Wellsite Diagnosis of Pumping Problems Using Minicomputers

Abstract

The truck-mounted computer system described here greatly enhances the efficiency of the sucker rod diagnosis technique. Using an example well, the paper shows how the method and the equipment can be used to increase production and decrease lifting costs. With this system, more definitive production and decrease lifting costs. With this system, more definitive and timely results can be obtained more efficiently, thus lowering the cost of applying the technique. Introduction The Sucker Rod Diagnostic Technique was perfected by Shell during the 1960's. Its concept was suggested by the work of British physicians who wanted to analyze human electrocardiograms more accurately and definitively. To do this, they subjected cardiograms to Fourier analysis, hoping to reveal subtle indications of heart disease that might be overlooked if only visual interpretations were made. Similarly the sucker rod method was designed to derive the maximum amount of information from a pumping-well dynamometer card and to make the analysis of the card a science rather than an art. This paper describes a portable computer system for implementing the sucker rod method. Brief Theoretical Review The basis for the diagnostic technique is a stress wave propagation problem based on the one-dimensional propagation problem based on the one-dimensional wave equation (1) The wave equation models the rod string and permits the use of surface data to deduce down-hole conditions in pumping wells. This is directly analogous to the human cardiogram where easy-to-measure surface data are used to infer conditions within the body. The boundary conditions measured at the surface are time histories of the load and position of the polished rod. These are expressed as truncated polished rod. These are expressed as truncated Fourier series of the following type: (2) (3) Solutions to the wave equation that satisfy the measured boundary conditions give operating conditions in a given well at a particular time in its producing life. The basic diagnostic solutions give producing life. The basic diagnostic solutions give displacement and load at arbitrary depths in the rod string. These are (4) and (5) The procedure for solving and generalizing for the case of tapered strings is detailed in Refs. 1 and 2. By cross-plotting the solution for displacement (Eq. 4) vs load (Eq. 5) at a given depth, a dynamometer card at that depth is obtained, This is equivalent to the card that would be measured with a dynamometer instrument placed at that depth. JPT P. 1319