The relative significance of the various well elements In determining the dynamic load on the sucker rods was evaluated by a lumped-parameter analysis, and the rod string was then analyzed as a distributed system to determine the loads and velocities throughout the length of the string . The equations derived were programmed for an IBM 650 computer for calculating loads on both the upstroke and downstroke, and the static and coulomb friction loads were added to the dynamic loads. The effects of varying pumping speed, length of stroke, viscosity, net lift , and friction and specific gravity were computed by means of the program. The polished-rod load increases exponentially with increasing speed and linearly with Increasing stroke length. Low-viscosity fluids have little effect on the load, but as the viscosity approaches 10-2, the load increases rapidly . Both the dynamic and total loads increase slightly with net lift . friction affects primarily the static load, and specific gravity affects primarily the dynamic load. The measured load for 33 wells is within 10 percent of the calculated load for 30 of the cases.
Over the years considerable effort has been devoted toward a better understanding of the nature of sucker-rod pumping. This problem was investigated by Coberly l Mills 2 Kemler, 3 Slonneger, 4 and other during the 30's and 40's. Since World War I1 the trend has been to extend the lumped-parameter analytical approach by considering the rods, fluid, and tubing as continuous or distributed systems This approach under the directions of Howe 5 and Kemler has led to a set of equations considered to be beyond analytical solution. These investigations , together with Halderson, 6 been instrumental in the present impetus toward simulation and analog solutions
In the lumped-parameter method of analysis the entire mass of the element is assumed to be concentrated at a point, and the elastic effects are assumed to be in a massless spring connecting the mass and the driving element The continuous or distributed method of analysis assumes the mass and elasticity to be uniformly distributed throughout-the element.
It is generally recognized that a complete analysis must consider the surface equipment , the rod string, fluid column , tubing , and bottom-hole pump. To make an analysis which would consider all these elements requires that the nature of the various elements must be known or characteristics. An objective of this paper is to determine the characteristics of the rods Another objective is to determine the relative importance of other well elements In contributing to the load on the rods. Realization of these objectives would, of course, only be another step toward a more complete analysis where consideration would be given to the surface equipment as well as subsurface equipment. It should be noted, however, that the rods are the most significant of the well elements in determining the nature of the overall system.
The primary emphasis of this paper is to investigate the dynamic loads in the rods