Kinetic parameter estimation with nonlinear mixed-effects models

Applications of fixed-effects models for kinetic parameter estimation using multiple batch experiments assume that all batches are independent. Multiple longitudinal batch experiments with time series data often exhibit biased residuals, violating this assumption. Nonlinear mixed-effects models offer an alternative approach to account for the two types of random experimental variation resulting from longitudinal experiments: the measurement error for each data point and the random batch-to-batch variation between experiments. Our case study models a single response hydrogenation reaction of acetophenone to 1-phenylethanol over a copper catalyst in a trickle-bed batch reactor system. Implementation of a mixed-effects model using nonlinear programming to model the batch reactor system results in parameter estimates with less bias compared to a fixed-effects model. We then apply the Bayesian notion of probability shares as a methodology for model discrimination between several candidate mixed-effects models, and demonstrate the ability to elucidate additional model information through the application of mixed-effects models when the use of fixed-effects models is inappropriate.