Beam pumping unit

The dynamometer card tells you what the pump is doing a mile down.

A rod pump lifts fluid one stroke at a time. The load cell and the rod position draw a card on every stroke, and the shape of that card says whether the pump is full, pounding, gassy or worn. The twin turns the card into fillage, production and gearbox torque.

API 11E 640D-305-144, 8 spm, 1.75 in plunger at 7,000 ft

Built and run to API 11E, API RP 11L

Start with one station or field See how we prove results

Production, pump full: 289 bbl/d
Plunger stroke: 112 in
Peak rod load: 62% of rating
Peak torque: 43% of gearbox

Anatomy and nameplate

1Polished-rod load. Load cell under the carrier bar. One half of the card.
2Rod position. Inclinometer on the beam. The other half of the card.
3Motor current and speed. Power on each stroke and a second view of balance.
4Strokes per minute. Sets the production the pump can make when it is full.
5Pump-off controller state. Running, idle or tripped, and the idle time it chose.
6Tubing pressure. Back pressure the pump lifts against. A leak shows here.
7Casing pressure. Gas in the annulus. Rising pressure points to gas going to the pump.
8Downhole pump. Its card is worked out from the surface card through the rods.

Beam pumping unit nameplate
Unit
API 11E size	640D-305-144, conventional geometry
Gearbox rating	640,000 in·lb
Structure rating	30,500 lb polished rod load
Stroke	144 in
Speed	8 strokes per minute
Motor	50 hp, high-slip, with pump-off controller and load cell
Well and rods
Pump	1.75 in plunger, insert pump at 7,000 ft, tubing anchored
Rod string	API 76: 30% 7/8 in, 70% 3/4 in, Grade D
Fluid	60% water cut, specific gravity 0.97
Fluid load on plunger	7,008 lb
Rod weight	12,677 lb in air, 11,103 lb in fluid
Rod stretch and overtravel	40.2 in stretch, 8.6 in overtravel
Plunger stroke	112 in of the 144 in surface stroke
At design
Production, pump full	289 bbl/d gross, 116 bbl/d oil
Peak polished rod load	18,837 lb, 62% of structure rating
Minimum polished rod load	10,377 lb
Top rod stress	31,343 psi
Counterbalance effect	14,607 lb at the polished rod
Peak gearbox torque	275k in·lb, 43% of rating

From the well to market

Wells lift the fluid. The separator splits it. Oil goes to the tank battery and gas to the compressor station, and both leave by pipeline for processing.

Well fluid
Crude oil
Gas
Has its own twin page

The physics

The equations behind every curve on this page.

Production

Q = 0.1166·D²·S_p·N·E

bbl/d from plunger size, plunger stroke and speed. 289 bbl/d with the pump full.

Plunger stroke

S_p = S − e_r + e_o

The rods stretch 40 in under the fluid load, so the plunger moves less than the polished rod.

Pump fillage

fill = effective stroke / gross stroke

Read from the downhole card, where the load comes off.

Gearbox torque

T(θ) = TF(θ)·(F(θ) − B)

Rod load less counterbalance, through the torque factor of the unit. Kept under the rating.

Dynamometer cards

The surface card is what the load cell sees. The downhole card is what the pump does. Fluid pound changes both.

Surface card: full pump against fluid pound

Polished rod, 8 strokes a minute, 7,000 ft pump depth

Full pump
Fluid pound, 60% full

Peak load: 18,837 lb, 62% of rating
Minimum load: 10,377 lb

The loop is the rods picking up the fluid on the way up and letting it go on the way down. With fluid pound the load hangs on far into the downstroke, then drops all at once when the plunger hits liquid.

F = W_rf + F_o(stretch) + W_r·α·cos θ α = S·N² / 70,500

Downhole card: what the pump is doing

1.75 in plunger, 112 in gross plunger stroke

Full pump
Fluid pound, 60% full

Fluid load: 7,008 lb
Rod stretch: 40.2 in
Overtravel: 8.6 in

A full pump draws a rectangle: fluid load on the way up, none on the way down. Fillage is the width where the load comes off, divided by the full width.

fill = effective plunger stroke / gross plunger stroke S_p = S − e_r + e_o

Fillage and torque

Inflow sets how fast the pump should run. Counterbalance sets how hard the gearbox works to run it.

Fillage as the well draws down

Inflow falls from 310 to 170 bbl/d over 120 days

Fillage at 8 spm
Fillage with speed matched
Matched speed (right axis)

Speed on day 120: 5.2 spm

Once inflow drops below what the pump can lift, the barrel stops filling and the pump starts to pound. Slowing the unit to match inflow keeps it full and saves the rods and the gearbox.

fill = q_in / (0.1166·D²·S_p·N·E)

Gearbox torque against the rating

Net torque at the crank shaft through one stroke

Balanced
Counterweight 15% light

Peak, balanced: 275k in·lb, 43%
Peak, out of balance: 426k in·lb, 67%

Counterweights carry the rods on the way down so the gearbox sees two equal humps. A light counterweight piles the load onto the upstroke and eats into the gearbox rating.

T(θ) = TF(θ)·(F(θ) − B) TF ≈ (S/2)·sin θ

Failure modes

What breaks, what it looks like, what the twin does about it.

Failure mode	The physics	Signals that show it	How the twin catches it
Fluid pound	The barrel only part fills, so the plunger falls through gas and hits liquid on the downstroke.	Card shows the load staying on late in the downstroke, then a sharp drop. Fillage under 85%.	Reads fillage on every stroke and gives the speed or idle time that matches inflow.
Gas interference	Free gas enters the pump and compresses before the valves open.	Rounded load drop on the downstroke. Casing pressure up. Fillage low with fluid over the pump.	Tells gas from pump-off by the card shape and fluid level, and puts a number on the barrels deferred.
Worn pump, valve leaks	Fluid slips past the plunger or a leaking valve during the stroke.	Load falls off during the upstroke. Production down at the same fillage.	Runs traveling and standing valve checks from the card and trends pump efficiency.
Rod part	Fatigue or a worn coupling breaks the rod string.	Card collapses to rod weight only. Load far under the model. No production.	Flags the part within strokes and tracks rod stress against the allowable so fewer happen.
Out of balance	Counterweight too light or too heavy for the rod load.	Uneven motor current peaks. Torque higher on one stroke than the other.	Works out net torque from the card and gives the counterweight move that evens it out.

What the twin does not do

The pump-off controller keeps control of the unit. We suggest speed and idle time. Your people set them.
We never start or stop a well. TwinEdge is never in the safety loop.

How we catch it early

A physics twin and a PINN, working on one beam pumping unit.

The twin is a set of equations for this machine, tuned to its nameplate. Give it the flow, speed and conditions and it returns what every reading should be. It always gives the same answer for the same inputs.

A physics-informed neural network, or PINN, sits on top. It is trained on the plant’s own data and it is penalized whenever it breaks a physics rule. So it can only learn what the equations leave out: wear, fouling, friction. It cannot invent an answer that the machine could never produce.

Step 1
Measure
Flow, pressure, current, temperature, vibration. Whatever the asset already has.
Step 2
Physics twin
The equations of this machine, set to its nameplate. It says what the readings should be right now.
Step 3
Residual
Measured minus expected. Demand, weather and speed are already taken out.
Step 4
PINN
A small neural network that learns the cause of the gap, under the physics rules.
Step 5
Finding
A named cause, a date, and the kWh or hours at stake. An engineer reviews it.

loss = (measured − predicted)² + λ · (physics residual)²

The second term is the rulebook. It is zero when the network obeys the equations.

Why this beats black-box AI

A black-box model learns patterns from history. It needs examples of each failure, and it goes quiet when the pump runs at a point it has not seen. The twin starts from physics, so it works on day one. The PINN adds what physics cannot know about this particular machine.

That is also what makes the savings countable. The baseline is a calculation, not a guess, so the gap between baseline and meter is a number a customer can check.

What the twin checks on this asset

Fillage on every stroke from the downhole card
Production against 289 bbl/d with the pump full
Peak and minimum rod load against the rating and the rod allowable
Gearbox torque and balance from the card

	Fixed alarm	Black-box AI	Twin + PINN
Needs failure history to learn	No	Yes, lots	No
Says what is wrong	No	Rarely	Yes, by name
Works at a flow it has never seen	No	Often fails	Yes, the equations still hold
Puts a number on the saving	No	No	Yes, in kWh and dollars
Lead time on slow wear	Late	Varies	Weeks to months
Every number can be traced	Yes	No	Yes, to an equation

What the twin puts a number on

Energy and cost, from the equations.

Gas interference, pump 72% full

32 bbl/d oil

81 bbl/d gross deferred, $2,265 a day at $70 per bbl

One rod part

578 bbl oil

5 days waiting for a rig, $40,447

Counterweight 15% light

67% of gearbox

Against 43% when balanced

Pounding starts

Day 47

As inflow falls at a fixed 8 strokes a minute

What we do for you

We watch it. We catch it. We prove it.

Our reliability engineers run the twin on your beam pumping unit, review every finding, and help your crew fix it. After the repair we compare the meter to the baseline and write the result in the ledger.

Start with one station or field See the 90-day pilot

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