Friction Losses in Vertical Tubing as Related to Hydraulic Pumps

Abstract

Abstract In a previous paper, the authors showed that the viscosity of the fluid in a well varies in an exponential manner with well depth due to the temperature and pressure gradients of the well. A viscosity gradient, , was introduced as a means to integrate the friction loss in the tubing string of a well. This paper presents the accepted relations for friction loss in circular sections in a form suitable for oilfield use. Hydraulically operated pumps may also involve the flow in an annulus between a large and small-diameter tubing or between a tubing and casing. Where annular flow is involved, the inner tube usually will be eccentric to the outer tube or casing. The available literature was reviewed on this subject, and correction factors proposed by several different writers were combined in the friction loss relations for both laminar and turbulent flow. To simplify calculations in annular sections, equivalent diameters are introduced that take into consideration these factors. These diameter may then be used in the normal friction loss relations for circular section. They are tabulated for the more common combinations of tubing and casing sizes. Charts and nomographs are presented. Together with the nomographs of the previous paper, they enable the petroleum engineer to quickly estimate tubing sizes and to determine the friction losses in a given system. Introduction In an ordinary hydraulic system, the conduit is normally circular in cross section, the viscosity of the fluid and the specific gravity are constant and the static head probably is small. In a hydraulically operated oil-well pumping system, the conduit may be either circular or annular. Also the fluid is subjected to a high static head and large temperature gradient and, as a result, viscosity and specific gravity will vary with well depth. Because of this large variation of viscosity, the flow in the tubing strings may be both turbulent and laminar. Therefore, the calculation of friction losses in hydraulic pumping installations poses a number of problems not encountered in ordinary hydraulic systems.