Modelling of tubular reverse osmosis systems (1991)

Reverse osmosis and nanofiltration membranes can be used for the separation and concentration of aqueous solutions. As such, they are often used in desalination and in water treatment of mainly industrial effluents (Amjad, 1993, Brouckaert and Buckley, 1992). Usually, the design of a membrane process involves a long series of experiments on labscale and with a pilot plant. It is, however, impossible to test a pilot plant under every single possible condition. Formulating a model of the transport across the membrane and using this in order to predict membrane performance can be a way of saving time and money otherwise spent on experiments. As the model has to be verified, experiments cannot be omitted completely, but a model should at least be able to tell the engineer what kinds of experiments have to be done and thus reduce the number of experiments. (Mason and Lonsdale, 1990)

The Pollution Research Group of the university of Natal, Durban, has been involved in a number of investigations into modelling of membranes. The most recent project concerned the use of nanofiltration membranes for the treatment of coloured wastewater from the textile industry. The idea was to separate the dyehouse effluent into a retentate containing the dyestuff and the divalent ions and a permeate containing the water and the monovalent ions. A model was designed for this process. It is based on the extended Nernst-Planck equations and can take two or more layers into account, by using the two-layer model and the multilayer model, respectively. Using the multilayer model, reasonably good fittings of the species rejections of the dye effluent could be obtained, but the flux decline could not be fitted very well using either of the models. In order to make the model useful in practice, it will have to be run with a number of further test data sets and it will probably have to undergo some modifications. (Machenbach, 1997)

Research objectives
There are a number of uncertainties about the model. It is very elaborate and uses a lot of parameters and although it certainly provides a good insight into the processes that occur in nanofiltration, it is hard to say if the estimated values of the parameters have any physical meaning. Especially if the multilayer model is used for more than three layers, the number of parameters grows so big that parameter values may be exchanged between each other without changing the fitting of the model. Also, the parameters are probably not all equally meaningful. It is necessary to find a way to distinguish between the identifiability of different parameters, if values obtained with this model are to be used elsewhere.
The goal of this research was, therefore, to alter the program in such a way that it would yield information about the identifiability of the model.