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2.3 Phase Equilibrium Modeling 2.3.1 Bulk Mass Transportation Creating models that can predict experimental data is important to analyze systems that are difficult to run experimentally. Once an accurate model has been achieved, it can be used to check the accuracy of experiments, resulting in the need for fewer experiments. By using bulk transportation of carbon dioxide and water the mass transfer coefficient (Kla) of the reactor system can be determined (Wade & Simek, 2011). The simple two-film theory can be used to help understand the transfer coefficients seen in Figure 2.3 (Wade & Simek, 2011). Figure 2.3: Two film theory diagram (Modified from Wade & Simek, 2011) Applying the two film theory to the reactor system, the mass balance of butanol in the scCO2 phase (Equation 2.1) and in the water phase (Equation 2.2) are shown. (2.1) ππ ππΆπ = βπΊπΆπ + π1πΎππ(ππΆπ β πΆπ ) ππ‘ (2.2) ππΆπ = βπΎππ(ππΆπ β πΆπ ) ππ‘ These two equations can be solved for using Laplace transform (where s is the Laplacian variable) and the initial reactor conditions given in Equation 2.3. (2.3) πΆπ =πΆπ0ππ‘π‘=0 This gives equations 2.4 and 2.5. (2.4) ππ π πΆπ (π ) = βπΊπΆπ (π ) + πππΎππ(ππΆπ(π ) β πΆπ (π )) 20PDF Image | Extraction of Bio-Butanol using Supercritical Carbon Dioxide
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