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cross sectional area of the reactor and total bubble surface area to determine an estimate for the interfacial area. These values were obtained from taking videos and pictures of a pressurized (1500 PSI) view cell (sight gage) that is located after the pump, to then measure and count the bubble size and quantity. One major problem with this calculation was that the impact of stirring was not fully taken into account, which could have lead to a larger a-value. In order to remedy the shortcomings of this simple calculation, more robust correlations were researched to produce reasonable interfacial area values. Table 4.3 shows the correlations that were used to search for the interfacial area and their results. Correlation for a Equation a- value (m2) (2.1) Calculation based π βπ π» πβπ2 (4.4) π=ππ βπΏβ π΅ π π π΄βπ»+ππ π΅π΅πΏπ΅π΅ 226022 (2.2) Video/Picture based π βπ π» πβπ2 (4.5) π=ππ βπΏβ π΅ π π π΄βπ»+ππ π΅π΅πΏπ΅π΅ 995 (2.3) Gas holdup approach (4.6)π= 6 β(π )β0.5β(π βπ )0.25β(π βπ3)0.125βπ πΏπΏπΊπΏπΏ (4.7) πβπ4 πΊ πΏπΏπΏ ππΊ = ππΊ 0.3+2βππΊ 2.5 π βπ π 0.00000015 Assumed a-value β 0.0007 Table 4.3: Comparison of interfacial area correlations trying to generate assumed a-value The results of Table 4.3 range from being unreasonably large to fairly close to the assumed a-value but none of them are sufficient in matching the reasonable value we assumed. The first correlation (2.1) is based off of an area equation that uses separate correlations to determine both the bubble size (dB) and velocity (UB) as shown in equations 4.8 and 4.9 (Painmanakul, Wachirasak, Jamnongwong, & Hebrard, 2009). (4.8) (4.9) ππ΅ =0.32βπ π0.425 β( ππ ) Ξπβπ ππ΅ = ππΏ β (π½ β 0.857) β ππβ0.149 ππΏβππ΅ π2 βπ 1/4 55PDF Image | Extraction of Bio-Butanol using Supercritical Carbon Dioxide
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