Modeling derivative properties and binary mixtures with CO2 using the CPA and the quadrupolar CPA equations of state

Abstract

The cubic plus association (CPA) equation of state (EoS) is extended to include quadrupolar interactions. The quadrupolar term is based on a modification of the perturbation terms by Larsen et al. (Mol. Phys. 1977, 33, 4, 987) for a hard sphere fluid with a symmetric point quadrupole moment. The new quadrupolar CPA (qCPA) can be used without introducing any additional pure compound parameters. Alternatively a single additional adjustable parameter can be employed.To evaluate qCPA several pure compound properties are predicted. The model is furthermore evaluated for its ability to predict and correlate binary vapor-liquid equilibria (VLE) and liquid-liquid equilibria (LLE) of mixtures containing CO 2 and hydrocarbons, water, alcohols, or selected quadrupolar compounds.The results indicate that most pure compound property predictions are satisfactory but similar to other CPA approaches. When binary mixtures are con- qCPA can accurately correlate both the phase behaviour of CO 2 + hydrocarbon mixtures as well as mixtures of CO 2 + a self-associating compound.

Uncertainty analysis of the CPA and a quadrupolar CPA equation of state – With emphasis on CO2

“…We note that, as expected from the work of Tsivintzelis et al [28] and Bjørner and Kontogeorgis [33], excellent agreement to saturated vapor pressures and It can be seen from table 3 that small confidence intervals are obtained as well as low correlations between b 0 and both Γ and c 1 for approach E. A Table 2: Correlated pure compound parameters and %AADs in saturated liquid density and saturated pressure for CO 2 with the CPA EoS (Approaches A-D) and the qCPA (Approaches E-F). The parameters are correlated in the temperature range Tr = 0.7 − 0.9.…”

“…Each subsample is subsequently used to calculate output properties of interest. It is assumed that the error distribution of the input parameters follow the kernel distribution obtained from bootstrapping, although It is well-known that the isochoric heat capacity is a challenging property to predict even with modern equations of state [33,56]. It is believed that this is primarily due to structural issues with the temperature dependence of the for approach D, smaller, but still present, for approaches E and F and almost non-existent for approach A.…”

“…for the approaches using more adjustable parameters, result in higher uncertainties in the non-fitted derivative properties. The large uncertainties for the isochoric heat capacity in figure 7b suggest that the uncertainty in pure compound parameters lead to significant uncertainties in the temperature is such a difficult property to calculate for many equations of state [33,56]. However, the deviation from the pseudo-experimental data is One of the primary objectives of most equations of state is the accurate description of phase equilibria [56,57].…”

“…In the latter case we employ the quadrupolar CPA (qCPA) which is a recent extension of CPA to quadrupolar fluids suggested by Bjørner and Kontogeorgis [33]. Equations for CPA and qCPA can be found in appendix Appendix A or 95 in the literature [1,[33][34][35][36].…”

“…Equations for CPA and qCPA can be found in appendix Appendix A or 95 in the literature [1,[33][34][35][36]. Two cases are evaluated when CO 2 is considered to be a quadrupolar molecule, one where no additional adjustable parameter is employed and one where an additional volumetric parameter is employed.…”