The U.S. Interior Secretary recently approved drilling of natural gas wells near

Question

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 8 miles directly west and then 16 miles south and finally 40 miles east to the refinery (see figure below). Cost for materials, labor and fees to run the pipeline across BLM ground is $480,000 per mile.

Cost of drilling through the existing mountain would be a one-time cost of $4,500,000 on top of the normal costs ($480,000 per mile) 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 $600,000 and will delay the project by 8 months costing the company another $100,000 per month.

For any pipeline run across private ground, your company incurs an additional $360,000 per mile cost for right-of-way fees.

Your company has asked you to do the following:

b) Determine the cost of running the pipeline:

i) The shortest distance across the private ground to the refinery.

ii) Straight south across the private ground, then straight east to the refinery.

the qustion is B

Explanation / Answer

We have 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 fees for drilling through the mountain would be

C= 4,500,000+600,000+(100,000*8)

C=5,900,000

The other route running west, south and then east to the refinery would require 64 miles of pipe. This would cost

C=480,000*64

C=30,720,000

The shortest distance across the private ground to the refinery is

c=(32^2+16^2)^1/2 (look at the figure in the question we have calculated c by using pythogorus threom from the =(1280)^1/2 triangle in the figure)

C=480,000*x + 840,000*y

C=480,000*0 + 840,000*(1280^1/2)

C= 3,005,273

So it is significantly more than running the pipe around the perimeter of the private ground, this route isn't suggested.

By using the knowledge of calculus we can determine the optimal place to run the pipeline to minimize the cost.

By considering a triangle from the figure given in the question

let the angle be a

tan(a)= x/16

y^2=x^2+16^2

y=(256+x^2)^1/2

C=480,000x+840,000y

C(x)=480,000(32-x)+840,000(256+X^2)^1/2

now differentiate with x and equal to zero

d/dx(C(x)) = -480,000+420,000(2x)/(256+x^2)^1/2

0=840,000x(256+x^2)^1/2-480,000

12=21x/(256+x^2)^1/2

12*(256+x^2)^1/2=21x

256=2.06x^2

x=11.14

tan(a)=11.14/16

angle a= 34.83

y=(256+11.14^2)^1/2

y=19.5

32-(11.14) =

C=480,000(11.14) + 840,000(19.5)

C=21,727,200

So if we were to lay the pipe in a southeast direction at a 34.83° from due south you will lay about 19.5 miles of pipe across the private ground. Leaving about 20.86 miles of pipe to lay due east to connect to the refinery. This will cost about $21,727,200, this will minimize the cost for laying the pipe. This is the route that I suggest you lay the pipe.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.