The use of Excel spreadsheets in the modelling of the dynamics of tracer washout in continuous pans

The use of spreadsheets in technical computation in the sugar industry has been very successful. Highly sophisticated modelling has been made possible with the use of the solver and custom developed iteration techniques. The technique has been used by the industry since the early 1990s for solution of steady state non-linear equations. However, the solution of partial differential equations or a set of simultaneous ordinary differential equations (ODEs) to solve dynamic problems presents an extra level of difficulty for spreadsheet techniques. The authors developed a spreadsheet to solve the ODEs describing the dynamics of tracer movement through continuous pans. The use of tracers to test the fluid dynamics of process equipment has a long history in science and technology. It has been used in the sugar industry to identify inefficient use of holdup in continuous equipment. Time dependent processes, such as crystallisation, require a knowledge of residence time distribution. Residence time distribution can be predicted from equipment geometry and the equations of fluid flow (conservation of mass and momentum). Some process equipment requires very sophisticated software to solve these equations, while some useful results can be obtained with a relatively simple formulation amenable to solution by spreadsheet techniques. This paper presents the results of such an analysis applied to the Macknade low grade continuous pan. The analytical solution of the dynamic equations relating to well stirred tanks in series. with varying holdup and flow rates is not an easy task. A solution of the appropriate difference equations yields results which are compared to experimental data. More valid conclusions can be drawn regarding short-circuiting and/or dead spots in the equipment compared to an analysis involving the classical assumption of equal size, well stirred cells in series. Experimental data support the predictions and suggests that this method is more appropriate than the classical model in establishing a residence time distribution benchmark, which can then be used to compare against experimental tracer data.