Problem 2 A reactor system having various feeds and products is listed in the table below. The capacity to run gas feeds through this reactor is 200,000 lb/stream hour. Ethane uses the equivalent of 1.1 lb of capacity per pound of ethane; propane 0.91b; gas oil 0.91b/lb; and DNG 1 The downstream operation is limited to 50000lb/stream hour (ethylene), and 20000 lb/stream hour for propylene. DNG Gas oil Propanc Ethane Recycle J(Ethane) Thermal cracker Fuel (Propane) Methanc Fuel oil Ethylene Propylene Butadiene Gasoline Yield table: (e.g: methane product needs the following feed: 0.07 ethane +0.25 propane + 0.1 gas oil + 0.15 DNG) Feed Ethane 0.07 Product Methane Ethane Ethylene Propane Propylene Butadiene Gasoline Fuel Oil 0.4 0.5 0 Propane 0.25 0.06 0.35 0.10 0.15 0.02 0.07 Gas oil 0.1 0.04 0.2 0.01 0.15 0.04 0.25 0.21 DNG 0.15 0.05 0.25 0.01 0.18 0.05 0.3 0.01 0.01 0.01 0.01 0 0 The fuel requirement to run the reactor with respect to each feed type are given as follow: Heating values (Heat produced) Feed type Recycled feed The fuel requirement to run the reactor with respect to each feed type Fuel requirement (BTU/lb) Ethane 8364 Propane 5016 Gas oil 3900 DNG 4553 Natural gas Fuel Produced (BTU/lb) 21520 21520 18000 Methane Fuel oil Price for feeds, products and fuel are listed below Feed type Ethane Propane Gas oil DNG Price (S/Ib) 6.55 9.73 12.50 10.14 Products Methane Ethylene Propylene Butadiene Gasoline Fuel oil Price ($/lb) 5.38 17.75 13.79 26.64 9.93 4.5 The fixed fuel requirement is 20*10^6 Btu/stream hour Assume an energy fuel cost of 2.50$/(10^6 Btu). 1. Set up the objective function and constraints to maximize profit by writing all necessary equalities, imequalities, bounds. Etc... when they exist. The variables to be optimized are the amounts of stream feed in to the reactor. (hint estimate product value, feed and energy costs, This is a linear problem) Recycled methane is considered to contribute to the fuel source not significantly to the mass Problem 2 A reactor system having various feeds and products is listed in the table below. The capacity to run gas feeds through this reactor is 200,000 lb/stream hour. Ethane uses the equivalent of 1.1 lb of capacity per pound of ethane; propane 0.91b; gas oil 0.91b/lb; and DNG 1 The downstream operation is limited to 50000lb/stream hour (ethylene), and 20000 lb/stream hour for propylene. DNG Gas oil Propanc Ethane Recycle J(Ethane) Thermal cracker Fuel (Propane) Methanc Fuel oil Ethylene Propylene Butadiene Gasoline Yield table: (e.g: methane product needs the following feed: 0.07 ethane +0.25 propane + 0.1 gas oil + 0.15 DNG) Feed Ethane 0.07 Product Methane Ethane Ethylene Propane Propylene Butadiene Gasoline Fuel Oil 0.4 0.5 0 Propane 0.25 0.06 0.35 0.10 0.15 0.02 0.07 Gas oil 0.1 0.04 0.2 0.01 0.15 0.04 0.25 0.21 DNG 0.15 0.05 0.25 0.01 0.18 0.05 0.3 0.01 0.01 0.01 0.01 0 0 The fuel requirement to run the reactor with respect to each feed type are given as follow: Heating values (Heat produced) Feed type Recycled feed The fuel requirement to run the reactor with respect to each feed type Fuel requirement (BTU/lb) Ethane 8364 Propane 5016 Gas oil 3900 DNG 4553 Natural gas Fuel Produced (BTU/lb) 21520 21520 18000 Methane Fuel oil Price for feeds, products and fuel are listed below Feed type Ethane Propane Gas oil DNG Price (S/Ib) 6.55 9.73 12.50 10.14 Products Methane Ethylene Propylene Butadiene Gasoline Fuel oil Price ($/lb) 5.38 17.75 13.79 26.64 9.93 4.5 The fixed fuel requirement is 20*10^6 Btu/stream hour Assume an energy fuel cost of 2.50$/(10^6 Btu). 1. Set up the objective function and constraints to maximize profit by writing all necessary equalities, imequalities, bounds. Etc... when they exist. The variables to be optimized are the amounts of stream feed in to the reactor. (hint estimate product value, feed and energy costs, This is a linear problem) Recycled methane is considered to contribute to the fuel source not significantly to the mass