A evaporation-crystallization process is used to obtain solid potassium sulfate from an aqueous solution of this salt. The fresh feed to the process contains 19.6% potassium sulfate by mass. The wet filter cake consists of solid K2SO4 crystals and a 40.0% potassium sulfate solution, in a ratio of 10 kg crystals/kg solution. The filtrate, also a 40.0% solution, is recycled to join the fresh feed. Of the water that feeds the evaporator, 45.0% is evaporated. The evaporator has a maximum capacity of 175 kg of evaporated water/s. (a) Consider that the process operates at its maximum capacity. Draw and label the flow diagram and perform the degree of freedom analysis for the overall system, the fresh feed-recycle mixing point, the evaporator, and the crystallizer. Then write, in an efficient order (minimizing simultaneous equations), the equations you would use to solve for the unknowns. In each equation, indicate the variable to be determined, but do not perform the calculations yet. (b) Calculate the maximum production rate of solid K2SO4, the flow rate at which the fresh feed must be supplied to ensure this production rate, and the ratio of recycle to fresh feed in kg/kg. Answer: 221 kg/s; 41.6 kg/s; 1.60. (c) Calculate the composition and flow rate of the stream entering the crystallizer if the process is scaled to 75% of its maximum capacity. Answer: 299 kg (46.3% K2SO4, 53.4% H2O).
A evaporation-crystallization process is used to obtain solid potassium sulfate from an aqueous solution of this salt. The fresh feed to the process contains 19.6% potassium sulfate by mass. The wet filter cake consists of solid K2SO4 crystals and a 40.0% potassium sulfate solution, in a ratio of 10 kg crystals/kg solution. The filtrate, also a 40.0% solution, is recycled to join the fresh feed. Of the water that feeds the evaporator, 45.0% is evaporated. The evaporator has a maximum capacity of 175 kg of evaporated water/s.
(a) Consider that the process operates at its maximum capacity. Draw and label the flow diagram and perform the degree of freedom analysis for the overall system, the fresh feed-recycle mixing point, the evaporator, and the crystallizer. Then write, in an efficient order (minimizing simultaneous equations), the equations you would use to solve for the unknowns. In each equation, indicate the variable to be determined, but do not perform the calculations yet.
(b) Calculate the maximum production rate of solid K2SO4, the flow rate at which the fresh feed must be supplied to ensure this production rate, and the ratio of recycle to fresh feed in kg/kg. Answer: 221 kg/s; 41.6 kg/s; 1.60.
(c) Calculate the composition and flow rate of the stream entering the crystallizer if the process is scaled to 75% of its maximum capacity. Answer: 299 kg (46.3% K2SO4, 53.4% H2O).
Step by step
Solved in 2 steps with 2 images
