Extrapolated ILDF stage requirements
Using the permeate removal data for the initial pass of the five starting ethanol concentrations examined, a continuous ILDF (Figure 1C) was modelled and the number of passes/stages for the target ethanol removal calculated. Figure 4A shows the permeate removed for each of the measured initial ethanol concentration passes with an extrapolated curve/function. This function was used to model each independent pass/stage of a continuous ILDF process until the target ethanol removal was achieved (Figure 4B). Each pass/stage was modelled using the following equations:
\(c_{p+1}=\frac{c_{p}R-c_{p}f\left(c_{p}\right)}{R}\) (Equation 4)\(f\left(c_{p}\right)=-5.696\ln\left(c_{p}\right)-3.8359\)(Equation 5)
where \(c_{p}\)= ethanol concentration at the beginning of a pass,\(c_{p+1}\)= ethanol concentration at the end of a pass, \(R\)= mass of the retentate, and \(f(c_{p})\) = the extrapolated ethanol concentration dependent permeate removal function. Using Equations 4 and 5, starting ethanol concentrations were selected and the ethanol concentrations calculated after each subsequent pass/stage. The calculation continued until the target ethanol removal was achieved and the number of passes/stages determined.
The number of passes needed when starting at different concentrations was calculated and are shown in Figure 4B. Figure 4C compares the calculated pass/stage data to the pass/stage data determined with the Figure 1D set up. The modelled continuous ILDF passes required are significantly less than the Figure 1D set up, but the difference becomes smaller with lower initial ethanol concentrations. This shows that the impact of carrying through the Figure 1D initial ethanol concentration limitation on permeability was mitigated by calculating the passes independently. Note that the continuous ILDF ethanol reduction curve does not follow the diafiltration equation, while the Figure 1D set up did. This is most likely due to the Figure 1D reuse of the same hollow fibers for each run, which caused the permeability limitations similar to a CVDF batch process. The extrapolated ILDF model’s use of new hollow fibers for each pass/stage leveled out the rejection coefficient effect into a linear reduction as the permeability of each pass/stage was set independently. Overall, this showed that a continuous ILDF process would minimize any impact of the ethanol rejection coefficient or permeability reduction as compared to the batch CVDF process.