Oil Pipeline Hydraulics: How Much Pressure Do We Need, and When Do We Add a Pump Station?
Key takeaways
- Pump discharge pressure must cover three things: friction along the line, elevation difference, and the pressure required on arrival.
- Friction is calculated with the Darcy-Weisbach equation and grows roughly with the square of velocity.
- In our example, a 20 in line, 150 km long, carrying 100,000 bbl/d needs about 37 bar at the pump.
- Doubling the flow raises friction loss about 3.5 times, so an intermediate pump station may be needed to stay below MAOP.
- Fast valve closure creates a pressure wave (surge) that can exceed design pressure, so closure times are limited and protection systems installed.
Educational content only: procedures and operating values vary between companies and sites. Always follow your company’s approved procedures, your supervisor’s instructions and the permits in force at your site.
From the field to the port: why pressure matters
After processing in the central facility (CPF), stabilized crude leaves through a long transmission line that may run hundreds of kilometres to a refinery or port. Oil does not move by itself: pumps give it pressure, and that pressure is used up along the way. The pipeline engineer answers two questions: how much pressure is needed at the start, and can the pipe take it?
The pressure a line can safely carry is the maximum allowable operating pressure, or MAOP. It is set by wall thickness, steel grade and design factor, then proven by a hydrostatic test before start-up.
Required pressure = three parts
At the pump station we need a pressure equal to the sum of:
- Friction loss: the fluid rubs against the pipe wall and against itself, losing energy over every kilometre.
- Elevation difference: if the delivery point is higher than the start, extra pressure is needed to lift the column. If it is lower, some pressure is recovered.
- Delivery pressure: the minimum needed at the end of the line, for example to enter a tank or another pump, and also to keep pressure above vapour pressure at every point.
The Darcy-Weisbach equation
Friction loss in a pipe of length L and inside diameter D:
ΔP = f × (L ÷ D) × (ρ × v² ÷ 2)
where ρ is fluid density, v the mean velocity and f the friction factor. f depends on the Reynolds number and the wall roughness. In turbulent flow it comes from the Colebrook equation or an approximation such as Swamee-Jain.
The key point: the loss is roughly proportional to the square of velocity. Doubling the flow in the same pipe doubles the velocity, so the loss grows about four times, slightly less because f falls as the Reynolds number rises.
Data: inside diameter D = 0.489 m (20 in line), flow 100,000 bbl/d, density ρ = 830 kg/m³, viscosity 5 cP, roughness 0.045 mm, delivery 100 m higher, required delivery pressure 5 bar.
Q = 100,000 × 0.159 ÷ 86,400 = 0.184 m³/s
A = π × 0.489² ÷ 4 = 0.188 m² → v = 0.98 m/s
Re = 830 × 0.98 × 0.489 ÷ 0.005 ≈ 79,500
The flow is turbulent, and Swamee-Jain gives f ≈ 0.0192.
ΔP/km = 0.0192 × (1,000 ÷ 0.489) × (830 × 0.98² ÷ 2) ≈ 15.7 kPa
Over 150 km the loss is about 23.5 bar. Add the elevation:
ρ × g × h = 830 × 9.81 × 100 ≈ 8.1 bar
So the pump needs about 23.5 + 8.1 + 5 ≈ 36.6 bar. If the MAOP is, say, 70 bar, the line runs with one station and a good margin.
What if we want twice the flow?
At 200,000 bbl/d the velocity becomes 1.96 m/s and f drops to about 0.0170. Friction over 150 km rises to about 83 bar, roughly 3.5 times the previous value. With elevation and delivery pressure we would need about 96 bar, above the MAOP in our example.
Possible solutions:
- Intermediate pump station: placed roughly mid-line, so each station runs below MAOP, as shown in the figure.
- Drag reducing agents (DRA): polymers injected in very small amounts that damp turbulence near the wall and cut friction loss.
- Looping: laying part of a second line alongside the first to share the flow.
- Heating viscous crude: for heavy crudes, lower viscosity means lower friction.
Surge (water hammer)
If a valve closes quickly at the end of a liquid line, the fluid stops suddenly and its kinetic energy becomes a pressure wave travelling back upstream. A first estimate comes from the Joukowsky equation:
ΔP = ρ × a × Δv
where a is the pressure wave speed in the pipe, about 1,000 to 1,200 m/s for crude in steel pipe. In our example:
ΔP = 830 × 1,100 × 0.98 ≈ 8.9 bar
This adds to the operating pressure at that point. That is why minimum valve closure times are specified, surge relief valves are used, and a transient analysis is run when the line is designed.
What does the pipeline operator watch?
- Suction and discharge pressure at each station: low suction pressure can cause pump cavitation.
- Pressure at high points: it must not fall below vapour pressure, or a vapour pocket breaks the liquid column (slack flow).
- Volume balance: comparing volume in and volume out detects leaks early.
- Temperature and viscosity: in winter crude viscosity rises, and so does friction loss.
Takeaway for the engineer
Pipeline design balances three things: the required flow, the pressure the pipe can take, and the number and cost of pump stations. The Darcy-Weisbach equation, the MAOP and a transient study are the three tools every decision starts from.
Test your understanding
Related lessons
- Hydrostatic Pressure, Gradient and ECD for Engineers: Formulas and Worked Examples
- Pigging: cleaning and inspecting pipelines
- Huge Pressure and Trapped Oil: The Answer in Darcy's Law
Sources
- Technical Toolboxes - Liquid pipeline hydraulics: pressure and friction gradient
- Technical Toolboxes - Liquid pipeline hydraulics: elevation pressure drop
- Atmos International - Steady states in a pipeline (pipeline simulation, chapter 5)
- Pump station spacing, velocity limits and transient pressure analysis for crude pipelines
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