Design a heat exchanger for a chemical process that requires heating of 50 kg/hr of water from 25°C to 80°C using steam as the heating medium. The available steam is at a pressure of 1.5 MPa and a temperature of 300°C. The overall heat transfer coefficient between the water and the steam is 600 W/m2K. The heat exchanger should be designed to accommodate a temperature drop of 5°C for both the water and the steam. Determine the required surface area of the heat exchanger and the mass flow rate of steam required to meet the process requirements.

Question

Design a heat exchanger for a chemical process that requires heating of 50 kg/hr of water from 25°C to 80°C using steam as the heating medium. The available steam is at a pressure of 1.5 MPa and a temperature of 300°C. The overall heat transfer coefficient between the water and the steam is 600 W/m2K. The heat exchanger should be designed to accommodate a

Answer 1

To design the heat exchanger, we first need to determine the heat duty  Q  required to heat the water from 25C to 80C. We can use the formula:Q = m  Cp  Twhere m is the mass flow rate of water  50 kg/hr , Cp is the specific heat capacity of water  4.18 kJ/kgK , and T is the temperature change  80C - 25C = 55C .Q = 50 kg/hr  4.18 kJ/kgK  55 K = 11495 kJ/hrNow, we need to convert the heat duty to watts:Q = 11495 kJ/hr   1000 W/kW    1 hr/3600 s  = 3.194 kWNext, we need to determine the log mean temperature difference  LMTD  for the heat exchanger. The LMTD is given by the formula:LMTD =  T1 - T2  / ln T1/T2 where T1 is the temperature difference between the steam and water at the inlet  300C - 25C = 275C  and T2 is the temperature difference between the steam and water at the outlet  295C - 80C = 215C , considering a 5C temperature drop for both the water and the steam.LMTD =  275C - 215C  / ln 275/215  = 243.4CNow, we can determine the required surface area  A  of the heat exchanger using the formula:Q = U  A  LMTDwhere U is the overall heat transfer coefficient  600 W/mK .A = Q /  U  LMTD  = 3.194 kW /  600 W/mK  243.4 K  = 0.0219 mTo determine the mass flow rate of steam required, we need to find the heat capacity of the steam. The specific heat capacity of steam at 1.5 MPa and 300C is approximately 2.1 kJ/kgK. We can use the formula:Q = m_steam  Cp_steam  T_steamRearranging the formula to find the mass flow rate of steam  m_steam :m_steam = Q /  Cp_steam  T_steam  = 3.194 kW /  2.1 kJ/kgK  5 K  = 0.303 kg/sConverting to kg/hr:m_steam = 0.303 kg/s  3600 s/hr = 1090.8 kg/hrIn summary, the required surface area of the heat exchanger is 0.0219 m, and the mass flow rate of steam required is 1090.8 kg/hr.