The value of \(\mathrm{E}_{\mathrm{MD}}=0.927\) in Example 16-5 is lower than the 0.95 value your supervisor expects. You are tasked to see if the current mixer with the current feed rate can be coaxed into operating at \(\mathrm{E}_{\mathrm{MD}}=0.95\) by reducing solvent flow rate \(\mathrm{S}\). Your immediate answer is no, but your supervisor wants proof.
a. Find solvent flow rate that gives \(\mathrm{E}_{\mathrm{MD}}=0.95\).
b. Calculate new values of \(\mathrm{x}_{\mathrm{D}, \text { out }}\) and \(\mathrm{x}_{\mathrm{C}, \text { out }}\).
c. Find new value of \(\varphi_{D}\).
d. Estimate new values of \(\mathrm{d}_{\mathrm{p}}\) and \(\mathrm{a}\).
e. Estimate new values of \(\mathrm{k}_{\mathrm{C}}\) and \(\mathrm{K}_{\mathrm{O}-\mathrm{ED}} \mathrm{a}\).
f. Estimate new values of \(\mathrm{n}_{\mathrm{O}-\mathrm{ED}}\) and \(\mathrm{E}_{\mathrm{MD}}\).
g. Suggest operating changes that might work.
Data are listed in Example 16-5, and although the mixer is a different size, the physical property data in Example 13-7 also apply to this system. The controlling resistance is continuousphase mass transfer. Assume drops are rigid.

Example 16-5

Example 13-7

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Treybal (1980) estimates the overall mass transfer coefficient and stage efficiency for a mixer (0.5-m high and 0.5-m diameter, Amixer = 0.1963 m, Vmixer = 0.09817 m) extracting benzoic acid from water into pure toluene solvent. The water plus benzoic acid flow rate is QF = 0.003 m/s, and toluene flow rate is Qp = 0.0003 m/s. The tank is well mixed. Toluene is dispersed, and QD is estimated as 0.0824. The estimated dispersed-phase surface to volume ratio ap = 1940.0 m dispersed phase/m dispersed phase. The estimated overall dispersed-phase mass transfer coefficient KLD = 2.01 x 10-5 kmol benzoic/[ms(kmol benzoic/m)]. Additional data: Ptoluene = 865 kg/m, MW toluene = 92.14 kg/kmol. Equilibrium is Cextract = 20.8 Craffinate (Cextract is kmol benzoic/m extract); since solvent is the dispersed phase, McD 0.0481 [see Eq. (16-80c analog) listed in the solution to part a]. A. Convert the mass transfer coefficient to the units used in this section. B. Calculate the stage efficiency using the completely mixed model. C. Calculate the stage efficiency using the differential equation approach. = 1/20.8= = D. Calculate the exiting raffinate and extract mole fractions for a completely stirred mixer if entering solvent contains no benzoic acid and entering feed is 0.03 mol% benzoic acid in water.