Viscosity: zyxw A Critical Review of Practical Predictive and Correlative Methods zy WAYNE D. MONNERY*, WILLIAM Y. SVRCEK and ANIL K. MEHROTRA Deparhnent of Chemical and Petroleum Engineering, The University of Calgary, Calgary, Alberta T2N IN4 This paper reviews methods for the prediction and correlation of Newtonian viscosity for pure components and mix- tures of dilute gases, dense gases and liquids, focussing on those which are suited for practical engineering use. The methods reviewed were chosen because they are well known and accepted or appear potentially promising. They are categorized as theoretical, semi-theoretical or empirical and further distinguished as predictive or correlative. Brief derivations with relevant equations and discussions on limitations and reliability of results are presented. In addition, the applicability and average deviations for each method are tabulated, with the recommended methods clearly stated. Furthermore, some gaps in viscosity predictionkorrelation are identified and promising approaches are discussed. On examine dans cet article des methodes de prediction et de correlation de la viscositt newtonienne pour des com- posants purs et des melanges de zyxwvuts gaz dilues, de gaz denses et de liquides, en particulier celles qui sont bien adapttes zy i la pratique du genie. Les methodes examinees ont ttC choisies parce qu’elles sont bien connues et accepttes ou pour leur potentiel; on les a classifikes selon leur nature theorique, semi-theorique ou empirique, puis on a introduit une sous-classification selon leur capacite predictive ou correlante. Une brkve demonstration des equations pertinentes est presentee ainsi qu’une analyse des limites et de la fiabilite des rksultats. Par ailleurs, pour chaque methode, I’applicabilite et les Ccarts moyens sont tabules et les methodes recom- mandks sont clairement identifiees. Enfin, certains ecarts de prediction ou de correlation de la viscositk sont signales et des techniques prometteuses sont discuttes. Keywords: viscosity, prediction, correlation, dilute gases, dense gases, liquids, pure components, mixtures. zy ‘ n the chemical and petroleum industries, viscosity of pure I components and mixtures is an important property in hydraulics calculations for surface facilities, pipeline systems and flow through porous media. With the increased popularity of process and reservoir simulators, there is a need for a consistent, reliable and accurate analytical predictive method for viscosity calculations. Gas phase viscosity is primarily a function of momentum transfer by translation of the molecules with relatively few collisions and has been described by kinetic theory of gases. In dense gases and liquids, however, the momentum transfer is dominated by collisions and interacting force fields between the densely packed molecules. The theoretical description of liquids is difficult due to these intermolecular forces, which consist of short range effects such as repulsions and hydrogen bonding, wide range effects such as electrostatic effects (mul- tipole moments) and long range effects such as attractions. Inclusion of these effects in models is typically through a simplified treatment. zyxwvutsr A further complication is the structure and degree of disorder between the molecules. There is no widely accepted simple theoretical method to calculate vis- cosity of liquids. Several models for predicting the viscosity of pure com- ponents and mixtures are available in an abundance of liter- ature with excellent reviews available by Reid et al. (1977, 1987) Touloukian et al. (1973, Stephan and Lucas (1979) and Viswanath and Natarajan (1989). The available models range from highly theoretical to entirely empirical. Viscosity prediction models for pure components can be categorized as shown in Figures 1 and 2. Mixtures can be categorized as shown in Figure 3. Semi-theoretical models refer to those which have a theoretical basis or framework but the parameters are adjustable and determined from experimental data. Mixture viscosity equations refer to the mixture vis- cosity as a function of the viscosities of the pure components which comprise the mixture. *Author to whom correspondence should be addressed. This paper critically reviews the most widely known and accepted models from each category. Detailed discussions are presented and, for completeness, relevant equations have been provided in most cases. The models have been summarized in Table 1. The main text discusses our current state of knowledge. Important gaps in our knowledge and some pmmis- ing research directions are discussed at the end of the paper. Gases and Vapours THEORETICAL METHODS The theoretical models for gas or vapour phase viscosi- ties are based on the lunetic theory of gases described in detail in many references of which two of the most well known are Hirschfelder et al. (1954) and Chapman and Cowling (1952, 1970). The most simple kinetic model for gases assumes all molecules to be noninteracting rigid spheres of diameter zyxwv u and mass m moving at some mean velocity and colliding with other such molecules after moving a “mean free path” distance. Simple kinetic theory gives the following expression for dilute gas viscosity: zyx 770 = (2/3P) [ (rnk7)%7*] . . . . . . . . . . . . . . . . . (1.1) If the molecules attract or repel one another due to inter- molecular forces, the Chapman-Enskog (CE) theory is typi- cally applied. The Chapman-Enskog theory treats the interactions between colliding molecules in detail and is well described in the above references as well as by Reid and Gubbins (1973) and McQuarrie (1976). In general terms, the solution for the viscosity is written: qc- = (5/16*”2)[(mk~”2/(u2n2,2(T*))] . . . . . . (1.2) which is very similar to the simplified treatment except for the constant and the inclusion of the collision integral n2*2(r*). In practical units, Equation (1.2) may be written as : THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 73, FEBRUARY, 1995 3