Multi-effect Evaporators: Screencasts
Describes the operation of a triple-effect evaporator to concentrate a solute liquid solution using significantly less energy than a single-effect evaporator.
We suggest that after watching this screencast, you list the important points as a way to increase retention.
Describes how a triple-effect evaporator with backward feed concentrates a dilute solution.
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)
\(\dot{Q}_1 = U_1A_1(T_s – T_{evap\, 1})\)
\(\dot{Q}_i\) = heat transfer rate (kJ/s) for evaporator \(i\) (\(i\) = 1, 2, … up to n)
n = number of effects
\(U_i\) = overall heat transfer coefficient (kJ/(m2 s K) for evaporator \(i\) (\(i\) = 1, 2, … up to n)
\(A_i\) = heat transfer area (m2) for evaporator \(i\) (\(i\) = 1, 2, or 3)
\(T_s\) = steam temperature (ºC)
\(T_{evap\, i}\) = temperature (ºC) of liquid and vapor in evaporator \(i\) (\(i\) = 1, 2, … up to n)
\(\dot{Q}_i = U_iA_i(T_{evap\, i-1} – T_{evap\, i})\) for evaporator \(i\) (\(i\) = 2, 3, … up to n)
Mass balances
\(\dot{m}_f = \dot{m}_{V1} + \dot{m}_{L1}\) for evaporator 1
\(\dot{m}_f\) = mass flow rate of liquid feed (kg/s)
\(\dot{m}_{Vi}\) = mass flow rate of vapor leaving evaporator \(i\) (kg/s)
\(\dot{m}_{Li}\) = mass flow rate of concentrated liquid leaving evaporator \(i\) (kg/s)
\(x_f\dot{m}_f = x_{L1}\dot{m}_{L1}\)
\(x_f\) = mass fraction of solute in liquid feed
\(x_{Li}\) = mass fraction of solute in concentrated liquid leaving evaporator \(i\)
\(\dot{m}_{L(i-1)} = \dot{m}_{Vi} + \dot{m}_{Li}\) for evaporator \(i\) (\(i\) = 2, 3, … up to n)
\(x_{L(i-1)}\dot{m}_{L(i-1)} = x_{Li}\dot{m}_{Li}\) for evaporator \(i\) (\(i\) = 2, 3, … up to n)
Energy balances
\(\dot{m}_fH_f + \dot{m}_sH_s^V = \dot{m}_{V1}H_{V1} + \dot{m}_sH_s^L + \dot{m}_{L1}H_{L1}\) for first evaporator
\(\dot{m}_s\) = 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)
\(H_s^L\) = specific enthalpy of condensed steam (saturated liquid) leaving evaporator (kJ/kg)
\(H_{Vi}\) = specific enthalpy of vapor leaving evaporator \(i\) (kJ/kg)
\(H_{Li}\) = specific enthalpy of concentrated liquid leaving evaporator \(i\) (kJ/kg)
\(\dot{Q}_1 = \dot{m}_s(H_s^V – H_s^L) = \dot{m}_s\Delta H_s^{vap}\)
\(\Delta H_s^{vap}\) = enthalpy of vaporization of steam (per kg) at temperature \(T_s\)
\(\dot{m}_{L(i-1)}H_{L(i-1)} + \dot{m}_{V(i-1)}H_{V(i-1)} = \dot{m}_{Vi}H_{Vi} + \dot{m}_{Li}H_{Li} + \dot{m}_{V(i-1)}H_{Ci}\) for evaporators 2 to n
\(H_{Ci}\) = specific enthalpy of condensed vapor leaving evaporator \(i\)
steam economy = \(\frac{\sum{\dot{m}_{Vi}}}{\dot{m}_s}\)