Published in Petroleum Transactions, AIME, Vol. 219, 1960, pages 415–417.
A method based on an approach by Hurst is developed for calculating water influx behavior. Using this method, superposition calculations may be eliminated. The principal difference between this method and that of Hurst is that, over finite intervals of time, constant oil-production rates are assumed by Hurst whereas constant water influx rates are assumed in the presently described method.
By adopting the assumption of constant water influx rate for finite time periods, a method is developed for calculating water influx behavior which lends itself to convenient combination with the material balance equation in the Schilthuis form. Above the bubble point, an equation is given for the explicit step-wise calculation of pressure history for a prescribed oil-production history. Use of this method of calculating water influx behavior should result in a considerable saving of time as compared to superposition calculations when the calculations must be made without using a digital computer.
The connection is shown between the method described herein and the method developed by van Everdingen and Hurst (which requires superposition calculations). Also, results obtained using the two methods are compared.
While the method of van Everdingen and Hurst is in many respects a satisfactory way of calculating water influx behavior, the superposition calculations involved make it a tedious procedure when the work is done without using a digital computer.
Hurst has presented an approach to the problem which eliminates superposition calculations, in many cases at small expense to accuracy. It is the purpose of this paper to present a method of calculating water influx which is based on the approach of Hurst and which may be conveniently combined with the material balance equation in the Schilthuis form. The relation will be discussed between the method of van Everdingen and Hurst and the method described herein. Examples of results using the two methods are given.