An excess Gibbs free energy based model to calculate viscosity of multicomponent liquid mixtures

https://doi.org/10.1016/j.ijggc.2015.09.003Get rights and content

Highlights

  • We propose a correlation to calculate the viscosity of multicomponent mixtures.

  • The model uses an analogy to excess Gibbs energy (GE) models.

  • In this work, we chose the functional form of the NRTL model to represent the GE.

  • The resulting model is called NRTL-DVIS and it requires few adjustable parameters.

  • The model represented the tested systems with good accuracy.

Abstract

Solution densities and viscosities are important parameters for the design and simulation of absorption processes. Accurate models are needed and in this work, a new model for calculating the liquid viscosity of mixtures is presented. The model uses an analogy to excess Gibbs energy models to account for the deviation from a simple mixing rule based on the pure component viscosities. In this work, we chose the functional form of the NRTL model to represent the excess Gibbs energy and the resulting model is referred to as NRTL-DVIS. Eleven systems (eight binaries and three ternary) were chosen for testing the accuracy of the model. The ternary systems were built from the optimized binaries and pure component systems. With few adjustable parameters, the NRTL-DVIS model represented the tested systems with good accuracy. With few exceptions the calculated total deviation (AARD) was within 3.5%. The NRTL-DVIS model shows better accuracy than other models proposed in the literature.

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.

lnη=A+BT+C·lnT

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).

lnη=i=1NCxilnηi

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, ηH2O is the viscosity of pure water in mPa.s and T is the temperature in K. The studied systems are given in Table 1.

ϕ=2.1482T281.585+8078.4+(T

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

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