CN112214935A - Method and system for calculating fluid phase state in porous medium - Google Patents
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Abstract
A method and system for calculating the phase state of fluid in porous medium are disclosed. The method can comprise the following steps: step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores; step 2: calculating the phase state parameter of each size pore; and step 3: and normalizing the phase parameters of each size pore to obtain the final phase parameters. The invention determines the change process of the fluid phase along with the size pore by calculating the phase state characteristics of the fluid under the condition of the porous medium, deepens the knowledge of the fluid phase change under the actual oil reservoir condition and provides technical support for oil field production and decision.
Description
Technical Field
The invention relates to the field of oil and gas field development, in particular to a method and a system for calculating a fluid phase state in a porous medium.
Background
The fluid phase calculation plays a vital role in the fields of fluid PVT analysis fitting, oil reservoir numerical simulation, condensate gas reservoir development, CO2 oil displacement, burial and the like.
The conventional cubic state equation (PR, SRK and the like) is widely applied to fluid phase calculation, and the fitted state equation can accurately represent the phase state characteristics of the fluid under large space conditions (PVT kettle). However, the interaction between the fluid molecules in the porous medium and the surface of the porous medium causes the fluid phase state to be significantly different from that under the conventional large space condition.
In dense pore, especially nanoporous media, the critical parameter of the fluid is shifted compared to the large space, and the influence of the shift of the critical parameter on the phase state characteristics should be considered in the calculation. The heterogeneity in the porous medium is serious, especially the pore size in the shale is between 1 nm and 100nm, the span is large, and different distribution modes can cause the difference of the calculation results. In addition, the pore radius in the dense pore medium is small, the capillary force is large, so that the oil-gas two-phase pressure is unequal, and the phase state characteristics are also influenced. There is also adsorption in the porous media, which affects the composition of the fluid, and at the same time, the presence of the adsorption layer leads to a reduction in the effective pore diameter, which also leads to differences in the phase equilibrium calculations, which need to be taken into account.
Although a great deal of research is conducted on the phase calculation aspect of the porous medium at home and abroad, due to a plurality of influencing factors and complex action mechanism, the research results are often in contradiction. At present, no systematic fluid phase calculation method considering the condition of the porous medium exists. Therefore, there is a need to develop a method and system for calculating the fluid phase in porous media.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention provides a method and a system for calculating a fluid phase state in a porous medium, which can determine the change process of the fluid phase state along with size pores by calculating the phase state characteristics of a fluid under the condition of the porous medium, deepen the knowledge of the fluid phase state change under the actual oil reservoir condition and provide technical support for oil field production and decision.
According to one aspect of the invention, a method for calculating a fluid phase in a porous medium is provided. The method may include: step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores; step 2: calculating the phase state parameter of each size pore; and step 3: and normalizing the phase parameters of each size pore to obtain final phase parameters.
Preferably, the step 2 includes: step 201: calculating the amount of adsorbed substances of each component under the given conditions of temperature and pressure; step 202: calculating the critical temperature and critical pressure of each component according to the amount of the substance adsorbed by each component; step 203: calculating an initial equilibrium ratio according to the adsorbed total composition, the critical temperature and the critical pressure, and calculating a gas phase mole fraction according to the initial equilibrium ratio so as to calculate an oil phase component and a gas phase component; step 204: calculating the fugacity of each component according to the oil phase component and the gas phase component, and further calculating the fugacity error; step 205: judging whether the fugacity error is less than or equal to an error threshold, if so, performing step 206, otherwise, updating the initial balance ratio, performing step 206, and if so, outputting the current phase state parameter; step 206: calculating the average molar mass, volume fraction and density of the oil phase component and the gas phase component, and further calculating the plane interfacial tension; step 207: calculating capillary pressure, replacing the pressure in the step 201 with the capillary pressure, and repeating the step 201 and the step 207; wherein the phase parameters include the average molar mass, the volume fraction, the density, and the planar interfacial tension.
Preferably, the amount of adsorbed substance of each component is calculated by the formula (1):
na,i＝Va,iWs (1)
wherein n isa,iAmount of substance to which i component is adsorbed, WsIs the mass of the adsorbent, Va,iIs the adsorption capacity at equilibrium of the i component.
Preferably, the critical temperature of each component is calculated by equation (2):
the critical pressure of each component was calculated by equation (3):
wherein, Delta TcIs the critical temperature offset, σeffDenotes the effective diameter of the molecule, DeffDenotes the effective diameter of the pores, TcpAnd TcbRepresenting the critical temperature, Δ p, of the fluid in the porous medium and the large space, respectivelycIs the critical pressure offset, pcpAnd pcbRepresenting the critical pressure of the fluid in the porous medium and the large space, respectively.
Preferably, the fugacity of the components of the oil phase is calculated by equation (4):
the fugacity of the components in the gas phase is calculated by equation (5):
wherein Z isL,jAnd ZV,jRespectively representing the compression factors of the oil phase and the vapor phase mixture in the jth capillary bundle,
am,jand bm,jRespectively the average attraction constant and the repulsion constant of the mixture system in the jth capillary bundle,
ai,j(T)＝aci,jαi,j(T)，
ωi,jis the eccentricity factor of the component i in the jth capillary bundle,
Tci,jand pci,jRespectively showing the critical temperature and the critical pressure of the component i in the jth capillary bundle,
is a binary interaction coefficient.
Preferably, the average molar mass of the oil phase component and the gas phase component is calculated by the formula (6):
calculating the density of the oil phase component and the gas phase component by formula (7):
wherein M isLIs the average molar mass of the oil phase components, MVIs the average molar mass of the gas-phase components, MiDenotes the molar mass of the i component, pLIs the density of the oil phase component, pVIs the density of the gas phase component.
Preferably, the planar interfacial tension is calculated by equation (8):
wherein, γ∞Is a plane interfacial tension, [ P ]i]Is the isospecific volume of component i.
Preferably, the capillary pressure is calculated by equation (9):
wherein p isca,jIs the capillary pressure in the jth capillary bundle, theta is the included angle between the oil-gas interface and the pore surface, gammajRepresenting the actual interfacial tension of the j-th bundle.
Preferably, the method further comprises the following steps: and calculating the dew point pressure according to the final phase state parameter.
According to another aspect of the present invention, there is provided a computing system for calculating a fluid phase in a porous medium, the system comprising: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores; step 2: calculating the phase state parameter of each size pore; and step 3: and normalizing the phase parameters of each size pore to obtain final phase parameters.
Preferably, the step 2 includes: step 201: calculating the amount of adsorbed substances of each component under the given conditions of temperature and pressure; step 202: calculating the critical temperature and critical pressure of each component according to the amount of the substance adsorbed by each component; step 203: calculating an initial equilibrium ratio according to the adsorbed total composition, the critical temperature and the critical pressure, and calculating a gas phase mole fraction according to the initial equilibrium ratio so as to calculate an oil phase component and a gas phase component; step 204: calculating the fugacity of each component according to the oil phase component and the gas phase component, and further calculating the fugacity error; step 205: judging whether the fugacity error is less than or equal to an error threshold, if so, performing step 206, otherwise, updating the initial balance ratio, performing step 206, and if so, outputting the current phase state parameter; step 206: calculating the average molar mass, volume fraction and density of the oil phase component and the gas phase component, and further calculating the plane interfacial tension; step 207: calculating capillary pressure, replacing the pressure in the step 201 with the capillary pressure, and repeating the step 201 and the step 207; wherein the phase parameters include the average molar mass, the volume fraction, the density, and the planar interfacial tension.
Preferably, the amount of adsorbed substance of each component is calculated by the formula (1):
na,i＝Va,iWs (1)
wherein n isa,iAmount of substance to which i component is adsorbed, WsIs the mass of the adsorbent, Va,iIs the adsorption capacity at equilibrium of the i component.
Preferably, the critical temperature of each component is calculated by equation (2):
the critical pressure of each component was calculated by equation (3):
wherein, Delta TcIs the critical temperature offset, σeffDenotes the effective diameter of the molecule, DeffDenotes the effective diameter of the pores, TcpAnd TcbRepresenting the critical temperature, Δ p, of the fluid in the porous medium and the large space, respectivelycIs the critical pressure offset, pcpAnd pcbRepresenting the critical pressure of the fluid in the porous medium and the large space, respectively.
Preferably, the fugacity of the components of the oil phase is calculated by equation (4):
the fugacity of the components in the gas phase is calculated by equation (5):
wherein Z isL,jAnd ZV,jRespectively representing the compression factors of the oil phase and the vapor phase mixture in the jth capillary bundle,
am,jand bm,jRespectively the average attraction constant and the repulsion constant of the mixture system in the jth capillary bundle,
ai,j(T)＝aci,jαi,j(T)，
ωi,jis the eccentricity factor of the component i in the jth capillary bundle,
Tci,jand pci,jAre respectively provided withThe critical temperature and the critical pressure of the component i in the jth capillary bundle are shown,
is a binary interaction coefficient.
Preferably, the average molar mass of the oil phase component and the gas phase component is calculated by the formula (6):
calculating the density of the oil phase component and the gas phase component by formula (7):
wherein M isLIs the average molar mass of the oil phase components, MVIs the average molar mass of the gas-phase components, MiDenotes the molar mass of the i component, pLIs the density of the oil phase component, pVIs the density of the gas phase component.
Preferably, the planar interfacial tension is calculated by equation (8):
wherein, γ∞Is a plane interfacial tension, [ P ]i]Is the isospecific volume of component i.
Preferably, the capillary pressure is calculated by equation (9):
wherein p isca,jIs the capillary pressure in the jth capillary bundle, theta is the included angle between the oil-gas interface and the pore surface, gammajRepresenting the actual interfacial tension of the j-th bundle.
Preferably, the method further comprises the following steps: and calculating the dew point pressure according to the final phase state parameter.
The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
Fig. 1 shows a flow chart of the steps of a method of calculating the phase of a fluid in a porous medium according to the invention.
FIG. 2 shows a schematic of dew point pressures for different sized pores according to one embodiment of the invention.
FIG. 3 shows a schematic of dew point pressures for different critical parameters according to one embodiment of the present invention.
FIG. 4 shows a schematic of a distribution of 3 size pores according to one embodiment of the invention.
Fig. 5 shows a schematic of the dew point pressure for the 3 size pore distribution according to fig. 4.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Fig. 1 shows a flow chart of the steps of a method of calculating the phase of a fluid in a porous medium according to the invention.
In this embodiment, the method for calculating the fluid phase state in the porous medium according to the present invention may include: step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores; step 2: calculating the phase state parameter of each size pore; and step 3: and normalizing the phase parameters of each size pore to obtain the final phase parameters.
In one example, step 2 comprises: step 201: calculating the amount of adsorbed substances of each component under the given conditions of temperature and pressure; step 202: calculating the critical temperature and critical pressure of each component according to the amount of the substance adsorbed by each component; step 203: calculating an initial equilibrium ratio according to the adsorbed total composition, the critical temperature and the critical pressure, and calculating a gas phase mole fraction according to the initial equilibrium ratio so as to calculate an oil phase component and a gas phase component; step 204: calculating the fugacity of each component according to the oil phase component and the gas phase component, and further calculating the fugacity error; step 205: judging whether the fugacity error is less than or equal to the error threshold, if so, performing step 206, otherwise, updating the initial balance ratio, performing step 206, and if so, outputting the current phase state parameter; step 206: calculating the average molar mass, volume fraction and density of the oil phase component and the gas phase component, and further calculating the plane interfacial tension; step 207: calculating capillary pressure, replacing the pressure in the step 201 with the capillary pressure, and repeating the step 201 and the step 207; wherein the phase parameters include average molar mass, volume fraction, density, and planar interfacial tension.
In one example, the amount of adsorbed species for each component is calculated by equation (1):
na,i＝Va,iWs (1)
wherein n isa,iAmount of substance to which i component is adsorbed, WsIs the mass of the adsorbent, Va,iIs the adsorption capacity at equilibrium of the i component.
In one example, the critical temperature of each component is calculated by equation (2):
the critical pressure of each component was calculated by equation (3):
wherein, Delta TcIs the critical temperature offset, σeffDenotes the effective diameter of the molecule, DeffDenotes the effective diameter of the pores, TcpAnd TcbRepresenting the critical temperature, Δ p, of the fluid in the porous medium and the large space, respectivelycIs the critical pressure offset, pcpAnd pcbRepresenting the critical pressure of the fluid in the porous medium and the large space, respectively.
In one example, the fugacity of the oil phase components is calculated by equation (4):
the fugacity of the components in the gas phase is calculated by equation (5):
wherein Z isL,jAnd ZV,jRespectively representing the compression factors of the oil phase and the vapor phase mixture in the jth capillary bundle,
am,jand bm,jRespectively the average attraction constant and the repulsion constant of the mixture system in the jth capillary bundle,
ai,j(T)＝aci,jαi,j(T)，
ωi,jis the eccentricity factor of the component i in the jth capillary bundle,
Tci,jand pci,jRespectively showing the critical temperature and the critical pressure of the component i in the jth capillary bundle,
for a binary interaction coefficient, for hydrocarbon-hydrocarbon systems,
in one example, the average molar mass of the oil phase component to the gas phase component is calculated by equation (6):
the densities of the oil phase component and the gas phase component are calculated by formula (7):
wherein M isLIs the average molar mass of the oil phase components, MVIs the average molar mass of the gas-phase components, MiDenotes the molar mass of the i component, pLIs the density of the oil phase component, pVIs the density of the gas phase component.
In one example, the planar interfacial tension is calculated by equation (8):
wherein, γ∞Is a plane interfacial tension, [ P ]i]Is the isospecific volume of component i.
In one example, capillary pressure is calculated by equation (9):
wherein p isca,jIs the capillary pressure in the jth capillary bundle, theta is the included angle between the oil-gas interface and the pore surface, theta is zero and gamma is zero when considering the existence of the adsorption layerjRepresenting the actual interfacial tension of the j-th bundle.
In one example, further comprising: and calculating the dew point pressure according to the final phase parameters.
Specifically, the method for calculating the fluid phase state in the porous medium according to the present invention may include:
step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores, wherein the model hypothesis comprises: (1) the oil-gas two-phase system is a closed system; (2) the phase equilibrium process between the oil phase and the gas phase is completed instantly; (3) considering the influence of the capillary force on the pressure of the oil-gas two-phase system; (4) considering the influence of adsorption on components and the influence of the thickness of the adsorption layer on the effective pore diameter; (5) considering the shift of critical parameters of components in the porous medium; (6) considering the effect of size pore distribution; assuming that the oil and gas system has N in commoncSeed component, total composition of system in j-th capillary bundle is Zi,j(i＝1,2,…,Nc；j＝1,2,…,Nb) Total amount of substance is Fj(j＝1,2,…,Nb) At equilibrium, the oil phase has a molar fraction LjThe oil phase is Xi,jGas phase mole fraction of VjThe gas phase composition being Yi,j。
Step 2: calculating the phase state parameter of each size pore, which specifically comprises the following steps:
step 201: to study the interaction of a fluid in a porous medium with the surface of the porous medium, adsorption was considered. Because the adsorption characteristics of different hydrocarbons in dense pores are different, two adsorption models are established for characterization: light hydrocarbon (C)4And below), a Langmuir monolayer adsorption model was used; heavy hydrocarbons (C)5And above) using the BET multilayer adsorption model.
The Langmuir single-layer adsorption model can well simulate the adsorption process of light hydrocarbon:
in the formula, VaAnd VmRespectively represents the adsorption amount and the maximum adsorption amount at equilibrium, p represents the equilibrium pressure, bLIs the isothermal adsorption constant.
When multi-component competitive adsorption is considered, a modified Langmuir model is employed:
in the formula, C1,iIs the adsorption coefficient of a component, which is related to the component, temperature, and physical properties of the surface of the porous medium. p is a radical ofiDenotes the partial pressure of the i component:
pi＝p·Yi(12)
for the larger hydrocarbons (C)5And above) calculated using BET multilayer adsorption model:
in the formula, p0Saturated vapor pressure of adsorbate at given temperature, C2Is a constant.
Therefore, the amount of the substance adsorbed by each component is calculated by the formula (1) under the given temperature and pressure conditions.
Step 202: the thickness of the adsorbed layer generated by adsorption can be calculated according to the equation set forth by Dong (2016):
in the formula, raAnd rmRespectively, the adsorption layer thickness and the maximum adsorption layer thickness at a given pressure.
While, when considering the case where the adsorption completely covers the surface, the maximum adsorption layer thickness can be calculated by the following formula:
in the formula, vlDenotes the liquid molar volume, NARepresents the Avogadro constant.
The effective diameter of the pores can be further obtained according to the calculated thickness of the adsorption layer:
Deff＝2(r-ra) (15)
the critical parameters of the confining fluid in a dense porous medium can shift from those under conventional conditions. Zargagoicoechea and Kuz (2004) suggest a relationship between critical parameters and pore diameter, but the formula applies only to
The case (1). It is not suitable for large molecules and very small pores. Therefore, in consideration of the difference in size pores, the critical temperature and the critical pressure of each component are calculated by the formula (2) and the formula (3) using the relationship proposed by Ma and Jin (2013), that is, the amount of the substance adsorbed by each component.
Step 203: calculating an initial equilibrium ratio by the formula (16) based on the total composition after adsorption, the critical temperature and the critical pressure:
according to the law of conservation of substances, the method comprises the following steps:
Lj+Vj＝1 (17)
Xi,jLj+Yi,jVj＝Zi,j (18)
wherein, each phase composition meets the following normalization conditions:
the balance ratio of the components i in the jth capillary bundle in the balance process is as follows:
the oil phase composition obtained by the simultaneous four formulas (17), (18), (19) and (20) is as follows:
substituting the formula (21) into the formula (20) to obtain a gas phase composition:
combining the three formulas (19), (21) and (22) to obtain:
according to a given Ki,jValues, vapor phase mole fraction V can be calculated by Newton-Raphson iterative method using equation (23)jBased on the above, the liquid phase mole fraction L is calculated by the formulas (17), (21) and (22) respectivelyjAnd a vapor-liquid two-phase composition Xi,jAnd Yi,j。
Step 204: calculating the fugacity of each component of the oil phase by formula (4) and calculating the fugacity of each component of the gas phase by formula (5) according to the components of the oil phase and the gas phase, wherein ZL,jAnd ZV,jThe compression factors, which represent the mixture of oil and gas phases in the j-th bundle, respectively, can be calculated by the following formula:
the formula (24) has three roots, wherein the largest positive root is the compression factor Z of the gas phase mixtureV,jThe minimum root is the compression factor Z of the oil phase mixtureL,j。
And calculating the fugacity error as follows:
step 205: judging whether the fugacity error is less than or equal to the error threshold value epsilon0If yes, go to step 206, otherwise, update the initial balance ratio to
And step 206, if yes, outputting the current phase state parameter.
Step 206: the average molar mass of the oil phase component and the gas phase component is calculated through formula (6), the density of the oil phase component and the gas phase component is calculated through formula (7), and the volume of the oil-gas two-phase mixture can be calculated after the oil-gas two-phase composition is determined:
the volume fractions of the oil phase and the gas phase are respectively as follows:
and calculating the plane interfacial tension through a formula (8), wherein the phase parameters comprise average molar mass, volume fraction, density and plane interfacial tension.
Step 207: considering the scale effect of surface tension, in a tiny pore, the influence of the curvature of the interface on the actual interface tension cannot be ignored:
in the formula, γ represents an actual interfacial tension in the micropores, and δ represents a Tolmann length.
Ahn (1972) proposes a relation for calculating the length of torman:
in the formula, vsRepresents the molar volume of the solid.
Further, the capillary pressure is calculated by the formula (9), the capillary pressure is used to replace the pressure in the step 201, and the step 201 and the step 207 are repeated.
And step 3: and normalizing the phase parameters of each size pore to obtain the final phase parameters. Calculating the dew point pressure according to the final phase parameters: and (2) calculating the gas phase mole fraction of the system at the same temperature and different pressure levels, wherein the gas phase mole fraction is 1 (namely all gas phases) when the pressure is higher, and when the pressure is gradually reduced, the gas phase mole fraction is suddenly reduced to below 1 (namely oil phase appears) at one pressure point, and the pressure point at the moment is the dew point pressure of the current system and the temperature.
The method determines the change process of the fluid phase along with the size pore by calculating the phase state characteristics of the fluid under the condition of the porous medium, deepens the knowledge of the fluid phase change under the actual oil reservoir condition and provides technical support for oil field production and decision.
Application example
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
The method for calculating the fluid phase state in the porous medium comprises the following steps:
step 1: and establishing a porous fluid component adsorption model, and further determining a plurality of size pores.
Step 2: calculating the phase state parameter of each size pore, which specifically comprises the following steps:
step 201: under the conditions of given temperature and pressure, calculating the amount of adsorbed substances of each component through the formula (1); step 202: calculating the critical temperature of each component by formula (2) and the critical pressure of each component by formula (3) according to the amount of the substance adsorbed to each component; step 203: calculating an initial equilibrium ratio according to the adsorbed total composition, the critical temperature and the critical pressure, and calculating a gas phase mole fraction according to the initial equilibrium ratio so as to calculate an oil phase component and a gas phase component; step 204: calculating the fugacity of each component of the oil phase through a formula (4) and calculating the fugacity of each component of the gas phase through a formula (5) according to the components of the oil phase and the gas phase, and further calculating the fugacity error; step 205: judging whether the fugacity error is less than or equal to the error threshold, if so, performing step 206, otherwise, updating the initial balance ratio, performing step 206, and if so, outputting the current phase state parameter; step 206: calculating the volume fractions of the oil phase component and the gas phase component, calculating the average molar mass of the oil phase component and the gas phase component through a formula (6), calculating the density of the oil phase component and the gas phase component through a formula (7), and further calculating the plane interfacial tension through a formula (8); step 207: calculating capillary pressure by the formula (9), replacing the pressure in the step 201 with the capillary pressure, and repeating the step 201 and the step 207; wherein the phase parameters include average molar mass, volume fraction, density, and planar interfacial tension.
And step 3: and normalizing the phase parameters of each size pore to obtain the final phase parameters.
The original gas phase components and critical parameters of a fluid sample obtained from a condensate gas reservoir after conventional PVT physical simulation experiments and phase fitting are shown in table 1.
TABLE 1
The test shows that the dew point pressure at 110.4 ℃ is 26.3MPa under the conventional conditions.
FIG. 2 shows a schematic of dew point pressures for different sized pores according to one embodiment of the invention.
The capillary pressure under different pore diameters was calculated and the phase results were calculated considering the capillary pressure, as shown in fig. 2, it can be seen that: capillary forces decrease with increasing pore diameter; the dew point pressure of condensate gas is improved by considering the action of capillary force; the capillary force has a more significant effect when the pore diameter is less than 10nm, and is negligible when the pore diameter is greater than 100 nm.
FIG. 3 shows a schematic of dew point pressures for different critical parameters according to one embodiment of the present invention.
Calculating the influence of the critical parameter deviation on the condensate gas phase state calculation result under the condition of different pore diameters, as shown in fig. 3, the result shows that the dew point pressure of the condensate gas is reduced when the critical parameter deviation is considered; the influence degree of the phase calculation result is as follows: critical parameter deviation is greater than capillary pressure; the critical parameter shift has little influence on the phase result when the pore diameter is more than 100nm, and the influence generated by the critical parameter shift is very obvious when the pore diameter is less than 10 nm.
FIG. 4 shows a schematic of a distribution of 3 size pores according to one embodiment of the invention.
Fig. 5 shows a schematic of the dew point pressure for the 3 size pore distribution according to fig. 4.
The simulation calculates the condensate gas phase characteristics (only considering capillary action) under three different size pore distribution modes (average pore diameter is 10 nm). The size pore distribution pattern is shown in fig. 4, and the phase calculation results are shown in fig. 5. The results show that the heterogeneity of the size pore distribution further leads to an increase in the condensate dew point pressure; the effect of size pore distribution on the condensate dew point is primarily dependent on the smallest size pores, regardless of the distribution pattern.
In conclusion, the invention determines the change process of the fluid phase along with the size pore by calculating the phase state characteristics of the fluid under the condition of the porous medium, deepens the knowledge of the fluid phase change under the actual oil reservoir condition and provides technical support for oil field production and decision.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
According to an embodiment of the present invention, there is provided a computing system for a fluid phase in a porous medium, the system comprising: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores; step 2: calculating the phase state parameter of each size pore; and step 3: and normalizing the phase parameters of each size pore to obtain the final phase parameters.
In one example, step 2 comprises: step 201: calculating the amount of adsorbed substances of each component under the given conditions of temperature and pressure; step 202: calculating the critical temperature and critical pressure of each component according to the amount of the substance adsorbed by each component; step 203: calculating an initial equilibrium ratio according to the adsorbed total composition, the critical temperature and the critical pressure, and calculating a gas phase mole fraction according to the initial equilibrium ratio so as to calculate an oil phase component and a gas phase component; step 204: calculating the fugacity of each component according to the oil phase component and the gas phase component, and further calculating the fugacity error; step 205: judging whether the fugacity error is less than or equal to the error threshold, if so, performing step 206, otherwise, updating the initial balance ratio, performing step 206, and if so, outputting the current phase state parameter; step 206: calculating the average molar mass, volume fraction and density of the oil phase component and the gas phase component, and further calculating the plane interfacial tension; step 207: calculating capillary pressure, replacing the pressure in the step 201 with the capillary pressure, and repeating the step 201 and the step 207; wherein the phase parameters include average molar mass, volume fraction, density, and planar interfacial tension.
In one example, the amount of adsorbed species for each component is calculated by equation (1):
na,i＝Va,iWs (1)
wherein n isa,iAmount of substance to which i component is adsorbed, WsIs the mass of the adsorbent, Va,iIs the adsorption capacity at equilibrium of the i component.
In one example, the critical temperature of each component is calculated by equation (2):
the critical pressure of each component was calculated by equation (3):
wherein, Delta TcIs the critical temperature offset, σeffDenotes the effective diameter of the molecule, DeffDenotes the effective diameter of the pores, TcpAnd TcbRepresenting the critical temperature, Δ p, of the fluid in the porous medium and the large space, respectivelycIs the critical pressure offset, pcpAnd pcbRepresenting the critical pressure of the fluid in the porous medium and the large space, respectively.
In one example, the fugacity of the oil phase components is calculated by equation (4):
the fugacity of the components in the gas phase is calculated by equation (5):
wherein Z isL,jAnd ZV,jRespectively representing the compression factors of the oil phase and the vapor phase mixture in the jth capillary bundle,
am,jand bm,jRespectively the average attraction constant and the repulsion constant of the mixture system in the jth capillary bundle,
ai,j(T)＝aci,jαi,j(T)，
ωi,jis the eccentricity factor of the component i in the jth capillary bundle,
Tci,jand pci,jRespectively showing the critical temperature and the critical pressure of the component i in the jth capillary bundle,
is a binary interaction coefficient.
In one example, the average molar mass of the oil phase component to the gas phase component is calculated by equation (6):
the densities of the oil phase component and the gas phase component are calculated by formula (7):
wherein M isLIs the average molar mass of the oil phase components, MVIs the average molar mass of the gas-phase components, MiDenotes the molar mass of the i component, pLIs the density of the oil phase component, pVIs the density of the gas phase component.
In one example, the planar interfacial tension is calculated by equation (8):
wherein, γ∞Is a plane interfacial tension, [ P ]i]Is the isospecific volume of component i.
In one example, capillary pressure is calculated by equation (9):
wherein p isca,jIs the capillary pressure in the jth capillary bundle, theta is the included angle between the oil-gas interface and the pore surface, gammajRepresenting the actual interfacial tension of the j-th bundle.
In one example, further comprising: and calculating the dew point pressure according to the final phase parameters.
The system determines the change process of the fluid phase along with the size pores by calculating the phase state characteristics of the fluid under the condition of the porous medium, deepens the knowledge of the fluid phase change under the actual oil reservoir condition and provides technical support for oil field production and decision making.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (10)
1. A method for calculating a phase of a fluid in a porous medium, comprising:
step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores;
step 2: calculating the phase state parameter of each size pore;
and step 3: and normalizing the phase parameters of each size pore to obtain final phase parameters.
2. The method for calculating the phase state of a fluid in a porous medium according to claim 1, wherein the step 2 comprises:
step 201: calculating the amount of adsorbed substances of each component under the given conditions of temperature and pressure;
step 202: calculating the critical temperature and critical pressure of each component according to the amount of the substance adsorbed by each component;
step 203: calculating an initial equilibrium ratio according to the adsorbed total composition, the critical temperature and the critical pressure, and calculating a gas phase mole fraction according to the initial equilibrium ratio so as to calculate an oil phase component and a gas phase component;
step 204: calculating the fugacity of each component according to the oil phase component and the gas phase component, and further calculating the fugacity error;
step 205: judging whether the fugacity error is less than or equal to an error threshold, if so, performing step 206, otherwise, updating the initial balance ratio, performing step 206, and if so, outputting the current phase state parameter;
step 206: calculating the average molar mass, volume fraction and density of the oil phase component and the gas phase component, and further calculating the plane interfacial tension;
step 207: calculating capillary pressure, replacing the pressure in the step 201 with the capillary pressure, and repeating the step 201 and the step 207;
wherein the phase parameters include the average molar mass, the volume fraction, the density, and the planar interfacial tension.
3. The method for calculating a fluid phase state in a porous medium according to claim 2, wherein the amount of the substance to which each component is adsorbed is calculated by formula (1):
na,i＝Va,iWs (1)
wherein n isa,iAmount of substance to which i component is adsorbed, WsIs the mass of the adsorbent, Va,iIs the adsorption capacity at equilibrium of the i component.
4. The method for calculating a phase state of a fluid in a porous medium according to claim 2, wherein the critical temperature of each component is calculated by formula (2):
the critical pressure of each component was calculated by equation (3):
wherein, Delta TcIs the critical temperature offset, σeffDenotes the effective diameter of the molecule, DeffDenotes the effective diameter of the pores, TcpAnd TcbRepresenting the critical temperature, Δ p, of the fluid in the porous medium and the large space, respectivelycIs the critical pressure offset, pcpAnd pcbRepresenting the critical pressure of the fluid in the porous medium and the large space, respectively.
5. The method for calculating a phase state of a fluid in a porous medium according to claim 2, wherein the fugacity of each component of the oil phase is calculated by formula (4):
the fugacity of the components in the gas phase is calculated by equation (5):
wherein Z isL,jAnd ZV,jRespectively representing the compression factors of the oil phase and the vapor phase mixture in the jth capillary bundle,
am,jand bm,jRespectively the average attraction constant and the repulsion constant of the mixture system in the jth capillary bundle,
ai,j(T)＝aci,jαi,j(T)，
ωi,jis the eccentricity factor of the component i in the jth capillary bundle,
Tci,jand pci,jRespectively showing the critical temperature and the critical pressure of the component i in the jth capillary bundle,
is a binary interaction coefficient.
6. The method for calculating a fluid phase in a porous medium according to claim 2, wherein the average molar mass of the oil phase component and the gas phase component is calculated by formula (6):
calculating the density of the oil phase component and the gas phase component by formula (7):
wherein M isLIs the average molar mass of the oil phase components, MVIs the average molar mass of the gas-phase components, MiDenotes the molar mass of the i component, pLIs the density of the oil phase component, pVIs the density of the gas phase component.
7. The method for calculating a fluid phase state in a porous medium according to claim 2, wherein the plane interfacial tension is calculated by formula (8):
wherein, γ∞Is a plane interfacial tension, [ P ]i]Is the isospecific volume of component i.
8. The method for calculating a phase state of a fluid in a porous medium according to claim 2, wherein the capillary pressure is calculated by equation (9):
wherein p isca,jIs the capillary pressure in the jth capillary bundle, theta is the included angle between the oil-gas interface and the pore surface, gammajRepresenting the actual interfacial tension of the j-th bundle.
9. The method for calculating the phase state of a fluid in a porous medium according to claim 1, further comprising: and calculating the dew point pressure according to the final phase state parameter.
10. A computing system for a fluid phase in a porous medium, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
step 1: establishing a porous fluid component adsorption model, and further determining a plurality of size pores;
step 2: calculating the phase state parameter of each size pore;
and step 3: and normalizing the phase parameters of each size pore to obtain final phase parameters.
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