(311c) 19th Century Meet the 21st Century: Scaling Batch Reactors

The heart of every chemical process is the reactor. The majority of chemical reactions in the chemical processing industry occur in batch reactors. At the laboratory scale, batch reactors are reaction rate limited because they have large heat transfer surface area to reacting volume ratios. The same is generally true for pilot plant batch reactors. However, most commercial-size batch reactors are heat transfer rate limited because their heat transfer surface area to reacting volume ratios are small.

Since the mid-1950â??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-1980â??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/m³) and R is the formation of P by chemical reaction (moles/m³*s or moles/m³*min). Our task is to determine R by one of four methods. Those methods are

1. 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;
2. determine the concentration dependence of R_P using the initial concentration experimental method, then calculate k;
3. determine the concentration dependence of R_P using the initial time central difference method, then calculate k;
4. 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.