A Three-Dimensional Model For Predicting Natural Gas Reserves And Availability

Abstract

Abstract A model is presented which analyzes the discovery and subsequent appreciation of natural gas in Alberta using data compiled by the Alberta Oil and Gas (now Energy Resources) Conservation Board. This model is then used for the prediction of new discoveries and subsequent appreciation of existing discoveries. This means that the volumes of gas discovered are analyzed and predicted both as a function of discovery year and year since discovery. Introduction PREVIOUS ATTEMPTS at statistically estimating natural gas reserves have dealt with the problem as a process which analyzed and subsequently predicted reserves as a cumulative quantity. No attempt was made at separating the appreciation of present reserves and the prediction of new reserves. Noteworthy of the studies that have been performed are two approaches. The first approach, presented by Hubbert(1) and Moore(2), uses cumulative gas reserves tabulated by calendar year and involves the fitting and extrapolation of S-shaped curves of either logistic or Gompertz form, respectively, with the latter curve giving a slightly better fit to the data presented here. The second approach, presented by the Alberta Oil and Gas Conservation Board(3,4) uses cumulative gas reserves tabulated by years since discovery and analyzes the growth pattern of the appreciation of existing gas reserves. This method does not predict an ultimate initial established marketable gas reserves, but does provide a very good fit on a cumulative basis of the appreciation of existing reserves. This paper is aimed at statistically analyzing the way estimates of natural gas reserves grow. The model used for the analysis is referred to as a three-dimensional model because it is a function of three factors - the calendar year, the year since discovery and the amount of reserves known at these times. Alberta Oil and Gas Conservation Report data(3) used in this study are shown in Table 1. The Table shows) by year since discovery and by calendar year, the recognized reserves of some 400 natural gas pools discovered subsequent to 1950 which have initial reserves greater than 10 billion cubic feet. In total, it is estimated that these pools represent 72 per cent of the total reserves that have been recognized as being discovered prior to December 30, I970. GENERAL STRUCTURE OF THE MODEL Appreciation of Existing Reserves Once given the amount of gas discovery in any one particular year (t), the appreciation of this gas is a very regular process which slows down exponentially with time and hence the cumulative growth has the form of a limited exponential of the following form. (Equation Available In Full Paper) Applying this model to the data presented in Table 1 for the years of discovery 1951 to 1960, the following results were obtained by non-linear least-squares techniques. (Equation Available In Full Paper) As can be seen from the above results, each individual model as well as the cumulative model provides a good description of the data.