Parametric sensitivity in tubular polymerization reactors

Abstract

A recent technique for studying the parametric sensitivity of chemical reactors is applied to tubular chain homopolymerization reactors. The sensitivities of the temperature maxima with respect to various parameters of the model are computed. Using conditions typically encountered for high-pressure polyethylene systems, it is found that the temperature sensitivities with respect to all the nine parameters have their maxima at approximately the same value of the feed initiator concentration, thus leading to a generalized sensitivity-based constraint for design. It is also found that, under usual conditions of operation, no significant design constraints on the feed temperature are indicated. Detailed sensitivity plots are presented, which could be used to obtain "safe" operating conditions. The effects of changing the most important parameters, the dimensionless heat of reaction and the dimensionless activation energy (ε), on the sensitivity envelope are also investigated. Our studies reveal that better estimates of ε than are available presently are required. Sensitivities of the number-average chain length maxima with respect to the same nine parameters are also computed. Under conditions where the steady-state hypothesis applies, estimates of ε these sensitivities can be obtained analytically. However, for the usual values of the parameters, and close to "sensitive" values of the feed initiator concentration, this hypothesis does not apply, and the chain length sensitivities need to be obtained numerically. In the absence of the gel effect, chain length sensitivities do not usually provide design constraints because of the very low monomer conversions encountered.