Oil Refinery Optimization

A refinery has a distillation capacity of 100,000 barrels of crude/day in its fractionater. Here crude oil is basically heated and as the temperature increases different products called DN (distillation naptha), DHO (distillation heating oil), DGO (distillation gas oil), and P (Pitch), are given off in vapor form, and are collected at various levels. The refinery gets crude oil from three different countries, these are called crudes 1,2,3. All the crudes and the various products are measured by volume in barrels. The output statistics from the distillation of each of the available crudes are given in Table 1.

  
Table 1: Distillation Output

It can be verified that the total volume of outputs from the distillation of one barrel of crude is <1. The loss is due to evaporation and unusable heavy residuals.

DHO can be sold directly as heating oil. DGO can be sold directly as diesel fuel. Sale prices of these products are given in Table 3.

  
Table 2: Cracker Output

DHO and DGO can also be processed further in a catalytic cracker. The catalytic cracker can either process a maximum of 100,000 barrels/day of DHO, or a maximum of 50,000 barrels/day of DGO, or a combination of these in proportion of these levels adding up to 1. Also, when processing DHO the catalytic cracker can be run either at a normal level or at a high severity level. The high severity level helps to convert more of the DHO into naptha as seen from Table 2. In processing DGO the catalytic cracker is run at normal level only and never on high severity level.

The cracking process converts the feed into products whose density is smaller than that of the feed, that's why the volume of outputs from this process is greater than the feed volume.

The pitch (from fractionater and catalytic cracker) can be combined with CHO (two parts of CHO to 17 parts of pitch) and sold as heavy fuel oil. DN and CN can be combined (20 parts of DN with 17 parts or greater of CN) and sold as gasoline. The quality of the gasoline improves with the proportion of CN in this blend. Table 3 gives the selling prices and demand for the various final products.

  
Table 3: Final Prices

The processing cost on the fractionater is estimated to be $0.60/barrel of crude processed. On the catalytic cracker the processing costs are $1.50/barrel of fresh feed at the high severity level, and $0.95/barrel of fresh feed at the normal level. Formulate the problem of determining how much of each final product to produce daily in order to maximize daily net profit, as an LP.

 
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