An Investigation of Experimental Methods of Determining Sucker-rod Loads

The problem of determining the most desirable operating conditions of anoil-well pumping unit, the selection of the proper material and size of suckerrods, and the design of the pumping unit, requires that the sucker-rod loads beknown with a reasonable degree of accuracy. In production practice, it is alsodesirable to know the effects of operating speeds and strokes on a plungermotion, as well as on the rod loads. For a particular well, data on rod loads can be obtained by measuring the loadin sucker rods with a dynamometer. This method is not satisfactory because itdoes not permit the various factors to be investigated independently. It isalso impossible to measure the plunger motion simultaneously with rod motionunder operating conditions. The mathematical solution is impractical because ofthe simplifications that have to be made to get a solution and the tremendousamount of numerical work that is necessary after such a simplified solution hasbeen attained. This paper shows how analogies and models can be applied to thesolution of these problems. The loads set up in a sucker-rod string during the ordinary pumping cycle aremade up of the weight of the rods, force required to accelerate the rods, weight of the oil and force required to accelerate the oil on the upstroke, rodfriction, stuffing-box friction, plunger friction, friction of the oil in thetubing and rods, and friction loss through the valves. The problem ofdetermining the sucker-rod load is further complicated by the fact that thelong oil column and the sucker-rod column act as springs, which affect thetransmission of the polished-rod motion. A further complication is the factthat the motion cannot be transmitted at a speed greater than that of thevelocity of sound in the material, and this means that there will be a time lagin the transmission in the motion, as well as a modification of its magnitudeand a phase displacement.