## Example Economical Pipe Size

As a result of the conflict in the Persian Gulf, Kuwait is studying the feasibility of running a steel pipeline across the Arabian Peninsula to the Red Sea. The pipeline will be designed to handle 3 million barrels of crude oil per day at optimum conditions. The length of the line will be 600 miles. Calculate the optimum pipeline diameter that will be used for 20 years for the following data at i = 10%:

• Pumping power = 1.333QAP/1,980,000 horsepower

• Power cost, \$0.015 per horsepower hour

• Pump and motor costs, \$195 per horsepower

The salvage value of the steel after 20 years is assumed to be zero considering the cost of removal. (See Figure 17.6.1 for relationship between D and t.)

Cross-sectional view of pipeline

Cross-sectional view of pipeline

FIGURE 17.6.1 Designing economical pipe size to handle 3 million barrels of crude oil per day (Example 17.6.1).

Discussion. In general, when progressively larger-size pipe is used to carry a given fluid at a given volume flow rate, the energy required to move the fluid will progressively decrease. However, as we increase the pipe size, the cost to construct the pipe will increase. In practice, to obtain the best pipe size for a particular situation, you may choose a reasonable, but small, starting size. Compute the energy cost of pumping fluid through this size and the total construction cost. Compare the difference in energy cost with the difference in construction cost. When the savings in energy cost exceed the added construction cost, you may repeat the process with progressively larger pipe sizes until the added construction cost exceeds the savings in energy cost. As soon as this happens the best pipe size to use in the particular application is identified. However, we can simplify this search process by using the minimum cost concept as explained through Equations (17.6.3) and (17.6.4).

Solution. We will solve the pipe sizing problem in 8 steps:

1. Since the pipe size will be measured in inches, we will assume the following basic conversion units:

2. To determine the operating cost in pumping oil, we first need to determine power (electricity) required to pump oil:

• Volume flow rate per hour:

Q = 3,000,000 barrels/day x 5.6146 ft3/barrel = 16,843,800 ft3/day = 701,825 ft3/hr

_ 128QmL gpD

_ 128 x 701,825 x 8500 x 3,168,000 _ 32.2 x 12,960,000 x 3.14159D4

Pumping power required to boost the pressure drop: 1.333QDP

power =

1,980,000

1,845,153,595

1.333x 701,825 x-

1,980,000

871 818 975

power cost _-' ^-hp x \$0.015/hp.hr x 24 hr/day x 365 days/year

3. Pump and motor cost calculation

871,818,975 ^nr„ pump and motor cost =-^-x \$195/hp

4. Required amount and cost of steel

cross-sectional area =---

= 0.032D2 ft2 total volume of pipe = 0.032D2 ft2 x 3,168,000 ft

= 101,376D2 ft3 total weight of steel = 101,376D2 ft3 x 490.75 lb/ft3 = 49,750,272D2 lb total pipeline cost =\$1.00/lb x 49,750,272D2 lb = \$49,750,272 D2

5. Annual equivalent cost calculation capital cost \$49,750,272 D2 + \$170,00y00,125 j((,10%,20) |2 19,968,752,076

annual power cost 6. Economical pipe size

\$114,557,013,315

AE(10%) = 5,843,648 D2 + 19,968,752,076 + \$114,557f3,315 \ ) • • d4 D4

To find the optimal pipe size (D) that results in the minimum annual equivalent cost, we take the first derivative of AE(10%) with respect to D, equate the result to zero, and solve for D.

11,687,297D6 = 538,103,061,567 D6 = 46,041.70 D' = 5.9868 ft

Note that velocity in a pipe should be ideally no more than around 10 ft/sec due to friction wearing in the pipe. To check to see if the answer is reasonable, we may compute

Q = velocity x pipe inner area

V = 6.93 ft/sec which is less than 10 ft/sec. Therefore, the optimal answer as calculated can be practical. 7. Equivalent annual cost at optimal pipe size • Capital cost:

capital cost =

5.98684 2 19,968,752,076

5.98684