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ioe510hw3 - ‘vlil HW 3 Winter 2000 Fermulation due-on 30...

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Unformatted text preview: ‘vlil HW 3, Winter 2000, Fermulation due-on 30 Jan. class. , - ‘ 7 Formulate the .foloowing problem using an LP model. BetUrn your formulation in the caiss on'30 Jan. tohe' grede‘d' as HW. " _‘ .- Later you are asked to solve the'sameproblem. using AMPL software, and write a report on the optimum schition to be implemm. Tour report should contain (1) Model and data files for solving this problem usingA-MPL, (2) output sheet containing AMPL output and (3) A report written by you interpreting the Optimum sol. to implement from AMPL output and any other useful planning information that you can get from the AMPLcutput. _ You Can discuss this process with others,lbut you haveto solve the problem by yourself, and Write the reporttoo by yourself. " The final project report is due on 8 April 2002 in class. . Oil Refinery Optin'flzation 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 difl'erent 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 difl’erent 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 tabulated below. Distillation output Yield (barrels/ barrel) from distillation of . Crude 1 Crude 2 Crude 3 DN 0.19 ' 0.16 0.02 DHO 0.27 ' 0.32 0.24 D'Go 0.38 0.27 ' 0.26 P 0.05 7 0.13 , 0.30 Price ($/barrel) Available 60,000 90,000 80,000 (barrels/day) It can be verified that the total volume of outputs from the distillation of one barrel of crude is < l. 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 below. 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 the table below. In processing DGO the catalytic cracker is run at normal level only and never on high severity level. Catalytic cracker outputs Output (bands/barre: of_ feed) Catalytic naptha‘_(CN), ‘ ' Catalytic heatingoil (CHO) 0 80 0,69 0 52 ' Pitch (P). . . ' O 11 0.10 0 15 The cracking process converts the feed into prodncts whose density is smaller than that-of the feed, that’s why the Volume of outputs from this process is greaterthan (two parts of GHQ to 17 parts of pitch) and sold as heavy fuel oil, DN and ON can be combined (20 parts of DN with 17 parts or greater {if-ON) and sold as gasoline. The quality of the gasoline improves with the proportion of ON in this blend. The following table gives the sellingprices and demand-for the venous final products. Up to 40,000 barrels Anyamount Any amount 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/barre1 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. 2&1. (Pl/VIM QM; rflonomyka FWFgV-Hfls‘ Important Properties 1. Sum of convex functions is convex. _ 2. Positive combination of convex functions is convex. 3. Pointwise supremurn of convex functions is convex. ...
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ioe510hw3 - ‘vlil HW 3 Winter 2000 Fermulation due-on 30...

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