SHORTER COMMUNICATION DENSITY VARIATIONS IN A REACTOR DURING LIQUID FULL DIMERIZATION M. GOLOMBOK (MEMBER) and J. DE BRUIJN Shell Research and Technology Centre, Amsterdam, The Netherlands I n a liquid full plug ¯ow reactor during lower ole®n dimerization, the assumption of constant density is not validÐthe volume of a plug changes as it proceeds along the reactor. The observed kinetics depend on the density variation in the reactor as the conversion proceeds towards a distribution of oligomersÐand this in turn is a function of the reactor conditions for the ole®n dimerization. The net effect of considering density changes in elucidating global kinetics is to increase the effective reaction order; this is a function of the degree of oligomerization. The effects are demonstrated with a simple analytical model based around varying conditions during dimerization of 1-butene over an amorphous catalyst. Keywords: kinetics; packed bed; polymerization; reaction engineering; liquid-liquid tubular reactors; density INTRODUCTION Liquid reactions occur at a number of crucial points in the petrochemical industry and are reasonably well characterized both in batch and ¯ow reactors 1 . In most cases, the reactions occur in well stirred tanks and any changes in density arising from reaction or temperature variations are small enough to be ignored. Tubular reactors are used predominantly for continuous gas phase reactions. However, they are also used for packed bed gas to liquid conversions such as oligomer- ization (i.e., low degree polymerization). In general, polymer products are quite different in form and property from their monomer starter material. Product may be dissolved or suspended in the reactant or precipitate out. Low degree polymerizations, such as the dimerization associated with a number of homogeneous catalytic processes to produce high octane gasoline 2 have a less clear distinction between reactant and product and under typical process conditions, monomer and oligomer (principally dimer) may be well mixed. The distinguishing characteristic in these reactions is the change in density that occurs along the reactor. During light ole®n dimerization, the reaction is carried out at an elevated pressureÐfor thermodynamic reasons and also to avoid the problems of gas to liquid conversions which would be encountered at atmospheric pressure. The dimer product (containing some trimer and tetramer) has a different density and this results in modi®cations to the apparent kinetics, which are demonstrated below. This effect is also seen in the synthesis of ethylene glycols from ethylene oxide and water where an extra level of complication arises from the aqueous and organic liquid phases. Although strictly, this is an addition rather than polymerization process, the effects of liquid density variation on the kinetics still apply. DENSITY VARIATIONS IN A LIQUID FULL REACTOR The volume of a plug changes as it proceeds along the reactor, because the conservation of mass and different densities of reactant (butene) and product (octene and higher oligomers) require that this volume changes as it passes through the reactor. This problem is well known for gases and the solution is relatively simple using Charles’s law, where the change in the number of moles during a fractional conversion dX determines the change in volume, and thus in density 3 . In a liquid full system, the problem is somewhat more complex and surprisingly is not handled in any of the standard references or textbooks. The effects of spatial ¯uctuations of density on bimolecular kinetics have been discussed 4 . A recent study considered density effects on kinetics in tank reactors 5 . Because the rate is determined by reaction between moles rather than mass which is conserved, the concentration of reactant must be determined at an arbitrary conversion X. By de®nition N r = N r0 (1 ê X ) (1) The volume of a mixture can be calculated where XN r 0 moles of reactant will have reacted to yield XN ro /2 moles of product where the reaction is taken to be exclusively dimerization. (By comparing the densities of lower order oligomers below, it can be shown that this assumption is valid.) Since alkenes are forming other alkenes and are thus of a similar molecular and non polar character, it is reasonable to assume that there will be negligible volume change on mixingÐparticularly at high pressures where repulsive forces presumably dominate. The volume may thus be estimated by adding the volume of each individual component using the molar volumes n m . which are simply the inverse of the pure liquid molar densities M/», i.e. the 145 0263±8762/00/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol 78, Part A, January 2000