heat transfer

One method for distributing heat in refineries and petrochemical plants is to heat the oil in a central furnace and pump it to various heat exchangers where heating is required. The attached Figure shows a hot-oil loop that serves three boilers. The furnace, reboilers, and pumps are to be selected so that the total present worth of costs for the economic life of the facility is a minimum. Oil data: Oil chemically stable up to 370C Specific heat, 2.OKJ/Kg-K Density, 850Kg/m3 Reboiler data: Duty in KW Temperature of oil U values in being heated C W/m2.K Reboiler 1 1700 200 1410 Reboiler 2 | 1500 150 410 Reboiler 3 2300 175 410 Temperature of fluid heated in each boiler is essentially constant. Cost of the reboiler is $92 per square meter of heat exchanger area Furnace data Treat the furnace as a combination of a combustion chamber and a counter flow heat exchanger Combustion air is heated to temperature Th in the combustion chamber and then flows over heat- exchanger surface U value of furnace heat exchanger, 32W/mK First cost of furnace, $32 per square meter of heat -exchanger area. Cost of heating by natural gas, $1.20 per gigajoule Flow rate of combustion gas, 6.0Kg/s Specific heat of combustion gas, 1.2KJ/Kg. K Pump, motor and electric data Efficiency of pump(P), 87 percent Efficiency of electric motor for the pump, 92 percent First cost of pump, $160 for each Kilogram per second of oil flow. First cost of electric motor, $52 per Kilowatt shaft power output Cost of electricity, 11 cents per kilowatt-hour. An approximate measure of the pressure drop throughout the loop is given by Ap, KPa = 7.2w1.8 where w is the system flow rate in Kilograms per second. Economic data Plan on full-time operation for the 10-year economic life of the facility Interest rate, 3.3 percent. Under these conditions, determine the best possible (optimum) values of the total oil flow rare w and the flow rate in each reboiler, the leaving temperature of oil from each reboiler; Ta, T5, Th, Tg; the system oil pressure-drop; and the size of the electric motor. Heat distribution Network w Kg/s Air, 25C Natural gas, fuel Combustio Flow regulqtor Chamber 150C 0 200c www W Furnace 175 150C wa w, Reboiler T. T. Flue gas to stack To Pump and motor One method for distributing heat in refineries and petrochemical plants is to heat the oil in a central furnace and pump it to various heat exchangers where heating is required. The attached Figure shows a hot-oil loop that serves three boilers. The furnace, reboilers, and pumps are to be selected so that the total present worth of costs for the economic life of the facility is a minimum. Oil data: Oil chemically stable up to 370C Specific heat, 2.OKJ/Kg-K Density, 850Kg/m3 Reboiler data: Duty in KW Temperature of oil U values in being heated C W/m2.K Reboiler 1 1700 200 1410 Reboiler 2 | 1500 150 410 Reboiler 3 2300 175 410 Temperature of fluid heated in each boiler is essentially constant. Cost of the reboiler is $92 per square meter of heat exchanger area Furnace data Treat the furnace as a combination of a combustion chamber and a counter flow heat exchanger Combustion air is heated to temperature Th in the combustion chamber and then flows over heat- exchanger surface U value of furnace heat exchanger, 32W/mK First cost of furnace, $32 per square meter of heat -exchanger area. Cost of heating by natural gas, $1.20 per gigajoule Flow rate of combustion gas, 6.0Kg/s Specific heat of combustion gas, 1.2KJ/Kg. K Pump, motor and electric data Efficiency of pump(P), 87 percent Efficiency of electric motor for the pump, 92 percent First cost of pump, $160 for each Kilogram per second of oil flow. First cost of electric motor, $52 per Kilowatt shaft power output Cost of electricity, 11 cents per kilowatt-hour. An approximate measure of the pressure drop throughout the loop is given by Ap, KPa = 7.2w1.8 where w is the system flow rate in Kilograms per second. Economic data Plan on full-time operation for the 10-year economic life of the facility Interest rate, 3.3 percent. Under these conditions, determine the best possible (optimum) values of the total oil flow rare w and the flow rate in each reboiler, the leaving temperature of oil from each reboiler; Ta, T5, Th, Tg; the system oil pressure-drop; and the size of the electric motor. Heat distribution Network w Kg/s Air, 25C Natural gas, fuel Combustio Flow regulqtor Chamber 150C 0 200c www W Furnace 175 150C wa w, Reboiler T. T. Flue gas to stack To Pump and motor