A hydraulically driven walking beam pumping jack is introduced which differs from the conventional pumping jack in that the walking beam is activated by two telescopic joints. To analyze the performance of sucker rod pumping systems (both standard and hydraulic), a mathematical model and a numerical simulation were developed. Seven performance criteria were used to characterize the pumping systems. Full scale laboratory type experiments were performed to verity the mathematical model. Both computer generated and experimental results indicate that the hydraulic pumping jack consumes less energy at the polished rod than does the conventional pumping jack.


To obtain oil by sucker rod pumping, a certain amount of energy is consumed to drive the installation. With low oil prices, low production wells may not be economical to operate. It is apparent that reducing the input energy by optimizing operational practices (stroke length, pumping speed, etc.) or/and introducing more efficient production technology and equipment is of critical importance. Since the performance of a sucker rod pumping system is affected by many variables, the analysis and prediction of real systems is very difficult. In the early 1960's, Gibbs developed two techniques which are widely used now. The first technique is used for predictive purposes and is based on the numerical solution of the partial differential equation describing the motion of a sucker rod string. The second technique is used for diagnostic aims. The Fourier series approach is used to arrive at the desired solution of the same equations. More recently, Gibbs incorporated the variation in prime mover speed in his considerations. In his study, Gibbs used the governing differential equation of the sucker rod motion as proposed by Langer and Lamberger (1942). Doty and Schmidt (1983) have made an attempt to incorporate the viscous friction effects on sucker rod motion, rather than using the overall dumping factor as suggested by Gibbs, and utilized the method of characteristics to solve the system of partial differential equations which constitute their mathematical model.

Chacin and Purcupile (1987) used a discrete model composed of masses, springs, and dashpots to simulate various pumping conditions. In fact, such an approach is similar to the analog model used by the Midwest Research Institute in the late 1960's.

Schafer and Jennings (1987) have used both the analytical and numerical approaches to study the effect of the number of Fourier coefficients, the damping coefficient, and the number of sucker rod elements on the numerical transients associated with the initial start-up of the simulator, and the shape of dynamometer cards. Gault (1987) analyzed the energy requirements for various pumping conditions. He concluded that a considerable decrease in pumping cost can be achieved by designing production systems that consume less energy. The literature related to the sucker rod production system performance analysis and modeling is ample and an in depth analysis is not attempted here.

The objectives of this study are to:

  1. introduce the hydraulic pumping jack (HPJ);

  2. present a mathematical model and the results of a numerical simulation;

  3. analyze the various factors affecting the pumping system performance; and

  4. make a preliminary comparison with a conventional pumping jack (CPJ).


A hydraulic pumping jack differs from the conventional pumping jack in that the walking beam is forced to follow a reciprocating motion. Instead of using a gear reducer, a crank, and a pitman to change rotary motion of the crank to the reciprocating motion of the walking beam, two hydraulically driven telescopic joints are employed.

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