LearnChemE

#### Single-effect Evaporators: Screencasts

Describes the operation of a single-effect evaporator that is used to concentrate a solution and shows mass balances.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

Explains the energy balance for a single-effect evaporator, which is used to increase the concentration of a solute in a feed stream by evaporating some of the liquid in the feed. A feed stream of saturated steam supplies heat to evaporate the liquid.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

Heat transfer (assumes liquid is well mixed)

$$\dot{Q} = UA(T_s – T_{evap})$$

$$\dot{Q}$$ = heat transfer rate (kJ/s)

$$U$$ = overall heat transfer coefficient (kJ/(m2 s K)

$$A$$ = heat transfer area (m2)

$$T_s$$ = steam temperature (ºC)

$$T_{evap}$$ = temperature of liquid and vapor in evaporator (ºC)

Mass balances

$$\dot{m}_f = \dot{m}_V + \dot{m}_L$$

$$\dot{m}_f$$ = mass flow rate of liquid feed (kg/s)

$$\dot{m}_V$$ = mass flow rate of vapor leaving evaporator (kg/s)

$$\dot{m}_L$$ = mass flow rate of concentrated liquid leaving evaporator (kg/s)

$$x_f\dot{m}_f = x_L\dot{m}_L$$

$$x_f$$ = mass fraction of solute in liquid feed

$$x_L$$ = mass fraction of solute in concentrated liquid leaving evaporator

Energy balance (assumes saturated steam enters and saturated liquid water leaves evaporator)

$$\dot{m}_fH_f + \dot{m}_sH_s^V = \dot{m}_VH_V + \dot{m}_sH_s^L + \dot{m}_LH_L$$

$$\dot{m}_s$$ = mass flow rate of steam entering evaporator (kg/s)

$$H_f$$ = specific enthalpy of liquid feed (kJ/kg)

$$H_s^V$$ = specific enthalpy of steam entering evaporator (kJ/kg)

$$H_V$$ = specific enthalpy of vapor leaving evaporator (kJ/kg)

$$H_s^L$$ = specific enthalpy of condensed steam (saturated liquid) leaving evaporator (kJ/kg)

$$H_L$$ = specific enthalpy of concentrated liquid leaving evaporator (kJ/kg)

$$\dot{Q} = \dot{m}_s(H_s^V – H_s^L) = \dot{m}_s\Delta H_s^{vap}$$

$$\Delta H_s^{vap}$$ = enthalpy of vaporization of steam at temperature $$T_s$$

steam economy = $$\frac{\dot{m}_V}{\dot{m}_s}$$