Single-Effect Evaporator

This simulation shows the efficacy of single-effect evaporation of a dilute sugar solution. The saturated or unsaturated liquid is fed into a tank, which contains a steam-fed heat exchanger. The user may adjust the feed flow rate and feed temperature of the feed solution. The conditions of each inlet and outlet stream are shown in colored boxes, with green boxes representing the sugar solution or vapor from the sugar solution, and red boxes representing the steam fed into the heat exchanger.

The rate of a heat exchange $ (Q) $ in Watts in a single-effect evaporator is:

$$ [1] \quad \dot{ Q } = U A \; ( T_{ h } - T_{ conc } ) $$

where $ U $ is the overall heat transfer coefficient [2,500 W/(m²K)], $ A $ is the area of heat transfer (56 m²), $ T_{conc} $ is the temperature of the concentrated sugar solution (K), and $ T_{h} $ is the temperature of the steam (K), which is saturated. In real-life situations, the value of $ U $ depends on the fluids' density, viscosity, velocity, thermal conductivity, and heat capacity, but $ U $ is assumed to be constant in this simulation. The values of $ T_h $ and $ T_{conc} $ are obtained from Antoine's equations:

$$ [2] \qquad \mathrm{ log }_{ 10 } \left( P \right) = A - \frac{ B }{ T + C } $$

where $ P $ is the pressure (Pa), $ A $, $ B $, and $ C $ are constants (obtained from reference 1), and $ T $ is the temperature (K). The concentrated solution was assumed to be pure water initially. The required mass flow rate of steam $ F_h $ (kg/s) was calculated from:

$$ [3] \quad F_{ h } = \frac{ \dot{ Q } }{ \Delta H_{ vap, h } } $$

where $ \Delta H_{vap,h} $, which is the heat of vaporization (assumed to be 1,835 kJ/kg at the pressure in this simulation) of steam, was determined using an approximation from reference 2. The mass flow rate (kg/s) of water vapor ($ F_{evap} $) was calculated from:

$$ [4] \quad F_{ evap } = \frac{ \dot{ Q } - F_{ in } \, C_{ p, c } \, \left( T_{ conc } - T_{ in } \right) }{ \Delta H_{ vap, c } } $$

where $ F_{in} $ is the mass flow rate of the feed solution (kg/s), $ C_{p,c} $ is the temperature-dependent heat capacity of the solution [J/(kg K), calculated using an equation from reference 3], $ T_{in} $ is the temperature of the feed solution (K), and $ \Delta H_{vap,c} $ is the heat of vaporization of the solution (assumed to be 2,014 kJ/kg, calculated from reference (1)). The flow rate of the concentrated solution (kg/s) was determined from a mass balance:

$$ [5] \quad F_{ conc } = F_{ in } - F_{ evap } $$

where $ F_{conc} $ is the flow rate (kg/s) of concentrated solution. The mass fraction of solute in the concentrated solution was also determined from a mass balance:

$$ [6] \quad x_{ conc } = \frac{ x_{ in } \, F_{ in } }{ F_{ conc } } $$

where $ x_{conc} $ is the mass fraction of solute in the concentrates solution, and $ x_{in} $ is the mass fraction of solute in the feed solution. The steam economy $ ( SE ) $ is the ratio of the mass flow rate of liquid evaporated to the mass flow rate of steam (assuming saturated water leaves the heat exchanger):

$$ [7] \quad SE = \frac{ F_{ evap } }{ F_{ h } } $$

An initial estimate of the concentration of solute in the concentrated sugar solution was obtained from equations [1] - [6]. and the flow rate of each stream. Raoult's law was then used to obtain the saturated pressure of the concentrated sugar solution:

$$ [8] \quad P_{ sat, conc } = \frac{ P_{ evap } }{ 1 - x_{ conc } } $$

where $ P_{sat,conc} $ is its saturation pressure, and $ P_{evap} $ is the pressure in the evaporator. Antoine's Equation [2] was then used to calculate $ T_{conc} $. Equations [1] and [3] - [7] were then recalculated using the updated $ T_{conc} $.

References:

(1) National Institute of Standards and Technology (2021). Water phase change data. Retrieved from NIST's website.
(2) My Chemical Engineering Musings (2019). Handy equations to calculate Heat of Evaporation and Condensation of Water/Steam.
Click here to download the article.
(3) Mohos, F.Á. (2017). Data on Engineering Properties of Materials Used and Made by the Confectionery Industry. In Confectionery and Chocolate Engineering, F.Á. Mohos (Ed.). https://doi.org/10.1002/9781118939741.app1.