Surface and steam requirements for multiple effect chemical evaporation can be computed by imposing the energy balance across each effect individually and material balance over the whole system.
So here is discussed energy balance across each effect
4.4.1: First Effect
Heat entering the system:
Latent heat of steam = m. λ = 27931 * 1886
= 52677866 kJ
Enthalpy of steam = Latent heat + Sensible heat
= 52677866 + {27931 * 4.225 * (486-298)}
= 74863459 kJ/hr
Enthalpy of feed entering = 129286 * 4.24 *(468-298)
= 93189348 kJ/hr
Heat added to the system by flashing of feed = 129286 * 1.98 * (468-455)
= 3327821 kJ/hr
Total Heat Input = 74863459 + 3327821 +93189348
= 1.7 * 108 kJ/hr
= 47200 kW
Heat leaving the system:
Enthalpy of bottom product leaving = 98634 * 4.23 * (955-298)
= 65503825KJ/hr
Enthalpy of evaporated stream = enthalpy of superheat + enthalpy of latent heat
= 30652*1.943*(455-451) + 30652*2020+30652*4.35*(451-298)
= 82555705
Enthalpy of condensate = 27931*4.225*(486-298)
= 22185593
Total heat output = 22185593 + 82555705 + 65503825
= 1.7*108 kJ/hr
= 47200 kW
| Stream: | Flow Rate (kg/hr) | Temp. (K) | Saturation Temp. (K) | Latent Heat (kJ/kg) | Heat Capacity (kJ/kg K) |
| Steam: | 27931 | 486 | 486 | 1886 | ----- |
| Condensate | 27931 | 486 | 486 | ------ | 4.225 |
| Liquor (feed): | 129286 | 468 | 455 | ------ | 4.24 1.98* |
| Concentrate (bottom product): | 98634 | 455 | ------- | ------ | 4.23 |
| Evaporated stream (top product): | 30652 | 455 | 451 | 2020.2 | 1.943* |
Note: “*” means for superheated stream
4.4.2: Second Effect
Heat entering the system:
Enthalpy of steam = enthalpy of evaporated stream from 1st effect = 82555705 kJ/hr
Enthalpy of liquor = enthalpy of bottom product from 2nd effect = 65503825 kJ/hr
Heat added due to flash (removal of superheat) = 98634*1.88*(455-405)
= 9283185
Total heat input = 9283185 + 65503825 + 82555705
= 1*108 kJ/hr
Heat leaving the system:
Enthalpy of concentrate = 76440*4.033*(405-298)
= 32986229
Enthalpy of concentrate = 30652*4.35*(451-298)
= 20400438
Enthalpy of top product = 22194 *2*(405-401) + 22194*2179 + 22194*(401- 298)*1.01*4.183
= 58196163
Total heat output = 58196163 + 20400438 + 32986229
= 1.0*108 kJ/hr
| Stream: | Flow Rate (kg/hr) | Temp. (oK) | Sat. Temp. (oK) | Latent Heat (kJ/kg) | Heat Capacity (kJ/kg. K) |
| Steam: | 30652 | 455 | 451 | 2020.2 | 1.943 |
| Condensate | 30652 | 451 | 451 | ------ | 4.35 |
| Liquor (feed): | 98634 | 455 | 405 | ------ | 4.23 1.88* |
| Concentrate (bottom product): | 76440 | 405 | ------- | ------ | 4.033 |
| Evaporated stream | 22194 | 405 | 401 | 2179 | 2.0* |
Note: “*” means for superheated stream
4.4.3: Third Effect
Heat entering the system:
Enthalpy of steam = enthalpy of evaporated stream leaving the effect 2
= 58196163
Enthalpy of liquor entering = 32986229
Heat added due to flash = 76440*4.033*(405-350)
= 169555
Total heat input = 1.0*108 kJ/hr
Heat leaving the system:
Enthalpy of product leaving = 42513*3.48*(350-298)
= 7693152
Enthalpy of condensate leaving = 22174*4.2*(401-298)
= 9592472
Enthalpy of evaporated stream = 33927*1.9*(350-346) + 33927*2326 +
33927*4.20*(346-298)
= 86011730
Total heat output = 1.0*108 kJ/hr
| Stream: | Flow Rate (kg/hr) | Temp (K) | Sat. Temp (K) | Latent Heat (kJ/kg) | Heat Capacity (kJ/kg. K) |
| Steam: | 22194 | 405 | 401 | 2179 | 2.0* |
| Condensate | 22194 | 401 | ------- | ------ | 4.2 |
| Liquor (feed): | 76440 | 405 | 350 | ------ | 4.033 |
| Concentrate (bottom product): | 42513 | 350 | ------- | ------ | 3.48 |
| Evaporated stream (top product): | 33927 | 350 | 346 | 2326 | 1.8939* |
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