Math 1210- Pipeline Project
The U.S. Interior Secretary recently approved drilling of natural gas wells near Vernal, Utah. Your company has begun drilling and established a high-producing well on BLM ground. They now need to build a pipeline to get the natural gas to their refinery. While running the line directly to the refinery will be the least amount of pipe and shortest distance, it would require running the line across private ground and paying a right-of-way fee. There is a mountain directly east of the well that must be drilled through in order to run the pipeline due east. Your company can build the pipeline around the private ground by going 3 mile directly west and then 8 miles south and finally 25 miles east to the refinery (see figure above). Cost for materials, labor and fees to run the pipeline across BLM ground is $500,000 per mile. For any pipeline run across private ground, your company incurs an additional $350,000 per mile cost for right of way fees. Cost of drilling through the existing mountain would be $1,200,000 on top of the normal costs of the pipeline itself. Also the BLM will require an environmental impact study before allowing you to drill through the mountain. Cost for the study is estimated to be $240,000 and will delay the project by 4 months costing the company another $140,000 per month.
Dear CEO,
I'm sure that you are aware of the above situation. I was asked to determine two different ways of running the pipeline strictly on BLM with two different cases, one heading east through the mountain and then south to the refinery and the other running west, south and then east to the refinery.
The mountain route would require 30 miles of pipe, but the fees for drilling through the mountain would make it cost about $17,000,000.
Dear CEO,
I'm sure that you are aware of the above situation. I was asked to determine two different ways of running the pipeline strictly on BLM with two different cases, one heading east through the mountain and then south to the refinery and the other running west, south and then east to the refinery.
The mountain route would require 30 miles of pipe, but the fees for drilling through the mountain would make it cost about $17,000,000.
The other route running west, south and then east to the refinery would require 36 miles of pipe. This would cost $18,000,000.
I have also calculated the cost of running the pipeline the shortest distance across the private ground to the refinery. This would cost $19,897,989.85. So significantly more than running the pipe around the perimeter of the private ground, this route isn't suggested.
Using my knowledge of calculus I determined the optimal place to run the pipeline to minimize the cost. I have clearly showed all work and included a drawing the pipeline on the figure below.
So if you were to lay the pipe in a southeast direction at a 36.03° from due south you will lay about 9.89 miles of pipe across the private ground. Leaving about 16.18 miles of pipe to lay due east to connect to the refinery. This will cost about $16,499,090.83, this will minimize the cost for laying the pipe. This is the route that I suggest you lay the pipe.
Included is a sketch of the cost function for this pipeline for any configuration involving crossing some private ground as well as some BLM ground.