Evaporation Single-stage and Multi-stage Evaporation Processes Section A – Single Stage Evaporation Ashleen Marshall 28th April 2021 Section A – Single-stage Evaporation Evaporation is defined as an operation whereby a fluid changes from a liquid state into the vapor state. The mixture consists of a volatile component and a non-volatile component Processes Involved heat and mass transfer Heat is supplied to the process to provide the latent heat of vaporisation The volatile component (liquor) vaporises The vapor is removed (mass transfer) Equipment used for evaporation Open pans – expose a large surface area to the sun’s rays Horizontal tube evaporators – steam tubes arranged horizontally inside the evaporator body, which supplies heat indirectly to the liquor Forced circulation evaporator – vertical tubes through which liquor is forced, surrounded by steam. Long tube vertical evaporators used with natural circulation. The liquid rises up through the tubes because of the decrease in liquid density with the increase in temperature Heat Transfer in Evaporators Heat transfer The general equation for heat transfer is: Q = heat transferred per unit time U = overall heat transfer coefficient A = heat transfer surface T = temperature difference between two streams The Temperature Difference Driving Force Represents the difference between the temperature of the boiling liquid and the condensing steam. The temperature of the boiling liquid is not constant because of the effect of liquid head. It is therefore necessary to choose a standard basis for defining temperature of the boiling liquid ∆𝑇 = 𝑇𝑠𝑡𝑒𝑎𝑚 − 𝑇𝑣𝑎𝑝𝑜𝑢𝑟 To determine the temperature of the vapour, the pressure in the vapour space needs to be determined. The corresponding temperature of the vapour space is determined using a table (steam table) or a graph (duhring plot) Standard temperature difference The temperature of the boiling liquid in an evaporator body is the temperature of the boiling solution at the pressure of the vapor space, i.e. the temperature of the boiling liquid at the exposed surface of the liquid Therefore, the standard (net) temperature difference is: The difference between the temperature of the condensing steam in the steam chest, and the temperature of the boiling solution at the liquid-vapor interface in the evaporator body Apparent temperature difference The difference between the steam temperature and the apparent saturation temperature of the vapor leaving the evaporating mixture Apparent saturation temperature – the temperature of the vapor assuming it is saturated at the existing pressure This is only an estimate though because it is based on the assumption that the liquid is pure water Boiling Point Rise Due to Material in Solution A pure liquid exerts a certain vapor pressure at a given temperature If another substance is dissolved in this pure liquid, the vapor pressure of the mixture will be less than that of the pure substance at the same temperature. A solution boils when its vapor pressure equals the pressure of the surroundings A solution of a nonvolatile material in water must be heated above the boiling point of pure water before boiling can occur. The boiling point rise due to material in solution – the actual surface temperature of the mixture minus the temperature of the pure solvent if it exerted the same vapor pressure as the mixture. Duhring’s Rule An empirical law developed for determining BPR due to material in solution Rule A plot of the temperature of a constant concentration solution versus the temperature of a reference substance, where the reference substance and the solution exert the same pressure, results in a straight line. Raoult’s Law A generalisation for BPR due to material in solution Law The equilibrium vapor pressure which is exerted by a component in a liquid solution equals the mole fraction of that component in the solution times the equilibrium vapor pressure the component would exert if it were pure and at the same temperature as the solution pa = equilibrium vapor pressure of component a in solution with components a, b, c, .. Pa0 = equilibrium vapor pressure of component a if it were pure at the same temperature as the solution na, nb, nc, = moles of components a, b, c, … in the solution xa = mole fraction of component a in the liquid solution Application – only to mixtures in which the components are similar chemically and the molecules do not interact in any way. Boiling point rise due to Hydrostatic Head Evaporators where the heat source is submerged below the surface of the evaporating liquid (e.g. stem tubes) The solution at the outside of the steam tubes is at a higher pressure than the solution at the top surface of the liquid due to the presence of an existing head of liquid If boiling occurs at the steam tubes, the liquid temperature at this point of higher pressure must be greater than that at the top liquid surface. The difference in temperature of the liquid at the heat source and the liquid at the top of the evaporating surface Need to determine BPR due to hydrostatic head – average density of the liquid solution average concentration of the liquid solution NB: Usually the presence of BPR due to hydrostatic head has little effect on overall heat transfer coefficients In practise a corrected heat transfer coefficient is used – assumes the temperature of the boiling liquid to be the point halfway between the top and the bottom of the boiling material Standard Overall Coefficients To avoid confusion a standard overall coefficient is used Based on the difference in temperature between the steam in the steam chest and the boiling liquid at the liquid-vapor interface in the evaporator body. In the general heat transfer equation T = standard (net) temperature difference = the apparent temperature difference minus the BPR due to material in solution ASSUMPTIONS IN EVAPORATOR CALCULATIONS The standard temp. diff. is based on the temperature of the boiling liquid at the liquid-vapor interface in the evaporator body The heat required to vaporise 1kg of solvent is taken as the latent heat of vaporisation at the exposed surface temperature of the solution For feeds of inorganic salts in water, the heat capacity may be assumed as equal to that of the water alone The effect of BPR due to hydrostatic head is commonly neglected BPR calculations for continuous evaporators are based on a mixture having the same concentration as the liquid leaving the evaporator The sensible heat necessary to heat the feed to the boiling point may be approximated by assuming the heat capacity of the original feed is constant until the feed has reached the boiling temperature of the mixture Example 1 – Illustrative 30% by weight solution of sodium hydroxide-in-water solution at a surface temperature of 1750F. If the solution was pure water at the temperature, the water-vapor pressure would be 6.715 lb/in2 abs. The actual vapor pressure of the solution containing 30% by weight of sodium hydroxide at the given temperature is 3.718 lb/in2 abs. The steam-table temperature of water corresponding to 3.718 lb/in2 is 1500F. pure water at 1500F would exert exactly the same vapor pressure as the solution at 1750F. B.P.R. = 175 – 150 =250F Example 2 – Illustrative An evaporator producing a 30 weight % solution of NaOH in water when the pressure in the evaporator vapor space is 3.718 lb/in2 abs, and the steam chest pressure is 25 lb/in2 abs. The steam-table temperature for saturated water vapor exerting a pressure of 3.718 lb/in2 abs, is 1500F. The temperature of the saturated steam at 25 lb/in2 abs is 2400F. The apparent temp. diff. is 240 – 150 = 900F The actual BPR due to material in solution is 250F. The temperature of the liquid at the liquid-vapor interface is actually 150 + 25 = 1750F The standard temp. diff. is 240 – 175 = 650F. Example A continuous single stage evaporator is to concentrate 25000 kg/hr of a 5% by weight sodium hydroxide in water solution to a final concentration of 20 weight % sodium hydroxide. The vapor space of the evaporator will be maintained at atmospheric pressure (1 atm), and the steam pressure will be kept at 238 kPa gauge. The standard overall heat transfer coefficient can be assumed as 1500Btu/(hr)(ft2)(0F). The feed enters the evaporator at 21.10C Determine the area of heat transfer theoretically necessary to carry out the evaporation.
