Pump Fillage and Pump Efficiency on a Rod-Pumped Well

Pump displacement vs. actual production

Displacement is the volume the plunger sweeps per stroke, times strokes per minute. In field units, with plunger diameter D and plunger stroke S in inches and N strokes per minute, it works out to about 0.1166 × D² × S × N barrels per day.

The constant is plain unit conversion: the plunger's area (π/4 × D²) times its stroke gives cubic inches per stroke, a day has 1,440 minutes, and a barrel holds 9,702 cubic inches (42 gallons of 231 cubic inches each). Pump designers use the same relation in reverse: divide the maximum expected production by strokes per minute times stroke length to get the pump constant, and from that the bore. ⁵

Two details matter when you compare displacement with a well test:

• Use the plunger's stroke, not the polished rod's. On each upstroke the rods stretch until the fluid load transfers from the standing valve to the travelling valve, so the plunger travels less than the surface stroke. ⁴ If the tubing isn't anchored, the pump barrel also moves up with the plunger, which shortens the effective stroke again. ³ The effective pump stroke can be calculated from the measured surface card. ¹
• Compare like with like. Displacement is measured at pump conditions; the well test is in stock-tank barrels. Oil carrying gas in solution occupies more volume at the pump than in the tank. ¹

Volumetric efficiency is then simply the tested production divided by the pump's displacement.

Reading pump fillage from the card

Pump fillage is the share of each downstroke the plunger spends in liquid: the filled stroke divided by the gross pump stroke, read off the downhole pump card.

On a full pump, the load comes off at the top of the stroke. On an incompletely filled pump, the load stays on into the downstroke until the plunger meets liquid, then drops. The distance from the bottom of the stroke to that drop is the filled stroke. The dynamometer card atlas shows how fillage looks against the other card shapes, including the rounded corner of gas interference.

Fillage tells you how much of each stroke is wasted. It doesn't tell you why: a card with low fillage can mean the well is pumped off or that the barrel is filling with gas. That takes a fluid level (see below).

Where the rest goes: the causes of low pump efficiency

Production falls short of displacement in a fixed order along the way, from the surface stroke to the stock tank.

Rod and tubing stretch

Every upstroke starts with the rods stretching to pick up the fluid load, so part of the polished rod's stroke never reaches the plunger. ⁴ With unanchored tubing, the barrel rides up with the plunger and the effective stroke shrinks further. Anchoring the tubing removes that loss by stopping the barrel from moving. ³ The one exception is a well where overtravel makes the plunger travel more than the surface stroke and pump efficiency exceeds 100%. Even there, the extra production is more than offset by wear. ³

Incomplete fillage: pump-off or free gas

• Pump-off. The pump's displacement is larger than the well's inflow, the fluid level falls to the pump, and the barrel can't fill. The cure is matching displacement to inflow; see fluid pound.
• Free gas. Below the bubble point, the pump stroke must compress gas before it can displace liquid, which means poor pump efficiency and reduced production. ⁶ Free gas takes up space liquid could fill and delays the valves opening. How much it costs depends on how well gas is separated downhole, the intake conditions and the fluid properties. ² In most cases, the production lost to gas interference far exceeds the loss to leakage in pump components. ² See gas-locked rod pump.

Slippage and leaks

Slippage is liquid that slips back between the plunger and the barrel into the pump chamber while the travelling valve is on its seat. ¹ Some is necessary: 2–3% slippage is required to lubricate the pump. ⁵

How much slips depends on the clearance and the conditions:

• Clearance. In the Permian Basin, standard plunger fits run 0.005 to 0.008 inches. ⁵ Operators often run clearances too large for the well, and the cause of the low production can be hard to identify. ¹
• Depth. Slippage rises significantly with depth, because higher temperature thins the water and the pressure difference across the plunger is larger. ¹
• Speed. Slippage rises with pumping speed, but displacement rises faster, so efficiency improves at higher speed. With large clearances, efficiency can drop dramatically at slow speeds. ¹

The Patterson slippage equation calculates the slippage volume, and the authors recommend designing clearances with it rather than with a rule-of-thumb table. ¹ Leaking valves also return fluid. A static travelling-valve load test is a common field check for a leaky pump, which can make a pump card lean much like unanchored tubing does. ⁴

Shrinkage

Oil with gas in solution has more volume at pump pressure than in the stock tank. ¹ This isn't a fault to fix, but it belongs in the comparison: otherwise it looks like a lost barrel.

A worked case: a new pump at 70% efficiency

A published field case shows how the gap breaks down. ¹ A Permian Basin oil well ran a new 2.25-inch pump with 0.009-inch clearance, installed a few weeks earlier.

• The pump card showed a full pump with an effective stroke of 103 inches, calculated from the surface card. That gave a displacement of 580 barrels a day, before correcting for slippage or for oil swell.
• The well tested 106 barrels of oil and 296 barrels of water a day: 178 barrels a day less than the displacement.
• The card showed no gas interference, and a new pump shouldn't leak much. The Patterson equation put slippage at 169.8 barrels a day for this clearance, a 30% loss of displacement that the operator considered excessive.
• Gas in solution swelled the oil volume at the pump by 4.4%, about 5 barrels a day.
• Corrected, production was 70% of the 576-barrel displacement, and most of the loss was slippage.

The lesson: the pump was full, new and gas-free, and still lost almost a third of its displacement, because the clearance was too open for the well.

The order to fix them in

Measure first, then work from the biggest and cheapest losses to the most expensive change.

1. Measure three things together: a pump card (fillage, plus a valve check), a fluid level, and a well test. Work out displacement from the effective plunger stroke, not the surface stroke. ¹⁴
2. Low fillage, fluid at the pump: the well is pumped off. Match displacement to inflow (speed, stroke, control) before touching the pump. See fluid pound.
3. Low fillage, fluid well above the pump: gas is getting in. Improve downhole gas separation and the pump's compression ratio. It is usually a bigger loss than leakage. ²⁶ See gas-locked rod pump.
4. Full card, production still short: check the tubing anchor. Set it by pulling inches of stretch, not by a load gauge. ³⁴ Then check slippage and leaks: run a travelling-valve test, and size the clearance for the well's depth, temperature and speed with the slippage equation. ¹⁴
5. Only then resize the pump. Use the pump constant to choose the bore ⁵, and the rod pump types guide to choose the pump.

Where SRABS fits

SRABS is built around the measurements this guide asks for. SRABS Echo is "an automated acoustic edge device" that reads fluid level, fully remote. "Brain reads every dynamometer card, motor current and Echo fluid level, and checks them against the physics of your rod string." In the words of the proof page: "You set the guardrails, SPM range, fillage targets, kill conditions, and Brain runs the well inside them." See the platform and solutions.

To estimate what fewer failures would mean for your fleet, run the ROI calculator. Its default 100-well scenario is modelled, not a field result.

The bottom line

Displacement minus production is a measurement problem before it is a pump problem. Read fillage off the card, take a fluid level, and compare the test with displacement from the effective stroke. Then fix pump-off, gas, tubing movement and slippage, in that order, before you change the pump.

See it measured on a real well.

FAQ

Sources

1. Rowlan, O. L., McCoy, J. N., Lea, J. F., "Use of the Pump Slippage Equation to Design Pump Clearances," Southwestern Petroleum Short Course, 2012. https://www.swpshortcourse.org/sites/default/files/papers/2012021.pdf
2. Robles, J., Podio, A. L., "Effects of Free Gas and Downhole Separation Efficiency on the Volumetric Efficiency of Sucker Rod Pumps and Progressing Cavity Pumps," Southwestern Petroleum Short Course, 1999. https://www.swpshortcourse.org/paper/effects-free-gas-and-downhole-separation-efficiency-volumetric-efficiency-sucker-rod-pumps
3. Logan, J. L., "Tubing Movement and Tubing Anchor Payout in Pumping Wells," Southwestern Petroleum Short Course, 1964. https://www.swpshortcourse.org/sites/default/files/papers/1964017.pdf
4. Rowlan, O. L., Fernandez, G., Taylor, C. A., Wang, S., "How to Determine if Tubing Is Unanchored in Rod Pump Wells by Analyzing Dynamometer Data," Southwestern Petroleum Short Course, 2023. https://www.swpshortcourse.org/paper/2023010-how-determine-if-tubing-unanchored
5. Monk, A., Thompson, L., Smith, Z., Roderick, R., "Sucker-Rod Pump Selection and Application," Southwestern Petroleum Short Course, 2018. https://www.swpshortcourse.org/sites/default/files/papers/2018018.pdf
6. Chokshi, R., Lane, B., "Reciprocating Rod Lift (RRL)," SPE Artificial Lift webinar series, webinar 2, September 23, 2014. https://file.streaming.spe.org/wp-content/uploads/2024/02/22131640/Reciprocating-Rod-Lift-RRL-.pdf