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)

     ${\dot{m}}_f{H}_f+{\dot{m}}_s{H}_s^V={\dot{m}}_V{H}_V+{\dot{m}}_s{H}_s^L+{\dot{m}}_L{H}_L$

     ${\dot{m}}_s$ = 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)

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

     $\mathrm{\Delta }{H}_s^{vap}$ = enthalpy of vaporization of steam at temperature $T_s$

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