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(2.5) π πΆπ(π ) β πΆπ0 = βπΎππ(ππΆπ(π ) β πΆπ (π )) Rearranging Equation 2.4 in terms of Cs(s) and plugging it into equation 2.5 gives, Where, (2.6) πΆ(π )= (π +π΄)πΆπ0 π π 2+π1π +π2 (2.7) π΄ = πΊ + ππ β πΎππ ππ ππ (2.8) π1 =πΎππβπ+πΊ +ππ βπΎππ ππ ππ (2.9) π2 =πΎππβπβππΊ π Rearranging equation 2.6 gives the final concentration of butanol inside the reactor at any time (t) Where, (2.10) πΆπ=πΆπ,0β(π½1βπβ1βπ‘+π½2βπβ2βπ‘) (2.11) πΌ1 = βπ1+βπ12β4βπ2 2 (2.12) πΌ2 = βπ1 ββπ12 β4βπ2 2 (2.13) π½1 = β1+π΄ πΌ1βπΌ2 (2.14) π½2 = β2+π΄ πΌ2 βπΌ1 By rearranging equation 2.13, the mass transfer coefficient (Kla) can be calculated using β1β(1+β1βππ ) (2.15) πΎπ=β πΊ π πβ((β1βππ )+1)+β1βππ πΊπΊ Where, Ξ±1 is the slope of the Ln (Ca/Co) and is determined from experimental data m is the partition coefficient and is 2.2 (Laitinen & Kaunisto, 1999b) VS is the volume of scCO2 in the reaction G is the scCO2 flow rate Vl is the volume of butanol/water mixture in the reaction Kla is the mass transfer coefficient Cl is the final concentration in the reactor Cl,0 is the initial concentration in the reactor By using equations 2.1-2.15 and collected experimental data, the final concentration of butanol in the reactor can be calculated at any time. The effects on Kla from changing pressure, initial concentration and flow rate can be determined. Once a model has been 21PDF Image | Extraction of Bio-Butanol using Supercritical Carbon Dioxide
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