The solution of the wave equation applied to sucker rod pumping makes possible the prediction of a dynamometer card of considerable accuracy, for all beam pumping geometries, aver any application. Development of the net crankshaft torque history of the predicted dynagraph, along with the accompanying cyclic load factor and surface efficiency also permits the forecasting of an optimum size electric motor prime mover for the particular unit geometry and application in question. Using the performance curves of the optimum size motor selected, along with the torque history. and utility company rate schedule involved – accurate electric energy and demand costs can also be forecast. Determination of the optimum size electric prime mover and the accurate prediction of electrical costs for various beam pumping combinations enables the operator to select the mast efficient and economical beam pumping system.
The impact of the energy crisis on much of the free world has recently changed the status of fuel conservation, from desirable, to imperative. Because a great proportion of the world's oil is produced by artificial lift, it becomes increasingly important to expend minimal energy in producing this vital commodity. Since large numbers of wells are produced by electrically driven, beam pumping units, it is more necessary than ever that the prime mover be properly sized, and unit geometry and pumping mode optimized – not only to reduce costs, but to maximumly conserve primary energy as well. It is of further importance to accurately predictelectrical demand and energy costs for various combinations of prime mover, unit geometry, downhole hardware, and pumping mode – so that the most efficient and economical combination can be selected. The development of these two techniques:
optimum prime mover selection, and
accurate prediction of electrical costs – is based on the ability to forecast a particular dynamometer card (for the proposed application) which closely matches the actual measured dynagraph, eventually taken in the field.
Forecasting an accurate dynamometer card shape is based on the solution of the wave equation applied to sucker rod pumping. This predictive method was developed independently by the Sucker Rod Research Institute (SRI) and Dr. S. G. Gibbs of the WABLA Corporation, and is outlined in Gibbs' paper, "PREDICTING THE BEHAVIOR OF SUCKER ROD PUMPING SYSTEMS"(Ref, I). Gibbs' powerful technique makes possible the prediction of an accurate dynamometer card profile for different pump unit geometries under all conditions of operation.
The same mathematical model is used for all geometries and pumping modes, and requires only the insertion of the actual kinematic linkage dimensions of the particular pumping unit geometry in question.
Fig. 1 shows a typical beam pumping application applied to five different geometries. The Gibbs technique not only predicts accurate torsional and structural loads, and pump displacements, but also forecasts a precise dynamometer card profile for each of the different geometries considered. Because arious pumping unit geometries develop significantly different torsional and structural loads and pump displacements, this type of information is important in selecting the proper geometry, pumping mode, nd prime mover size, for any application.