Issue 059 - Energy supply chains - Pipeline pumping power
How much power does it take to move millions of barrels of oil through a pipeline?
Recent drone attacks damaged pumping stations on Saudi Arabia's East-West Pipeline, temporarily disrupting a major route used to bypass the Strait of Hormuz. The pipeline stretches about 1,200 km and had recently been transporting roughly 4 to 5 million barrels of crude oil per day.
The problem
Estimate the mechanical pumping power required to move roughly 4 to 5 million barrels of crude oil per day through a 1,200-km pipeline.
You will need to make your own assumptions about the diameter of a major oil pipeline, the density of crude oil, the resulting speed of the oil through the pipe, how much pressure the pumping system must supply to overcome friction and terrain, and the efficiency of the pumps.
Then estimate the pipeline's total pumping-energy requirement over one day, and compare that with the chemical energy contained in the oil being transported.
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
This is a great question because it highlights how little I know about pressure required to move liquids through pipes. I do not know where to begin, so I have to do a wild approximation.
I first assumed a barrel of crude oil was about 45 gallons, and at 3.8 L per gallon that is about 170 L per barrel, or 7.7 x 10^8 L crude oil per day.
daily oil volume
~= 4.5 x 10^6 barrels/day x 45 gal/barrel x 3.8 L/gal
~= 7.7 x 10^8 L/dayNext I assumed you could move a liter of crude oil with about 1 lb of force, which I approximated as 1/2 kg or 5 N. Scaling that up, that is about 5 N x 7.7 x 10^8 L to get about 3.9 x 10^9 N to move that full amount.
estimated total force
~= 5 N/L x 7.7 x 10^8 L
~= 3.9 x 10^9 NFor work done, that force is applied for a distance of 1.2 x 10^6 m, which gives about 4.7 x 10^15 J expended.
work
~= 3.9 x 10^9 N x 1.2 x 10^6 m
~= 4.7 x 10^15 JIf this takes place over the span of about a day, that is about 86,000 seconds, so 4.7 x 10^15 J divided into 86,000 seconds gives about 5.5 x 10^10 W, or 55 GW of power maintained to move that volume of crude oil that distance daily.
power
~= 4.7 x 10^15 J / 8.6 x 10^4 s
~= 5.5 x 10^10 W
~= 55 GWCalibration Score
Matt's Calibration Score: 45 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 10/30. The barrel volume and crude-density instincts were close enough, but the force/pressure peg was too high and the pipe geometry was not used.
Model: 15/30. Work divided by time is a legitimate energy route, but a pipeline problem is better modeled as pressure drop times volumetric flow, with pipe diameter and friction setting the pressure requirement.
Math: 10/10. The arithmetic followed from the assumptions without a major numerical slip.
Result: 10/30. The 55 GW estimate was high by roughly two orders of magnitude, but it still landed in the broad neighborhood that the task was asking about.
Grounding facts
AP reports that Saudi Arabia's East-West Pipeline stretches about 1,200 km and recently carried an average of roughly 2.6 million to 4 million barrels per day through the Red Sea outlet after late August. The article also notes that 4 million barrels per day is about 4% of global oil supply.
Global Energy Monitor lists the pipeline's capacity as 5 million barrels per day, length as 1,200 km, and diameter as 56/48 inches. Its background note says the system consists of two pipelines, one 48 inches and one 56 inches, with pumping and breaking stations along the line.
A petroleum barrel is 42 U.S. gallons, or about 159 L. Crude oil density varies, but a Fermi value of 850 kg/m3 is a useful middle peg. A barrel of oil equivalent is roughly 6 GJ of chemical energy.
After checking sources
Check and recalibrate
Start by turning the flow into SI units. Using 4.5 million barrels per day as the midpoint:
flow volume per day
~= 4.5 x 10^6 barrels/day x 0.159 m3/barrel
~= 7.2 x 10^5 m3/day
volumetric flow rate
~= 7.2 x 10^5 m3/day / 8.6 x 10^4 s/day
~= 8.3 m3/sThat is already a striking flow: several cubic meters of crude oil every second.
Now estimate the pipe speed. A 48-inch pipe is about 1.2 m in diameter, and a 56-inch pipe is about 1.4 m in diameter. Their combined cross-sectional area is about 2.7 m2.
oil speed
~= 8.3 m3/s / 2.7 m2
~= 3 m/sThe oil is not crawling, but it is not moving like a jet either. At a few meters per second, a parcel of oil would take several days to cross 1,200 km.
travel time
~= 1.2 x 10^6 m / 3 m/s
~= 4 x 10^5 s
~= 5 daysA compact pressure-based estimate is:
pump power = pressure drop x flow rate / efficiencyFor a huge long crude pipeline, a plausible total effective pressure requirement is on the order of tens of megapascals after summing friction and terrain through multiple pump stations. Use 50 MPa as a round Fermi pressure-drop peg and 70% overall pumping efficiency:
pump power
~= 5 x 10^7 Pa x 8.3 m3/s / 0.7
~= 6 x 10^8 W
~= 600 MWIf the effective pressure requirement were 30 MPa instead of 50 MPa, the answer would be about 350 MW. If it were 80 MPa, the answer would be close to 1 GW. So the right scale is probably hundreds of megawatts to roughly 1 GW, not a few MW and not tens of GW.
The daily pumping energy is then:
daily pumping energy
~= 6 x 10^8 W x 8.6 x 10^4 s
~= 5 x 10^13 J/day
~= 14 GWh/dayNow compare that with the energy inside the oil:
chemical energy moved per day
~= 4.5 x 10^6 barrels/day x 6 x 10^9 J/barrel
~= 2.7 x 10^16 J/day
pumping share
~= 5 x 10^13 / 2.7 x 10^16
~= 2 x 10^-3
~= 0.2%The scale lesson is that the pipeline is a major industrial machine. Keeping several million barrels per day moving can require the output of a mid-sized power plant. But the energy required to transport the oil is still only a tiny fraction of the chemical energy contained in the oil itself.
Post-check reflection
Matt's reflection
I knew this one was going to be brutal. I just do not know enough about pressure differences and liquids being pressed through tunnels. My answer ended up about two orders of magnitude high, mainly because my estimate of force necessary to move a unit of the crude oil was too high. I just do not do enough problems involving pressure.
Recommended memory peg
For pipeline and pump problems, remember: pump power = pressure difference x volumetric flow / efficiency. A flow of 1 m3/s pushed through 1 MPa requires 1 MW of hydraulic power before efficiency losses.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.