Simultaneous estimation of the heat of reaction and the heat transfer coefficient by calorimetry: estimation problems due to model simplification and high jacket flow rates—theoretical development

Abstract

In batch and semi-batch reactors, the heat of reaction Q ˙ R is normally estimated using calorimetry. If all temperatures and volumes are measured correctly and the measurements are filtered sensibly, the results are usually very good. For many applications, the overall heat transfer coefficient k also needs to be known. In heat balance calorimetry k and Q ˙ R can be calculated simultaneously, if the correct model is used. It is shown that the commonly used model simplifications pose serious problems for large reactors. Subsequently a sensible model extension is discussed. For this extension we propose the application of an Extended Kalman Filter (EKF) to estimate the heat of reaction ( Q ˙ R ) and the heat transfer coefficient ( k) simultaneously, as the EKF can handle the model extension well. Our emphasis lies on three important factors. Firstly and mainly, the jacket of a jacketed reactor is generally modelled as a stirred tank. When looking at real jacketed reactors, the jacket behaves more like a plug-flow reactor. We propose a model extension to overcome this problem. Secondly, the heat transfer coefficient ( k) is for many reactions strongly dependent on the batch time and should therefore also be estimated. With the usual models, errors may result which can be corrected by the model extension. Thirdly, the flow rate through the jacket and the hold-up in the reactor strongly influence the estimation quality. With a lower jacket flow rate estimation quality increases but cooling decreases, a trade-off has to be made. Using an EKF, good estimation quality can still be achieved for high flow rates. However, the trade-off is considered and the tuning is adjusted to the flow rate. An optimal flow rate calculation is suggested. Finally, it will be shown that adding measurements in the jacket rather than in the reactor will improve calorimetric estimation for the proposed model extension.