Rod Pump Sucker Rod Sizing

Overview

Sucker rod pumping (beam pumping) is the most common artificial lift method, used on over 80% of artificially lifted wells worldwide. The system consists of a surface pumping unit (beam), sucker rod string, and downhole pump. Key design parameters include rod loads, pump displacement, counterbalance, and polished rod horsepower. The API RP 11L method provides a systematic approach to rod pump design.

Theory

The sucker rod string transmits reciprocating motion from the surface beam pump to the downhole plunger pump. During the upstroke, the traveling valve closes, the plunger lifts fluid, and rods carry the fluid load plus rod weight. During the downstroke, the standing valve closes, the traveling valve opens, and fluid transfers above the plunger.

Formulas

Pump Displacement

PD = 0.1166 * Ap * Sp * N  (bbl/d)

where Ap = plunger area (in²), Sp = effective plunger stroke (in), N = pumping speed (spm).

Plunger Area

Ap = π/4 * Dp^2

Common sizes: 1.25" (1.227 in²), 1.50" (1.767 in²), 1.75" (2.405 in²), 2.00" (3.142 in²).

Volumetric Efficiency

q = PD * Ev

Typical Ev: 70–90% (affected by gas interference, pump slippage, rod stretch).

Peak Polished Rod Load (PPRL)

PPRL = Wrf + Fo + (Wr * Sp * N^2 * C)

Simplified (API RP 11L):

PPRL = Wrf + Fo * (1 + F1)

where Wrf = weight of rods in fluid, Fo = fluid load, F1 = acceleration factor.

Minimum Polished Rod Load (MPRL)

MPRL = Wrf - Fo * F2

Weight of Rods in Fluid

Wrf = Wr * (1 - ρf/ρsteel) = Wr * (1 - SG_fluid/7.85)

Fluid Load

Fo = 0.052 * ρf * H * Ap = 0.433 * SG * H * Ap

where H = fluid level depth (ft), or net lift if pumped off.

Rod Stretch

ΔL_rod = Fo * L / (Ar * E)

where Ar = rod cross-sectional area, E = Young's modulus (30 × 10⁶ psi for steel).

Effective Plunger Stroke

Sp = S + ΔL_rod - ΔL_tubing

(Anchored tubing: ΔL_tubing ≈ 0.)

Polished Rod Horsepower

PRHP = F_avg * S * N / 33,000 * 12  (hp)

or:

PRHP = 2.53e-6 * G * D * S * N

where G = fluid specific gravity, D = net lift (ft).

Worked Example

Given: 1.75" pump, 5,000 ft setting depth, 7/8" rods, S = 86" stroke, N = 8 spm, SG = 0.85, pump fully submerged.

Step 1: Plunger area:

Ap = π/4 * 1.75^2 = 2.405 in²

Step 2: Pump displacement:

PD = 0.1166 * 2.405 * 86 * 8 = 192.9 bbl/d

Step 3: Fluid load:

Fo = 0.433 * 0.85 * 5,000 * 2.405 = 0.368 * 5,000 * 2.405 = 4,427 lbf

Step 4: Rod weight (7/8" rods, 2.224 lb/ft):

Wr = 2.224 * 5,000 = 11,120 lb
Wrf = 11,120 * (1 - 0.85/7.85) = 11,120 * 0.892 = 9,919 lb

Step 5: Peak load (simplified, F1 ≈ 0.15):

PPRL ≈ 9,919 + 4,427 * 1.15 = 9,919 + 5,091 = 15,010 lb

With Ev = 80%: q = 192.9 * 0.80 = 154 bbl/d

Valid Ranges

References

1. API RP 11L — Design Calculations for Sucker Rod Pumping Systems.
2. Takacs, G. (2015). Sucker-Rod Pumping Handbook. Gulf Professional Publishing.
3. Brown, K.E. (1980). The Technology of Artificial Lift Methods, Vol. 2b. PennWell.
4. PetroWiki — Sucker rod pumping: https://petrowiki.spe.org/Sucker_rod_pumping