Mathematical Modeling of Arborescent Polyisobutylene Production in Continuous and Semi-Batch Reactors
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Mathematical models are developed for arborescent polyisobutylene (arbPIB) production in continuous-stirred-tank and semi-batch reactors. The objective of the research is to assess how reactor type influences final polymer properties and to use the new semi-batch model for parameter estimation with existing literature data. A multidimensional method-of-moments technique is used to predict number and weight-average molecular weights and branching levels. The continuous stirred-tank reactor (CSTR) model developed is used to simulate arbPIB polymerization over a range of different residence times and inimer feed concentrations. It is shown that polydispersity and average branching level are higher for polymer produced in a CSTR compared to polymer produced in batch. It is also shown that operating a CSTR at long residence times and/or high inimer feed concentrations will result in an inability to reach steady-state operation due to the weight-average molecular weight increasing indefinitely. This range of instability for CSTR operation is larger for SCVCP than for inimer homopolymerization because of the relatively high apparent rate constant associated with the isobutylene comonomer reacting with an inimer branching agent. In addition, a semi-batch model is developed that incorporates a material balance on Lewis-acid concentration. Lumped parameters (containing true rate constants and equilibrium constants) are estimated using literature batch and semi-batch data for arbPIB. Two attempts are made to fit these data by applying different mechanistic assumptions. Unfortunately, parameters estimated from these studies are unable to provide simulation results that accurately fit the experimental data. It is recommended that additional experimental data be collected at various reaction conditions, including replicate semi-batch data, before improved modeling assumptions are developed.