# 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 |

Dt n,.1′

Where

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)

Where

Ki = (4.333 S

’ ”,

Equation (4.333) assumes a constant ratio.

The total mass is

N

 M = 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)

I

Defining

M° = (4.336)

N

M v = y x, Mt (4.337

_ v1ir±t

I

We obtain the following:

Y exp(-K, p]t)

Dm* o 1 ,• 4 -»•*>rvv

————- N——————— ‘ (4-3W!

I

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)

^x’Jcxpi-K’pU)

I

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) H

RT’

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).