Dynagrams help design, diagnose sucker-rod pumping systems

Robert J. Watson
Sheer Lea Pty Ltd. Applecross,
Western Australia

A spreadsheet designed by the author facilitates the design and diagnosis of sucker-rod pumping systems by wave-train analysis.

Incorporated within the spreadsheet are equations required for presenting quantitative, theoretical pump dynagrams, and pressure-vs.-stroke diagrams.

The spreadsheet allows the user to study the effects of a range of fluid properties and pump geometries.

Spreadsheet background

Gibbs, ¹ in 1963, published a mathematical wave-train-based method for designing and diagnosing sucker-rod pumping systems. With this method, the pump dynagram is the starting point for system design and the end point for diagnosis of the pumping action.

The pump dynagrams used in both design and diagnosis have to date been mostly empirical and qualitative.

Juch and Watson,2 in 1969, published theoretical, quantitative pump dynagrams. These were constructed graphically from pressure-volume-temperature (PVT) fluid properties and from the geometries of both single and two-stage pumps.

Both single and two-stage pump geometries combined with tabulated PVT properties are incorporated into a spreadsheet for designing and diagnosing sucker-rod pumping systems.

The spreadsheet greatly facilitates the study of the effects of those variables which impact most on the performance of rod pumps.

Dynagrams

Assumptions and limitations of the dynagrams are as follows:

• The free-gas rate through the pump can be measured or estimated.
• Pump suction and discharge pressures can be measured or estimated.
• Segregation of gas and liquid in the pump barrel does not affect the dynagram significantly.
• Isothermal PVT fluid properties are applicable. Oil compressibility above the bubble point and of water compressibility is small. Laboratory tests found that resolution of gas during recompression is slower than dissolution.2
• Leakage past valves and the plunger are neglected.
• Friction losses and dynamic forces such as fluid pound and the movement of unanchored tubing are excluded.
• If pump fluids are incompressible, pump fill may be incomplete.
• The volume of the plunger above and below the traveling valve is included in the top and bottom dead space.

Calculation method

The calculation method requires the following four steps:

1. Input to the spreadsheet appropriate PVT tables derived from laboratory experiments or from general correlations. The tables should cover the full range of pump pressures. Pressure increments should be 50 psi or less.
2. Input the single and/or two-stage pump geometry.
3. Modify the calculations of stroke vs. pump volume factor to suit the pump geometry and its discharge and intake pressures.
4. Chart the pressures and loads vs. stroke as shown in Sheets 2 and 3 of the spreadsheet. For the two-stage dynagram, only four key points can be plotted. Otherwise, curve fitting must be used.

The key points are sufficient to outline the shape of the dynagram.

Example

Sheet 1 of the spreadsheet [165,808 bytes] shows the calculations and the input PVT data, fluid rates, and pump geometries ( Table 1 [158,244 bytes]). Sheets 2 and 3 allow graphical comparisons of the pressure vs. stroke and the pump dynagrams before and after the addition of a ring valve ( Fig. 1 [155,968 bytes] and Fig. 2 [100,699 bytes]).

For the selected intake and discharge pressures, the two-stage pump in this case demonstrates greater efficiency and liquid capacity, while having a lower and better distributed load.²

Notice that for the single-stage dynagram, "pump off " control is affected on the downstroke. In the two-stage dynagram, "pump off" is controlled by the upstroke.

Either pump dynagram is suitable for design or diagnosis using the Gibbs methods.

References

1. Gibbs, S.G., "Predicting the Behavior of Sucker Rod Pumping Systems," JPT, July 1963.
2. Juch, A.H., and Watson, R.J., "New Concepts in Sucker Rod Pump Design," JPT, March 1969.

Editor's note: To obtain a free copy of the spreadsheet, subscribers can send a request by e-mail to [email protected]. The subscriber will receive a copy of the spreadsheet as an e-mail attachment.

This e-mail offer will expire Sept. 1, 1999.

The Author