Conclusions
A 1-D pressure filtration model for edible fats, focusing on the expression step, has been developed and described. The model comprises two differential equations one of which is a second-order diffusion equation with a non-constant consolidation coefficient while the second is a simple transient mass balance. The expression we derived for this consolidation (or diffusion) coefficient is essentially different from earlier proposals in the literature since we explicitly take the biporous character of our fat crystal slurry into account, in terms of intra-aggregate and inter-aggregate solidosities. In addition, our consolidation equation contains a source term which to the best of our knowledge is a novelty. In general terms, our set of two differential equations represents a rheological model composed of a series of two dashpots parallel to a spring. The double porous nature of the fat crystal aggregate filter cake can be conceived as a series of two dashpots described with the Meyer & Smith correlation for the permeability (rather than the Kozeny-Carman relation). The spring is due to the elastic modulus that can be determined experimentally with a constant load test.
The model was implemented in MATLAB with five unknown coefficients remaining, which were calibrated with the help of measured oil outflow rates in two filtration tests in a pilot scale membrane filter press. The model was then validated by using experimental data from five filtration tests. The model is capable of displaying porosities and solidosities, the solid fat content inclusively, as a function of time and of position in the filter cake. In addition, it can generate plots of overall features of the filtration process such as oil outflow velocity, solid fat content of the filter cake and aggregate oil volume, all as a function of time.
The overall conclusion is that the model gives very promising results, qualitatively realistic and obviously pretty reliable, with room for improvement in quantitative respect. Our simulations may also result in process information which is more consistent than data from pilot plant tests which suffer from several equipment technicalities and operational issues. Specific experiments may be helpful to find more reliable and accurate data for some cake features such as permeability and elasticity as a function of particularly aggregate properties of typical edible fats.
Finally, the model has been shown to have the potential of exploring the effect of typical process operation variables on eventual solid fat content of the filter cake, such as the rate of pressure increase and, related, the duration of the expression phase.