The aim of modeling polymerization processes of high-pressure low-density polyethylene (LDPE) in tubular reactors is to improve the processability of the polymers produced by varying the reaction conditions. As the processability is inherently coupled to the polymeric microstructure the model has to combine heat transfer and reaction kinetics to yield detailed information about molecular weight distributions and degrees of long- and short-chain branching. Furthermore it is highly desirable to obtain chain-length differentiated branching densities. Using the software package PREDICI a model has been developed that allows to compute temperature and pressure profiles and to obtain detailed information about the polymer microstructure. Due to the complexity of solving the coupled equations for the heat and material balance as well as differential equations needed to determine the chain-length differentiated quantities it is reasonable to use a two-stage toolkit. Therefore in a first step temperature and pressure profiles are computed which are then used for the calculation of chain-length differentiated observables.
As heat transfer processes are mainly governed by average reaction condition it is sufficient to compute the temperature and pressure profiles using moments kinetics. This ensures a fast convergence of iterative procedures needed to account for counter cooling. Complex cooling scenarios and multiple injections can be described. Special attention is dedicated to the transfer of kinetic data from independent laboratory experiments. By comparing model results with industrial data for different LDPE grades the model also serves as a test whether rate constants obtained on laboratory scale reactors can be directly transferred to large scale industrial plants. To compare computed distribution data directly with those from standard SEC and light scattering measurements, the results are modified to account for experimental band broadening effects assuming randomly distributed branches.
Having computed the temperature and pressure profiles using moment kinetics chain-length differentiated degrees of branching can be calculated using the concept of boundary density functions in combination with the h-p Galerkin method implemented in PREDICI. For statistical processes this approach allows to reduce the two-dimensional problem (chain length and number of branches) to two one-dimensional subproblems: the rigorous computation of the molecular weight distribution and the evaluation of the leading moments of the branching density distribution. Assuming a binomial or Wesslau distribution for the branching density bivariate chain-length/degree of branching distributions, which play a crucial role for structure-property relationships, can be obtained in a reasonable timeframe.
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