Jay Dickson sat at his desk mulling over his current assignment. Three months ago he had been hired by CalEnergy Canada, a major vertically integrated oil company, in their LPG (liquefied petroleum gas) department in downtown Calgary. He was quickly given the opportunity to take on a variety of challenging tasks. His latest assignment was especially demanding. CalEnergy had recently signed an agreement to buy pipeline capacity on the Interprovincial Pipeline (IPPL) from another company. This pipeline capacity would be used to transport natural gas liquids (NGLs) from Alberta to their processing plant in eastern Ontario. CalEnergy wished to optimize the use of this new pipeline capacity with regard to profits. The additional capacity came to a total of 6,250 barrels gas per day (bbl./day). CalEnergy had a number of different sources of NGLs from which it could choose to pipe downstream to the east. Of course, the company could choose to mix source streams if it wished (e.g. it could send 2,000 bbl./day from one source and another 3,000 bb1./day from another). All of these sources converged on an Alberta receiving point (RP), at which time CalEnergy chose whether to process the NGLs in Alberta or whether to pipe them down east for processing via the IPPL. The first source was an 8" pipeline connecting several of CalEnergy's gas plants to its Alberta receiving point. This source was simply known as High River. The second source was through an exchange deal with another oil and gas company. In exchange for delivering NGLs elsewhere in the province, CalEnergy receives NGLs at the RP via the Peace pipeline. Third, CalEnergy's refinery in Alberta provides them with a large volume of NGLs daily. Fourth and finally, another pipeline provides CalEnergy with pure normal propane (C) at the RP daily. The compositions of each of these streams and their daily capacities are shown in the table receiving point (RP), at which time CalEnergy chose whether to process the NGLs in Alberta or whether to pipe them down east for processing via the IPPL. The first source was an 8" pipeline connecting several of CalEnergy's gas plants to its Alberta receiving point. This source was simply known as High River. The second source was through an exchange deal with another oil and gas company. In exchange for delivering NGLs elsewhere in the province, CalEnergy receives NGLs at the RP via the Peace pipeline. Third, CalEnergy's refinery in Alberta provides them with a large volume of NGLs daily. Fourth and finally, another pipeline provides CalEnergy with pure normal propane (C3) at the RP daily. 1 The compositions of each of these streams and their daily capacities are shown in the table below. Each stream can be considered to be formed from five components: ethane, propane, normal-butane, iso-butane, and condensate (pentanes and up). It is this composition that is of interest because CalEnergy receives different profits for each of these components when they are processed down east as opposed to in Alberta. Ethane (C2) Propane (C3) n-Butane (nC4) iso-Butane (iC4) Condensate (Cs) Capacity (bbl./day) High River 1.1% 46.9% 27.0% 13.3% 11.7% 1,668 Peace 20.8% 35.2% 17.4% 8.6% 18.0% 418 Refinery 0.4% 22.0% 24.9% 50.7% 2.0% 4,956 Pure C 0% 100% 0% 0% 0% No effective limit Because of different physical pipeline constraints, it is always preferable to do final processing of the gas in the province in which it is to be sold. However, because costs of processing and shipping along with the market demand for each component differ from province to province, CalEnergy has what are known as "netbacks": the difference in profit for a cubic meter of gas processed and sold in the east versus Alberta. These factors are in a constant state of flux. However, the current forecasts indicate that it shall generally be more profitable to pipe down east. Ethane and normal-butane are predicted to each garner CalEnergy $3.50 in additional profits per cubic meter. Propane will be worth $5.50 more and iso-butane will be worth a whopping $10.00 more per cubic meter. However, condensate, a traditional loser in the eastern market is forecasted to lose $2.50 per cubic meter. In addition, it should be noted that it will cost $0.10 per barrel to ship the NGLs downstream and an additional $0.10 per cubic meter in fractionating costs (the plant in Ontario is older and not as cost efficient as the Alberta facility). Jay was also aware that because of a number of technical constraints having to do with the vapor pressure of the gas being piped, and because of the fact that this was not a continuous pipeline but rather a series of pipelines with several breakout and reinjection points, the composition of the NGL being piped had to fall within certain ranges. Ethane could not be more than 2% of the overall gas, propane could not be more than 50% nor less than 35% of the total gas; the total amount of butane (normal- and iso-) could not exceed 50% of the overall composition yet must exceed 30%; as well, the ratio of iso-butane to normal-butane could not exceed 2:3. Jay was also aware that because of a number of technical constraints having to do with the vapor pressure of the gas being piped, and because of the fact that this was not a continuous pipeline but rather a series of pipelines with several breakout and reinjection points, the composition of the NGL being piped had to fall within certain ranges. Ethane could not be more than 2% of the overall gas; propane could not be more than 50% nor less than 35% of the total gas, the total amount of butane (normal- and iso-) could not exceed 50% of the overall composition yet must exceed 30%; as well, the ratio of iso-butane to normal-butane could not exceed 2:3. Jay's boss had asked him this morning to optimize the use of this new pipeline capacity with the objective of maximizing profits. Realizing that the problem was suitable for linear programming, Jay began drawing upon his LP skills and started to formulate the problem. Questions In the role of Jay, prepare a report to your boss dealing with the following issues. 1. What are the contribution margins for each source? What is the solution to the problem and the resulting value of the objective function? How much of the total pipeline capacity is being used with this solution? 2. Management is considering acquiring more NGLs on the High River pipeline. Specifically, an additional 3,000 bbl./day of capacity is available, but at a cost of $0.70 more for each additional bbl. which will be piped east (to be clear: if only 1,000 bbl. are piped east, CalEnergy pays only $700 more). Should CalEnergy purchase some or all of the additional capacity? Jay Dickson sat at his desk mulling over his current assignment. Three months ago he had been hired by CalEnergy Canada, a major vertically integrated oil company, in their LPG (liquefied petroleum gas) department in downtown Calgary. He was quickly given the opportunity to take on a variety of challenging tasks. His latest assignment was especially demanding. CalEnergy had recently signed an agreement to buy pipeline capacity on the Interprovincial Pipeline (IPPL) from another company. This pipeline capacity would be used to transport natural gas liquids (NGLs) from Alberta to their processing plant in eastern Ontario. CalEnergy wished to optimize the use of this new pipeline capacity with regard to profits. The additional capacity came to a total of 6,250 barrels gas per day (bbl./day). CalEnergy had a number of different sources of NGLs from which it could choose to pipe downstream to the east. Of course, the company could choose to mix source streams if it wished (e.g. it could send 2,000 bbl./day from one source and another 3,000 bb1./day from another). All of these sources converged on an Alberta receiving point (RP), at which time CalEnergy chose whether to process the NGLs in Alberta or whether to pipe them down east for processing via the IPPL. The first source was an 8" pipeline connecting several of CalEnergy's gas plants to its Alberta receiving point. This source was simply known as High River. The second source was through an exchange deal with another oil and gas company. In exchange for delivering NGLs elsewhere in the province, CalEnergy receives NGLs at the RP via the Peace pipeline. Third, CalEnergy's refinery in Alberta provides them with a large volume of NGLs daily. Fourth and finally, another pipeline provides CalEnergy with pure normal propane (C) at the RP daily. The compositions of each of these streams and their daily capacities are shown in the table receiving point (RP), at which time CalEnergy chose whether to process the NGLs in Alberta or whether to pipe them down east for processing via the IPPL. The first source was an 8" pipeline connecting several of CalEnergy's gas plants to its Alberta receiving point. This source was simply known as High River. The second source was through an exchange deal with another oil and gas company. In exchange for delivering NGLs elsewhere in the province, CalEnergy receives NGLs at the RP via the Peace pipeline. Third, CalEnergy's refinery in Alberta provides them with a large volume of NGLs daily. Fourth and finally, another pipeline provides CalEnergy with pure normal propane (C3) at the RP daily. 1 The compositions of each of these streams and their daily capacities are shown in the table below. Each stream can be considered to be formed from five components: ethane, propane, normal-butane, iso-butane, and condensate (pentanes and up). It is this composition that is of interest because CalEnergy receives different profits for each of these components when they are processed down east as opposed to in Alberta. Ethane (C2) Propane (C3) n-Butane (nC4) iso-Butane (iC4) Condensate (Cs) Capacity (bbl./day) High River 1.1% 46.9% 27.0% 13.3% 11.7% 1,668 Peace 20.8% 35.2% 17.4% 8.6% 18.0% 418 Refinery 0.4% 22.0% 24.9% 50.7% 2.0% 4,956 Pure C 0% 100% 0% 0% 0% No effective limit Because of different physical pipeline constraints, it is always preferable to do final processing of the gas in the province in which it is to be sold. However, because costs of processing and shipping along with the market demand for each component differ from province to province, CalEnergy has what are known as "netbacks": the difference in profit for a cubic meter of gas processed and sold in the east versus Alberta. These factors are in a constant state of flux. However, the current forecasts indicate that it shall generally be more profitable to pipe down east. Ethane and normal-butane are predicted to each garner CalEnergy $3.50 in additional profits per cubic meter. Propane will be worth $5.50 more and iso-butane will be worth a whopping $10.00 more per cubic meter. However, condensate, a traditional loser in the eastern market is forecasted to lose $2.50 per cubic meter. In addition, it should be noted that it will cost $0.10 per barrel to ship the NGLs downstream and an additional $0.10 per cubic meter in fractionating costs (the plant in Ontario is older and not as cost efficient as the Alberta facility). Jay was also aware that because of a number of technical constraints having to do with the vapor pressure of the gas being piped, and because of the fact that this was not a continuous pipeline but rather a series of pipelines with several breakout and reinjection points, the composition of the NGL being piped had to fall within certain ranges. Ethane could not be more than 2% of the overall gas, propane could not be more than 50% nor less than 35% of the total gas; the total amount of butane (normal- and iso-) could not exceed 50% of the overall composition yet must exceed 30%; as well, the ratio of iso-butane to normal-butane could not exceed 2:3. Jay was also aware that because of a number of technical constraints having to do with the vapor pressure of the gas being piped, and because of the fact that this was not a continuous pipeline but rather a series of pipelines with several breakout and reinjection points, the composition of the NGL being piped had to fall within certain ranges. Ethane could not be more than 2% of the overall gas; propane could not be more than 50% nor less than 35% of the total gas, the total amount of butane (normal- and iso-) could not exceed 50% of the overall composition yet must exceed 30%; as well, the ratio of iso-butane to normal-butane could not exceed 2:3. Jay's boss had asked him this morning to optimize the use of this new pipeline capacity with the objective of maximizing profits. Realizing that the problem was suitable for linear programming, Jay began drawing upon his LP skills and started to formulate the problem. Questions In the role of Jay, prepare a report to your boss dealing with the following issues. 1. What are the contribution margins for each source? What is the solution to the problem and the resulting value of the objective function? How much of the total pipeline capacity is being used with this solution? 2. Management is considering acquiring more NGLs on the High River pipeline. Specifically, an additional 3,000 bbl./day of capacity is available, but at a cost of $0.70 more for each additional bbl. which will be piped east (to be clear: if only 1,000 bbl. are piped east, CalEnergy pays only $700 more). Should CalEnergy purchase some or all of the additional capacity