Mathematical Determination of Production Decline Curves

NUMEROUS papers have been published on the use of graphic methods to determine the best curve to be used in estimating the production decline of oil wells but, as far as the writer has been able to ascertain, nothing has been published dealing directly with the subject as to how curves may be worked out mathematically, which will conform most closely to the production data under consideration in any given instance; hence the writer has endeavored to show by means of a few concrete examples just how such appli-cation can be made. Among valuation engineers, two types of curves are in current use for the representation of the decline in production of oil wells. One may be represented by the equation, y = krx, sometimes known as a percentage curve, for the reason that the production for any period is multiplied by a constant rate or percentage to obtain the production for the succeeding period. This curve appears as a straight line on semi-logarithmic cross-section paper. The other curve may be represented by the equation, y = kxn, and is shown as a straight line on logarithmic cross-section paper. In each of these equations, y represents the number of barrels produced over a given period of time, and x the successive periods of time. The other letters are constants to be determined for each well or group of wells considered in arriving at the most probable curve to represent the rate of production for a given property; from which the underground reserves may be estimated by extrapolation, or the extending of the curve beyond the last known period of production to show the most probable production values for the future.