USE OF A TWO-DIMENSIONAL PSEUDO-HOMOGENEOUS MODEL FOR THE STUDY OF TEMPERATURE AND CONVERSION PROFILES DURING A POLYMERIZATION REACTION IN A TUBULAR CHEMICAL REACTOR UPORABA DVODIMENZIONALNEGA PSEVDOHOMOGENEGA MODELA ZA [TUDIJ TEMPERATURE IN PROFILA PRETV

Abstract

A two-dimensional pseudo-homogeneous model is used to study temperature and conversion profiles during the polymerization reaction of low-density polyethylene (LDPE) in a tubular chemical reactor. This model is integrated with the Runge-Kutta 4 th -order semi-implicit method, using orthogonal collocation to transform a system of complex equations into the ordinary differential ones, with respect to the heat and mass transfers involved. Ethylene polymerization has been simulated over a range of temperatures and pressures and according to the mechanisms of radical polymerization. The results of several tests, carried out under the conditions similar to those of an industrial-scale polymerization, are presented. The influences of the initial temperature T 0 , the total pressure P t and the ratio L/D (the main dimensions of the reactor) on the profiles of the temperature and conversion rates are tested and analyzed to predict the behavior and performance of the tubular chemical reactor considered. The focus was on the effect of an increase in the initial temperature T 0 since such a rise results in a decrease in T c (hot spot) appearing at the entrance of the reactor on the one hand, and in an improved conversion on the other hand. An opposite effect is observed for P t since a pressure increase will result in a rapid rise in T c and a decrease in the conversion. The ranges of pressures and temperatures are thus limited by the system performance: excessive pressures must be avoided and working temperatures must be chosen in the range where the polymerization reaction is very fast; such conditions allow not only a good conversion, but also a resulting polymer with a low crystallinity and, thus, a low density. In the present work the effect of the L/D ratio was also studied in order to find the most suitable ratio that permits the best evacuation of the heat released during the polymerization. Keywords: modeling, tubular reactor, simulation, low-density polyethylene, pseudo-homogeneous two-dimensional model Dvodimenzijski psevdohomogeni model je bil uporabljen za {tudij temperature in profila pretvorbe med reakcijo polimerizacije polietilena z nizko gostoto (LDPE) v cevastem kemijskem reaktorju. V model je bila vklju~ena Runge-Kuttova semiimplicitna metoda 4. reda z uporabo ortogonalne kolokacije za pretvorbo sistema kompleksnih ena~b v navadne diferencialne ena~be glede na vklju~en prenos toplote in mase. Simulirana je bila polimerizacija etilena v {ir{em podro~ju temperature in tlaka skladno z mehanizmom radikalne polimerizacije. Predstavljenih je ve~preizkusov polimerizacije, izvedenih v razmerah, podobnih industrijskim. Preizku{en in analiziran je bil vpliv za~etne temperature T 0 , celotnega tlaka P t in razmerja L/D (glavne dimenzije reaktorja) na profil temperature in hitrost pretvorbe, da bi bilo mogo~e napovedati pona{anje in zmogljivost uporabljenega cevastega reaktorja. Pozornost je bila usmerjena na u~inek povi{anja za~etne temperature T 0 , ker to po eni strani vpliva na zni`anje T c (vro~a to~ka) na vstopu v reaktor, po drugi pa na izbolj{anje pretvorbe. Nasproten u~inek je bil opa`en za P t , ker se narastek tlaka izra`a v hitrem povi{anju T c in zmanj{anju konverzije. Obmo~je tlaka in temperature je torej omejeno z zmogljivostmi sistema: treba se je izogibati prekomernemu tlaku, delovne temperature pa je treba izbrati v obmo~ju, kjer je reakcija polimerizacije zelo hitra; take razmere omogo~ajo dobro konverzijo, in nastali polimer ima majhno kristalini~nost in s tem nizko gostoto. V tem delu je bilo preu~evano tudi razmerje L/D, da bi dobili najbolj primerno razmerje, ki omogo~a najbolj{i odvod toplote, ki se spro{~a med polimerizacijo