Crude Petroleum - Loss Ratio Method of Extra olating Oil Well Decline Curves

The appraisal of oil wells, now that we have the age-size method of making composite decline curves, and the present worth of successive time units method of valuation, has its greatest remaining uncertainty in the difficulty of extending into the future the price curve and the composite production curve. The point of attack in this paper is the carrying on (or extrapolation) of the production curve. Led by the valuable discovery of Lewis and Beal that the decline curve is nearer the hyperbolic class, y = (x + a)-", than any other form, the current practice is the graphic method. The data are plotted on logarithmic paper and shifted with successive trials until the line becomes straight. This straight line can then be extended into the future. The method was a great help during the period when, for tax purposes, there was need for a quick method even though the errors were large. Now that we seek greater validity in our methods we find the following faults with the current method. 1. Where the shift is great (it exceeds 10 in some cases) the scale cannot be read with the necessary precision so that the resulting data would give a very irregular and inaccurate curve. 2. Where the curve cannot be straightened on logarithmic paper because of sigmoid shape the method has a serious systematic error. We believe the sigmoid curves to be more common than usually supposed, indeed when one considers the number of variable causative factors this is to be expected. We have therefore been seeking a method that is free from these difficulties and yet not so laborious as fitting a curve to the data and the calculation from the formula which, since it involves looking up logarithms, is unduly time-consuming. The method here described has been developed on the basis suggested by Earl Oliver, that the amount of oil produced per month or year for each reduction of production of a barrel of oil per day could be plotted to advantage. A step forward was made by Earl Carpenter in this laboratory, and some of the