The CPVC wetcake leaves the product centrifuge at 80°C and 1 atm and is fed to the elevated end of a rotary dryer (a rotating cylinder inclined about 35° from horizontal). A fresh air stream at 27°C, 1 atm, and 60% relative humidity is mixed adiabatically with an air stream recycled from the dryer exhaust, and the combined stream is heated in an air furnace and fed to the lower end of the dryer. Water evaporates from the wetcake moving downward in the rotating drum into the hot air moving in the opposite direction. The exhaust air leaves the dryer at 110°C, 1.3 atm, and 20% relative humidity. The dryer operates adiabatically. Ninety percent of the exhaust air is recycled, and the rest is vented to the atmosphere. The dried polymer resin leaves the dryer at 120°C containing 0.1 wt% water.

(a) In your own words, explain the purpose of this portion of the process. Your explanation should include statements about why the dryer must be tilted, why the air temperature drops as the air moves through the dryer, and why the preheater (air furnace) is necessary.

(b) Draw and fully label a flowchart of this portion of the process, substituting known variable values from previous calculations and including the required rate of heat transfer to the air in the preheater in the labeling. Use molar flow rates and mole fractions when labeling gas streams.

(c) Carry out the process degree-of-freedom analysis to verify that enough information is available to determine all unknown stream flow rates and component mole fractions (air) and mass fractions (wet resin), the temperature of the air entering the dryer, and the heat transferred to the air in the furnace. Write, in order, the equations you would solve to determine the unknown variables, circling in each equation the variable for which you would solve. Use as references for enthalpy calculations solid CPVC at 80°C, liquid water at 0°C, and dry air at 110°C (all at 1 atm), neglect the contribution of sodium chloride to the energy balance, use the steam tables to determine vapor pressures and the heat of vaporization of water, and use the following heat capacities: CPVC(s), 1.88 kJ/(kg•°C); dry air, 29.2 kJ/(kmol∙°C); H₂O(1), 4.2 kJ/ (kg∙°C); H₂O(v), 34.0 kJ/(kmol∙°C). Do not perform the calculations in this part.

(d) Solve the equations of part (c) for the unknown stream flow rates, component fractions and temperature of the air entering the dryer, and rate of heat transfer to the air in the furnace (kW).