An excess Gibbs free energy based model to calculate viscosity of multicomponent liquid mixtures
Introduction
Densities and viscosities of solutions are especially important when designing and simulating processes. In particular viscosity is important in processes where mass transfer is involved (e.g., absorbers and desorbers). Moreover, equipments such as pumps and heat exchangers are better modeled when the physical properties of the system are accurately calculated (Fu et al., 2012, Weiland et al., 1998).
Several properties of a system can be directly correlated to its viscosity. For instance, Versteeg et al. (1996) show that the diffusivity of alkanolamines can be estimated from viscosity with a modified Stokes–Einstein relation. Hence, a good representation of the viscosity of the solution is crucial. Proposed correlations for liquid viscosity available in the literature, unfortunately, do not share the same theoretical basis as for gas viscosity (Poling et al., 2000). Therefore, it is desirable to estimate the liquid viscosity from experimental data whenever available.
Many correlations are available in the literature to calculate the viscosity of both pure liquids and mixtures of liquid components. A number of proposed models use the pure liquid viscosity as a starting point and apply a mixing rule to calculate the viscosity of the mixture. In these cases, it is required that pure component liquid viscosities are known at given temperatures and pressures.
However, for solutions where the viscosity of at least one of the components is not known, the applicability of these types of equations is not straightforward. Aqueous solutions of hydroxide salts are examples of solutions where the liquid viscosity of one component (in this case, the hydroxide) is not known for a wide range of temperatures. These solutions are of interest for CO2 capture processes (see Yoo et al., 2013, Mahmoudkhani and Keith, 2009, Stolaroff et al., 2008).
When the pure viscosity of one (or more components) is not available, models which use a reference viscosity are usually applied (see, for instance, Först et al., 2002, Mathlouthi and Reiser, 1994, Vand, 1948). An extensive review on this type of viscosity models is found in Longinotti and Corti (2008). Alternatively, one can still use models which require the pure viscosity of the components by, for instance, setting the unknown viscosity to a constant value.
In this work, a new model for calculating the viscosity of multicomponent liquid mixtures is presented. The model is based on the fact that excess viscosities show similar behaviour as that observed for excess Gibbs energy. Hence, the functional forms of the many existing models capable of representing excess Gibbs energy can be used for representing excess viscosities. In particular, the functional form of the NRTL model was chosen in this work. By setting few binary interaction parameters, the model is able to accurately represent the viscosity of liquid mixtures. Eight binary systems and three ternary systems were tested to verify the accuracy of the model. Although the model has the same functional form as that of excess Gibbs energy models, it is important to stress that the fitted interaction parameters are not connected at all to the NRTL model and should not be used for activity calculations. Moreover, it is important to check if, at the desired conditions of composition, temperature and pressure, the mixture is a single phase liquid solution.
Section snippets
Liquid viscosity correlations
Several viscosity correlations are available in the literature. For a pure component in its liquid state, the Andrade type of equation (Andrade, 1930) is well accepted and is implemented in many process simulators. One of the forms of the Andrade equation is given in Eq. (1). Here η∘ is the dynamic viscosity of the liquid, T is the temperature of the system and A, B and C are the adjustable parameters of the model.
For multicomponent systems, the Grunberg–Nissan model (Grunberg
The functional form of excess Gibbs energy models
The viscosity of most liquid mixtures cannot be explained by a simple mixing rule as described by Eq. (9).
However, this simple mixing rule is the basis for several available models, as well as for the proposed model. The difference between the left- and right-hand sides of Eq. (9), except for pure components, is non-zero for most systems. In Fig. 1, the shape of this difference is shown for the H2O-MDEA system. This shape resembles the excess Gibbs energy function as
Optimization procedure
The parameters of the proposed model were estimated to fit the experimental viscosity data for some selected systems. The particle swarm optimization (Kennedy and Eberhart, 1995) algorithm was used in this work. As previously done in Pinto et al. (2014), the lbest topology was chosen with the inertia factor (ω = 0.7298) and the acceleration coefficients (ϕ1 and ϕ2 = 1.49618) (Poli et al., 2007). The particles were generated within the interval [−3, 3] and [−3000, 3000] for the adjustable
Results
In this section, 11 systems were chosen to be modeled using the NRTL-DVIS model. All the studied systems are aqueous solutions and the knowledge of the viscosity of pure water is required. The correlation given in Bingham and Jackson (1918) (Eqs. (17) and (18)) was used to calculate the viscosity of pure water where ϕ is the fluidity of water in P−1, is the viscosity of pure water in mPa.s and T is the temperature in K. The studied systems are given in Table 1.
Conclusions
The NRTL-DVIS model uses the NRTL model structure to correlate the excess viscosity of liquid mixtures. The NRTL model is relatively simple and presents only few binary adjustable parameters which are fitted to experimental data. The binary interaction parameters are assumed to have a simple temperature dependency to account for calculations at different temperatures.
The NRTL-DVIS model is able to correlate the viscosity of liquid mixtures with very good accuracy. The model is also able to
References (50)
- et al.
Pilot study-CO2 capture into aqueous solutions of 3-methylaminopropylamine (MAPA) activated dimethyl-monoethanolamine (DMMEA)
Int. J. Greenh. Gas Control
(2012) - et al.
Viscosities and excess viscosities of aqueous solutions of some diethanolamines
J. Mol. Liq.
(2010) - et al.
Modeling piperazine thermodynamics
Energy Procedia
(2011) - et al.
Experiment and model for the viscosity of carbonated MDEA-MEA aqueous solutions
Fluid Phase Equilib.
(2012) - et al.
Density, dynamic viscosity, and derived properties of binary mixtures of methanol or ethanol with water, ethyl acetate, and methyl acetate at T = (293.15, 298.15, and 303.15) K
J. Chem. Thermodyn.
(2007) - et al.
Low-energy sodium hydroxide recovery for CO2 capture from atmospheric air-thermodynamic analysis
Int. J. Greenh. Gas Control
(2009) - et al.
VLE data and modelling of aqueous N,N-diethylethanolamine (DEEA) solutions
Int. J. Greenh. Gas Control
(2013) - et al.
eNRTL parameter fitting procedure for blended amine systems: MDEA-PZ case study
Energy Procedia
(2013) - et al.
Density measurements and modelling of loaded and unloaded aqueous solutions of MDEA (N-methyldiethanolamine), DMEA (N,N-dimethylethanolamine), DEEA (diethylethanolamine) and MAPA (N-methyl-1,3-diaminopropane)
Int. J. Greenh. Gas Control
(2014) - et al.
CO2 post combustion capture with a phase change solvent. pilot plant campaign
Int. J. Greenh. Gas Control
(2014)
Carbon dioxide capture capacity of sodium hydroxide aqueous solution
J. Environ. Manage.
Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems
AIChE J.
Density and viscosity of monoethanolamine + water + carbon dioxide from (25 to 80) °C
J. Chem. Eng. Data
The viscosity of liquids
Nature
Viscosities for aqueous solutions of N-methyldiethanolamine from 313.15 to 363.15 K
J. Chem. Eng. Data
Standard substances for the calibration of viscometers
Bull. Bureau Standards
Solubility of N2O in and density, viscosity, and surface tension of aqueous piperazine solutions
J. Chem. Eng. Data
On the pressure dependence of the viscosity of aqueous sugar solutions
Rheol. Acta
Mixture law for viscosity
Nature
Physical properties of partially CO2 loaded aqueous monoethanolamine (mea)
J. Chem. Eng. Data
Volumetric properties and viscosities for aqueous AMP solutions from 25 ∘c to 70 ∘c
J. Chem. Eng. Data
Particle swarm optimization, Neural Networks, 1995.
Tables of the dynamic and kinematic viscosity of aqueous NaCl solutions in the temperature range 20-150 °C and the pressure range 0. 1-35 MPa
J. Phys. Chem. Ref. Data
Diffusivity of nitrous oxide in aqueous alkanolamine solutions
J. Chem. Eng. Data
Study on the change of refractive index on mixing, excess molar volume and viscosity deviation for aqueous solution of methanol, ethanol, ethylene glycol, 1-propanol and 1, 2, 3-propantriol at t = 292.15 k and atmospheric pressure
Res. J. Appl. Sci., Eng. Technol.
Cited by (12)
Modeling dynamic viscosities of multi-component aqueous electrolyte solutions containing Li<sup>+</sup>, Na<sup>+</sup>, K<sup>+</sup>, Mg<sup>2+</sup>, Ca<sup>2+</sup>, Cl<sup>−</sup>, SO<inf>4</inf><sup>2−</sup> and dissolved CO<inf>2</inf> under conditions of CO<inf>2</inf> sequestration
2022, Applied GeochemistryCitation Excerpt :Adopting thermodynamic models for solution can make viscosity models more predictive, but more parameters are used by some models. Leyendekkers (1979), Chandra and Bagchi (2000), Gering (2006), Aburto and Nägele (2013), Pinto and Svendsen (2015) proposed semi-empirical viscosity models different from the Eyring's absolute rate theory. By the way, some viscosity models, such as the Jones–Dole equation and the Goldsack–Franchetto model, can account for the initial decrease of viscosity of aqueous KCl (KBr, NH4Cl and so on) solution with increasing concentration.
Thermo-physical properties of CO<inf>2</inf> mixtures and their impacts on CO<inf>2</inf> capture, transport and storage: Progress since 2011
2019, Applied EnergyCitation Excerpt :Moreover, the SUPERTRAPP model was modified by changing reference fluid from propane to CO2. The NRTL-DVIS correlation was proposed by Pinto and Svendsen [58] to calculate the liquid viscosity of mixtures. The adopted mixing rule was a function of excess Gibbs energy, which was specifically represented using the NRTL model.
Viscosity measurements and modeling of loaded and unloaded aqueous solutions of MDEA, DMEA, DEEA and MAPA
2017, Chemical Engineering ScienceCitation Excerpt :Experiments for both unloaded and loaded solutions were performed with the exception of DMEA where loaded solutions were not measured. For both the unloaded and loaded solutions the NRTL-DVIS (Pinto and Svendsen, 2015) model was used to correlate the data. With the optimized parameters presented in this work, the model represents the experimental data within 5–6% deviation (AARD) in all cases but one.
Study of binary system glycerine-water and its colloidal samples of silver nanoparticles
2016, Journal of Molecular LiquidsDensity and Viscosity Calculation of a Quaternary System of Amine Absorbents before and after Carbon Dioxide Absorption
2021, Journal of Chemical and Engineering Data