Bottom-hole Measurements in Pumping Wells

THE fundamental hydrodynamic principles governing the production of oil from wells have been carefully studied and evaluated by many investigators. These prior studies are quite complete and cover virtually the entire field of oil production and recovery.1 One of the most impor-tant measurements in production studies is that of the bottom-hole pressure at various rates of production.2 It is the purpose of this paper to outline the technique and economics of fluid-level measurements as applied to pumping wells and to review briefly other methods for obtain-ing bottom-hole data. The applications of bottom-hole pressure or fluid-level measure-ments are based on simple hydrodynamic principles. Under equilib-rium conditions, pbh = hd + pg + pch [ l] when pbh = bottom-hole pressure, lb. per sq. in. absolute, h = height of fluid in well, ft., d = average fluid density, lb. per sq. in. per foot, pg = weight of section of gas column 1 in. square from fluid level to casing head, pch = casing-head pressure, lb. per sq. in. absolute. In words, equation 1 states that the bottom-hole pressure is equal to the weight hd of the column of fluid plus the weight of the column of gas between the fluid and the casing head plus the casing-head pressure. At moderate rates of flow, the rate of production is approximately proportional to the difference between the reservoir, or static bottom-hole, pressure and the flowing or producing pressure; i.e.: Q = c(pr - pbh) [2] pr = the reservoir pressure, c = the constant of proportionality. However, at production rates approaching zero and also at high rates the proportionality may break down. By combining equations 1 and 2 the