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Optimization of A Thermal Cracker Via Linear Programming

The document describes optimizing the operation of a thermal cracker that produces olefins from various feedstocks using linear programming. The cracker has constraints on its capacity to process gas feeds and downstream limits on ethylene and propylene production. Linear programming is used to maximize profit by determining the optimal amounts of each feedstock to use while satisfying all constraints. The yield matrix and relevant process information like fuel requirements and prices are provided to set up and solve the linear programming problem.

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Charly Jiménez
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248 views1 page

Optimization of A Thermal Cracker Via Linear Programming

The document describes optimizing the operation of a thermal cracker that produces olefins from various feedstocks using linear programming. The cracker has constraints on its capacity to process gas feeds and downstream limits on ethylene and propylene production. Linear programming is used to maximize profit by determining the optimal amounts of each feedstock to use while satisfying all constraints. The yield matrix and relevant process information like fuel requirements and prices are provided to set up and solve the linear programming problem.

Uploaded by

Charly Jiménez
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Optimization of a Thermal Cracker via Linear Programming

Reactor systems that can be described by “yield matrix” are potential candidates for the application of linear
programming. In these situations, each reactant is known to produce a certain distribution of products. When
multiple reactants are employed, it is desirable to optimize the amount of each reactant so that the products
satisfy flow and demand constraints. Linear programming has become widely adopted in scheduling production
in olefin units and catalytic crackers. In this example, we make use of linear programming to optimize the
operation of a thermal cracker sketched in Fig. 1. Table 1 shows various feeds and the corresponding product

Figure 1: Flow diagram of thermal cracker.

distribution for a thermal cracker that produces olefins. The possible feeds include ethane, propane, debutanized
natural gasoline (DNG), and gas oil, some of which may be fed simultaneously. Based on plant data, eight
products are produced in varying proportions according to the yield matrix (see Table 1). The capacity to
run gas feeds through the cracker is 200,000 lb/stream hour (total flow based on an average mixture). Ethane
uses the equivalent of 1.1 lb of capacity per pound of ethane; propane 0.9 lb; gas oil 0.9 lb/lb; and DNG 1.0.
Table 1: Yield structure: (wt. fraction).
Feed
Product Ethane Propane Gas oil DNG
Methane 0.07 0.25 0.10 0.15
Ethane 0.40 0.06 0.04 0.05
Ethylene 0.50 0.35 0.20 0.25
Propane − 0.10 0.01 0.01
Propylene 0.01 0.15 0.15 0.18
Butadiene 0.01 0.02 0.04 0.05
Gasoline 0.01 0.07 0.25 0.30
Fuel oil − − 0.21 0.01
Downstream processing limits exist of 50,000 lb/stream hour on the ethylene and 20,000 lb/stream hour on the
propylene. The fuel requirements to run the cracking system for each feedstock type are as follows.
Feedstock type Fuel requirement (Btu/lb)
Ethane 8364
Propane 5016
Gas oil 3900
DNG 4553
Methane and fuel oil produced by the cracker are recycled as fuel. All the ethane and propane produced is
recycled as feed. Heating values are as follows:
Recycled feed Heat produced (Btu/lb)
Natural gas 21520
Methane 21520
Fuel oil 18000

Because of heat losses and the energy requirements for pyrolysis, the fixed fuel requirement is 20×106 Btu/stream
hour. The price structure on the feeds and products and fuel costs is:
Feeds Price (c/lb) Products Price (c/lb)
Ethane 6.55 Methane 5.38(fuel value)
Propane 9.73 Ethylene 17.75
Gas oil 12.50 Propylene 13.79
DNG 10.14 Butadiene 26.64
Gasoline 9.93
Fuel oil 4.50(fuel value)
Assume an energy (fuel) cost of $2.5/106 Btu.
The procedure is to:
1. Set up the objective function and constraints to maximize profit while operating within furnace and
downstream process equipment constraints. The variables to be optimized are the amounts of the four
feeds.
2. Solve using linear programming.

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