Question

The intermediate product of a chemical process is a chemical paste that is saturated with water. The paste is rolled into a thin layer and placed to dry in a flat area 30m long 15m wide. Drying is enhanced by blowing hot air over the paste, and the mass transfer coefficient is 0.017 m/s. Diffusion of water through the paste is rapid so that the concentration of water vapor at the surface of the paste remains constant at 0.002 gmol/L. Water must be removed from the paste remains at a minimum rate of 9.5 L/min (liquid volume). (Note:MW water=18 and p water=1 g/cm^3.) a.) What mechanism controls the transfer of water from the paste in the air? b.) What is the molar rate of water removal that corresponds to a volumetric removal rate of 9.5 L/min? C.) What is the maximum concentration of water vapor allowable in the air (far from the paste surface) if water must be removed at a rate of at least 9.5 L/min? D.) Assuming that the mass transfer coefficient remains constant, what can be done to increase the rate of water removal from the paste?

Answer 1

a.) What mechanism controls the transfer of water from the paste in the air?
Evaporation
b.) What is the molar rate of water removal that corresponds to a volumetric removal rate of 9.5

L/min?
Molar mass of water, MW = 18 gm/mol
density of water, rho = 1 gm/cm3 = 1000gm/L
Mass rate of water, W = density*volumetric rate
Molar flow rate = W/MW = density*volumetric rate/MW = 1000*9.5/18=527.78 mol/min =527.78/60 mol/s =

8.8 mol/s

C.) What is the maximum concentration of water vapor allowable in the air (far from the paste

surface) if water must be removed at a rate of at least 9.5 L/min?
area, A = 30*15 = 450 m2
Molar flux of water from surface, J = Molar flow rate/area = 8.8/450 = 0.02 mol/m2-s
concentration of water vapor at the surface of the paste, cs = 0.002 gmol/L = 2mol/m3
concentration of water vapor in the air = cinf mol/m3

convective mass transfer coefficient, kc = 0.017 m/s

J = kc*(cs - cinf )
cinf = cs - J/kc = 2 - 0.02/0.017 = 0.8235 mol/m3 = 0.0008235 mol/L

D.) Assuming that the mass transfer coefficient remains constant, what can be done to increase the

rate of water removal from the paste?
Increasing,
(i) surface area
(ii)air velocity
(iii) air temperature