Nonlinear mixed-effects models for kinetic parameter estimation with batch reactor data

Traditional fixed-effects models based on nonlinear least squares or Bayesian methods of rate parameter estimation for batch reactor longitudinal data are problematic because such methods assume statistical independence between all measurements across multiple batches. For multiple longitudinal experiments, which yield time series data, such assumptions of independence are clearly inappropriate. Therefore, we investigate the application of nonlinear mixed-effects models for batch reactor experiments. Investigators in other fields use nonlinear mixed-effects models extensively to estimate accurate and nonbiased parameters for data sets with multiple correlated measurements. Such models may be superior for modeling batch reactor longitudinal experiments. Using single response data from a batch recycle trickle bed reactor system for the hydrogenation of acetophenone to 1-phenylethanol over a copper catalyst, we show less correlated parameters as well as improved lag plots and run sequence plots from a mixed-effects model relative to a fixed-effects Bayesian model.