the average saturation Sw of spontaneous imbibition wetting phase is 0.2239, and then research work of main influence factors can be carried out, as shown in fig. 8, the influence of wetting angle on imbibition extraction degree is carried out.

Claims (10)

1. A two-phase seepage dynamic simulation method based on a pore network model comprises the following steps:
setting initial capillary force of a pore or a throat on the basis of a pore network model, and acquiring wetting phase saturation corresponding to the initial capillary force;
on the basis of the saturation of the wetting phase corresponding to the initial capillary force, the saturation of the inlet end and the outlet end and the boundary conditions of the pressure are set on the basis of the material conservation of the two phases, and pressure data and saturation data are obtained for each time step on the basis of the capillary force and the relative permeability of each pore or throat change, so that the simulation of the seepage of the two phases is completed.
2. The method of claim 1, wherein the pressure data is obtained based on the material conservation of the two phases by the following equation:
Figure FDA0002625119290000011
wherein the content of the first and second substances,
Figure FDA0002625119290000012
pc is capillary pressure in Pa, SwIndicating the wetting phase saturation;
K＝0.6GA2(ii) a A is the area of the cross section of the aperture or throat in m2；
L is the length of the aperture or throat in m;
μ is viscosity in Pa · S;
p represents pressure in Pa;
k is the conductivity coefficient in m4；
i, j is the number of pores or roars;
r represents relative permeability;
w represents the wetting phase;
n represents a non-wetting phase.
3. The method of claim 1, wherein the saturation data is obtained by the following equation:
Figure FDA0002625119290000013
wherein S iswIndicating the wetting phase saturation;
l represents the current time step in units of s;
l +1 represents the next time step in units of s;
Δ t represents a time step in units of s;
v denotes the volume of the pore or throat in m3；
K is the conductivity coefficient in m4；
i, j is the number of pores or roars:
r represents relative permeability;
w represents the wetting phase;
p represents pressure in Pa.
4. The method of claim 3, wherein the wetting phase saturation for the initial capillary force is obtained by the following equation:
Figure FDA0002625119290000021
wherein S iswThe saturation of the wetting phase corresponding to the initial capillary force is zero dimension;
r is the radius of the inscribed circle of the aperture or throat, and the unit is m;
sigma is interfacial tension with the unit of N/m;
θ is the contact angle in degrees;
pc is capillary pressure in Pa;
Figure FDA0002625119290000022
g is the shape factor of the cross section of the aperture or throat, i.e. the square of the cross-sectional area divided by the cross-sectional perimeter in m2；
Beta is a half angle of one angle of the section, and the unit is an angle;
i is the index of the three corners of the triangular section of the aperture or throat;
θ is the contact angle in units.
5. The method of claim 4, wherein,
Figure FDA0002625119290000023
the wetting phase saturation is 1 and,
Figure FDA0002625119290000024
wherein θ is the contact angle in °;
sigma is interfacial tension with the unit of N/m;
Swthe wetting phase saturation corresponding to the initial capillary force;
r is the radius of the inscribed circle of the aperture or throat, and the unit is m;
PCcapillary pressure in Pa;
β1and beta2The half angle of the triangular cross section of the aperture or throat, respectively, is expressed in degrees.
6. The method of claim 1, wherein for each pore or throat, a varying capillary force is obtained:
saturation S for pore or throat wetting phasewThe process of the addition is that the process,
Figure FDA0002625119290000031
when the capillary force is
Figure FDA0002625119290000032
Sw<Sw1Then capillary tubeForce is
Figure FDA0002625119290000033
For wetting phase saturation SwThe process of the reduction is carried out in such a way that,
Figure FDA0002625119290000034
a capillary force of
Figure FDA0002625119290000035
Wherein
Figure FDA0002625119290000036
Sw<Sw2Capillary forces of
Figure FDA0002625119290000037
Wherein θ is the contact angle in °;
sigma is interfacial tension with the unit of N/m;
Swthe wetting phase saturation,%, corresponding to the initial capillary force;
pc is capillary pressure in Pa;
r is the radius of the inscribed circle of the aperture or throat in m.
7. The method according to claim 1, wherein for each pore or throat, a varying relative permeability is obtained:
for wetting phase saturation SwThe process of the addition is that the process,
Sw<Sw1then, then
Figure FDA0002625119290000038
Wherein
Figure FDA0002625119290000039
Sw>Sw1Then, thenKrw＝1，Krn＝0；
For wetting phase saturation SwThe process of the reduction is carried out in such a way that,
Sw>Sw2then, then
Figure FDA00026251192900000310
Wherein
Figure FDA00026251192900000311
Sw>Sw2Then Krw＝1，Krn＝0；
Where G is the shape factor of the cross-section of the aperture or throat, i.e. the square of the cross-sectional area divided by the cross-sectional perimeter in m2；
KrwRelative permeability of a wetting phase without dimension;
Krnrelative permeability of non-wetting phase, no dimension;
βithe half angle of the sectional area, in radians;
Gia shape factor of a single half angle, no dimension;
Gi *shape factor of the region occupied by the non-wetting phase, dimensionless;
Gcithe shape factor of the region occupied by the wetting phase, dimensionless;
θ is the contact angle in °;
Snindicating non-wetting phase saturation.
8. A two-phase seepage dynamic simulation device based on a pore network model, the device comprising:
the initial acquisition module is used for setting initial capillary force of a pore or a throat on the basis of the pore network model and acquiring wetting phase saturation corresponding to the initial capillary force;
and the dynamic simulation module is used for acquiring pressure data and saturation data on the basis of initialization to complete the simulation of the two-phase seepage.
9. The apparatus of claim 8, wherein in the dynamic simulation module, based on the conservation of material for the two phases, the pressure data is obtained by the following equation:
Figure FDA0002625119290000041
wherein the content of the first and second substances,
Figure FDA0002625119290000042
pc is capillary pressure in Pa, SwIndicates the wetting phase saturation,%;
K＝0.6GA2(ii) a A is the cross-sectional area of the aperture or throat in m2；
μ is viscosity in Pa · S;
l is the length of the aperture or throat in m;
p represents pressure in Pa;
k is the conductivity coefficient in m4；
K is the conductivity coefficient in m4；
i, j is the number of pores or roars;
r represents relative permeability;
w represents the wetting phase;
n represents a non-wetting phase.
10. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the computer program implements the steps of the two-phase percolation flow dynamic simulation method based on a pore network model according to any one of claims 1-7.
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Publication number Priority date Publication date Assignee Title
CN113569407A (en) * 2021-07-26 2021-10-29 中国石油大学(北京) Method and device for calculating capillary force and relative permeability curve

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