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.