Numerical Methods for Chemical Engineering: Applications in MATLAB
Written in a pedagogic style, this textbook unites the applications of numerical mathematics and scientific computing to the practice of chemical engineering.
TABLE OF CONTENTS Numerical Methods for Chemical Engineering: Applications in MATLAB
Example. Fitting Kinetic Parameters of a Chemical Reaction
Before proceeding, let us consider some simple examples of parameter estimation problems. We are studying the kinetics of the chemical reaction A + B ? C, which if assumed elementary, has the rate law
c A and c B are the concentrations of the two reactants in M, r R1 is the reaction rate per unit volume in M/s, and k 1( T) is a temperature-dependent rate constant in (Ms) ?1. We determine the value of k 1( T) by studying the behavior of well-characterized reactors such as a perfectly-mixed CSTR or a batch reactor (a well-mixed vessel with no inflow or outflow).
Fitting the rate law to steady-state measurements of a CSTR
For a CSTR, we measure k 1( T) by operating the reactor at steady state at constant volume V, constant volumetric flow rate ?, constant inlet concentrations 
, and measuring the outlet concentrations c j. We obtain a measurement of the rate though the balance on C,
Measurements of c A and c B are necessary to determine k 1( T) from (8.3). For each CSTR experiment, the set of predictor variables is x = [ c A c B]. The parameter that we wish to estimate is ? = [ k 1]. The response variable is y ( r) = [ r R1].
In...
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