Method for calculating viscosity of multi-component fluid in tight reservoir space

Abstract

The invention relates to a method for calculating viscosity of multi-component fluid in tight reservoir space, and belongs to the technical field of unconventional oil and gas reservoir development. The invention discloses a method for calculating viscosity of a multi-component fluid in a tight reservoir space. The method comprises the following steps: acquiring pore parameters in nanopores of a tight reservoir, components of the fluid and basic parameters of the components; constructing a two-phase flash evaporation calculation model coupled with the nanopore confinement effect; calculating a fugacity coefficient, a component equilibrium constant and the mole fraction of an equilibrium phase component in a gas-liquid phase according to the constructed two-phase flash calculation model coupled with the nanopore confinement effect; and calculating the fluid viscosity in the tight reservoir space when the nano confinement effect is considered according to the mole fraction of each component in combination with a phase equilibrium calculation model. According to the method, the flowing behavior of the fluid in the tight reservoir can be predicted more accurately, the mining scheme is optimized, and the mining efficiency is improved.

Description

Technical Field

[0001] The invention relates to a method for calculating the viscosity of a multi-component fluid in a tight reservoir space, and belongs to the technical field of unconventional oil and gas reservoir development. Background Art

[0002] With the in-depth exploration and development of tight reservoirs, it is increasingly important to accurately describe the physical properties of reservoir fluids. Among them, viscosity, as a key parameter, directly affects the fluidity and production efficiency of the fluid. In conventional reservoirs, due to the large pore size, the fluid viscosity can usually be regarded as a constant. However, in reservoirs with nanoscale pore throat structures such as tight sandstone and shale, the situation is quite different.

[0003] In tight reservoirs, due to the existence of nanopore confinement effect, the interaction between fluid molecules and pore walls is significantly enhanced, resulting in changes in fluid viscosity. Therefore, in order to accurately describe and predict the flow behavior of fluids in tight reservoirs, it is necessary to establish a viscosity calculation method that takes into account the nanopore confinement effect.

[0004] At present, commonly used viscosity models are often predicted based on the properties of bulk fluids. However, in nanopores, due to the influence of confinement effects, these models may not accurately reflect the actual situation. Summary of the invention

[0005] In order to overcome the defects in the prior art, the present invention aims to provide a method for calculating the viscosity of a multi-component fluid in a tight reservoir space. The present invention can more accurately predict the flow behavior of the fluid in the tight reservoir, thereby optimizing the mining plan and improving the mining efficiency.

[0006] The present invention provides a technical solution to solve the above technical problems: a method for calculating the viscosity of a multi-component fluid in a dense reservoir space, comprising the following steps:

[0007] Step 1, obtaining pore parameters, fluid components and basic parameters of the components in nanopores of a dense reservoir;

[0008] Step 2, constructing a two-phase flash evaporation calculation model coupled with nanopore confinement effect;

[0009] Step 3, calculating the fugacity coefficient, component equilibrium constant and the molar fraction of each component of the equilibrium phase in the gas and liquid phases according to the constructed two-phase flash calculation model coupled with the nanopore confinement effect;

[0010] Step 4, calculating the fluid viscosity in the tight reservoir space when considering the nano-confinement effect according to the mole fraction of each component combined with the phase equilibrium calculation model;

[0011] The Lohrenz-Bray-Clark model is used to calculate the fluid viscosity of the light component, and the Pedersen-Freenslund method is used to calculate the fluid viscosity of the heavy component.

[0012] A further technical solution is that the basic parameters of the components include critical pressure, critical temperature, critical volume, eccentricity factor, relative molecular mass, dimensionless volume offset parameter, and isotonic specific volume.

[0013] A further technical solution is that the two-phase flash evaporation calculation model includes:

[0014] The expanded PR state equation considering the nanoconfinement effect is:

[0015]

[0016] Where: P is the system pressure; T is the system temperature; R is the gas constant; a is the intermolecular attraction; b is the intermolecular repulsion; v is the component volume; σ LJ is the molecular size parameter; r is the pore radius;

[0017] The critical temperature inside the nanopores is calculated as:

[0018] T cn =T c (1-ΔT c )

[0019] The critical pressure inside the nanopores is calculated as:

[0020] P cn =P c (1-ΔP c )

[0021] Where: T cn is the critical temperature in the nanopores, P cn is the critical pressure in the nanopores, ΔTc and ΔPc are the offsets of the critical temperature and critical pressure of the components;

[0022] The equilibrium constant calculation formula of the component is:

[0023]

[0024] Where: P is the system pressure; T is the system temperature; P cn,i is the critical pressure in the nanopores of component i; T cn,i is the critical temperature in the nanopores of component i; ω i is the eccentricity factor of component i; K i is the equilibrium constant of component i;

[0025] The mass conservation equation:

[0026] z i =β L x i +β V y i

[0027] 1 = β L +β V

[0028]

[0029] Where: z i is the number of moles of component i; x i ,y i are the mole fractions of component i in the liquid phase and gas phase respectively; β L , β V are the phase fractions of liquid and gas phase, respectively;

[0030] The calculation formula of the fugacity coefficient of the component in the gas-liquid two phases is:

[0031]

[0032] Where: are the fugacity coefficients of component i in the liquid phase and gas phase respectively; x i ,y i are the mole fractions of component i in the liquid and gas phases, respectively.

[0033] A further technical solution is that the specific process of step 3 includes:

[0034] Step 31, calculating the system pressure, the critical temperature in the nanopores, and the critical pressure in the nanopores according to the expanded PR state equation considering the nanoconfinement effect;

[0035] Step 32, calculating the equilibrium constant of the component according to the equilibrium constant calculation formula of the component;

[0036] Step 33, calculating the Rachford-Rice equation according to the continuous iteration method and the Newton iteration method to obtain the gas phase mole fraction;

[0037] Step 34, obtaining the liquid phase mole fraction according to the mass conservation equation and the gas phase mole fraction;

[0038] Step 35, calculating the fugacity coefficient of the component in the gas-liquid two-phase according to the gas phase mole fraction, the liquid phase mole fraction and the fugacity coefficient calculation formula of the component in the gas-liquid two-phase;

[0039] Step 36, determine whether the fugacity coefficients in the gas and liquid phases are equal. If not, update the equilibrium constant and repeat steps 33-36 until they are equal, indicating that phase equilibrium is achieved, and output the mole fraction and fugacity coefficient of each component in the equilibrium gas and liquid phases.

[0040] A further technical solution is that the Rachford-Rice equation in step 33 is:

[0041]

[0042] Where: nc is the number of components.

[0043] A further technical solution is that the updating formula of the equilibrium constant in step 36 is:

[0044]

[0045] Where: are the fugacity of component i in the liquid phase and gas phase respectively; K i is the equilibrium constant of component i at the kth iteration; is the equilibrium constant of component i at the k+1th iteration; k is the number of iterations.

[0046] A further technical solution is that the Lohrenz-Bray-Clark model in step 4 is:

[0047]

[0048] Where: is the mixed viscosity of the diluted fluid at low pressure, ξ is the viscosity reduction parameter, ρ r is the relative density, a0-a4 are the correlation coefficients.

[0049] A further technical solution is that the calculation formula of the Pedersen-Freenslund method in step 4 is:

[0050]

[0051] Where: μ mix is the mixed viscosity of the diluted fluid at low pressure, μ o is the viscosity of the reference material, T cn,mix , P cn,mix , MW mix , a mix are the critical temperature, critical pressure, relative molecular mass, rotational coupling coefficient, T c,o , P c,o , MW o , a oThey are the critical temperature, critical pressure, relative molecular mass and rotational coupling coefficient of the reference substance methane respectively.

[0052] The present invention has the following beneficial effects: Based on the traditional viscosity calculation model, the present invention comprehensively considers the influence of the molecular-pore wall interaction force, the critical property deviation of the fluid and the capillary force in the tight reservoir. At the same time, the present invention introduces a solution strategy based on the continuous iteration method for accurately calculating the fluid viscosity under tight reservoir conditions.

[0053] This improved calculation method can overcome the limitations of the classical viscosity calculation model when applied in tight reservoirs, and fully considers the complex interaction effects of multi-component fluids. By accurately modeling the actual behavior of fluids under tight reservoir conditions, the present invention provides more reliable viscosity calculation results, especially when nanopore effects are considered. This technical solution not only improves the accuracy of viscosity calculations, but also helps to optimize the development and management strategies of tight reservoirs, provides a more scientific basis, and improves the development efficiency of unconventional oil and gas reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The flowchart of the calculation of the viscosity of multi-component fluid in a tight reservoir of the present invention;

[0055] Figure 2 This is a flow chart of the calculation of tight reservoir fluid phase equilibrium using a continuous iteration method taking into account the nanopore confinement effect of the present invention;

[0056] Figure 3 This is the calculation result diagram of gas phase viscosity in different pore sizes of the gas reservoir;

[0057] Figure 4 This is the calculation result of liquid viscosity in different pore sizes of the gas reservoir. DETAILED DESCRIPTION

[0058] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] A method for calculating the viscosity of a multi-component fluid in a dense reservoir space of the present invention comprises the following steps:

[0060] Step 1, obtaining pore parameters (pore radius), fluid components and basic parameters of the components in the nanopores of the dense reservoir;

[0061] The basic parameters of the components include the critical pressure P c , critical temperature Tc , critical volume V c , eccentricity factor ω, relative molecular mass MW, dimensionless volume offset parameter v s , isotonic volume [P];

[0062] Step 2, constructing a two-phase flash evaporation calculation model coupled with nanopore confinement effect;

[0063] The parameters required for the two-phase flash calculation model include fluid composition, component eccentricity factor, critical temperature, critical pressure, pore radius, binary interaction coefficient, system temperature and pressure;

[0064] The expanded PR state equation considering the nanoconfinement effect is:

[0065]

[0066] Where: P is the system pressure; T is the system temperature; R is the gas constant; a is the intermolecular attraction; b is the intermolecular repulsion; v is the component volume; σ LJ is the molecular size parameter; r is the pore radius;

[0067] The equation of state is expanded considering the nanoconfinement effect, and the critical property offset data in the nanopores are calculated, including the critical temperature and critical pressure of the components in the nanopores.

[0068] The calculation formula for the critical temperature of the components in the nanopores is:

[0069] T cn =T c (1-ΔT c )

[0070]

[0071] The critical pressure calculation formula of the components in the nanopores is:

[0072] P cn =P c (1-ΔP c )

[0073]

[0074] Among them, T cn is the critical temperature in the nanopores, P cn is the critical pressure in the nanopores, ΔTc and ΔPc are the offsets of the critical temperature and critical pressure of the component; r is the pore radius; Tc is the critical temperature of the component; Pc is the critical pressure of the component, σ LJ is the Lennard-Jones aperture parameter;

[0075] The equilibrium constant calculation formula of the component is:

[0076]

[0077] Where: P is the system pressure; T is the system temperature; P ci is the critical pressure of component i; T ci is the critical temperature of component i; ω i is the eccentricity factor of component i; K i is the equilibrium constant of component i;

[0078] The mass conservation equation:

[0079] z i =β L x i +β V y i

[0080] 1 = β L +β V

[0081]

[0082] Where: z i is the number of moles of component i; x i ,y i are the mole fractions of component i in the liquid phase and gas phase respectively; β L , β V are the phase fractions of liquid and gas phase, respectively;

[0083] The calculation formula of the fugacity coefficient of the component in the gas-liquid two phases is:

[0084]

[0085] Where: are the fugacity coefficients of component i in the liquid phase and gas phase respectively; x i ,y i are the mole fractions of component i in the liquid and gas phases, respectively;

[0086] The compression factor Z is obtained by solving the cubic state equation, and the calculation formula is:

[0087] Z 3 -(1-B)Z 2 +(A-2B-3B 2 )Z-(AB-B 2 -B 3 )=0

[0088] Among them, A and B are the mixing regularity coefficients;

[0089] For the gas phase, the coefficient is

[0090] For the liquid phase, the coefficient is

[0091] in, represents the logarithm of the gas phase fugacity coefficient, Represents the logarithm of the liquid phase fugacity coefficient, Z V is the gas phase compressibility factor, Z L is the liquid phase compressibility factor, P V is the gas phase pressure, P L is the liquid phase pressure; x i , xj represents the molar fraction of components i and j in the liquid phase, y i , yj represent the mole fractions of components i and j in the gas phase; κ i ,Ω a ,Ω b 、a V 、a L 、b V 、b L 、a i 、b i 、a ij All of them are parameters in phase equilibrium calculation; α i , α j represents the temperature-dependent gravitational correction term for components i and j, ω i is the eccentricity factor of component i, T ci is the critical temperature of component i, P ci is the critical pressure of component i;

[0092]

[0093] Ωa=0.457235530,Ωb=0.077796074

[0094] Step 3, calculating the fugacity coefficient, component equilibrium constant and the molar fraction of each component of the equilibrium phase in the gas and liquid phases according to the constructed two-phase flash calculation model coupled with the nanopore confinement effect;

[0095] Step 31, calculating the system pressure, the critical temperature in the nanopores, and the critical pressure in the nanopores according to the expanded PR state equation considering the nanoconfinement effect;

[0096] Step 32, calculating the equilibrium constant of the component according to the equilibrium constant calculation formula of the component;

[0097] Step 33, calculating the Rachford-Rice equation according to the continuous iteration method and the Newton iteration method to obtain the gas phase mole fraction;

[0098] The Rachford-Rice equation is:

[0099]

[0100] Where: nc is the number of components;

[0101] Step 34, obtaining the liquid phase mole fraction according to the mass conservation equation and the gas phase mole fraction;

[0102] Step 35, calculating the fugacity coefficient of the component in the gas-liquid two-phase according to the gas phase mole fraction, the liquid phase mole fraction and the fugacity coefficient calculation formula of the component in the gas-liquid two-phase;

[0103] Step 36, determine whether the fugacity coefficients in the gas and liquid phases are equal. If not, update the equilibrium constant and repeat steps 33-36 until they are equal, indicating that phase equilibrium is achieved, and output the mole fractions and fugacity coefficients of the components in the equilibrium gas and liquid phases;

[0104]

[0105] Where: are the fugacity of component i in the liquid phase and gas phase respectively; K i is the equilibrium constant of component i at the kth iteration; is the equilibrium constant of component i at the k+1th iteration; k is the number of iterations;

[0106] Step 4, calculating the fluid viscosity in the tight reservoir space when considering the nano-confinement effect according to the mole fraction of each component combined with the phase equilibrium calculation model;

[0107] The Lohrenz-Bray-Clark model is used to calculate the fluid viscosity of the light component;

[0108]

[0109] Where: is the mixed viscosity of the diluted fluid at low pressure, ξ is the viscosity reduction parameter, ρ r is the relative density, a0-a4 are the correlation coefficients; their values ​​are: a0=0.10230, a1=0.023364, a2=0.058533, a3=-0.040758, a4=0.0093324.

[0110] The viscosity reduction parameter ξ of the mixture is calculated as follows:

[0111]

[0112] Where: T ci MW i , P ci are the critical temperature, relative molecular mass, and critical pressure of component i, respectively.i is the mole fraction of component i. When calculating, the mole fraction of component i in the gas phase or liquid phase under equilibrium state is taken. Relative density ρ r Mixed viscosity of dilute fluid at low pressure The calculation of is as follows:

[0113]

[0114] Among them, Vci, are the critical volume of component i and the viscosity of the pure component at low pressure, respectively. ρ takes the mass density of the gas phase or liquid phase as needed. The calculation of the viscosity of the pure component at low pressure also requires the viscosity reduction parameter of the pure component, namely:

[0115]

[0116] ξi=Tcn,i1 / 6Mi-1 / 2Pcn,i-2 / 3

[0117] The Pedersen-Freenslund method is not affected by experimental data and can better calculate the viscosity of the heavy component (C10+). The process of calculating the gas-liquid phase viscosity combined with the phase equilibrium model proposed in this paper is as follows:

[0118]

[0119] Where: μ mix is the mixed viscosity of the diluted fluid at low pressure, μ o is the viscosity of the reference material, T cn,mix , P cn,mix , MW mix , a mix are the critical temperature, critical pressure, relative molecular mass, rotational coupling coefficient, T c,o , P c,o , MW o , a o They are the critical temperature, critical pressure, relative molecular mass and rotational coupling coefficient of the reference substance methane respectively.

[0120] The relative molecular mass MW of the mixture mix Determined by the following formula:

[0121]

[0122] MW w is the weight fraction average molecular mass, MW n is the average relative molecular mass by mole fraction, b1 and b2 are correlation coefficients. Their values ​​are: b1 = 1.304 × 10 -4 , b2=2.303;

[0123] The rotational coupling coefficient is calculated as follows:

[0124]

[0125] where ρ r is the relative density of the reference object, b3, b4, b5 are the correlation coefficients. Their values ​​are: b3 = 7.378 × 10 -3 , b4=1.847, b5=0.5173;

[0126] Example

[0127] The following is a specific example to illustrate a method for calculating the viscosity of a multi-component fluid in a tight reservoir space provided by an embodiment of the present invention. Taking a condensate gas reservoir as an example, the fluid viscosity is calculated.

[0128] The fluid in the nanopores of the tight reservoir is affected by the capillary force and the interaction between the pore wall. The components of the condensate gas reservoir fluid are obtained, specifically CO2, N2, CH4, C2H6, C3H8, IC4, NC4, IC5, NC5, FC6, and FC7. The critical pressure P of each component is obtained by querying from the knowledge base. c , critical temperature T c , critical volume V c , eccentricity factor ω, relative molecular mass MW, dimensionless volume offset parameter v s , isotonic volume [P], the above data are shown in Table 1:

[0129] Table 1 Physical properties of each fluid component

[0130]

[0131]

[0132] The binary interaction coefficient data of the fluid are shown in Table 2

[0133] Table 2 Binary interaction coefficients of fluids (×10 -3 )

[0134]

[0135] According to the calculation steps mentioned in the manual, the viscosity calculation results of the gas phase at different pore radii are as follows: Figure 3 As shown in the figure, the calculated results of the viscosity of the liquid phase are as follows: Figure 4 shown.

[0136] The above description is not intended to limit the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the viscosity of a multi-component fluid in a tight reservoir space, characterized in that: The following steps are involved: Step 1, obtaining pore parameters, fluid components and basic parameters of the components in the nanopores of the dense reservoir; Step 2, constructing a two-phase flash evaporation calculation model coupled with nanopore confinement effect; Step 3, calculating the fugacity coefficient, component equilibrium constant and the molar fraction of each component of the equilibrium phase in the gas and liquid phases according to the constructed two-phase flash calculation model coupled with the nanopore confinement effect; Step 4, calculating the fluid viscosity in the tight reservoir space when considering the nano-confinement effect according to the mole fraction of each component combined with the phase equilibrium calculation model; The Lohrenz-Bray-Clark model is used to calculate the fluid viscosity of the light component, and the Pedersen-Freenslund method is used to calculate the fluid viscosity of the heavy component.

2. The method for calculating the viscosity of a multi-component fluid in a dense reservoir space according to claim 1, characterized in that: The basic parameters of the components include critical pressure, critical temperature, critical volume, eccentricity factor, relative molecular mass, dimensionless volume shift parameter, and isotonic specific volume.

3. The method for calculating the viscosity of a multi-component fluid in a dense reservoir space according to claim 1, characterized in that: The two-phase flash calculation model includes: The expanded PR state equation considering the nanoconfinement effect is: Where: P is the system pressure; T is the system temperature; R is the gas constant; a is the intermolecular attraction; b is the intermolecular repulsion; v is the component volume; σ LJ is the molecular size parameter; r is the pore radius; The critical temperature inside the nanopores is calculated as: T cn =T c (1-ΔT c ) The critical pressure inside the nanopores is calculated as: P cn =P c (1-ΔP c ) Where: T cn is the critical temperature in the nanopores, P cn is the critical pressure in the nanopores, ΔTc and ΔPc are the offsets of the critical temperature and critical pressure of the components; The equilibrium constant calculation formula of the component is: Where: P is the system pressure; T is the system temperature; P cn,i is the critical pressure in the nanopores of component i; T cn,i is the critical temperature in the nanopores of component i; ω i is the eccentricity factor of component i; K i is the equilibrium constant of component i; The mass conservation equation: z i =β L x i +β V y i 1＝β L +β V Where: z i is the number of moles of component i; x i ,y i are the mole fractions of component i in the liquid phase and gas phase respectively; β L , β V are the phase fractions of liquid and gas phase, respectively; The calculation formula of the fugacity coefficient of the component in the gas-liquid two phases is: Where: are the fugacity coefficients of component i in the liquid phase and gas phase respectively; x i ,y i are the mole fractions of component i in the liquid and gas phases, respectively.

4. The method for calculating the viscosity of a multi-component fluid in a tight reservoir space according to claim 3, characterized in that: The specific process of step 3 includes: Step 31, calculating the system pressure, the critical temperature in the nanopores, and the critical pressure in the nanopores according to the expanded PR state equation considering the nanoconfinement effect; Step 32, calculating the equilibrium constant of the component according to the equilibrium constant calculation formula of the component; Step 33, calculating the Rachford-Rice equation according to the continuous iteration method and the Newton iteration method to obtain the gas phase mole fraction; Step 34, obtaining the liquid phase mole fraction according to the mass conservation equation and the gas phase mole fraction; Step 35, calculating the fugacity coefficient of the component in the gas-liquid two-phase according to the gas phase mole fraction, the liquid phase mole fraction and the fugacity coefficient calculation formula of the component in the gas-liquid two-phase; Step 36, determine whether the fugacity coefficients in the gas and liquid phases are equal. If not, update the equilibrium constant and repeat steps 33-36 until they are equal, indicating that phase equilibrium is achieved, and output the mole fraction and fugacity coefficient of each component in the equilibrium gas and liquid phases.

5. The method for calculating the viscosity of a multi-component fluid in a tight reservoir space according to claim 4, characterized in that: The Rachford-Rice equation in step 33 is: Where: nc is the number of components.

6. The method for calculating the viscosity of a multi-component fluid in a tight reservoir space according to claim 4, characterized in that: The updating formula of the equilibrium constant in step 36 is: Where: f i L 、f i V are the fugacity of component i in the liquid phase and gas phase respectively; K i is the equilibrium constant of component i at the kth iteration; is the equilibrium constant of component i at the k+1th iteration; k is the number of iterations.

7. The method for calculating the viscosity of a multi-component fluid in a tight reservoir space according to claim 1, characterized in that: The Lohrenz-Bray-Clark model in step 4 is: Where: is the mixed viscosity of the diluted fluid at low pressure, ξ is the viscosity reduction parameter, ρ r is the relative density, a0-a4 are the correlation coefficients.

8. The method for calculating the viscosity of a multi-component fluid in a tight reservoir space according to claim 1, characterized in that: The calculation formula of the Pedersen-Freenslund method in step 4 is: Where: μ mix is the mixed viscosity of the diluted fluid at low pressure, μ o is the viscosity of the reference material, T cn,mix , P cn,mix , MW mix , a mix are the critical temperature, critical pressure, relative molecular mass, rotational coupling coefficient, T c,o , P c,o , MW o , a o They are the critical temperature, critical pressure, relative molecular mass and rotational coupling coefficient of the reference substance methane respectively.

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