Prediction of Vapor and Liquid Viscosities from the Lawal-Lake-Silberberg Equation of State

ABSTRACT A difficulty in modeling multicontact miscibility processes is achievement of consistent, stable convergence of gas and oil phase compositions, densities, and viscosities as the critical point is approached. The use of an equation of state offers the advantage of a single, consistent source of calculating K-values and phase densities. The criterion of stable convergence viscosity in the vicinity of critical regions is not often met without fine tuning with laboratory data as phase viscosity correlations are usually developed independent of each other. The present study extends the van der Waals model to viscosity by drawing an analogy between the graphs of PVT and PμT. Vapor and liquid viscosities based solely upon pure component critical data and acentric factor were derived from the Lawal-Lake-Silberberg (LLS) equation of state for methane through eicosane, i-butane, neo-pentane, carbon dioxide, and nitrogen. The 6718 experimental data used cover a range of temperatures from −183°F to 482°F and pressure up to 20,000 psia. For the twenty-four components, the average absolute deviation of the predicted viscosities from experimental is 5.9%. A mixing rule which relates mixture parameters to composition and pure component constants is proposed and comparisons of 9,000 experimental data with computed viscosities for several binary, multicomponents, natural gases and complex systems resulted in an average absolute deviation of 3.5%. The extension of the mixing rules to predictions of reservoir oil viscosity was generally within +8% of the experimental values. Extensive comparisons of the LLS viscosity equation with other methods of predicting reservoir oil viscosity are made and found to be generally superior in ease of use and in accuracy. The prediction of vapor and liquid viscosities from the LLS equation of state makes the present work very attractive for compositional reservoir simulators and other applications which are repetitive in nature. The use of an equation of state to predict phase viscosities offers an opportunity to make calculations in the critical region without the computational problems commonly associated with that effort. The internal consistency and the convergence of vapor and liquid viscosities at the critical point have heretofore been unattainable.