A diffusion coefficient calculation method considering nano confinement effect

Abstract

The application discloses a diffusion coefficient calculation method considering nano confinement effect and belongs to the technical field of oil and gas field development. The method comprises the following steps: correcting a Peng-Robinson state equation by considering the nano confinement effect; carrying out oil / gas phase balance calculation based on the corrected Peng-Robinson state equation; calculating the molar density of the oil / gas two-phase; and correcting a SIGMUND empirical formula to calculate the diffusion coefficient according to the molar density calculated in the step S3. By means of the above method, the molecular diffusion phenomenon in the dense reservoir such as shale can be accurately described, and the gas injection stimulation and the recovery prediction accuracy are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil and gas field development, and in particular to a diffusion coefficient calculation method considering nano confinement effect. BACKGROUND

[0002] Molecular diffusion plays a key role in the process of oil and gas migration in tight shale reservoirs. In the ultra-low permeability shale reservoirs with nano-scale pores, molecular diffusion is comparable to convective viscous flow, and the mass transfer process is dominated by diffusion. However, there is currently a lack of diffusion coefficient calculation methods suitable for nano-porous porous media such as shale.

[0003] Traditional methods for calculating diffusion coefficients are mainly based on Sigmund's empirical correlation formula, which are widely used in conventional oil and gas reservoirs, but do not consider the nano confinement effect. In nano-scale pores, the nano confinement effect changes the phase behavior and physical parameters of the reservoir fluid.

[0004] Existing state equations such as the Peng-Robinson equation perform well in describing the phase behavior of conventional oil and gas reservoir fluids, but when directly applied to nano-porous systems without modification, the accuracy is insufficient. Phase equilibrium calculation is the basis for determining the composition of gas-liquid two-phase, but the traditional method fails to consider the influence of nano-pores on phase equilibrium. The calculation of oil and gas two-phase molar density is a key step in determining the diffusion coefficient, and although the SIGMUND empirical formula can well predict the binary diffusion coefficient of gas-liquid mixture under high pressure conditions, it also fails to consider the influence of nano confinement effect.

[0005] Experimental studies have shown that the effective diffusion coefficient in porous media is 1-2 orders of magnitude lower than that in the bulk phase, which is closely related to the intrinsic characteristics of the rock, but the traditional calculation method is difficult to accurately characterize this difference.

[0006] Therefore, it is necessary to establish a complete method that systematically integrates state equation modification, phase equilibrium calculation, molar density determination, and diffusion coefficient calculation. SUMMARY

[0007] The purpose of the present application is to provide a diffusion coefficient calculation method considering nano confinement effect, which integrates state equation modification, phase equilibrium calculation, molar density determination, and diffusion coefficient calculation, and systematically incorporates nano confinement effect into the whole process of diffusion coefficient calculation, overcoming the calculation bias caused by ignoring nano effect in traditional methods, and significantly improving the accuracy of fluid diffusion coefficient prediction in tight reservoirs such as shale.

[0008] To achieve the above purpose, the present application provides a diffusion coefficient calculation method considering nano confinement effect, comprising the following steps:

[0009] S1, modifying the Peng-Robinson state equation considering the nano confinement effect;

[0010] S2, carrying out oil / gas phase equilibrium calculation based on the corrected Peng-Robinson state equation;

[0011] S3, calculating the molar density of oil / gas two-phase;

[0012] S4, correcting the SIGMUND empirical formula to calculate the diffusion coefficient according to the molar density calculated in step S3.

[0013] Preferably, step S1 specifically comprises:

[0014] The Peng-Robinson state equation is adopted, and the nano confinement effect is considered to correct the critical temperature and critical pressure of the fluid in the Peng-Robinson state equation;

[0015] The formula of the Peng-Robinson state equation is:

[0016] Z 3 +(B-1)Z 2 +[A-3B 2 -2B]Z-[AB-B 2 (B+1)]=0;

[0017] Wherein,

[0018]

[0019] A ij =(1-δ ij )(A i A j ) 0.5 ;

[0020]

[0021] In the formula, Z is the compressibility factor, which represents the degree of deviation of the actual gas from the ideal gas; A is the attraction parameter, which is related to the intermolecular attraction; B is the volume parameter, which is related to the molecular volume; m i is the eccentric factor function of component i, which is related to the molecular shape; P ri is the normalized pressure of component i; T ri is the normalized temperature of component i; δ ij is the binary interaction coefficient between components i and j; P ci is the critical pressure of component i in the mixture; T ci is the critical temperature of component i in the mixture; A ij is the interaction parameter between components i and j; A i is the attraction parameter of component i; A j is the attraction parameter of component j; ci is the mole fraction of component i; c j is the mole fraction of component j; n c is the number of components; T is the system temperature; P is the system pressure;

[0022] The critical pressure correction coefficient and the critical temperature correction coefficient The formula is:

[0023]

[0024]

[0025] In the formula, σ i is the Lennard-Jone size parameter, r p is the pore radius;

[0026] According to the critical pressure correction coefficient and the critical temperature correction coefficient The corrected critical pressure P cpi and the critical temperature T cpi in the nanopore component i are obtained, instead of the critical pressure P ci and the critical temperature T ci , and the formula is:

[0027]

[0028] Preferably, step S2 specifically comprises:

[0029] According to the initial K i value estimated according to the Wilson empirical formula:

[0030]

[0031] In the formula, ω i is the eccentric factor of component i;

[0032] According to the Rachford-Rice formula, the mole fraction f ng of the gas phase in the system is calculated based on the Newton iteration method, and the formula is:

[0033]

[0034] Based on the obtained K i and f ng , the phase composition of the liquid phase x i and the gas phase y i is calculated, and the formula is:

[0035]

[0036] The fugacity fraction of the gas phase and the fugacity coefficient of the liquid phase are calculated by using the modified Peng-Robinson equation of state The formula is as follows:

[0037]

[0038] Wherein, Z V and Z L are the compressibility factors of the gas phase and the liquid phase calculated based on the modified Peng-Robinson equation of state, x i and y i are the phase compositions of the liquid phase and the gas phase respectively;

[0039] According to the phase compositions and the fugacity coefficients, the liquid phase fugacity f i L and the gas phase fugacity f i V are calculated respectively, and the formula is as follows:

[0040]

[0041] Wherein, P is the pressure of the system;

[0042] When the oil and gas phases are in phase equilibrium, the gas phase fugacity f i V and the liquid phase fugacity f i L are equal, and the convergence condition is met, and the convergence condition is as follows:

[0043]

[0044] When the convergence condition is not met, the equilibrium constant K i needs to be updated, and the continuous replacement method is used to calculate the new equilibrium constant K i , and the formula is as follows:

[0045]

[0046] After the equilibrium constant meets the convergence condition, the gas / liquid phase compositions y i and x i after reaching the phase equilibrium are recalculated.

[0047] Preferably, the step S3 specifically comprises the following steps.

[0048] The liquid phase molar density ρ L and the gas phase molar density ρ V are calculated, and the formula is as follows:

[0049]

[0050] ​

[0051] where R is the gas constant, R = 8.314 x 10 7 erg / (mol·K); T is the system temperature.

[0052] Preferably, the step S4 specifically comprises:

[0053] The diffusion coefficient is calculated by using SIGMUND empirical formula, considering the nano confinement effect.

[0054] The binary diffusion coefficient calculation formula between component i and component j is:

[0055]

[0056] where, is the product of the density and the diffusion coefficient of phase k at low pressure, k is the liquid phase or the gas phase, ρ kr is the reduced density of phase k, λ ij is the Lennard-Jones size parameter, representing the collision diameter, Ω ij is the collision integral of the Lennard-Jones potential, both of which are related to the critical properties of the component; ξ ik is the mole fraction of component i in phase k, the mole coefficient in the gas phase is y i , and the mole coefficient in the gas phase is x i ; v ci is the critical volume of component i; M i and M j are the molecular weights of component i and component j;

[0057] The Lennard-Jones parameters are calculated, the Lennard-Jones collision diameter between component i and j in the mixture is calculated by the arithmetic mean of the collision diameters of the two components, and the formula is:

[0058]

[0059] The Lennard-Jones energy parameter between component i and j in the mixture is calculated by the geometric mean of the energy parameters of the two components, and the formula is:

[0060]

[0061] The Lennard-Jones collision diameter λ i and the Lennard-Jones energy parameter ε i of pure component i are calculated, and the formula is:

[0062]

[0063] ε i = k B (0.7915+0.1963ω i )T cpi ;

[0064] where k B is the Boltzmann constant, k B = 1.3805E-16 erg / K;

[0065] Based on the Lennard-Jones energy parameter, the collision integral Ω ij , which is a function of dimensionless temperature , is calculated as:

[0066]

[0067] According to the above formula, the diffusion coefficient of component i in phase k in a multi-component mixture is obtained when considering the nano-confinement effect based on the Wilke formula, and the formula is:

[0068]

[0069] Therefore, the diffusion coefficient calculation method considering the nano-confinement effect is adopted, the Peng-Robinson state equation is first corrected, the critical temperature and critical pressure adjustment items are introduced, so that the state equation can accurately describe the special phase behavior of the fluid in the nanopore, secondly, based on it, the oil / gas phase equilibrium calculation is carried out, the initial K value is determined by using the Wilson empirical formula, the gas-liquid phase composition under the nano-confinement condition is accurately calculated through iteration, then the molar density of the oil / gas two phases is calculated according to the equilibrium calculation result and the ideal gas state equation, finally, the SIGMUND empirical formula is corrected to adapt to the nano environment, combined with the Lennard-Jones parameter and the collision integral calculation, the diffusion coefficient of component i in phase k considering the nano-confinement effect is finally obtained, through this method, the molecular diffusion phenomenon in the tight reservoir such as shale can be accurately described, and the gas injection stimulation and the recovery prediction accuracy are improved.

[0070] The technical solutions of the present application will be further described in detail below with the help of the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0071] Figure 1 is a method flowchart of an embodiment of the present application;

[0072] Figure 2 is a flowchart of calculating the diffusion coefficient considering the nano-confinement effect of an embodiment of the present application;

[0073] Figure 3A schematic diagram of the diffusion coefficient Dco2-g of the CO2 component in the gas phase in the embodiment of the present application is shown in the figure;

[0074] Figure 4 A schematic diagram of the diffusion coefficient Dco2-G of the C5C6 component in the gas phase in the embodiment of the present application is shown in the figure;

[0075] Figure 5 A schematic diagram of the diffusion coefficient Dco2-l of the CO2 component in the liquid phase in the embodiment of the present application is shown in the figure;

[0076] Figure 6 A schematic diagram of the diffusion coefficient Dco2-L of the C5C6 component in the liquid phase in the embodiment of the present application is shown in the figure;

[0077] Figure 7 A diagram showing the change of the diffusion coefficient of different components in the gas phase in the Bakken shale oil with pressure in the embodiment of the present application is shown in the figure;

[0078] Figure 8 A diagram showing the change of the diffusion coefficient of different components in the liquid phase in the Bakken shale oil with pressure in the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations. In the description of the present application, it should be noted that the orientation or position relationship indicated by the terms “up”, “down”, “inner”, “outer” and the like is based on the orientation or position relationship shown in the drawings, or the orientation or position relationship commonly used when the product of the present application is used, and is only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0080] EMBODIMENT

[0081] As shown in the figure, the present application provides a diffusion coefficient calculation method considering nano confinement effect, and the steps include: Figure 1

[0082] S1, correcting the Peng-Robinson state equation considering nano confinement effect.

[0083] S2, carrying out oil / gas phase equilibrium calculation based on the corrected Peng-Robinson state equation.

[0084] ​S3, calculating the molar density of the oil / gas two-phase.

[0085] S4, correcting the SIGMUND empirical formula to calculate the diffusion coefficient according to the molar density calculated in step S3.

[0086] In this embodiment, the Peng-Robinson state equation is modified considering the nano-confinement effect, which specifically includes:

[0087] The Peng-Robinson state equation is used to correct the critical temperature and critical pressure of the fluid in the Peng-Robinson state equation considering the nano-confinement effect. The formula of the Peng-Robinson state equation is:

[0088] Z 3 +(B-1)Z 2 +[A-3B 2 -2B]Z-[AB-B 2 (B+1)]=0 (1)

[0089] Wherein,

[0090]

[0091] A ij =(1-δ ij )(A i A j ) 0.5 (3)

[0092]

[0093] In the formula, Z is the compressibility factor, which represents the degree of deviation of the actual gas from the ideal gas; A is the attraction parameter, which is related to the intermolecular attraction; B is the volume parameter, which is related to the molecular volume; m i is the eccentric factor function of component i, which is related to the molecular shape; P ri is the normalized pressure of component i; T ri is the normalized temperature of component i; δ ij is the binary interaction coefficient between components i and j; P ci is the critical pressure of component i in the mixture; T ci is the critical temperature of component i in the mixture; A ij is the interaction parameter between components i and j; A i is the attraction parameter of component i; A j is the attraction parameter of component j; c i is the mole fraction of component i; c j is the mole fraction of component j; n c is the number of components; T is the system temperature; P is the system pressure;

[0094] The critical pressure correction coefficient and the critical temperature correction coefficient The formula is:

[0095]

[0096] In the formula, σ i is the Lennard-Jone size parameter, r p is the pore radius.

[0097] According to the critical pressure correction coefficient and the critical temperature correction coefficient The corrected critical pressure P cpi and the critical temperature T cpi in the nanopore component i are obtained, which replace the critical pressure P ci and the critical temperature T ci in the formula (7) (8), and the formula is:

[0098]

[0099] In this embodiment, the oil / gas phase equilibrium calculation based on the corrected Peng-Robinson state equation specifically includes:

[0100] According to the initial K i value estimated according to the Wilson empirical formula:

[0101]

[0102] In the formula, ω i is the eccentric factor of component i.

[0103] According to the Rachford-Rice formula, the molar fraction f ng of the gas phase in the system is calculated based on the Newton iteration method, and the formula is:

[0104]

[0105] Based on the obtained K i and f ng , the phase composition of the liquid phase x i and the gas phase y i is calculated, and the formula is:

[0106]

[0107] Using the corrected Peng-Robinson state equation, the fugacity fraction of the gas phase and the fugacity coefficient of the liquid phase are calculated respectively, and the formula is:

[0108]

[0109] wherein, Z V and Z L are the gas and liquid compressibility factors calculated based on formula (1), x i and y i are the phase compositions of the liquid and gas phases, respectively.

[0110] According to the phase compositions and the fugacity coefficients, the liquid fugacity f i L and the gas fugacity f i V are calculated, respectively, and the formulas are as follows:

[0111]

[0112] wherein, P is the pressure of the system.

[0113] When the oil and gas phases are in phase equilibrium, the gas fugacity f i V and the liquid fugacity f i L are equal, and the convergence condition is satisfied, and the convergence condition is as follows:

[0114]

[0115] When the convergence condition is not satisfied, the equilibrium constant K i needs to be updated, and the continuous replacement method is used to calculate the new equilibrium constant K i , and the formula is as follows:

[0116]

[0117] After the equilibrium constant satisfies the convergence condition, i.e., the convergence condition formula (22) is satisfied, the gas / liquid phase compositions y i and x i after reaching the phase equilibrium are recalculated through formulas (16) and (17).

[0118] In this embodiment, the calculation of the molar densities of the oil and gas phases specifically includes the following steps.

[0119] The liquid molar density ρ L and the gas molar density ρ V are calculated, and the formulas are as follows:

[0120]

[0121] wherein, R is the gas constant, R = 8.314 × 10 7 erg / (mol·K); and T is the temperature of the system.

[0122] In this embodiment, the diffusion coefficient is calculated according to the SIGMUND empirical formula modified by the molar density calculated in step S3, and the calculation specifically includes:

[0123] The SIGMUND empirical formula is used to calculate the diffusion coefficient by considering the nano confinement effect.

[0124] The binary diffusion coefficient calculation formula between component i and component j is:

[0125]

[0126] In the formula, is the product of the density and the diffusion coefficient of phase k at low pressure, k can be a liquid phase or a gas phase, ρ kr is the reduced density of phase k, λ ij is the Lennard-Jones size parameter, representing the collision diameter, Ω ij is the collision integral of the Lennard-Jones potential energy, both of which are related to the critical properties of the components; ξ ik is the molar fraction of component i in phase k, for the molar fraction of component i in the liquid phase, that is, x i , for the molar fraction of component i in the gas phase, that is, y i ; v ci is the critical volume of component i; M i and M j are the molecular weights of component i and component j.

[0127] The Lennard-Jones parameters are calculated, the Lennard-Jones collision diameter between components i and j in the mixture is calculated, which is calculated by the arithmetic mean of the collision diameters of the two components, and the formula is:

[0128]

[0129] The Lennard-Jones energy parameter between components i and j in the mixture is calculated, which is calculated by the geometric mean of the energy parameters of the two components, and the formula is:

[0130]

[0131] The Lennard-Jones collision diameter λ i and the Lennard-Jones energy parameter ε i of pure component i are calculated, and the formula is:

[0132]

[0133] In the formula, k B is the Boltzmann constant, k B=1.3805E-16erg / K.

[0134] Calculate the collision integral Ω based on the Lennard-Jones energy parameters. ij It is a dimensionless temperature. The function is given by the formula:

[0135]

[0136] Based on the above formula, the diffusion coefficient of component i in phase k of a multi-component mixture, considering the nanoconfinement effect according to the Wilke formula, can be obtained as follows:

[0137]

[0138] To verify the effectiveness of the method of the present invention, Bakken shale oil samples were used as reservoir fluids for illustration.

[0139] The fluid composition of Bakken shale oil is shown in Table 1.

[0140] Table 1. Mole fractions of components in Bakken shale oil

[0141] Component [C1] [C2] [C3] [C4] [C5 C6] [C7C 12 ]]> [C 13 C 21 ]]> [C 22 C 80 ]]> Mole fraction 0.36736 0.14885 0.09334 0.05751 0.06406 0.15854 0.0733 0.03704

[0142] Figure 2 This is a flowchart illustrating the calculation of the diffusion coefficient using the aforementioned diffusion coefficient calculation formula, considering the nanoconfinement effect. Using the modified PR equation of state, the diffusion coefficients Dco2-g and Dco2-G of CO2 and C5C6 components in the gas phase of the Bakken shale oil system at a pressure of 1500 psi are calculated as follows: Figure 3 and Figure 4 As shown, at a pressure of 3000 psi, the diffusion coefficients Dco2-l and Dco2-L of CO2 and C5C6 components in the liquid phase are as follows: Figure 5 and Figure 6 As shown.

[0143] pass Figure 3 It can be seen that the diffusion coefficient of CO2 decreases significantly in both cases with increasing CO2 mole fraction. Considering the nanoconfining effect, the overall diffusion coefficient is lower than that without considering the nanoconfining effect. The difference between the two curves is larger at low CO2 mole fractions, and gradually decreases as the CO2 mole fraction increases. When the CO2 mole fraction approaches 90%, the two curves almost overlap. Figure 4It can be seen that with the increase of CO2 mole fraction, the diffusion coefficient of C5C6 also presents a downward trend as a whole. In the low CO2 mole fraction region (<10%), the diffusion coefficient without considering the nano-confinement effect is higher than that considering the nano-confinement effect; in the medium CO2 mole fraction region (about 50%), the two curves cross, indicating that the influence of the nano-confinement effect changes; in the high CO2 mole fraction region (>60%), the diffusion coefficient considering the nano-confinement effect is higher than that without considering the nano-confinement effect, especially when the CO2 mole fraction is close to 90%, the curve considering the nano-confinement effect appears a slight upward trend.

[0144] Figure 3 and Figure 4 The common embodiment is that the diffusion coefficient of CO2 is higher than that of C5C6 as a whole, which conforms to the general rule that the diffusion ability of light components is stronger than that of heavy components. The nano-confinement effect has significant differences on the two components: for CO2, the nano-confinement effect mainly reduces its diffusion coefficient; for C5C6, the nano-confinement effect reduces the diffusion coefficient at low CO2 content, and increases the diffusion coefficient at high CO2 content. This difference may be related to the changes of intermolecular interaction and phase behavior of each component under nano-confinement conditions, indicating that the influence of nano-confinement effect on different components is nonlinear and differentiated. For CO2 flooding / oil / gas process, these results mean that in the high CO2 content region, the nano-confinement effect is beneficial to the diffusion transmission of heavy components, but not conducive to the diffusion of CO2 itself, which has a complex impact on the displacement efficiency.

[0145] Figure 5 The common embodiment is that the diffusion coefficient of CO2 is higher than that of C5C6 as a whole, which conforms to the general rule that the diffusion ability of light components is stronger than that of heavy components. The nano-confinement effect has significant differences on the two components: for CO2, the nano-confinement effect mainly reduces its diffusion coefficient; for C5C6, the nano-confinement effect reduces the diffusion coefficient at low CO2 content, and increases the diffusion coefficient at high CO2 content. This difference may be related to the changes of intermolecular interaction and phase behavior of each component under nano-confinement conditions, indicating that the influence of nano-confinement effect on different components is nonlinear and differentiated. For CO2 flooding / oil / gas process, these results mean that in the high CO2 content region, the nano-confinement effect is beneficial to the diffusion transmission of heavy components, but not conducive to the diffusion of CO2 itself, which has a complex impact on the displacement efficiency.

[0146] Figure 6It is embodied that in the consideration of nano confinement effect, in the low CO2 mole fraction region (<30%), the diffusion coefficient slightly rises, reaches the peak at 30%, and then rapidly decreases with the increase of CO2 mole fraction. Without considering the nano confinement effect, the overall trend is relatively flat, and the decline rate accelerates in the high CO2 mole fraction region. The difference between the two curves is the largest in the low CO2 mole fraction region, and is significantly higher when considering the nano confinement effect. With the increase of CO2 mole fraction, the difference gradually decreases, and at 80% CO2 mole fraction, the two curves are close to overlap.

[0147] Figure 5 and Figure 6 It can be seen from the comparative analysis that the influence of nano confinement effect on the diffusion coefficient in the liquid phase is more significant than in the gas phase. In the liquid phase, the diffusion coefficient considering the nano confinement effect is nearly twice as high as that without considering the nano confinement effect in the low CO2 mole fraction region, which indicates that the nano confinement effect may promote molecular diffusion in the liquid phase. The diffusion behavior of CO2 and C5C6 in the liquid phase is similar, both showing a trend of first stable / rising and then sharply decreasing when considering the nano confinement effect, and a relatively flat downward trend when not considering the nano confinement effect. The diffusion coefficients of the two components are of similar order of magnitude, indicating that the influence of molecular weight difference on the diffusion coefficient is weakened in the liquid phase. C5C6 shows a peak in the diffusion coefficient at 30% when considering the nano confinement effect, which may be related to the solvation effect or microfluid structure change caused by the increase of CO2 content.

[0148] Figure 7 The diffusion coefficient curves of 8 different components in the gas phase are shown. It can be observed that light components (such as C1 methane) have higher diffusion coefficients, while heavy components (such as C 22 C 80 ) have lower diffusion coefficients. At 1000 psia, the diffusion coefficient of C1 is almost an order of magnitude higher than that of the heaviest component C 22 C 80 With the increase of pressure, the diffusion coefficients of all components show a downward trend, and the difference between light and heavy components gradually narrows.

[0149] Figure 8 The diffusion coefficient curves of 8 components in the liquid phase are shown. It can be observed that the diffusion coefficient in the liquid phase is about two orders of magnitude smaller than in the gas phase. In the liquid phase, the trend of diffusion coefficient change with pressure is different from that in the gas phase, they slightly decrease with pressure, which is contrary to the case of shale gas. When reaching the bubble point pressure (2860 psia), the diffusion coefficient shows an almost linear downward relationship with pressure, and the difference in diffusion coefficient between different components still exists in the liquid phase.

[0150] Therefore, the application adopts the above diffusion coefficient calculation method considering nano confinement effect, and can accurately describe the molecular diffusion phenomenon in the dense reservoir such as shale by correcting the Peng-Robinson state equation and SIGMUND empirical formula to calculate the diffusion coefficient, and improve the prediction accuracy of gas injection stimulation and recovery factor.

[0151] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application rather than limiting them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for calculating a diffusion coefficient considering a nanorestriction effect, characterized by the steps of Comprise: S1, considering the nano confinement effect correction Peng-Robinson equation of state, the specific process includes: Using Peng-Robinson equation of state, considering the nano confinement effect, the fluid critical temperature and critical pressure in Peng-Robinson equation of state are corrected: Peng-Robinson equation of state formula is: Z 3 +(B-1)Z 2 +[A-3B 2 -2B]Z-[AB-B 2 (B+1)]=0; Wherein, A ij = (1 - δ ij )(A i A j ) 0.5 ; where Z is the compressibility factor, which indicates the degree to which the real gas deviates from the ideal gas; A is the attractive parameter, which is related to the intermolecular attraction; B is the volume parameter, which is related to the molecular volume; m i is the eccentric factor function of component i, which is related to the molecular shape; P ri is the normalized pressure of component i; T ri is the normalized temperature of component i; δ ij is the binary interaction coefficient between i and j components; P ci is the critical pressure of component i in the mixture; T ci is the critical temperature of component i in the mixture; A ij is the interaction parameter between component i and j; A i is the attractive parameter of component i; A j is the attractive parameter of component j; c i is the mole fraction of component i; c j is the mole fraction of component j; n c is the number of components; T is the system temperature; P is the system pressure; A critical pressure correction coefficient is calculated and a critical temperature correction coefficient The formula is: where σ i is the Lennard-Jone size parameter, r p is the pore radius; According to the critical pressure correction coefficient and the critical temperature correction coefficient the corrected critical pressure P cpi and the critical temperature T cpi in the nanopore component i are obtained, instead of the critical pressure P ci and the critical temperature T ci , according to the formula: S2, based on the modified Peng-Robinson equation of state to carry out oil / gas phase equilibrium calculation; S3, the molar density of oil / gas two-phase is calculated; S4, according to the molar density calculated in step S3, the SIGMUND empirical formula is used to correct the diffusion coefficient.

2. The method of claim 1, wherein the method is characterized by, Step S2 specifically includes: Initial K estimated according to Wilson empirical formula i value: wherein ω i is the eccentricity factor of component i; The mole fraction of the gas phase, f, in the system was calculated based on the Newton iteration method according to the Rachford-Rice formula ng , which is: Based on the obtained K i and f ng , the phase composition of liquid phase x i and gas phase y i is calculated, and the formula is: The fugacity fraction of gas phase and the fugacity coefficient of liquid phase are calculated by the modified Peng-Robinson equation of state respectively The formula is: wherein Z V and Z L are the gas and liquid compressibility factors calculated based on the modified Peng-Robinson equation of state, x i and y i are the phase compositions of the liquid and gas phases, respectively; According to the phase composition and the fugacity coefficient, the liquid phase fugacity f i L and the gas phase fugacity f i V is calculated, and the formula is: In the formula, P is the pressure of the system; When the oil and gas two phases are in phase equilibrium, the gas phase fugacity f i V and the liquid phase fugacity f i L are equal, the convergence condition is met, and the convergence condition is: When the convergence condition is not satisfied, the balance constant K needs to be updated i The new balance constant K is calculated by using the continuous replacement method i The formula is: After the convergence condition is met for the equilibrium constant, the gas / liquid phase compositions y and x are recalculated to reach phase equilibrium i and x i .

3. The method of claim 2, wherein the method is characterized by, Step S3 specifically includes: The liquid molar density p is calculated L and the gas molar density p V with the formula: where R is the gas constant, R = 8.314 x 10 7 erg / (mol K); T is the system temperature.

4. The method of claim 3, wherein the method is characterized by, Step S4 specifically includes: Using SIGMUND empirical formula, considering the nano confinement effect, the diffusion coefficient is calculated; The binary diffusion coefficient calculation formula between component i and component j is: where is the product of the density and the diffusion coefficient at low pressure for phase k, p kr is the reduced density of phase k, λ ij is the Lennard-Jones size parameter, representing the collision diameter, Ω ij is the collision integral for the Lennard-Jones potential, both of which are related to the critical properties of the components; ξ ik is the mole fraction of component i in phase k; v ci is the critical volume of component i; M i and M j are the molecular weights of component i and component j, respectively; The Lennard-Jones parameters are calculated, the Lennard-Jones collision diameter between component i and j in the mixture is calculated, which is calculated by the arithmetic mean of the collision diameter of the two components, and the formula is: The Lennard-Jones energy parameter between component i and j in the mixture is calculated, which is calculated by the geometric mean of the energy parameter of the two components, and the formula is: The Lennard-Jones collision diameter λ of the pure component i is calculated i and the Lennard-Jones energy parameter ε i , which is given by the formula: ε i = k B (0.7915 + 0.1963ω i )T cpi ; where k B is the Boltzmann constant, k B = 1.3805E-16 erg / K; Based on the Lennard-Jones energy parameters, the collision integrals Ω are calculated ij which is a dimensionless temperature function given by the formula: According to the above formula, the diffusion coefficient of component i in k phase in multi-component mixture is obtained based on Wilke formula considering nano confinement effect, and the formula is:

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