Surface Card vs Downhole Card: How the Pump Card Is Calculated

Surface card vs downhole card: the short answer

The surface card is measured: load and position at the polished rod, recorded by a load cell and a position sensor on every stroke. The downhole card, or pump card, is calculated from it. A wave-equation model of the rod string strips out stretch, weight and dynamics, leaving the load the pump puts on the bottom of the rods. ¹⁷

Both are dynamometer cards, drawn from the same data. The surface card tells you what the pumping unit is carrying; the downhole card tells you what the pump is doing. Surface cards come in so many shapes that the original patent calls downhole diagnosis from them frequently impossible. ¹ The fault shapes are read on the pump card; see the dynamometer card interpretation guide. This guide covers the step before: how one card becomes the other, and where that goes wrong.

What the surface card measures

The surface card plots polished rod load against polished rod position. Load usually comes from a load cell between the carrier bar and the polished rod clamp, or from a strain gauge on the walking beam. Position comes from a crank switch, Hall-effect sensors or an inclinometer on the beam. Every later calculation depends on those two signals. ⁶

A polished rod load cell sits on the polished rod above the carrier bar and below the clamps, so the whole rod string weight bears on it. Its output is directly proportional to load and temperature-compensated. A beam-mounted strain gauge is only approximately proportional, useful as a qualitative picture of rod load. ⁶ Load inferred from motor torque or speed adds assumptions and is usually not accurate enough. ²⁶ Position is usually worked out from the crank or beam and the unit's geometry. ⁶

The surface card carries everything the surface equipment feels: peak and minimum polished rod load, gearbox torque, structure loading and the rod stresses near the top of the string. ⁶

What the downhole pump card shows

The pump card is the load the pump applies to the bottom of the rod string, plotted against plunger position. It cannot practically be measured on a producing well, so it is calculated. From it you read fluid load, gross and net plunger stroke, pump fillage, leaks, gas and tubing movement. ³⁷¹²

Downhole load cells have been run in test wells to check the calculation, and a measured pump card agreed closely with the calculated one. ⁷ Everyday surveillance relies on the calculation. ³

The 1967 patent lists fluid load, gross pump stroke, displacement and volumetric efficiency, plus tubing leaks, defective tubing anchors, gas separation problems and leaky pumps. ¹ A later patent adds fillage and pump-off detection. ² For fillage on its own, see pump fillage and pump efficiency.

Why the two cards look different

Between the polished rod and the pump hang thousands of feet of steel rod. It stretches under load, it has mass spread along its whole length, and it loses energy to friction with the fluid. Loads travel down it as stress waves. The rod string behaves less like a rigid link and more like a long, damped spring. ¹³

Gibbs' patent names the cause: a long sucker rod has "considerable stretch, distributed mass," so pump motion may differ greatly from surface motion. He treated the rod as a transmission line. ¹ Three effects stack up:

• Rod stretch. When the traveling valve closes and the fluid load comes onto the rods, the string stretches before the plunger starts to move. So the plunger stroke differs from the polished rod stroke. ¹
• Inertia. Accelerating and stopping the string adds load at the polished rod that the pump never feels. ¹
• Damping. Fluid friction along the rods takes energy out on every stroke, and the surface has to supply it. ¹³

Add the rod weight, which the load cell carries and the pump does not, and the surface card is the pump card filtered through the rod string. The downhole card removes the ambiguities of the surface card and the obscuring effects of friction along the rods. ²

How a downhole card is calculated

The textbook method models the rod string with the one-dimensional damped wave equation. The measured surface load and position over a stroke become its boundary conditions. Solving the equation carries load and position down the string, taper by taper, to the pump. Plot the result and you have the pump card. ¹³

The model

The equation describes how displacement travels along a slender elastic rod. It has three ingredients: the speed of sound in steel, which sets how fast a load change travels down the string; the distance from the polished rod; and a damping coefficient that stands in for friction. ¹ The rod weight is subtracted from the measured polished rod load first, because the equation has no gravity term. ¹

The two published solution methods

1. Fourier series (the Gibbs method). The measured load-versus-time and position-versus-time curves are approximated by truncated Fourier series, with coefficients found by numerical integration over the recorded points. The wave equation is solved by separation of variables, and recursive formulas carry the solution through each section of a tapered rod string down to the pump. ¹
2. Finite differences. The rod string is split into short elements, and the equation is stepped from element to element, surface to pump. Later patents describe this method, iterating on net stroke and damping. ³⁵

It can run in real time, point by point, so a complete pump card is ready at the end of each stroke. ² For what a controller then does with that card, see pump-off controller vs. AI well control.

Choosing the damping factor

The model replaces real friction with an equivalent viscous force that removes as much energy per cycle. The 1967 patent sets it from a curve of field measurements, or from polished rod horsepower against pump hydraulic horsepower. ¹

Later work made that an iteration. The pump card's area is the work the pump does. ⁷ If it comes out higher than the hydraulic work of lifting the fluid, the card is under-damped and damping goes up; if lower, damping comes down. Because fluid flows with the rods on one half-stroke and against them on the other, one patent uses separate upstroke and downstroke damping factors. ³ An SWPSC paper finds the damping coefficient directly, without iterating. ⁵

What each card is good for diagnosing

Use the surface card for loads on the surface equipment and the top of the string: peak load, minimum load, gearbox torque and structure loading. Use the pump card for the pump itself: fillage, valve action, gas, leaks, tubing movement, and compression at the bottom of the rods. ¹²⁶⁷

The reference: a full-pump downhole card, close to a rectangle.

Common pitfalls: damping and bad input data

A pump card is only as good as the surface data and the damping behind it. Wrong damping makes a card fat or makes it loop over itself. A load cell with a zero offset shifts the whole card up or down. A position error rotates it, faking tubing movement or changing fillage. Unmodelled friction distorts it. ³⁴⁶

Damping set wrong. An under-damped pump card looks fat; an over-damped one can loop over itself or show a concave upstroke or downstroke. A well-damped card should have roughly flat upstroke and downstroke load lines. ³

Mechanical friction in deviated wells. The wave equation's damping term covers viscous friction only. In deviated wells, rods and couplings rub on the tubing, and that dry friction does not scale with velocity the way viscous friction does. Ignoring it distorts the card, and raising the viscous damping to hide it makes the card stop representing the pump. ⁴

Load errors. Questionable inputs are common, and they feed wrong numbers into rod stress, torque and pump intake pressure. ⁶ The checks:

• Zero offset. Skip the load cell's zero calibration and every point on the card shifts up or down by the offset. ⁶
• Strain gauge drift. Beam gauges drift with temperature, so controllers that run on the downhole card need frequent load recalibration. ⁶
• The zero-load check. Plot the pump card in effective load and, with little downhole friction, the minimum downstroke load should sit on the zero line. A minimum above zero always means a zero offset error; a negative minimum can mean friction or an offset. ⁶

Position errors. A crank switch gives one reference point per stroke, and assuming sinusoidal motion between switch closures gives pump cards a jagged look or loops at the top and bottom of stroke. ⁶ A wrong top-of-stroke or phase setting rotates both cards. In one well it faked almost 25 inches of tubing movement and understated net stroke, which can stop a well early. ⁶ A downhole card that leans to the left almost always points to a position problem, often a lagging, filtered inclinometer. ⁶ Fix it in the wellsite controller, not just in office software. ⁶

What a negative load on the downhole card means

A negative effective load on the pump card means the pump is pushing up on the bottom of the rods: the rods are in compression. A rod string behaves like a slender column and can buckle under very small compressive loads, so a pump card below zero on the downstroke is a buckling warning. Check the load basis first. ⁷

On both strokes the rods should be in tension. But any upward force from the plunger and pump can put the bottom rods, which carry only the plunger weight, into compression, and a rod string behaves as a slender Euler column that buckles under very small compressive loads. ⁷

The catch is how the card is plotted. A pump card plotted in true load sits below the zero line by roughly the buoyancy force on the rods. Plotted in effective load, the minimum sits near zero. ⁷ Buoyancy does not make rods buckle, so only a negative effective load is a buckling signal. Showing large negative loads has caused confusion and led to sinker bars sized against a buoyancy force that does not buckle rods. ⁷ Before acting on a negative minimum:

1. Confirm the card is in effective load, so zero is a real reference. ⁶⁷
2. Rule out a load cell zero offset (see above). ⁶
3. Then read a remaining negative downstroke load as compression from the pump. ⁷

What causes that compression, where the neutral point sits and what it does to the string is covered in the sucker rod buckling guide; the usual weight-based mitigation is in sinker bars and rod guides.

Where SRABS fits

SRABS works from the same surface data every rod-lift engineer already records. On the monitoring side, SRABS Brain reads the cards. On the mechanical side, the SRABS Pump takes away the downstroke compression that a negative effective load on the pump card warns about.

In the words of the platform page, Brain "reads every dynamometer card, motor current and Echo fluid level, and checks them against the physics of your rod string." On buckling, how it works puts it this way: "Buckling shows on the surface dynamometer card, and SRABS Brain flags it from the surface card alone." The SRABS Pump "keeps the rod string in tension at every stroke, so the bottom of the string never goes into compression." See the system, and run the ROI calculator for your fleet. Its default 100-well scenario is modelled, not a field result.

The bottom line

The surface card is what the unit feels; the pump card is what the pump does. A calculated pump card is only as good as its load cell, position data and damping. Check the zero line and the lean before you trust it, and read a negative effective load as compression at the bottom of the string.

If your pump cards keep dipping below zero on the downstroke, test that on one well.

FAQ

Sources

1. Gibbs, S. G., US Patent 3,343,409, "Method of determining sucker rod pump performance" (Shell Oil Co., 1967). https://patents.google.com/patent/US3343409
2. Gibbs, S. G., US Patent 5,252,031, "Monitoring and pump-off control with downhole pump cards" (1993). https://patents.google.com/patent/US5252031
3. Pons, V. M., US Patent 9,810,214, "Calculating downhole pump card with iterations on dual damping factors" (Weatherford, 2017). https://patents.google.com/patent/US9810214
4. Pons, V. M., US Patent 9,897,083, "Calculating downhole cards in deviated wells" (Weatherford, 2018). https://patents.google.com/patent/US9897083
5. Bastian, M., Keating, J., Jennings, J. W., "A Method to Find the Viscous Damping Coefficient and a Faster Diagnostic Model," Southwestern Petroleum Short Course, paper 1990023. https://www.swpshortcourse.org/paper/method-find-viscous-damping-coefficient-and-faster-diagnostic-model
6. Allison, A., "Accurate Load & Position Measurement Is Critical to Quality Dynamometer Analysis," Southwestern Petroleum Short Course, paper 2015001. https://www.swpshortcourse.org/paper/2015001-accurate-load-position-measurement-critical-quality-dynamometer-analysis
7. Rowlan, O. L., "Effect of Fluid Buoyancy on Rod String Loads and Stresses," Southwestern Petroleum Short Course, paper 1999013. https://www.swpshortcourse.org/paper/effect-fluid-buoyancy-rod-string-loads-and-stresses