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464752 19th Century Meet the 21st Century: Scaling Batch Reactors

Since the mid-1950’s, the cost of computation via digital computers has decreases annually. With the invention of the personal computer and user friendly software since the mid-1980’s, the cost of computation has become miniscule. The chemical processing industry has embraced computation as a means for modifying its historic process development procedure. Today, we use reaction data gathered from a laboratory-sized batch reactor to model as large a batch reactor as deemed safe to commission and operate based on that laboratory data.

To model a batch reactor via computation, we first derive the differential equation d[P]/dt = R where [P] is the concentration of product P (moles/m^{3}) and R is the formation of P by chemical reaction (moles/m^{3}*s or moles/m^{3}*min). Our task is to determine R by one of four methods. Those methods are

- guess the concentration dependence of R
_{P}, solve the above differential equation analytically, plot the resulting dependent variable as a function of time, then calculate k, the rate constant, from the slope of the line; - determine the concentration dependence of R
_{P}using the initial concentration experimental method, then calculate k; - determine the concentration dependence of R
_{P}using the initial time central difference method, then calculate k; - determine the concentration dependence of R
_{P}using the initial time polynomial method, then calculate k.

These procedures were developed between 1890 and 1940. Today's computing power and user-friendly software allow us to develop a different procedure for determining the kinetics of a batch reaction and to scale that reaction into ever-larger batch reactors.

This presentation discusses a new method for determining the kinetics of a reaction occurring in a batch reactor and it discusses how to use this new method to scale the heat transfer requirements of a commercial-sized reactor designed for the reaction in question.

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