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ENERGY BALANCE Energy balance on Extractor Since the extractor does not contain any heating equipment, the energy balance around the extractor is not required. Energy balance on the 1st condenser The stream coming out of the stripping section as solvent at top of the stripping column. Latent heat of components at inlet of the condenser (T=140oC) HB = 1062.6 kJ/kg HT = 37.99 kJ/kg HX = 39.56 kJ/kg Latent heat of components at outlet of the condenser (T=75oC) HB = 627.32 kJ/kg HT = 7.054 kJ/kg HX = 16.013 kJ/kg Therefore total heat load on the condenser is given by; Q = ∑minputH - ∑moutputH Where , m – mass flow rate of feed in kg/s min = mout = 100kg/h = 0.028kg/s ∴Q = 0.028 ( 0.15191x 1062.6 + 0.4235 x 37.99 + 0.40232 x 39.56) - 0.028 ( 0.15191x 627.32 + 0.4235 x 7.054 + 0.40232 x 16.013) = 2.48kW
Energy balance on the 2nd condenser The side stream coming out of solvent stripper. The condition is same with the first condenser but the flow rate is different. min = mout = 820kg/h = 0.228kg/s Q = ∑minputH - ∑moutputH ∴Q = 0.228 ( 0.15191x 1062.6 + 0.4235 x 37.99 + 0.40232 x 39.56) - 0.228 ( 0.15191x 627.32 + 0.4235 x 7.054 + 0.40232 x 16.013) = 31.83kW
Energy balance on the 3rd condenser min = mout = 123.9434kg/h = 0.0344kg/s Q = ∑minputH - ∑moutputH ∴Q = 0.0344 (1062.6) – 0.0344 (627.32)= 14.97kW
Energy balance on the 4th condenser min = mout = 340.3536kg/h = 0.0945kg/s Q = ∑minputH - ∑moutputH ∴Q =0.0945 (37.99) – 0.0945 (7.054) = 2.93kW
Energy balance on Benzene Column Since water is added as washing liquid to the extracted aromatic stream, there will be a considerable temperature drop in the system and furthermore the energy losses in clay treater and separator also contributes to the temperature drop. ∴Assume the feed temperature to the condenser at the top of the column is 90oC and at the bottom temperature is 100oC the reference temperature is taken as =0oC ∴Heat capacity, (Cp)B = 1.856 kJ/kg.K (Cp)T = 1.809 kJ/kg.K (Cp)X = 1.841 kJ/kg.K ∴ (Cp)avg. = Σ (xi x Cpi) = 1.789 kJ/kg.K and, HB = 627.32 kJ/kg HT = 7.054 kJ/kg HX = 16.013 kJ/kg And F= W+D = 820kg/h D= 0.15191 x 820 = 124.5662kg/h = 0.0346kg/s W=695.4338kg/h ∴The heat load on the condenser (top of the column); Qc = mD x HB = 0.0346kg/s x 627.32kJ/kg = 21.7 kW To find Qb; Assume that heat loss in the distillation column is negligible. ∴The heat balance around the benzene column; (F x HF )+ Qb =( D x HD) +( W x HW) + Qc i.e, (0.228kg/s x 1.7887kJ/kg.K x 348K) + Qb = (0.0346kg/s x 1.856kJ/kg.K x 363K) + (0.1934kg/s x 1.831kJ/kg.K x 373K) + 21.7kW ⇒ Qb = 25.51 kW
Energy balance on Toluene Column: The feed to the column is assume to have temperature = 120oC F= 0.1932kg/s D= 0.4994 x 0.1932 = 0.09647kg/s W= F-D =0.09673 ∴The heat load on the condenser; Qc = mD x HT = 0.09647 x 37.99 = 3.67 kW For Qb, overall heat balance; (F x HF )+ Qb =( D x HD) +( W x HW) + Qc i.e, (0.1932kg/s x 1.7887kJ/kg.K x 393K) + Qb = (0.09647kg/s x 1.856kJ/kg.K x 396K) + (0.09673kg/s x 1.831kJ/kg.K x 396K) + 357.99kW ⇒ Qb = 363.22kW
