Abstract
In order to set up a subsequent optimization of the precoat filtration with body-feed cycles by supplying the slurry with a centrifugal pump, a fluid-dynamic analysis of the filter-pump system with variable supply pressure was performed. Consequently an ordinary differential equation was formulated. Then a closed-form solution was found to obtain an equation useful for both the optimization of the filtration and the filter design. The application of the new mathematical modelling was compared with the application of Carman equation, classically used in filtration, which assumes a constant pressure filtration. The simulation showed that, due to different permeability of the filter, some conditions of filtration can make unrealistic the results of the classic Carman equation. Therefore, in filtration practice it is confirmed the opportunity to have a more accurate equation for both the design and the optimization.
Highlights
The precoat filtration with body-feed is an unit operation of agricultural and food engineering. It is implemented by using centrifugal pump, which pump curve has a partial horizontal trend. In filtration theory, this prerogative of the centrifugal pumps leads to the simplifying assumption that filtration occurs with constant pressure
A better optimization of the precoat filtration with body-feed could be obtain, with some economic benefits, if an integration of the Darcy ODE was developed starting from actual trend of the pressure produced by the centrifugal pump, that is if a variable pressure was considered, as expected from the pump curve
The graphic procedure is tedious since it is iterative and not computerizable. For this reason the aim of this work was to find an analytical solution to the Darcy ODE for the filtration with variable pressure in order to obtain a quick and easy-to-use equation for the subsequent optimization calculations of filtration cycles, even if more complex of the Carman equation
Summary
The precoat filtration with body-feed is an unit operation of agricultural and food engineering. A better optimization of the precoat filtration with body-feed could be obtain, with some economic benefits, if an integration of the Darcy ODE was developed starting from actual trend of the pressure produced by the centrifugal pump, that is if a variable pressure was considered, as expected from the pump curve. The graphic procedure is tedious since it is iterative and not computerizable For this reason the aim of this work was to find an analytical solution to the Darcy ODE for the filtration with variable pressure in order to obtain a quick and easy-to-use equation for the subsequent optimization calculations of filtration cycles, even if more complex of the Carman equation
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