Evaporation from a Multicomponent Liquid System
In many industrial processes, the many components contained in the liquid evaporate simultaneously. Evaporation of individual components is easy to determine. For multicomponent liquid systems, the individual evaporation rates are summed to obtain the total evaporation rate.
Applying mass transfer theory to a component i in the liquid, assuming good mixing and neglecting atmospheric concentrations, the evaporation molar rate of a single component can be expressed as
Dnt kGJA s
— — ———- pin,, i’4.331 |
K(;4 is the mass transfer coefficient A is the surface area of the liquid nt is the total moles of liquid
P) is the saturation vapor pressure of pure component i
Integrating Eq. (4.331) and knowing that n°, is the initial number of moles of component i yields
«, = n’fexpi-Kip’t), (4.332)
Ki = (4.333 S
Equation (4.333) assumes a constant ratio.
The total mass is
= V n, M,, (4.334)
The total evaporation mass flow rate is obtained as
, N, N
~rilt = ~3jI = lLM’~Zt = ‘Ј~K’Mirfn°exP(-K,/?-r) . (4.335)
M° = (4.336)
M v = y x, Mt (4.337
We obtain the following:
Y exp(-K, p]t)
Dm* o 1 ,• 4 -»•*>rvv
————- N——————— ‘ (4-3W!
Where xi is the mole fraction of component i in the liquid phase, and M is the molecular weight.
The partial pressure of the component i is obtained from
P. = Xfp-expi-Kjp^t) (4.340)
For a nonideal liquid solution, multiplying Eq. (4.331 ) by the activity coefficient y gives
Drij kG tA s
JF = <434]>
For an ideal solution the activity coefficient is y, = 1.
KCi = ^, (4.342)
Where bm i is the mass transfer coefficient in m/s, which is calculated from the heat and mass transfer analogy correlations, R is the universal gas constant, and T is the absolute temperature (K).
Posted in INDUSTRIAL VENTILATION DESIGN GUIDEBOOK