**Overall material balances** = mass flow rate of fresh feed (kg/h)

= mass flow rate of water exiting evaporator (kg/h)

= mass flow rate of solid KCl crystals exiting the crystallizer and filter (kg/h)

= mass flow rate of slurry exiting the crystallizer and filter (kg/h)

= mass fraction of KCl in fresh feed

= mass fraction of water in fresh feed

**Material balance around crystallizer and filter** = mass flow rate of solution exiting evaporator (kg/h)

= mass flow rate of recycle (kg/h)

= mass fraction of KCl in stream exiting evaporator

= mass fraction of KCl in solution exiting crystallizer and filter

= mass fraction of water in solution exiting crystallizer and filter (this is equivalent to

as the exit stream from the crystallizer is split)

= mass fraction of KCl in recycle stream

**Material balances around mixing point** = mass flow rate entering evaporator (kg/h)

= mass fraction of KCl in stream entering evaporator

**Material balance around evaporator****Dependence of solubility on temperature**= solubility of KCl in 100 kg

= evaporator operating temperature (°C)

= solubility of KCl in 100 kg

= crystallizer and filter operating temperature (°C)

Note that

and

, where

is the stream.

Recovery rate

View the screencast video at [1] for more practice with material balances on a crystallizer.