Prediction interval-based modelling of polymerization reactor: a new modelling strategy for chemical reactors

Precise and reliable modelling of polymerization reactor is challenging due to its complex reaction mechanism and non-linear nature. Researchers often make several assumptions when deriving theories and developing models for polymerization reactor. Therefore, traditional available models suffer from high prediction error. In contrast, data-driven modelling techniques provide a powerful framework to describe the dynamic behaviour of polymerization reactor. However, the traditional NN prediction performance is significantly dropped in the presence of polymerization process disturbances. Besides, uncertainty effects caused by disturbances present in reactor operation can be properly quantified through construction of prediction intervals (PIs) for model outputs. In this study, we propose and apply a PI-based neural network (PI-NN) model for the free radical polymerization system. This strategy avoids assumptions made in traditional modelling techniques for polymerization reactor system. Lower upper bound estimation (LUBE) method is used to develop PI-NN model for uncertainty quantification. To further improve the quality of model, a new method is proposed for aggregation of upper and lower bounds of PIs obtained from individual PI-NN models. Simulation results reveal that combined PI-NN performance is superior to those individual PI-NN models in terms of PI quality. Besides, constructed PIs are able to properly quantify effects of uncertainties in reactor operation, where these can be later used as part of the control process. © 2014 Taiwan Institute of Chemical Engineers.

Animal Guts as Ideal Chemical Reactors: Maximizing Absorption Rates

I solved equations that describe coupled hydrolysis in and absorption from a continuously stirred tank reactor (CSTR), a plug flow reactor (PFR), and a batch reactor (BR) for the rate of ingestion and/or the throughput time that maximizes the rate of absorption (=gross rate of gain from digestion). Predictions are that foods requiring a single hydrolytic step (e.g., disaccharides) yield ingestion rates that vary inversely with the concentration of food substrate ingested, whereas foods that require multiple hydrolytic and absorptive reactions proceeding in parallel (e.g., proteins) yield maximal ingestion rates at intermediate substrate concentrations. Counterintuitively, then, animals acting to maximize their absorption rates should show compensatory ingestion (more rapid feeding on food of lower concentration), except for the lower range of diet quality fur complex diets and except for animals that show purely linear (passive) uptake. At their respective maxima in absorption rates, the PFR and BR yield only modestly higher rates of gain than the CSTR but do so at substantially lower rates of ingestion. All three ideal reactors show milder than linear reduction in rate of absorption when throughput or holding time in the gut is increased (e.g., by scarcity or predation hazard); higher efficiency of hydrolysis and extraction offset lower intake. Hence adding feeding costs and hazards of predation is likely to slow ingestion rates and raise absorption efficiencies substantially over the cost-free optima found here.

Animal Guts as Nonideal Chemical Reactors: Partial Mixing and Axial Variation in Absorption Kinetics

Animal guts have been idealized as axially uniform plug-flow reactors (PFRs) without significant axial mixing or as combinations in series of such PFRs with other reactor types. To relax these often unrealistic assumptions and to provide a means for relaxing others, I approximated an animal gut as a series of n continuously stirred tank reactors (CSTRs) and examined its performance as a Function of n. For the digestion problem of hydrolysis and absorption in series, I suggest as a first approximation that a tubular gut of length L and diameter D comprises n=L/D tanks in series. For n greater than or equal to 10, there is little difference between performance of the nCSTR model and an ideal PFR in the coupled tasks of hydrolysis and absorption. Relatively thinner and longer guts, characteristic of animals feeding on poorer forage, prove more efficient in both conversion and absorption by restricting axial mixing, in the same total volume, they also give a higher rate of absorption. I then asked how a fixed number of absorptive sites should be distributed among the n compartments. Absorption rate generally is maximized when absorbers are concentrated in the hindmost few compartments, but high food quality or suboptimal ingestion rates decrease the advantage of highly concentrated absorbers. This modeling approach connects gut function and structure at multiple scales and can be extended to include other nonideal reactor behaviors observed in real animals.

Chemical Reactors. Problem 1: A simple ODE (chaos in the atmosphere) (2011-2012 Course)

Wording of problem 1: A simple ODE (chaos in the atmosphere).

Chemical Reactors. Problem 2: Constant pressure adiabatic stirred batch reactor with variable heat capacities (2011-2012 Course)

Wording of problem 2 (week 3, 17/10/11).

Chemical Reactors. Problem 2: Constant pressure adiabatic stirred batch reactor with variable heat capacities. Solution (2011-2012 Course)

Chemical Reaction Engineering. Course 2011-12. Solution of problem 2: constant pressure adiabatic stirred batch reactor with variable heat capacities.

Chemical Reactors. Problem 3: Isothermal plug flow reactor with multiple reactions (2011-2012 Course)

Wording of problem 3: Isothermal plug flow reactor with multiple reactions.