Problem 8.59.- Seawater containing 3.5 wt% dissolved salts is to
be desalinated in an adiabatic six-effect evaporator. Backward feed
is to be used: the seawater is fed to the last evaporator, and
successively concentrated brine solutions flow countercurrent to
the direction of flow of steam from one effect to the next.
Saturated steam at P = 2 bar is fed to the tube bundle in the first
effect. The operating pressures in bars of the six effects are,
respectively, 0.9, 0.7, 0.5, 0.3, 0.2, and 0.1. The brine leaving
the first effect contains 30 wt% salt. The flowchart shows Effects
1, 5, and 6.
Following is a labeled diagram of the i th effect:
In terms of the variables defined in this diagram:
= 5000 kg/h, = 0.035 kg salt/kg, = 0.30 kg salt/kg and = feed
rate of steam to the first effect.
a) Use a salt balance to calculate . Then use this result to
determine how much fresh water is produced in the process.
b) Prepare a table as follows and fill in all known variable
values (do not calculate any yet), including values obtained from
the steam tables, assuming that the physical properties of the
brine solution are those of pure water.
c) Show that the following equations can be derived from
balances:
d) The missing entries in the table of part (b) may be
determined by solving Equations 1 through 3 for all effects
simultaneously, but this is a cumbersome task. Instead, a
relatively simple trial and error method may be used, which
consists of assuming a value for , calculating = , and successively
solving Equations 1 through 3 for , , , then , , , and so on, until
finally is calculated. If the calculated value of is less than the
known value of 0.3, a higher value of is assumed and the process is
repeated; if > 0.3. a lower value of is assumed. A reasonable
first guess for is 1/6 of the total rate of evaporation [determined
in part (a)]. Construct a spreadsheet program to perform these
calculations, using the goalseek tool to carry out the
trial-and-error search for the correct value of nV6. Fill in the
table of part (b).
e) Solve the equations of part (c) for all six effects using an
equation-solving program. Fill in the table of part (b).
