The study of systems using modelling techniques

Abstract

This thesis describes the methodologies and techniques underpinning computer modelling. It also describes how these methodologies and techniques are encapsulated in the SAAM/CONSAM computer modelling software, and highlights the utility of computer modelling for the investigation of actual systems for which unanalysed data exist. Four systems were studied here, and models were developed for each system. The revegetation of bauxite refining residue, red mud, produced from alumina refi·ning is extremely difficult because of the high amount Na+ in the desilication product (DSP). Hence, an understanding of the Na+ chemistry in red mud is important for successful revegetation of red mud. A five compartment model was developed to describe the kinetics of Na+ release from red mud for both Na-K and Na-Ca exchange. The modelling results showed that sodium located in the external sites was released in about 6 hours and 3 days for K+ and Ca2+ exchange respectively. The release of Na+ located in the internal sites was slow for both Na-K and Na-Ca exchanges. Using the rate constants obtained for the slowest reaction for both exchange systems, it was estimated that the time required for the release of all exchangeable Na+ in red mud (73 meq/1 00g red mud) to a level of 0.01 meq/1 00g was 21.9 days and 54.7 days for K+ and Ca2+ as replacement cations respectively. It is clear that computer program support needs to be enlisted to investigate chemical processes of even modest complexity. The utility of the SAAM/CONSAM computer software in the investigation of the solution to arbitrary order differential equations and also the solution to chemical kinetics was demonstrated. Corroboration of the results from the model with analytical 11 iii solutions bore out the modelling results. This gave rise to an efficient way for the investigation of arbitrary order differential equations and chemical kinetics without any need for solving the associated differential equations. Bergman's minimal model can fit the FSIGT (frequently sampled intravenous glucose tolerance test) data of non-diabetics, and can be used to simultaneously estimate SI and SG values in non-diabetics. Unfortunately, this model could not fit the FSIGT data of type II diabetics. In order to fit the FSIGT data of type II diabetics and to investigate the glucose kinetics of type II diabetics, we developed a modified minimal model. Our model fitted the FSIGT data of NIDDM subjects (both saline and noradrenaline study) well, and also the FSD of all parameters were less than 30%. The modelling results showed that there was insulin secretion in NIDDM subjects, but the effect of insulin on glucose disposal was delayed (around 50 min). We did not include the insulin offset part in our model because we had never seen insulin offset from the FSIGT data of NIDDM subjects. However, we simulated the insulin offset in type II diabetics by generating the plasma glucose and plasma insulin data after the end of the experimental measurement. Two models were developed to fit the data. Both two models fitted the insulin onset data as well as the insulin offset data well. The second model included not only the feedback of insulin on glucose but also the feedback oi glucose on insulin. For the investigation of the mutual solubility behaviour of water with liquid organics, it is generally desirable to describe the solubility as a function of temperature. Several equations were proposed and investigated for their ability to fit the mutual solubility data of water with liquid organics. The systems chosen for study include hydrocarbons, esters and alcohols since these show a wide diversity of solubility behaviour. Polynomial equations were generally unsatisfactory for describing solubility data except in the simplest cases, and also they lacked physical significance. Better results were obtained with thermodynamically derived equations. Good fits could be obtained from these models even for highly soluble systems by assuming a constant heat capacity of dissolution