CN116822391A - Heavy oil reservoir bulk phase fluid nonlinear seepage theory model - Google Patents
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Abstract
The application discloses a heavy oil reservoir bulk phase fluid nonlinear seepage theory model, and relates to the technical field of heavy oil reservoir exploitation. The model comprises a thick oil reservoir bulk fluid nonlinear seepage equation and a starting pressure gradient theoretical formula based on the influence of a thick oil adsorption boundary layer and yield characteristics according to the thick oil reservoir bulk fluid seepage characteristics, and verifies the theoretical model. The verification result shows that the average error of the calculation result of the theoretical formula of the starting pressure gradient and experimental data is 7.67%, the average error of the theoretical calculation formula of the bulk fluid seepage equation of the heavy oil reservoir and experimental data is 8.25%, and the seepage curve drawn by the calculation result of the theoretical formula has an obvious nonlinear section. The model has good universality and provides an important nonlinear seepage basic theory for heavy oil reservoir exploitation.
Description
Technical Field
The application relates to the technical field of heavy oil reservoir exploitation, in particular to a heavy oil reservoir bulk phase fluid nonlinear seepage theoretical model.
Background
The thick oil system mainly comprises saturated hydrocarbon, aromatic hydrocarbon, colloid and asphaltene, wherein the saturated hydrocarbon and the aromatic hydrocarbon are light components, and the colloid and the asphaltene are heavy components. The colloid and asphaltene in the thick oil system belong to macromolecules with three-dimensional network structure, and the thick oil system with the structure has the viscosity function of fluid and the elasticity function of solid, and shows the nonlinear seepage with the starting pressure gradient when the porous medium seeps. Sun Jianfang it is believed that a highly viscous and intermolecular force heavy oil system, with some additional resistance to flow within the formation pores, primarily from the interaction between rock solid particles and crude oil at the pore walls, causes such heavy oil to exhibit a percolation law that deviates from darcy's law. During heavy oil seepage there is a critical displacement pressure gradient for the fluid from a stationary state to a flowing state, this critical value being called the start-up pressure gradient. The reason for the initiation of the pressure gradient is believed by Tunne to be primarily the flow resistance of the water-absorbing layer on the surface of the medium to fluid seepage, the presence of which resistance requires a critical pressure gradient for fluid flow. The most fundamental reason why heavy oil reservoirs have a starting pressure gradient is that macromolecules constituting heavy oil have a three-dimensional network structure, and fluids having such structures have elastic characteristics of solids and yield stress, and there is a starting pressure gradient when flowing in a porous medium. Meujuan Yun et al, based on porous media pore properties and capillary pressure effects, propose an irregular model of the starting pressure gradient of the porous media bingham fluid. Wu et al have proposed a percolation model that considers bingham fluids by studying its rheological model and the correlation between apparent viscosity and fluid properties.
It is known that the polar component of heavy oil and the pore wall surface can generate an adsorption boundary layer, the property difference between boundary layer fluid and bulk fluid is very large, the mechanism and influencing factors of the initiation pressure gradient of bulk fluid and the initiation pressure gradient of boundary fluid are different, and the initial stage of oil reservoir exploitation is mainly the seepage process of bulk fluid. The theoretical formula for calculating the starting pressure gradient does not distinguish bulk fluid from boundary fluid in the conventional thick oil nonlinear seepage mathematical model.
Disclosure of Invention
Aiming at the defects, the application provides a thick oil reservoir bulk phase fluid nonlinear seepage theory model based on the influence of a thick oil adsorption boundary layer and yield characteristics, and the model has good universality.
The application adopts the following technical scheme:
a heavy oil reservoir bulk phase fluid nonlinear seepage theory model comprises a heavy oil reservoir bulk phase fluid nonlinear seepage equation based on heavy oil adsorption boundary layer and yield characteristic influence and a starting pressure gradient theory formula, wherein the equilibrium equation of bulk phase fluid stable seepage under the conditions of gravity neglected and fluid being bingham flow is the formula (1),
in the above formula, the left side is displacement pressure, the right side is internal friction force of thick oil, wherein τ 0 The unit of the yield stress of bulk fluid is Pa, R-delta is more than R and more than 0, R is the distance from the center of a pore to a thick oil adsorption boundary layer, the unit is mu m, R is the radius of the pore, the unit is mu m, and delta is the edgeThe unit of the boundary layer thickness is mu m, mu is the viscosity of bulk fluid, the unit is mPa.s, deltap is the displacement pressure difference unit is MPa, v is the speed unit is cm/s, and L is the core length unit is cm;
the method is obtained by deforming the formula (1),
the equation is integrated on both sides:
the flow rate of the bulk fluid is expressed as:
carrying out after-treatment of the formula (3) into the formula (4):
obtaining flow according to an equivalent capillary method:
Q＝NAq (6)
bringing formula (5) into (6) gives:
according to the theory of porosity and capillary model, the porosity is obtained by researching the seepage of bulk fluidRepresents the pore space occupied by the bulk fluid, permeability K h Representing bulk fluid permeability:
and (3) carrying out formula (8) into formula (9), and obtaining a heavy oil reservoir bulk phase fluid nonlinear seepage equation after finishing:
and (3) finishing to obtain:
in the heavy oil reservoir bulk fluid nonlinear seepage equation,is a flow resistance term due to bulk crude oil yield stress;
in (11), the bulk fluid permeability is changed along with the thickness change of the boundary layer, and in the practical application process, the bulk fluid permeability is converted from the effective permeability of the reservoir, and the bulk fluid permeability can be expressed as follows by a capillary theoretical model:
boundary fluid porosityThe relation expression between the porosity phi of the reservoir is as follows:
the relation between effective permeability and effective porosity is:
substituting the formula (14) to obtain the relation between the fluid seepage formula of the heavy oil reservoir bulk phase fluid and the effective permeability:
in the method, in the process of the application,the term represents the influence of boundary layer on the seepage flow, +.>The term represents the effect of yield stress during bulk fluid seepage, and when the above formula does not consider the yield characteristics of the boundary layer and the thick oil, the equation becomes a standard form of Darcy seepage, so that the problem that the yield characteristics of the boundary layer and the thick oil increase the seepage resistance of the thick oil and become nonlinear seepage is solved;
to get a simpler equation form, assume:
the method comprises the following steps:
wherein c 1 And c 2 Are coefficients related to the boundary layer thickness;
let q=0 in equation (14), we obtain the heavy oil reservoir bulk fluid start pressure gradient calculation equation:
and (3) connecting delta with (20) to obtain a relation equation of the starting pressure gradient and the reservoir physical property and crude oil property, wherein the equation set is as follows:
the thickness of the thick oil boundary layer corresponding to the thick oil initial state is the thickness of the thick oil reservoir initial effective boundary layer, and the calculation formula for obtaining the final thick oil reservoir bulk phase fluid starting pressure gradient is as follows:
the method is characterized in that the method is obtained through a heavy oil reservoir bulk fluid starting pressure gradient calculation formula, the starting pressure gradient is related to the yield stress and the boundary layer thickness of heavy oil, and when the yield stress is increased and the boundary layer thickness is increased, the starting pressure gradient is increased;
in addition, anotherCarrying-in formula (23) to obtain:
the deformation is simplified to obtain a thick oil reservoir bulk fluid start pressure gradient expression:
wherein,,
τ 0 is bulk fluid yield stress, pa;
c is a coefficient related to a boundary layer and is obtained by calculating the molar absorptivity of crude oil,
r is pore radius, μm;
ρ is the density of crude oil, g/cm 3 。
Preferably, the relationship between the physicochemical parameters of the crude oil and the boundary layer thickness is as follows,
δ＝a-B ln R (26)
where coefficients a and B depend on the displacement pressure gradient and the physicochemical properties of the crude oil;
the value of B is a constant of 0.0471, a is related to the displacement pressure gradient:
where Z and m depend on the coefficients of the physicochemical properties of the crude oil.
Z＝d 1 ρ-β 1 (28)
m＝d 2 K cΠ -β 2 (29)
Substituting Z with m into equation (26) yields:
wherein d 1 ＝5.5221、β 1 ＝4.5023、d 2 ＝0.00027、β 1 ＝0.0360；
The final boundary layer thickness calculation formula is:
wherein ρ is the density of crude oil, g/cm 3 ；To displace the pressure gradient, atm/m; k (K) cΠ The molar absorptivity of the crude oil is L/(mol.cm); r is pore radius, mum; delta is the boundary layer thickness, μm;
the relationship between pore radius and permeability and porosity was obtained from the poismillet She Gongshi:
the absorbance coefficient can be obtained according to lambert beer's law:
wherein, pi is absorbance; c is the molar concentration, mol/L; bringing formulae (32), (33) into (31) gives:
assuming a displacement pressure gradient of 0.0001MPa/m as the effective boundary layer thickness in the initial state of the oil reservoir, namely:
writing:
the application has the following beneficial effects:
according to the characteristics of heavy oil reservoir bulk phase fluid seepage, a heavy oil bulk phase fluid nonlinear seepage theoretical model and a starting pressure gradient theoretical formula based on the influence of a heavy oil adsorption boundary layer and yield characteristics are established, and the theoretical model is verified. The verification result shows that the average error of the calculation result of the theoretical formula of the starting pressure gradient and experimental data is 7.67%, the average error of the theoretical calculation formula of the bulk fluid seepage equation of the heavy oil reservoir and experimental data is 8.25%, and the seepage curve drawn by the calculation result of the theoretical formula has an obvious nonlinear section. The model has good universality and provides an important nonlinear seepage basic theory for heavy oil reservoir exploitation.
Drawings
FIG. 1 is a core initiation pressure gradient result for LW-7;
FIG. 2 is a LW-8 core initiation pressure gradient result;
FIG. 3 is a LW-25 core initiation pressure gradient result;
FIG. 4 is a graph showing comparison between measured data of a seepage curve of LW-7 core at 40 ℃ and 50 ℃ and calculation results of a model;
FIG. 5 is a graph showing comparison between measured data of a seepage curve of a core LW-8 at 40 ℃ and 50 ℃ and calculation results of a model.
Detailed Description
The following description of the embodiments of the application will be given with reference to the accompanying drawings and examples:
heavy oil contains a large amount of polar components, and when in contact with the solid pore surfaces, adsorption occurs to generate a boundary layer, the boundary layer is related to the physical and chemical properties of the heavy oil, and the thickness of the boundary layer is a function of the physical and chemical properties. The greater the thickness of the boundary layer of crude oil at the same displacement differential pressure and unit load, the greater the gum and asphaltene content therein. The presence of the boundary layer can on the one hand alter the wettability of the reservoir and on the other hand increase the resistance to fluid seepage and it has been found during previous studies that under the influence of the boundary layer the seepage rate decreases by 15% to 20% over time. Therefore, the effect of the boundary layer during crude oil seepage is not negligible.
The thickness of the boundary layer affects fluid seepage to some extent, and is related to reservoir permeability, crude oil properties, and displacement pressure. In 1977, ma Erha cine, based on a great amount of experimental data and mathematical analysis methods, has compiled the relationship between the physicochemical parameters of crude oil and the thickness of the boundary layer by using the method of the nomogram as follows,
δ＝a-B ln R (26)
where coefficients a and B depend on the displacement pressure gradient and the physicochemical properties of the crude oil;
the value of B is a constant of 0.0471, a is related to the displacement pressure gradient:
where Z and m depend on the coefficients of the physicochemical properties of the crude oil.
Z＝d 1 ρ-β 1 (28)
m＝d 2 K c∏ -β 2 (29)
Bringing Z and m into equation (26) above yields:
wherein d 1 ＝5.5221、β 1 ＝4.5023、d 2 ＝0.00027、β 1 ＝0.0360；
The final boundary layer thickness calculation formula is:
wherein ρ is the density of crude oil, g/cm 3 ；To displace the pressure gradient, atm/m; k (K) cΠ The molar absorptivity of the crude oil is L/(mol.cm); r is pore radius, mum; delta is the boundary layer thickness, μm;
the relationship between pore radius and permeability and porosity was obtained from the poismillet She Gongshi:
the absorbance coefficient can be obtained according to lambert beer's law:
wherein, pi is absorbance; c is the molar concentration, mol/L; bringing formulae (32), (33) into (31) gives:
assuming a displacement pressure gradient of 0.0001MPa/m as the effective boundary layer thickness in the initial state of the oil reservoir, namely:
writing:
as can be seen from the above equation, the thickness of the boundary layer has an important relationship with crude oil properties, reservoir properties and displacement pressure gradients, and increases with increasing crude oil density, increases with decreasing reservoir permeability, and increases the displacement pressure gradients can reduce the boundary layer thickness.
A heavy oil reservoir bulk phase fluid nonlinear seepage theory model comprises a heavy oil reservoir bulk phase fluid nonlinear seepage equation based on heavy oil adsorption boundary layer and yield characteristic influence and a starting pressure gradient theory formula, wherein the equilibrium equation of bulk phase fluid stable seepage under the conditions of gravity neglected and fluid being bingham flow is the formula (1),
in the above formula, the left side is displacement pressure, the right side is internal friction force of thick oil, wherein τ 0 The unit is Pa, R-delta is more than R is more than 0, R is the distance from the center of a pore to a thick oil adsorption boundary layer, the unit is mu m, R is the pore radius, delta is the thickness unit of the boundary layer, mu is the viscosity of bulk fluid, the unit is mPa.s, delta p is the displacement pressure difference unit is MPa, v is the speed unit is cm/s, and L is the core length unit is cm;
the method is obtained by deforming the formula (1),
the equation is integrated on both sides:
the flow rate of the bulk fluid is expressed as:
carrying out after-treatment on the formula (3) in the formula (4) to obtain the compound:
obtaining flow according to an equivalent capillary method:
Q＝NAq (6)
bringing formula (5) into (6) gives:
according to the theory of porosity and capillary model, the porosity is obtained by researching the seepage of bulk fluidRepresents the pore space occupied by the bulk fluid, permeability K h Representing bulk fluid permeability:
and (3) carrying out formula (8) into formula (9), and obtaining a heavy oil reservoir bulk phase fluid nonlinear seepage equation after finishing:
and (3) finishing to obtain:
in the heavy oil reservoir bulk fluid nonlinear seepage equation,is a flow resistance term due to bulk crude oil yield stress;
in (11), the bulk fluid permeability is changed along with the thickness change of the boundary layer, and in the practical application process, the bulk fluid permeability is converted from the effective permeability of the reservoir, and the bulk fluid permeability can be expressed as follows by a capillary theoretical model:
boundary fluid porosityThe relation expression between the porosity phi of the reservoir is as follows:
the relation between effective permeability and effective porosity is:
substituting the formula (14) to obtain the relation between the fluid seepage formula of the heavy oil reservoir bulk phase fluid and the effective permeability:
in the method, in the process of the application,the term represents the influence of boundary layer on the seepage flow, +.>The term represents the effect of yield stress during bulk fluid seepage, and when the above formula does not consider the yield characteristics of the boundary layer and the thick oil, the equation becomes a standard form of Darcy seepage, so that the problem that the yield characteristics of the boundary layer and the thick oil increase the seepage resistance of the thick oil and become nonlinear seepage is solved;
to get a simpler equation form, assume:
the method comprises the following steps:
wherein c 1 And c 2 Are coefficients related to the boundary layer thickness;
let q=0 in equation (14), we obtain the heavy oil reservoir bulk fluid start pressure gradient calculation equation:
and (3) connecting delta with (20) to obtain a relation equation of the starting pressure gradient and the reservoir physical property and crude oil property, wherein the equation set is as follows:
the thickness of the thick oil boundary layer corresponding to the thick oil initial state is the thickness of the thick oil reservoir initial effective boundary layer, and the calculation formula for obtaining the final thick oil reservoir bulk phase fluid starting pressure gradient is as follows:
the method is characterized in that the method is obtained through a heavy oil reservoir bulk fluid starting pressure gradient calculation formula, the starting pressure gradient is related to the yield stress and the boundary layer thickness of heavy oil, and when the yield stress is increased and the boundary layer thickness is increased, the starting pressure gradient is increased;
in addition, anotherCarrying-in formula (23) to obtain:
the deformation is simplified to obtain a thick oil reservoir bulk fluid start pressure gradient expression:
wherein,,
τ 0 is bulk fluid yield stress, pa;
c is a coefficient related to a boundary layer and is obtained by calculating the molar absorptivity of crude oil,
r is pore radius, μm;
ρ is the density of crude oil, g/cm 3 。
In order to verify the reliability of the bulk fluid seepage equation of the heavy oil reservoir and the theoretical calculation formula of the starting pressure gradient, the core seepage experiment and the starting pressure gradient experiment result are carried out for calculation and fitting, and the experiment result and the model calculation result are compared.
The heavy oil sample is dehydrated crude oil from the wellhead of a certain domestic oil field, the specific parameters of the heavy oil are shown in the following table 1, the core is artificial sandstone core with different permeability levels, and the basic parameters of the core are shown in the following table 2. The starting pressure gradient and the non-linear seepage experimental temperature of the thick oil are respectively 30 ℃, 40 ℃, 45 ℃ and 50 ℃.
TABLE 1
TABLE 2
As can be seen from the starting pressure gradient experiment and the model calculation results in the figures 1-3, the starting pressure gradient theoretical formula calculation result is better in fit with experimental data, and the average error is 7.67%, so that the model has better application value.
As can be seen from the starting pressure gradient experiments and model calculation results of fig. 4 and 5, the theoretical calculation formula of the bulk fluid seepage equation of the heavy oil reservoir is better in fitting experimental data, and the average error is 8.25%. And the nonlinear segments can be clearly seen from the results calculated in fig. 5, which shows that the model has good universality.
By the characteristics of thick oil nonlinear seepage and the existence mechanism of a starting pressure gradient, a bulk fluid nonlinear seepage equation taking boundary layer and yield stress into consideration and a theoretical formula of the starting pressure gradient are provided. (1) The thick oil in the pore canal of the reservoir is divided into boundary fluid and bulk fluid, and the corresponding starting pressure gradients in different stages of the exploitation of the thick oil reservoir are different. At the beginning of production, there is mainly a starting pressure gradient that the bulk fluid has. In the later period of production, when the bulk fluid is produced under a certain displacement pressure gradient, the rest part is boundary fluid, and the starting pressure gradient at the moment is the starting pressure gradient of the boundary fluid. (2) And establishing a thick oil phase fluid nonlinear seepage theoretical model based on boundary layer and yield characteristic influence and a starting pressure gradient theoretical calculation formula. The model mainly aims at the nonlinear seepage characteristics of bulk fluid flow in pores at the initial stage of oil reservoir exploitation, the yield characteristic of the fluid and the influence of the thickness of a boundary layer on seepage are considered, and when the influence of the boundary layer and the yield characteristic of thick oil is not considered in a bulk fluid nonlinear seepage equation, the equation is changed into a standard form of Darcy seepage. The seepage model and the starting pressure gradient theoretical formula are more in line with the actual oil reservoir development process. (3) And verifying the applicability of a theoretical formula of the bulk fluid start pressure gradient and a nonlinear seepage equation. The comparison of the actually measured starting pressure gradient, the nonlinear seepage curve result and the bulk fluid starting pressure gradient and the nonlinear seepage theoretical equation calculation result shows that the deviation between the actually measured result and the theoretical calculation result is within 10 percent, and the method has good universality.
It should be understood that the above description is not intended to limit the application to the particular embodiments disclosed, but to limit the application to the particular embodiments disclosed, and that the application is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the application.
Claims (2)
1. A heavy oil reservoir bulk phase fluid nonlinear seepage theory model is characterized by comprising a heavy oil reservoir bulk phase fluid nonlinear seepage equation based on heavy oil adsorption boundary layer and yield characteristic influence and a starting pressure gradient theory formula, wherein the equilibrium equation of bulk phase fluid stable seepage under the conditions that gravity is ignored and fluid is bingham flow is formula (1),
in the above formula, the left side is displacement pressure, the right side is internal friction force of thick oil, wherein τ 0 The unit is Pa, R-delta is more than R is more than 0, R is the distance from the center of a pore to a thick oil adsorption boundary layer, the unit is mu m, R is the pore radius, delta is the thickness unit of the boundary layer, mu is the viscosity of bulk fluid, the unit is mPa.s, delta p is the displacement pressure difference unit is MPa, v is the speed unit is cm/s, and L is the core length unit is cm;
the method is obtained by deforming the formula (1),
the equation is integrated on both sides:
the flow rate of the bulk fluid is expressed as:
q＝∫ 0 R-δ v·2πrdr (4)
carrying out after-treatment on the formula (3) in the formula (4) to obtain the compound:
obtaining flow according to an equivalent capillary method:
Q＝NAq (6)
bringing formula (5) into (6) gives:
according to the theory of porosity and capillary model, the porosity is obtained by researching the seepage of bulk fluidRepresents the pore space occupied by the bulk fluid, permeability K h Representing bulk fluid permeability:
and (3) carrying out formula (8) into formula (9), and obtaining a heavy oil reservoir bulk phase fluid nonlinear seepage equation after finishing:
and (3) finishing to obtain:
in the heavy oil reservoir bulk fluid nonlinear seepage equation,is a flow resistance term due to bulk crude oil yield stress;
in (11), the bulk fluid permeability is changed along with the thickness change of the boundary layer, and in the practical application process, the bulk fluid permeability is converted from the effective permeability of the reservoir, and the bulk fluid permeability can be expressed as follows by a capillary theoretical model:
boundary fluid porosityThe relation expression between the porosity phi of the reservoir is as follows:
the relation between effective permeability and effective porosity is:
substituting the formula (14) to obtain the relation between the fluid seepage formula of the heavy oil reservoir bulk phase fluid and the effective permeability:
in the method, in the process of the application,the term represents the influence of boundary layer on the seepage flow, +.>The term represents the effect of yield stress during bulk fluid seepage, and when the above formula does not consider the yield characteristics of the boundary layer and the thick oil, the equation becomes a standard form of Darcy seepage, so that the problem that the yield characteristics of the boundary layer and the thick oil increase the seepage resistance of the thick oil and become nonlinear seepage is solved;
to get a simpler equation form, assume:
the method comprises the following steps:
wherein c 1 And c 2 Are coefficients related to the boundary layer thickness;
let q=0 in equation (14), we obtain the heavy oil reservoir bulk fluid start pressure gradient calculation equation:
and (3) connecting delta with (20) to obtain a relation equation of the starting pressure gradient and the reservoir physical property and crude oil property, wherein the equation set is as follows:
the thickness of the thick oil boundary layer corresponding to the thick oil initial state is the thickness of the thick oil reservoir initial effective boundary layer, and the calculation formula for obtaining the final thick oil reservoir bulk phase fluid starting pressure gradient is as follows:
the method is characterized in that the method is obtained through a heavy oil reservoir bulk fluid starting pressure gradient calculation formula, the starting pressure gradient is related to the yield stress and the boundary layer thickness of heavy oil, and when the yield stress is increased and the boundary layer thickness is increased, the starting pressure gradient is increased;
in addition, anotherCarrying-in formula (23) to obtain:
the deformation is simplified to obtain a thick oil reservoir bulk fluid start pressure gradient expression:
wherein,,
τ 0 is bulk fluid yield stress, pa;
c is a coefficient related to a boundary layer and is obtained by calculating the molar absorptivity of crude oil,
r is pore radius, μm;
ρ is the density of crude oil, g/cm 3 。
2. The method according to claim 1, wherein the relationship between the physical and chemical parameters of the crude oil and the thickness of the boundary layer is as follows,
δ＝a-BlnR (26)
where coefficients a and B depend on the displacement pressure gradient and the physicochemical properties of the crude oil;
the value of B is a constant of 0.0471, a is related to the displacement pressure gradient:
where Z and m depend on the coefficients of the physicochemical properties of the crude oil.
Z＝d 1 ρ-β 1 (28)
m＝d 2 K cΠ -β 2 (29)
Substituting Z with m into equation (26) yields:
wherein d 1 ＝5.5221、β 1 ＝4.5023、d 2 ＝0.00027、β 1 ＝0.0360；
The final boundary layer thickness calculation formula is:
wherein ρ is the density of crude oil, g/cm 3 ；To displace the pressure gradient, atm/m; k (K) cΠ The molar absorptivity of the crude oil is L/(mol.cm); r is pore radius, mum; delta is the boundary layer thickness, μm;
the relationship between pore radius and permeability and porosity was obtained from the poismillet She Gongshi:
the absorbance coefficient can be obtained according to lambert beer's law:
wherein pi is absorbance; c is the molar concentration, mol/L; bringing formulae (32), (33) into (31) gives:
assuming a displacement pressure gradient of 0.0001MPa/m as the effective boundary layer thickness in the initial state of the oil reservoir, namely:
writing:
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| CN117782943B (en) * | 2024-02-26 | 2024-05-28 | 中国石油大学(华东) | Testing method for non-linear seepage start pressure gradient of emulsion |
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