A van der Waals-type equation of state for fluids with associating molecules

Abstract

The basic assumptions of van der Waals theory are contained in two well-known concepts: excluded volume (repulsive forces) and a homogeneous, isotropic field potential (attractive forces). We have superimposed on these, one more well-known concept: the existence of dimers, trimers, etc., at chemical equilibrium. With Following the basic concepts of van der Waals, we postulate that when nT moles of fluid occupy volume V at temperature T, the pressure P can be expressed by P = Phs + Pa t [1] where subscript hs stands for hard sphere (repulsive forces) and subscript att stands for attractive forces.We rewrite the first contribution in terms of the compressibility factor Zhs Ph, = nTRTZhS/ V [2] where R is the gas constant. We introduce the reduced density t defined byThe attractive-force contribution to the pressure is rewritten in the form Patt = -(a/b2)7ratt(4) [4] where lratt is a function only of {. Xj+l.There is abundant experimental evidence which indicates that molecular clusters, as postulated, exist not only for polar and hydrogen-bonded molecules, but also for nonpolar molecules such as argon (7-9).Let .3 stand for the mole fraction of species i (monomer, dimer, etc.) [7] where a and b refer to the monomer.We also introduce the following reasonable simplifying assumptions bj= jb a1 = ja [3] [8] [9] where b is proportional to the volume of the hard-sphere molecules.The total number of moles nT is not a constant because, for an associating fluid, it depends on the density and the temperature. That is, the "pure" fluid is considered here to be a mixture of monomers, dimers, trimers, etc. Therefore, 1 depends on the "true" composition of the fluid. In the limit (all molecules are monomers) b = 7r NAV &3/6, where NAV is Avogadro's number and a is the collision diameter.where a and b refer to the monomer.Conservation of mass requires that the total number of moles nT is related to no (the number of moles that would exist if there were no association) by[10] nTEj&a = nOCombining Eq. 10 with Eqs. 6-9, we obtain a = (no/nT)2a and b = (nO/nT)b.[11] [12]

Chemical, quasi‐chemical and perturbation theories for associating fluids

“…Panayiotou (1 989, 1990) combined chemical theory into the Sanchez-Lacombe equation of state (Sanchez and Lacombe, 1976;Lacombe and Sanchez, 1976), a lattice fluid theory, to describe thermodynamic properties and phase equilibria of pure alcohols and mixtures of alcohols with alkanes. His hydrogen bonding expressions are similar to those derived by Heidemann and Prausnitz (1976) and by Ikonomou and Donohue (1986).…”

“…When physical interactions are considered, the equations for chemical equilibria and physical equilibria usually are solved simultaneously by a trial-and-error procedure. Heidemann and Prausnitz (1976) showed that it is possible to solve for the chemical equilibria analytically and combine the results into the equation of state to solve for phase equilibria.…”

“…If there is more than one associating component in the system, this approach becomes cumbersome. Heidemann and Prausnitz (1976) showed that it is possible to solve analytically for the chemical equilibria within the equation of state so that the conditions of the phase equilibria can be solved directly; this has led to the development of several new equations of state for hydrogen-bonding systems. Ikonomou and Donohue (1986Donohue ( , 1988 applied this approach using the perturbed-anisotropic-chain theory (PACT) and obtained a closed form equation of state, the associated-PACT (APACT).…”

“…7. The ratio P+,+,/+,+, finally is obtained (Heidemann and Prausnitz, 1976): where p is the density, p = l/uo. In Eq.…”

Supercritical thermodynamics of sulfur and nitrogen species. Final technical report, October 1, 1991--September 30, 1994

“…In order to satisfy this last condition, and the considerations of an infinite equilibrium model, Heidemann and Prausnitz (1976) developed a new mixing rule as follows considering this series of equilibria:…”