## Evaporation

To reduce load times, this material is divided into three files, corresponding to the numbered points below. The present file (evap3.html) contains point 3 only.

## Evaporator Calculations

Evaporator problems require solution of the system material and energy balances with the accompanying property and heat transfer equations. Solution would be rather straightforward, except that often the required thermodynamic properties are only available in tabular or graphical form.

### Single Effect Calculations:

Single effect evaporator calculations are fairly basic. Usually it is possible to solve the material and energy balances analytically by a sequential approach.

Typically, the operating temperature is not provided. Usually, the operating pressure or temperature of the vapor condenser is known, and can be used to determine the temperature using steam tables, etc. You may need a different steam table than you normally use, since not many textbook tables have good coverage of the vacuum range commonly used in evaporators.

Don't forget to allow for boiling point elevation. Remember that when BPE is present, the vapor will be superheated.

You also should be prepared for side calculations -- steam consumption, evaporator economy, etc.

### Multiple Effect Calculations

Typically, multiple effect evaporator calculations require an iterative solution procedure because so many of the required properties, etc., depend on unknown intermediate temperatures. Fortunately, the overall approach is basically the same for the majority of problems, requiring only minor adjustments to compensate for problem quirks.

In a typical evaporator problem, you are given the steam supply pressure, the operating pressure of the final effect, values for the overall heat transfer coefficient in each effect, the feed pattern, and the feed and product compositions. You also know that the effects are all to have the same heat transfer area.

You typically want to find the steam consumption and the heat transfer area, and one or more of the temperatures, flows, and compositions from within the system.

The overall strategy is to estimate intermediate temperatures, solve the material balances for the solvent vapor flow rates, use these to determine the heat transferred in each effect, and from that information find the heat transfer area. If the areas are not equal, you revise the temperature estimates and repeat the procedure.

The steps in the procedure can be summarized as:

1. Use the overall component balance to completely determine the feeds and product streams. These numbers are fixed and are not changed by iteration.
2. Calculate the total amount of solvent vaporized (another fixed number). Divide this up into estimated amounts for each effect; usually it is convenient to split it equally.
3. Use component and material balance to get estimates for the remaining flowrates within the system and the compositions of the intermediate streams. These (and all the estimated quantities) will change each iteration.
4. Use the compositions to estimate BPEs and other properties. Be sure to keep track of which properties depend on composition, temperature, or both.
5. Determine the overall temperature drop between the steam and the saturation temperature of the last effect (remember to subtract off the BPEs). Note that the BPE values may depend on the concentrations, so the overall Delta T can vary with each iteration.
6. Allocate the overall drop among the various effects. Since the areas are the same, the temperature difference in each effect is roughly proportional to the overall transfer coefficients. 7. Use the Delta T and BPE values to obtain estimates for all the temperatures in the system. Typically, you do this starting with the steam to the first effect, subtracting a Delta T, adding a BPE, etc. You can use the saturation temperature of the last effect as a check -- it should match the value for your final effect operating pressure.
8. Use the temperature and composition estimates to get enthalpy values. You can get these from specific heat calculations or from data. Be sure to use the same reference temperatures for all streams, including those taken from steam tables, etc.
9. Set up the process side enthalpy balances. Use material balances to eliminate the liquid flows from the enthalpy equations. Do enough algebra so that the only unknowns left in the balances are the vapor flow rates and the steam to the first effect.
10. Solve the set of equations that is made up of one enthalpy balance for each effect and the total vapor material balance for the unknown vapor flows (one off each effect and the steam to the first).
11. Use heat transfer equations to calculate the heat transfer area for each effect. 12. Compare the areas. If they are not equal, you need to repeat the calculation. Begin by using the areas you obtained to revise the temperature estimates. The recommended approach is to use the ratio of the calculated heat transfer area for an effect to the arithmetic mean of the calculated areas. 13. Repeat the calculations (from step 7) until the system converges. If your BPEs, enthalpy data, etc., depends on composition, you will need to include steps 3 and 4 in each cycle as well.
14. Once the system has converged, answer questions. Be sure to use values from the final iteration to calculate your answers.

A sample triple effect evaporator calculation may be downloaded as a Mathcad file. The example neglects BPE in order to show the algorithm clearly.

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