Chemical Engineering Science 58 (2003) 4185–4195 www.elsevier.com/locate/ces Dynamicpredictionofmilkultraltrationperformance: Aneuralnetworkapproach S.M.A.Razavi a ; * ,S.M.Mousavi b ,S.A.Mortazavi a a Department of Food Science and Technology, University of Ferdowsi, Mashad P.O.Box: 91775-1163, Iran b Department of Chemical Engineering, University of Ferdowsi, Mashad P.O.Box: 91775-1111, Iran Received 6 November 2002; received in revised form 30 April 2003; accepted 14 May 2003 Abstract Neural network models were tested in connection with the dynamic prediction of permeate ux ( JP ), total hydraulic resistance (RT ) and the solutes rejection for the crossow ultraltration of milk at dierent transmembrane pressure (TMP) and temperature (T ). This process has complex non-linear dependencies on the operating conditions. Thus it provides demanding test of the neural network approach to the process variables prediction. Two neural network models with single hidden layer were constructed to predict the time dependent rate of JP =RT and rejections from a limited number of training data. The modelling results showed that there is an excellent agreement between the experimental data and predicted values, with average errors less than 1%. The experimental results showed that the RT and solutes rejection (except for protein) increased greatly with time at each value of TMP and T , whereas the JP decreased signicantly for the same conditions. Increasing TMP at constant T led to an increase in the JP , RT and solutes rejection, but increasing T at constant TMP had no signicant eect on the JP , RT and rejection of components. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Membrane; Food processing; Neural network; Flux; Total hydraulic resistance; Rejection 1. Introduction Ultraltration (UF) is the most commonly used mem- brane process in the dairy industry. Ultraltration has been used at an increasing rate in the dairy processing since its initial application in the early 1970s. Total membrane area for UF in the dairy industry has been estimated approxi- mately 140; 000m 2 in 1988. About 35% (40; 000m 2 ) of this membrane area was devoted to milk processing, while the remaining 65% (110; 000m 2 ) was used for whey pro- cessing (Horst, 1990). The major problem of ultraltration processing is fouling, which results in ux decline and changing retention characteristics. Fouling limit membrane performance, reduce the working life of membrane and increases cleaning costs (Grandison, Youravong, & Lewis, 2000). Thus predicting the performance of UF process is necessary for the design of a new process and optimisation of present process. In the practical situations, some laboratory or pilot plant tests are carried out over a wide range of conditions. This ∗ Corresponding author. Tel.: +98-511-8795-618; fax: +98-511-8787-430. E-mail address: s.razavi@ferdowsi.um.ac.ir (S. M. A. Razavi). method is both time consuming and expensive. Meanwhile this leads to a simple calculation of the membrane area though the reliability of the result is questionable, be- cause the conditions are not the same in all stages of the process. A precise estimation of the membrane area can be made by using the equations describing the dependence of per- meate ux and rejection on the process variables. In fact, there have been some theoretical approaches to predict the ultraltrationperformanceofcolloidalsolutions(e.g.milk). These are based on some models such as mass transfer model (lm theory), gel-polarization model, osmotic pres- suremodel,boundarylayer-adsorptionmodel,Browniandif- fusion model, shear-induced diusion model, inertial lift modelandsurfacetransportmodel(Samuelssonetal.,1997; Cheryan,1998).Inadditiontothecomplexityofmathemat- ical equations involved, each of these models has a number of limitations: (i) They demand some experimental data for determining the input parameters. Perhaps this is always possibleinpractice,buttheequipmentrequiredarespecially sensitive instruments which might not be readily available. (ii)Noneofthesecandescribethefullux-timebehaviourof process;theyoftenpredictthesteadyorpseudo-steady-state 0009-2509/$-see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0009-2509(03)00301-4