Exercise 11
Assume that 0.2 mol/s of gas A is to be absorbed into a coalescing type of aqueous solution of B in
a baffled vessel of 2 m3 liquid capacity with a torispherical base. What is the required design if 99%
of gas A is to be absorbed and reacted?
The temperature of the gas is 300 K; the pressure at the sparger is 1.52 bar (absolute), and the inlet
concentration of A in gas, yA0 , is 0.1 mol/mol. Henry’s constant He = 10−8 mol fr./Pa; molar
volume of liquid MV = 50 000 g-mol/m3 .
Tips.
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The overall strategy is to determine from the requirements of the task the power needed to
fulfill the required mass transfer. From the power, you get the impeller speed.
Calculate the dimensions of the stirred tank, gas superficial velocity, the mass transfer
coefficient kLa required, shaft power required
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Volume of the vessel = 0.732 * Diameter vessel^2 * Height of the vessel (This relation takes
into account the torispherical base)
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When calculate the mean concentration driving force, assume that the reaction is rapid such
that the concentration of A in the bulk liquid phase is approximately zero. Assume also that
the gas recirculation ratio α is low (=0), approaching plug flow.
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Use the following correlation for estimate kLa (Middleton, 1997):
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Assume a Rushton turbine as impeller:
Exercise 2:
It is proposed to recover a fermentation product by solvent extraction. The broth has a viscosity of μ
c = 0.3 Pa·s. While the broth is viscous, the drop phase is not. The bulk or mixture viscosity is μ =
0.0386 Pa·s. The interfacial tension is σ = 0.003 N/m. The broth has density ρc = 1000 kg/m3, but the
bulk or mixture density is 1100 kg/m3. The vessel volume is 3.54 m3. The vessel has a diameter T =
1.524 m and is equipped with an Rushton Disk Turbine (RDT) with D/T = 0.4. Laboratory studies
have shown that acceptable extraction results are obtained if the mean drop size is d32 = 50 μm. (Mean
Sauter Diameter -> mean diameter with respect to the total interfacial area). Determine the Reynolds
number, the required impeller speed and power draw.
Tips.
Exercise 3:
It is desired to prepare a 25◦C aqueous solution of potassium sulfate containing 0.09 g K2SO4/g
solution in an agitated 48 in. diameter stainless steel reactor with an axial impeller A-310 (D=T/2).
Calculate:
(a) The solid–liquid mass transfer kSL coefficient at Njs, the minimum impeller speed required to
suspend the potassium particles completely.
(b) The rate of dissolution of the solids at Njs.
The required data for solving this problem include:
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Solid loading 0.05 g/cm3 of solid free liquid
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Solution viscosity 1.01 cP or 0.00101 kg/(m·s)
Solution density 1.08 g/cm3 or 1080 kg/m3
K2SO4 density 2.66 g/cm3 or 2660 kg/m3
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K2SO4 particles size 324 μm or 0.000324 m Solubility of K2SO4 0.12 g/g of solution
Bulk concentration 0.09 g K2SO4/g solution
Diffusivity of K2SO4 in water 9.9×10−6 cm2/s
Tips.
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Use the Zwietering correlation for estimate the Njs, the “just suspended” speed of the stirrer,
the speed at which no particle remaining at the base of the vessel for more than 1 to 2 s:
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To calculate the mass transfer coefficient kSL according to the following correlation:
To do this, you need to calculate the settling velocity Vt:
With a trial and error procedure, identify the appropriate expression for CD, for calculating both Vt
and Rep (you will need an iterative solver).
Then you can calculate kSL at Njs.
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To calculate the rate of dissolution of the solid, the initial dissolution rate corresponds to the
case where [A] = 0: