Analog Computer Simulation Of Sucker Rod Pumping Systems
Authors: Snyder Warren E. , Bossert Alfred J. 
Published: December 2007

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This paper was prepared for the Rocky Mountain Joint Regional Meeting in Denver, Colo. May 27–28, 1963, and is considered the property of the Society of Petroleum Engineers. Permission to published is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of the Journal of Petroleum Technology or the Executive Secretary. Such abstract should contain conspicuous acknowledgement of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request providing proper credit is given that publication and the original presentation of the paper.
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Abstract
A method is presented for simulating complete sucker rod pumping systems on an analog computer. Polished rod cards, pump cards and crank torque cards, as well as time histories of these and many other forces and displacements, can be obtained for a wide range of pumping conditions by simple adjustments available in the analog.

Introduction
The analog computer is well suited to the study of complex systems which have many variable parameters. The computer circuitry described here was used to record more than 9,000 dynamometer cards covering a wide range of pumping conditions. Included in the study were the effects of pump load, pumping speed, prime mover slip and inertia, pumping unit geometry, counter- weighting, tapered rod strings and tubing anchors. The many tests completed could not be made on a single well and only with a great expenditure of time and money could they have been completed on a large number of wells.

THE PUMPING SYSTEM
Fig. 1 is a schematic drawing of a sucker rod pumping installation. The principal parts of the system are the prime mover, pumping unit, sucker rod, pump, tubing and fluid column. Each of these parts responds to the forces acting upon it to produce some new motion in the system. The principal parts may include several mechanical parts as in the instance of the prime mover which includes the motor,, belt drive and gear reducer. Fig. 2 is a block diagram of the system as it was arranged for study on the analog computer. For clarity, the two signal paths of the crank are treated separately.

CRANK MOTION
Fig. 3[b] shows the circuit used to compute the motion of the crank. It is a simple harmonic oscillator, as shown by the heavy lines, modified for variable velocity and amplitude stability. With the notation of Fig. 3[a], the basic equations of the crank are:
and
For satisfactory operation, the crank circuit must have extreme amplitude stability. over a long period of time, small errors in the oscillator cause a gradual change in amplitude.