Chemical Engineering Science 61 (2006) 3818 – 3829 www.elsevier.com/locate/ces Numerical modelling of fixed-cavity plate-and-frame filtration: Formulation, validation and optimisation Anthony D. Stickland a , Ross G. de Kretser a , Peter J. Scales a , ∗ , Shane P. Usher a , Peter Hillis b , Martin R. Tillotson c a Particulate Fluids Processing Centre, Department of Chemical and Biomolecular Engineering, The University of Melbourne, Victoria, Australia 3010 b United Utilities PLC, Lingley Mere, Lingley Green Avenue, Warrington, WA5 3LP, United Kingdom c Yorkshire Water Services Ltd, Halifax Road, Bradford, BD6 2LZ, United Kingdom Received 31 August 2005; received in revised form 12 January 2006; accepted 12 January 2006 Available online 3 March 2006 Abstract A model of fixed-cavity plate-and-frame filter presses is developed based on the theoretical framework developed by Buscall and White (1987. The consolidation of concentrated suspensions. Part 1. The theory of sedimentation. Journal of the Chemical Society. Faraday Transactions. I, Physical Chemistry in Condensed Phases 83, 873–891) and the piston-driven filtration model of Landman et al. (1991. Dewatering of flocculated suspensions by pressure filtration. Physics of Fluids. A, Fluid Dynamics 3(6), 1495–1509). The model properly accounts for compression of the suspension network structure within a filter cake in one dimension over a fixed cavity and allows for the effect of membrane resistance and ramping pressures. The model is validated by comparing on-site measurements of actual process performance at two water treatment plants with model predictions based on fundamental material properties of the feed slurries, the operating conditions and the press dimensions. The material properties are measured using laboratory based filtration tests. The model is then used to investigate the optimisation of press throughput and cake solids for a ferric water treatment slurry.  2006 Elsevier Ltd. All rights reserved. Keywords: Filtration; Mathematical modelling; Optimisation; Plate-and-frame filter; Separations; Slurries; Validation 1. Introduction Plate-and-frame filter presses are used extensively in a wide range of industries to dewater various types of slurries. They consist of a vertical or horizontal concertina of plates, which are indented, such that a cavity of width d is formed between two plates when the press is closed. Semi-permeable membranes, or filter cloths, are mounted to the faces of the plates. Through the introduction of a suspension under pressure, a cake forms against the membrane and dewatering occurs. The membrane separation may be fixed or variable, depending on whether or not the press has an air- or water-driven squeeze phase. The operation of a plate-and-frame filter press depends upon the size and shape of the press, the applied pressure, the ∗ Corresponding author. Tel.: +61 3 8344 6480; fax: +61 3 8344 4153. E-mail address: peterjs@unimelb.edu.au (P.J. Scales). 0009-2509/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.01.020 resistance of the membrane, and the material characteristics of the feed slurry (including concentration, compressibility and permeability). The throughput and the final cake solids give measures of the performance of such presses. Traditionally, plate-and-frame presses are designed from scale-up of pilot- scale tests or laboratory measurements of specific resistance to filtration (SRF) (Tarleton and Wakeman, 1994). Neither ap- proach properly accounts for changes to operating conditions such as the initial solids concentration or the applied pres- sure (Tarleton and Willmer, 1997), while SRF does not account for cake compression and requires a priori knowledge of ma- terial property functional forms (Tiller and Shirato, 1964). A more general approach applicable to compressible materials is needed. A model to describe the volume fraction distribution during one-dimensional fixed-cavity filtration (including the effect of membrane resistance) is developed here based on the piston- driven filtration model of Landman et al. (1991) who used