A General Method For Predicting Rod Pumping System Performance
Authors: Gibbs S.G. 
Published: December 2007

Introduction
Although it looks simple, rod pumping equipment requires complex simulation methods to mimic the variety of actual conditions encountered in the field. This paper describes such a method which relates the influence of unit geometry, prime mover slip, rod design and downhole pump condition. The method is mathematical, but non-technical means such as dynamometer cards and electrical terms are used to describe it.
The standard predictive method sanctioned by the API is designed to simulate the following types of conditions:
Conventional units Low slip (relatively) prime movers Full liquid fillage Anchored tubing
Owing to the diversity of equipment available and the wide variety of downhole conditions prevalent in the field, the API method is limited and applies to only a small percentage of pumping wells.
The method described in this paper is designed to be more flexible so that a wider class of real problems can be solved. The subject method is problems can be solved. The subject method is formulated to simulate the following conditions:
Arbitrary beam unit geometries such as
Air balanced BG Conventional Mark II Clockwise or counterclockwise motion
Arbitrary rod designs and materials
Steel Fiber glass Stranded cable Sinker bar combinations
Arbitrary prime movers (for which torque-speed curves and electrical data are available)
Arbitrary downhole conditions (API pumps)
Anchored or unanchored tubing Full liquid fillage Fluid pound Gas interference Fluid inertia and friction effects
Portions of the subject method have been under development for nineteen years. Some of the theoretical details are shown in Reference 1. Recent additions to the technology have been in handling the effects of inertia on gearbox and prime mover loading. Most recent has been simulation of electrical performance of motors. performance of motors. The following examples illustrate a few of the practical problems that can be solved with the practical problems that can be solved with the technique. Referrals to the API method are unavoidable because it is widely used. No intent to unduly criticize the API method is intended, although limits in its applicability are mentioned.

STATE OF THE ART
To illustrate the type of predictions that are possible, Figure 1-a shows predicted surface and pump possible, Figure 1-a shows predicted surface and pump dynamometer cards for a 7850 ft. well being lifted with a conventional unit at 8.99 SPM with an ultra high slip prime mover in the low torque mode. Shown on the surface card is the permissible load diagram as modified by the effects of rotary and articulating inertia. Figure 1-b shows (predicted) net gearbox torque versus stroke and Figure 1-c shows (predicted) line current versus stroke. The torque plot shows at a glance the number of torque reversals and the severity of torque extremes. The current plot also has utility in evaluating motor load and unit balance. Tables 1 and 2 show the specific values of predicted items in a report format produced by the computer.
The predicted dynagraphs are compared with the actual measurements in Figure 2. The comparison between predicted and measured performance parameters is summarized in Table 3. The agreement is good.
The subject well was chosen impartially beforehand with no prior optimization efforts.