Helmholtz vs Entropy Scaling Approach for Viscosity Based on the GERG-2008 Equation of State

OSCAR THERAN; FEDERICO BENELLI; MARTÍN CISMONDI

Campinas

Congreso; XII IBEROAMERICAN CONFERENCE ON PHASE EQUILIBRIA AND FLUID PROPERTIES FOR PROCESS DESIGN; 2022

In the natural gas industry, furthermore to an accurate knowledge of thermodynamicproperties, it is of great importance to have a good approximation of transport properties suchas viscosity over a wide range of pressure and temperature conditions. The study of theseproperties has different industrial applications, ranging from processing to storage andtransport of natural gas.In the last decades, different approaches have been proposed to correlate fluidviscosities with different properties obtained from an equation of state. In parallel, Kunz andWagner developed a very accurate equation of state for the calculation of thermodynamicproperties of natural gas and related mixtures, known as GERG 2008. This equation of statecalculates Helmholtz’s free energy as a function of density, temperature, and composition. Inrecent work, Mairhofer presented a viscosity model with a residual entropy scaling approachbased on the GERG 2008 equation of state. On the other hand, Gonçalves et al. recentlyproposed a new Helmholtz energy scaling approach for viscosity calculation using the PCP-SAFT as the equation of state, whose fundamental idea we adopt to implement it with theGERG 2008 and compare with other approaches.In this work, a simple model based on the Helmholtz free energy is proposed tocalculate the viscosity of natural gases and related mixtures. This Helmholtz scaling approachwill apply the Chapman-Enskog relation as the reference viscosity and the GERG 2008 as theequation of state to calculate the viscosity of the fluid of interest.72This study aims to present the predictions of natural gas viscosities, evaluating theaccuracy of the Helmholtz scaling approach against other approaches such as residual entropyscaling. It is assumed that the deviations presented will have their origin in the approach usedto calculate the viscosity and not in the equation of state, since the GERG 2008 has beenadopted as an ISO standard, presenting very precise results in the calculation ofthermodynamic properties for natural gases and its mixtures. This will allow comparing suchapproaches on a more objective basis than in most works using engineering equations of statewith a certain level of error in the thermodynamic properties, which are highly dependent onpressure and temperature conditions.The calculation of the thermodynamic properties will be performed using PyForFluids(Python-Fortran-Fluids), a Python package focused on the calculation of multicomponentfluids properties and phase equilibrium based on Equations of State (EoS). PyForFluids,developed in our Fluids Thermodynamics Group (GTF-IPQA), will be presented in a separatework at EQUIFASE 2022 and includes the implementation of the GERG 2008 equation tocalculate both the ideal and residual Helmholtz free energy, used to calculate viscosities.- Cliff I. S. Gonçalves, Gabriel M. Silva, Papa M. Ndiaye and Frederico W. TavaresIndustrial & Engineering Chemistry Research 2021 60 (25), 9231-9245.- Jonas Mairhofer, Industrial & Engineering Chemistry Research 2021 60 (6), 2652-2662.- O. Kunz and W. Wagner, J. Chem. Eng. Data 2012, 57, 11, 3032–3091.Keywords: Viscosity model , GERG-2008, Helmholtz Free Energy, Natural Gas, PyForFluids.