Time needed for Evaporation

An apparent overall heat transfer coefficient is 735 Btu/(hr.sqft.oF) for a forced circulation evaporator concentrating sulfite liquor under certain special conditions. How long will it take to concentrate 20000 lb of a feed liquor containing 5% solute by weight to a final concentration of 15% if the steam temperature is 230.8oF and the temperature corresponding to the pressure in the vapor space is 210.7oF. The heating surface is 100 sqft. Indicate all the assumptions made in obtaining the result. How will the result be affected if each of the assumptions is not made.

Calculations:

Assumptions:

(i) Steady state operation

(ii) No elevation in boiling point due to solute concentration.

(iii) No elevation in boiling point due to hydrostatic head.

(iv) No sub-cooling of condensate.

(v) Feed is at the temperature of 210.7oF

Rate of heat transfer, Q = U A DT

= 735 x 100 x (230.8 - 210.7) / 3600 = 410.375 Btu/sec

Mass flow rate of steam, (mS):

mS lS = 410.375

lS = 958 Btu/lb (from Steam Tables - for the temperature 230.8oF )

Therefore,

mS = 410.375/958 = 0.42837 lb/sec

Making heat balance for the solution: (taking 210.7oF as the datum temperature)

By denoting mass flow rate of vapor as, mV,

mVlV = mSlS

lV = 971 Btu/lb (from Steam Tables - for the temperature 210.7oF )

Therefore,

mV = 410.375/971 = 0.42263 lb/sec

i.e., Mass of vapor evaporated = 0.42263 lb/sec

Time needed for evaporation:

Solute balance:

If the product is denoted as P,

20000 x 0.05 = P x 0.2

P = 5000 kg

Water in feed = water evaporated + water in concentrated solution

20000 x 0.95 = 0.42263 x Dt + P x 0.8

19000 = 0.42263 x Dt + 4000

Dt = 15000/0.42263 = 35492 sec = 9 hr 52 min

Time needed for evaporation = 9 hour and 52 minutes.

If the assumptions were not made:

If the assumption (i) is not made, then we have to make a unsteady balance (For Batch Evaporation). The results will be different for these two operations

If the assumption (ii) is not made, then the DT will be equal to, (Tsteam - Tboiling point of water corresponding to the pressure inside the evaporator - boiling point elevation). This will lead to the increase of time needed for evaporation.

Assumption (iii) also has the same effect of assumption (ii).

Assumption (iv): If sub-cooling of steam is allowed, it will give more heat to the solution, which in turn will reduce the time needed for evaporation.

Assumption (v): If feed temperature is less than this, it leads to more steam requirement. So with the available heat transfer rate, it leads to increased evaporation time.