Multiphase chemical and polymer phase equilibria calculations

A stoichiometric and a non-stoichiometric multiphase reactive flash algorithm were developed. These algorithms used a successive substitution mechanism to update fugacity coefficients in an outer loop. A nested inner loop solved the elemental balances and reaction equilibria requirements with a Newton-Raphson procedure. The inner loops in both cases were convex and quickly converged. Average chemical potentials for each species were used to define the reference phase chemical potentials.;The reactive flash routines were initiated with the maximum number of phases: one more than the number of components. Phases were combined as they became identical at each iteration. The tangent plane distance was incorporated into the unnormalized mole fractions of each phase so that phase stability could easily be examined during each iteration of the outer loop. This feature allowed incipient phases to be determined.;Both algorithms performed well in predicting the multiphase equilibria of methanol synthesis from carbon dioxide and hydrogen. An excess free energy mixing rule for a cubic equation of state was developed and used with the non-stoichiometric algorithm to calculate the conversion of methanol and isobutene to MTBE over a range of compositions. An association model for sulfur allotropes and sulfanes was used with the non-stoichiometric technique to successfully predict sulfur vapour pressures, enthalpies of vapourization and sulfur solubilities in hydrogen sulfide.;An algorithm to calculate isobaric lines of constant phase fraction in a polydisperse polymer/solvent system was developed. When a phase fraction of 0 or 1 was used, the lines represented the cloud and shadow point curves. A functional approach to continuous thermodynamics was employed using the Sanchez-Lacombe equation of state to model the components. Five scalar equations defined a single point on a curve and could be solved quickly using a Newton-Raphson method. Required integrations were done using a fifth order Runge-Kutta technique or a Gaussian quadrature technique.;The cloud point curves for a polyethylene/n-hexane system (Mn = 8000, Mw = 177000) showed an unstable critical point and a LLL point when the polyethylene was modeled with a log-normal distribution. Polyethylene modeled with the Shultz-Flory distribution did not show the same three phase point nor the unstable critical point.;A preliminary investigation into a multiphase polymer flash. using continuous thermodynamics was done. The Sanchez-Lacombe equation of state was used to represent the components. Both a successive substitution approach and a Newton-Raphson approach were used to solve the scalar equations that defined the equilibrium. The development of the algorithm allowed incipient phases to be determined.;It was found that a damped successive substitution method was more reliable than using a combination of the successive substitution and Newton-Raphson techniques. Additional studies into initiation techniques and the effective use of a Newton-Raphson step to decrease convergence time are recommended.