Evaporation

To reduce load times, this material is divided into three files, corresponding to the numbered points below. The present file (evap1.html) contains point 1 only.
  1. Evaporator Concepts
  2. Evaporator Modeling
  3. Evaporator Calculations

Evaporator Concepts

Single Effect Evaporator Evaporation is a special case of heat transfer to a boiling liquid. This particular heat transfer application is so common and important that it is treated as a separate unit operation.

The intent is to concentrate a non-volatile solute from a solvent, usually water. This is done by boiling off the solvent. Concentration by evaporation is normally stopped before the solute begins to precipitate; if not, the operation is better considered as crystallization.

Evaporation is usually treated as the separation of a liquid mixture into a liquid product (concentrate or thick liquor) and a vapor byproduct, although in special cases such as water treating and desalination, the vapor is the product instead of the thick liquor.

In this course, we will limit evaporation to systems with non-volatile solutes.

Evaporation is similar to drying in that both drive off volatiles, but is different in that the product is a liquid. Evaporation differs from distillation because both components in a distillation system are volatile. Evaporation normally produces a single vapor fraction, distillation several.

An evaporator consists of a heat exchanger for boiling the solution and a means to separate the vapor from the boiling liquid. Different types are categorized by the length and alignment (horizontal or vertical) of the evaporator tubes. The evaporation tubes may be located inside or outside of the main vessel where the vapor is driven off.

Because many materials cannot tolerate high temperatures, evaporators often operate at reduced pressure so that the boiling point will also be reduced.

In many (most?) cases, evaporators operate under a vacuum. This means that a vacuum pump or jet ejector vacuum system is required on the last effect.

Evaporators are commonly used in the inorganic and organic chemical, pulp and paper, and food industries (especially sugar). Examples are the concentration of fruit juices and of NaOH.

History:

The invention of the multiple effect evaporator is generally credited to Norbert Rillieux. Rillieux developed a multiple pan evaporation system for use in sugar refining. Rillieux was born in Louisiana and trained in France. Most of his working career was spent in the U.S., although he later returned to Europe where he is buried in the famous Pere Lachaise cemetery in Paris. Rillieux's achievements were little acknowledged during his lifetime, because according to the laws of the time he was "a free person of color." He was also the first cousin, once removed, of the painter Edgar Degas.

Performance Measures:

There are three main measures of evaporator performance:

  1. Capacity (kg vaporized / time)
  2. Economy (kg vaporized / kg steam input)
  3. Steam Consumption (kg / hr)
Note that the measures are related, since Consumption = Capacity/Economy.

Economy calculations are determined using enthalpy balances.

The key factor in determining the economy of an evaporator is the number of effects. The economy of a single effect evaporator is always less than 1.0. Multiple effect evaporators have higher economy but lower capacity than single effect.

The thermal condition of the evaporator feed has an important impact on economy and performance. If the feed is not already at its boiling point, heat effects must be considered. If the feed is cold (below boiling) some of the heat going into the evaporator must be used to raise the feed to boiling before evaporation can begin; this reduces the capacity. If the feed is above the boiling point, some flash evaporation occurs on entry.


Boiling Point Elevation

Since evaporators dealing with boiling solutions, and in particular with solutions with non-volatile solutes, any calculations must account for the effect of boiling point elevation.

The vapor pressure of an aqueous solution is less than that of pure water at the same temperature; so the boiling point of the solution will be higher than that of the water. This is called Boiling Point Elevation (BPE) or vapor pressure lowering.

The boiling point of a solution is a colligative property -- it depends on the concentration of solute in the solution, but not on what the solute and solvent are.

When working problems involving heat transfer to or from boiling solutions, it is necessary to adjust the temperature difference driving force for the boiling point elevation.

Note that the equilibrium vapor rising from a solution exhibiting boiling point elevation will exist at a temperature and pressure such that it is superheated with respect to pure vapor. The vapor rises at the solution boiling point, elevated with respect to the pure component boiling point. The vapor, however, is solute free, so it won't condense until the extra heat corresponding to the elevation is removed, thus it is superheated.

Justification

The equations in this section are being displayed using MINSE, a browser independent approach to displaying equations on the web. If the equations are not properly formatted by your browser, you need to render them (select this link) by invoking Ping's MINSE polymediator. This will run a special program that should cause them to appear in a more understandable format.

At equilibrium, we can write
p;solvent=?gamma?;solvent*'exp(p,sat);solvent*x;solvent
relating the partial pressure of solvent in a vapor phase to its thermodynamic activity coefficient, pure component vapor pressure, and mole fraction in the corresponding liquid phase. If we are dealing with ideal solutions, the activity coefficient is 1.0, Raoult's Law applies, and
p;solvent='exp(p,sat);solvent*x;solvent

If the solute is non-volatile, the vapor will be pure solvent, and
P='exp(p,sat);solvent*x;solvent
If the liquid phase is binary, then
x;solvent=1-x;solute , and P='exp(p,sat);solvent*(1-x;solute)
So as the solute fraction gets larger, the vapor pressure of the solvent must be higher to produce the same total pressure. The only way this can be true is if the boiling point of the solution increases to produce the needed pressure.

Determination

For strong solutions, one can take advantage of Duhring's Rule

The boiling point of a given solution is a linear function of the boiling point of water at the same temperature.
This lets us plot TBP solution against TBP water and get a straight line for each concentration. Another way of thinking of these plots -- they plot the temperature where the vapor pressure of the solution is equal to some fixed value against the temperature where the vapor pressure of water equals the same value.

For Duhring Plots to be valid, the range of boiling points must be relatively narrow and the solution must obey Raoult's Law.

A Duhring Plot for the NaOH/Water system can be found in McCabe et al. Fig. 16.3, p. 481 (also Foust et al. Fig 19.11, p. 502).

To use a Duhring plot:

  1. For a particular system pressure, determine the boiling temperature of pure water. This can be done from a vapor pressure equation or steam table.
  2. Enter the plot from the bottom (the water boiling point), trace up to the diagonal line representing the NaOH fraction, then trace left to read the solution boiling point from the vertical axis.
  3. The boiling point elevation is the difference between the two temperatures.

Felder & Rousseau (2nd ed., p. 264) give a method for estimating the BPE for dilute solutions (x close to zero). It does not apply to values of x greater than a few percent. The formula is:
?Delta?T;BPE=T;B;solution-T;B;solvent='quot(R*T;b;solvent^2,?Delta?H;vap)*x

BPE References


Multiple Effect Evaporators

Evaporators are classified by the number of effects. In a single-effect evaporator, steam provides energy for vaporization and the vapor product is condensed and removed from the system. In a double-effect evaporator, the vapor product off the first effect is used to provide energy for a second vaporization unit. Triple- effect evaporator problems are familiar to generations of engineering students. This cascading of effects can continue for many stages. Multiple-effect evaporators can remove much larger amounts of solvent than is possible in a single effect.

In a multiple effect arrangement, the latent heat of the vapor product off of an effect is used to heat the following effect. Effects are thus numbered beginning with the one heated by steam. It will have the highest pressure. Vapor from Effect I will be used to heat Effect II, which consequently will operate at lower pressure. This continues through the train: pressure drops through the sequence so that the hot vapor will travel from one effect to the next.

Normally, all effects in an evaporator will be physically the same in terms of size, construction, and heat transfer area. Unless thermal losses are significant, they will all have the same capacity as well.

Evaporator trains may receive their feed in several different ways. The feed order is NOT related to the numbering of effects. Effects are always numbered according to decreasing pressure (steam flow).

Forward Feed arrangements follow the pattern I, II, III. These require a single feed pump (reduced fixed costs). They typically have reduced economy (higher operating costs) since the cold feed must be raised to the highest operating temperature. These also tend to have the most concentrated liquour, which tends to be the most viscous, in the lowest temperature effects, so their may be difficulties getting a good overall heat transfer coefficient.

Backward Feed arrangements go III, II, I. These need multiple pumps to work against the pressure drop of the system; however, since the feed is gradually heated they usually have better economies. This arrangement also reduces the viscosity differences through the system and so is better for viscous solutions.

Mixed Feed arrangements offer a compromise, with the feed entering in the middle of the system (i.e. II, III, I). The final evaporation is done at the highest temperature so economies are still better than forward feed, but fewer pumps are required than in a backward feed arrangement.

Parallell Feed systems split the feed stream and feed a portion to each effect. This is most common in crystallizing evaporators where the product is likely to be a slurry.


References:

  1. Aven, R.E., Class Notes: Evaporation, unpublished, no date.
  2. Balchen, J.G. and K.I. Mumme', Process Control: Structures & Applications, Van Nostrand Reinhold, 1988, pp. 170-174, 508- 513.
  3. Foust, A.S. et al., Principles of Unit Operations, 2nd Edition, John Wiley, 1980, pp. 494-516.
  4. McCabe, W.L., J.C. Smith, P. Harriott, Unit Operations of Chemical Engineering, 5th Edition, McGraw-Hill, 1993, pp. 463- 489.


R.M. Price
Original: 12/17/96
Modified: 4/6/98, 4/5/99; 3/6/2003

Copyright 1996, 1998, 1999, 2003 by R.M. Price -- All Rights Reserved