An example of a cake washing calculation

Estimate the time and rate of washing of an initially saturated cake formed at constant pressure of 5 bar on a batch pilot pressure filter of filtration area equal to 0.5 m. Washing is to be done at the same pressure as filtration, the washing efficiency was determined experimentally at 77%, the required solute reduction in the cake is 95% and the wash liquid is pure water. The mother liquor is an aqueous solution of salt and other constants are as follows  

1 Try the simple approach by Choudhury and Dahlstrom in equation 10.1 which for E = 0.77 and / = 1 — 0.95 gives n = In (0.05)/In (0.23) = 2.0. This is within the applicability of this simple approach and = 2 is, therefore, our first estimate of the wash ratio needed. 

2 Equation 10.5 can be used to predict the washing curve but the washing rate has to be determined first, from the cake and medium resistance, using the general filtration equation 9.5 for Ap = 5 bar. As the mother liquor and the washing liquid have the same properties, the washing rate is equal to the final rate of filtration when the cake has been formed (i.e. after 0.028 m of the feed suspension has been filtered). The sequence of the calculations is as follows  

Using mass balance, the fraction of solute remaining in the cake R can now be calculated by integration, following equation 10.7  

Final remarks Wakeman and Attwood published pre-calculated graphs of washing curves c/cq and fractions retained R as functions of Pcc but these are unnecessary nowadays, given the ease of computing using packages such as spreadsheets (e.g. in the above example) for the hill calculation. Even the erf function is now widely available in spreadsheets such as Excel, for example. 

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