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A chemical production plant specializing in synthesizing high concentrated sulphuric acid for exports is performing its annual plant performance review. The main objective of this

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A chemical production plant specializing in synthesizing high concentrated sulphuric acid for exports is performing its annual plant performance review. The main objective of this review is to determine whether the production rate in the plant, P (ton/day) needs to be adjusted to maximize the annual profit obtained from the sales of the high concentrated sulphuric acid product. The process pathway for the production of high concentrated sulphuric acid, most commonly known as contact process involves 5 steps as listed below: 1. Production of sulphur dioxide through reaction between sulphur and oxygen 2. Purification of the sulphur dioxide 3. Addition of excess oxygen to sulphur dioxide to produce sulphur trioxide in the presence of vanadium (V) oxide as catalyst under 450 C and 1 atm 4. Combining sulphur trioxide with sulphuric acid to form oleum 5. Dilution of the oleum with water to produce concentrated sulphuric acid Based on the average expenses data gathered from the past 5 years, it is found that the cost for the raw material (RM/ton of sulphuric acid) can be correlated to the production rate, P given by 80P3- 150. The cost of the utilities (RM/ton of sulphuric acid) during the contact process is also depended on the production rate which is 50 + 3P. Meanwhile, the maintenance and inspection of the equipment in the plant requires RM 350 and RM 140 daily, respectively. The direct labor cost involved in the plant production requires RM 1200 per ton of sulphuric acid produced Other fixed charges resulted from the plant operation will usually amount to RM 1500 per month. The superproduction cost (RM) is estimated to incur additional 25P per ton of sulphuric acid produced. The sulphuric acid is packaged in drums which can load up to 2 ton of sulphuric acid each before sent for exportation. The average selling price per drum for the last 5 years is RM 4500. The plant is capable of operating for 365 days in a year but periodic maintenance requires the plant to shut down for 2 days every month. (a) Derive the equations for the operating cost and organization cost of the sulphuric acid production plant (6 marks) (b) Formulate the objective function with constraint and solve the optimization application for the plant to optimize the annual profit. (15 marks) (c) Please suggest TWO (2) feasible method to further improve the objective function formulated in Q4(b). (4 marks) A chemical production plant specializing in synthesizing high concentrated sulphuric acid for exports is performing its annual plant performance review. The main objective of this review is to determine whether the production rate in the plant, P (ton/day) needs to be adjusted to maximize the annual profit obtained from the sales of the high concentrated sulphuric acid product. The process pathway for the production of high concentrated sulphuric acid, most commonly known as contact process involves 5 steps as listed below: 1. Production of sulphur dioxide through reaction between sulphur and oxygen 2. Purification of the sulphur dioxide 3. Addition of excess oxygen to sulphur dioxide to produce sulphur trioxide in the presence of vanadium (V) oxide as catalyst under 450 C and 1 atm 4. Combining sulphur trioxide with sulphuric acid to form oleum 5. Dilution of the oleum with water to produce concentrated sulphuric acid Based on the average expenses data gathered from the past 5 years, it is found that the cost for the raw material (RM/ton of sulphuric acid) can be correlated to the production rate, P given by 80P3- 150. The cost of the utilities (RM/ton of sulphuric acid) during the contact process is also depended on the production rate which is 50 + 3P. Meanwhile, the maintenance and inspection of the equipment in the plant requires RM 350 and RM 140 daily, respectively. The direct labor cost involved in the plant production requires RM 1200 per ton of sulphuric acid produced Other fixed charges resulted from the plant operation will usually amount to RM 1500 per month. The superproduction cost (RM) is estimated to incur additional 25P per ton of sulphuric acid produced. The sulphuric acid is packaged in drums which can load up to 2 ton of sulphuric acid each before sent for exportation. The average selling price per drum for the last 5 years is RM 4500. The plant is capable of operating for 365 days in a year but periodic maintenance requires the plant to shut down for 2 days every month. (a) Derive the equations for the operating cost and organization cost of the sulphuric acid production plant (6 marks) (b) Formulate the objective function with constraint and solve the optimization application for the plant to optimize the annual profit. (15 marks) (c) Please suggest TWO (2) feasible method to further improve the objective function formulated in Q4(b). (4 marks)

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