Journal of Membrane Science 211 (2003) 59–70 Optimisation and graphical representation of multi-stage membrane plants Ken R. Morison ∗ , Xin She Department of Chemical and Process Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Received 4 May 2002; accepted 7 August 2002 Abstract A procedure is given for the design and optimisation of continuous multi-stage membrane plants using the example of whey ultrafiltration. During the design stage, the number of stages, area per stage, diafiltration water ratios and possible pressures can be varied to minimise capital and operating costs. The concept of an optimal or ideal plant was developed to provide a basis for comparison for the designs. To interpret the results, and check the validity of the optimisation results, a variety of graphical representations were developed. Graphical profiles of purity versus total solids, and of protein concentration versus lactose concentration were effective when interpreting design results and a graph of component mass flux helped identify yield losses. These and other graphs provided insight into the designs and often enable sensible improvements to them. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Multi-stage; Graphical; Design; Membrane; Optimisation 1. Introduction The design of batch and multi-stage membrane plants is well established in the commercial world and equations for the design of plants have been well documented [1–3]. Some efforts have been made to analyse and optimise multi-stage plants. Niemi and Palosaari [4] simulated multi-stage reverse os- mosis and ultrafiltration plants. Qi and Henson [5] gave a method for optimisation of gas separation in multi-stage spiral-wound plants by mixed integer non-linear programming (MINLP). A similar tech- nique [6] was used for the design of reverse osmosis networks. ∗ Corresponding author. Tel.: +64-3-364-2578; fax: +64-3-364-2063. E-mail address: k.morison@cape.canterbury.ac.nz (K.R. Morison). Although much of a design can be theoretical, it is very dependent on the equation for permeate flux which is normally obtained empirically for the particu- lar solution, membrane and operating conditions used. As a result optimality cannot be theoretically proven for a general case and results from one design are not necessarily true for another. The development of spreadsheets, such as Mi- crosoft Excel, with built in optimisation programs, such as Solver, bring to the engineer’s desktop the capability for fast and accurate calculation of plant designs. The result of such calculations, however, can be a mass of numbers and a design, of which the validity and optimality is uncertain. The un- certainty is likely to increase with the number of variables, e.g. when there are many stages and when diafiltration is used to achieve high purity in the product. 0376-7388/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0376-7388(02)00375-7