Application of Decline Curves to Gravity-Drainage Reservoirs in the Stripper Stage

Abstract

Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 275–280. Abstract In a recent publication it was shown that wells with a free surface in a homogeneous gravity-drainage reservoir have a hyperbolic decline with index n = 2, q/qi = 1/(1 + ?t)2. This paper reports efforts to extend this theory to practical field cases. As a first step in making the extension, a large number of lease production curves from gravity-drainage fields in the stripper stage were fitted with the general hyperbolic decline equation, q/qi = 1/(1 + ?t)n, ? and n in each case being determined by statistical methods. It was found that this equation is reliable for decline curve extrapolation for periods up to at least 25 years. The results obtained were disturbing in the sense that values for the index, n, were often smaller than one, which fact leads to the prediction that a well would produce an infinite amount of oil in infinite time. A theoretical investigation based on the results of the previous paper provides a suitable explanation for these low values of n. It suggests that these are obtained if production occurs from two or more layers of different permeability and thickness or two layers having different skin effects. It is predicted that as the more permeable layers are exhausted, the index of decline, n, will rise from a value smaller than 2, to n = 2. A practical method is given for fitting the general hyperbolic decline Eq. 6 to production decline data. When this method is used, the index of decline observed in gravity-drainage reservoirs in the stripper stage when using only data over early years of decline usually agrees quite closely with that determined using data over 25 years or more. This indicates that the hyperbolic decline equation is reliable for predicting behavior of such reservoirs. A method is also suggested for taking into account any changes in the value of the index of decline, n, which may be expected during the life of a well or lease.