F10. Evaporation Formulas

The evaporators may have single-effect or multi-effect. The multi-effect evaporators are used for steam economy. These evaporators may be classified as forward feed or backward feed. Application of the various types of evaporators is dependent upon the solution characteristics and the capacity required. In general, the evaporation problems involve the calculation of the material and heat balances, steam economy, and required heat-transfer surfaces.

The heat-transfer capacity of an evaporator is given by

where q = total heat transferred, U = overall heat-transfer coefficient, and ΔT = overall temperature difference. For a given heat input, the evaporation capacity is reduced if sensible heat is to be provided to bring the feed to its boiling point. The boiling point of a solution is higher than the boiling point of the solvent because of the dissolved salts. Duhring's rule states that the boiling point elevation of a given solution is a linear function of the boiling point of water. The other factor affecting the boiling point elevation of a solution in an evaporator is the liquid head or height of the liquid level (hydrostatic head).

Steam economy is defined as pounds of water evaporated per pound of steam. Steam is used only in one unit, whereas the vapor from one effect is used in the chest of the next effect. This requires using a vacuum in the system to have appreciable temperature differences. An optimum number of the effects is function of economy of steam savings weighted against the investment in the added number of effects.

It is assumed that there is no leakage or entrainment. It is further assumed that (1) non-condensable content of the steam or vapor; (2) superheating the steam or vapor from each effect; and (3) sub-cooling of the condensate are negligible.

Multi-effect Evaporation:

F_o = F₁ + D₁

F₁ = F₂ + D₂

F_o = D₁ + D₂ + F₂