Multiple Effect Evaporator.docx

Multiple-Effect Evaporators without Boiling Point Rise Evaporators are equipment used in concentrating solutions. Multiple-effect evaporators are commonly used due to higher steam economy although single-effect can also be used for some instances. Solving multiple-effect evaporator problem is an iterative time consuming process with the aim of equalizing the area of each effect. Usually, the given data are feed or product flow rate, feed and product composition, steam temperature or pressure and last effect pressure or temperature. With these, it is required to calculate the heating surface area, temperature, concentration and flow rates of each effect. The step by step solution is presented on figure 1.

Figure 1: Typical Process flow in solving Multiple-Effect Evaporation without boiling point rise The process starts by converting the operating pressures to saturation temperatures using steam tables. It is followed by performing overall material balance to determine the total rate of evaporation and the last effect product flow rate. Overall heat transfer coefficient is calculated using the formula

1 𝑈𝑡𝑜𝑡𝑎𝑙

=

1 1 1 + + ⋯+ 𝑈1 𝑈2 . 𝑈𝑛

Where U1, U2 and Un are the overall heat transfer coefficient of 1st, 2nd and nth effect, respectively. Total temperature difference is calculated using ∆𝑇𝑡𝑜𝑡𝑎𝑙 = 𝑇𝑠 − 𝑇𝑛 Where Ts and Tn are the temperature of the steam and nth effect, respectively. Temperature difference in its effect is determined using the formula 𝑈𝑡𝑜𝑡𝑎𝑙 ∆𝑇𝑖 = ( ) ∆𝑇𝑡𝑜𝑡𝑎𝑙 𝑈𝑖 Where Ti and Ui are the temperature and overall heat transfer coefficient of i th effect (e.g 1st, 2nd). Temperature of ith effect is determined by subtracting Ti from the temperature of the heating medium. As an example, for the 1 st effect, steam is the heating medium, thus, T1 = Ts - Ti. As an initial assumption, the rate of evaporation in each effect is assumed to be equal. Thus, 𝑉𝑖 =

𝑉𝑡𝑜𝑡𝑎𝑙 𝑛

Where Vi is the rate of evaporation in the first effect, Vtotal is the total rate of evaporation obtained from the overall mass balance and n is number of effects. After this, individual composition of each effect is calculated using a solute balance. To validate the assumption, enthalpy and mass balance in each effect is performed. If the computed values from the enthalpy and mass balance significantly differ to the assumption, then, the vapor flow rate calculated from the enthalpy and mass balance is used instead of equal rate of evaporation. The process is repeated until values converge. Area in each effect is calculated using the formula, 𝐴𝑖 =

𝑄𝑖 𝑈𝑖 ∆𝑇𝑖

Where Ai and Qi are the area and heat transfer rate of the ith effect evaporator. If the calculated areas in each effect differs significantly, the new temperature difference (T) in each effect is adjusted using the formula ∆𝑇𝑛𝑒𝑤 = (

𝐴1 ) ∆𝑇𝑜𝑙𝑑 𝐴𝑚

Where A1 is the calculated area and Am is the average area of all the effects. New temperature differences of all the effects are summed and compared with the total temperature difference. If the sum is not equal to the total temperature difference, the new temperature difference in each effect is normalized by ∆𝑇𝑛𝑒𝑤,𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = (

∆𝑇𝑡𝑜𝑡𝑎𝑙 ) ∆𝑇𝑛𝑒𝑤 ∆𝑇𝑛𝑒𝑤,𝑡𝑜𝑡𝑎𝑙

The normalized temperature difference is then used to determine the new temperature in each effect and the process above is repeated until the areas of all the effects are reasonably equal. From the methods discussed above, it can be seen that manual calculation is very tedious and time consuming. It is possible, however, to perform this method using Microsoft Excel. The process of calculation is almost the same with that of the manual method. The only difference is that enthalpy balance is no longer needed. So, how do we solve this problem in Excel? Excel solver will determine the concentrations in each effect that will satisfy the objective, which are areas in each effect is equal. To demonstrate the procedures consider Problem 8.5-2 in the book of Geancoplis, “Transport Processes and Unit Operations, 3 rd Edition”. A triple-effect evaporator with forward feed is evaporating a sugar solution with negligible boiling point rise (less than 1.0 K, which will be neglected) and containing 5 wt% solids to 25% solids. Saturated steam at 205 kPa abs is being used. The pressure in the vapor space of the third effect is 13.65 kPa. The feed rate is 22, 680 kg/h and the temperature 299.9 K. The liquid heat capacity is C p = 4.19 – 2.35x, where Cp is in kJ/kg K and x in wt. fraction. The heat transfer coefficients are U1 = 3123, U2 = 1987 and U3 1136 W/m2 K. Calculate the surface area of each effect if each effect has the same area, and the steam rate.

To solve this in Excel, first create a spreadsheet as shown in figure 2. Note, cells with yellow color are given values, those in white are calculated values and the blue ones are those which will change in the process of calculations.

Figure 2: Spreadsheet Calculation of Multiple Effect Evaporator in Excel Note! Don’t input the values, use formulas. For example, in calculating the heat capacity of the feed (C p = 4.19 – 2.35x), it should be on reference to the feed composition cell. This is shown below.

Figure 3: Inputting formulas in Excel