Fundamental equation of state correlation with hybrid data sets G. Rutkai, 1 M. Thol, 2 R. Lustig, 3 R. Span, 2 and J. Vrabec 1, a) 1) Lehrstuhl f¨ ur Thermodynamik und Energietechnik, Universit¨at Paderborn, 33098 Paderborn, Germany 2) Lehrstuhl f¨ ur Thermodynamik, Ruhr-Universit¨ at Bochum, 44801 Bochum, Germany 3) Department of Chemical and Biomedical Engineering, Cleveland State University, Cleveland, Ohio 44115, USA (Dated: 11 July 2013) A strategy is proposed for empirical fundamental equation of state correlations for pure fluids on the basis of hybrid data sets, composed of experimental and molecular simulation data. Argon and hydrogen chloride are used as examples. Keywords: equation of state, molecular simulation, argon, hydrogen chloride I. INTRODUCTION The fundamental equation of state (FEOS) can be ex- pressed with various thermodynamic potentials 1 , e.g. in- ternal energy E(N,V,S), enthalpy H(N,p,S), Helmholtz energy F (N,V,T ) or Gibbs energy G(N,p,T ), with num- ber of particles N , volume V , pressure p, temperature T and entropy S. Any other thermodynamic property, which may or may not be measurable in the laboratory, is a linear or non-linear combination of derivatives with respect to the independent variables. Conceptual details for the present context are outlined in references 2,3 . The form F/T (N,V, 1/T ) is preferred for empirical correla- tions due to practical reasons 4 . A definition for its deriva- tives may be ∂ m+n (F/(RT )) ∂β m ∂ρ n β m ρ n ≡ A mn = A i mn + A r mn , (1) where R is the gas constant, β ≡ 1/T and ρ ≡ N/V . A mn can be separated into an ideal part A i mn and a residual part A r mn 5 . The ideal part can usually be obtained by independent means, e.g. spectroscopic data or ab initio calculation 3,6,7 . It is the residual part which is of concern here. An empirical FEOS correlation needs carefully selected thermodynamic data to be used in a fitting procedure. Unfortunately, the data availability today is insufficient. FEOS correlations with technical accuracy 4 covering the entire fluid region of technological interest are available for about 100 of roughly 1000 pure compounds of indus- trial relevance. For the remaining compounds, data sets are at best scarce so that FEOS correlations are hardly feasible. For mixtures, of course, the data availability is much worse. It is to be expected that the accuracy of the Helmholtz energy surface representation will increase if more A mn are used in fitting eq. (1). Consequently, the accuracy of any other thermodynamic property obtained from the a) Electronic mail: jadran.vrabec@upb.de FEOS should also increase. However, the overall infor- mation on the whole possible range of Helmholtz en- ergy derivatives from laboratory measurements is lim- ited: A r 01 = p/(ρRT ) - 1, A i 10 + A r 10 = H/(RT ) - A r 01 - 1 and A i 20 + A r 20 = -C v /R, where C v is the isochoric heat capacity. A 11 and A 02 cannot be accessed individually, because the measurable quantities, isobaric heat capac- ity C p and speed of sound w, are non-linear combina- tions of A 01 , A 20 , A 11 and A 02 . In molecular simulation such constraints can be entirely removed. The statisti- cal mechanical formalism proposed by Lustig allows for the simultaneous sampling of any A r mn in a single NVT simulation for a given state point 2,3 . II. MOLECULAR SIMULATION AND FEOS CORRELATION Recent progress in molecular simulation has shown that molecular interaction models have powerful predic- tive capabilities with respect to thermodynamic data 8 . The current standard is to match molecular models to real compounds based on laboratory vapor-liquid equi- librium (VLE) data. The typical accuracy of reproduc- tion is ±5% for vapor pressure and ±1% for saturated liquid density 9–16 . However, it is usually not known how molecular interaction models perform in homoge- neous regions. We performed simulations for some ten molecular models 9–16 representing fluids of very differ- ent nature at various state points in the homogeneous regions, and compared A r mn results with the best avail- able FEOS correlations from the literature. The results for hydrogen sulfide are shown in figure 1 as an exam- ple. There is agreement with the FEOS of Lemmon and Span 17 throughout. Only A r 02 shows a deteriora- tion, which was not considered individually in the fits of the FEOS 17 . Tests for other fluids also show promis- ing behavior. Additional examples (including argon and hydrogen chloride) are given in the supplementary mate- rial. We conclude that molecular interaction models may perform well in the fluid region, based on comparisons to reference FEOS correlations. Therefore, a valid FEOS correlation can be established