Use of neural net computing for statistical and kinetic modelling and simulation of supercritical fluid extractors

An empirical kinetic model was developed for the extraction of black cumin (Nigella sativa L.) seed oil with supercritical carbon dioxide as solvent. Extraction conditions were up to 20 MPa and 333 K. Kinetic measurements provided by a neural-regressive hybrid prediction system allowed the simulation and design of a supercritical fluid extraction unit using differential laboratory data modelled with neural networks. Differential extraction yields were correlated with the factors that affected the rate (particle size, degree of milling, fluid flow rate, pressure, temperature, moisture, and time). Their influence on the extracted mass of oil (or system response) was determined by a statistical design of experiments. Response surface data were obtained by using non-parametric statistics. Thus, a neural net model was developed to predict extraction yields. It consisted in a feedforward multilayer neural network, conveniently trained with the backpropagation algorithm. Inputs to the neural net were: pressure, temperature and time. The system provided a single output (the amount extracted) as the only system response. The network architecture was kept to minimum complexity by carefully choosing the number of units of the hidden layer. The neural net computing program was intended as a design and simulation tool for SCF extractors. The bed was assimilated to a pile of layers, each corresponding to a neural net so that its extraction rate could be predicted by the associated neural network as a function of time. In the design stage, the neural-net system operates with numerical routines that carry out the integration of the fluid-phase mass balance equation. The intra-bed mass conservation equation takes into account solute accumulation, convective transport and transport by axial dispersion. Solution to the mass balance equation at each bed height and time was necessary for obtaining the breakthrough curve. By using certain scale-up rules, no fitting parameters were necessary to describe the actual breakthrough behaviour. A sensitivity analysis clearly pointed out the key process parameters, and how to use the model for design purposes. Predictions made with the present hybrid computing system (neural network in combination with pseudohomogeneous mass balance) successfully agreed with data.