Reserves Appreciation Factors
Authors: Davis James M. 
Published: December 2007

Abstract
Estimates of U. S. crude oil initial proved reserves made in the year of discovery are usually lower than those made in subsequent years as development proceeds. As the number of years from the discovery proceeds. As the number of years from the discovery year increases, the revised initial proved reserves estimates approach what is called the ultimate proved reserves estimate. This paper deals with the problem of determining the ultimate proved reserves estimate given an initial, or discovery year, proved reserves estimate.
Our analysis shows a decrease, though not statistically significant, in the ratio of ultimate to initial crude oil proved reserves estimates for latter discovery years, and a statistically significant indication of an increase in the rate at which reserves are developed.

Introduction
Ultimate recoverable crude oil reserves from all the discoveries of a given year can never be known until the last barrel has been produced. Until then, however, estimates of ultimate recoverable reserves are important for both government and private industry planning. Each year the American Petroleum Institute, planning. Each year the American Petroleum Institute, API, expends considerable effort in estimating crude oil proved reserves by year of discovery. In general, the estimates made in the year of discovery are lower than the estimates made in subsequent years due to extensions and revisions as development of fields proceeds. There has been interest in using proceeds. There has been interest in using initial proved reserves estimates to predict ultimate recovery for a typical discovery year.
This paper deals with the problem of determining the ultimate proved reserves (UPR) estimate from an initial proved reserves (IPR) estimate made in the discovery year. Trends in estimates of ultimate recovery by discovery year and the rate at which reserves are developed are also investigated.
The problem is approached by postulating a mathematical model describing the manner in which IPR estimates increase with time. The basic assumption is that the instantaneous increase in proved reserves is proportional to the reserves remaining to be proved. The model has two parameters. One is the ratio of the UPR estimate to the IPR estimate. The other is the proved reserves appreciation constant which is a proved reserves appreciation constant which is a measure of how fast reserves are being developed (proved).
The two model parameters are estimated for each discovery year from 1948 through 1973. Statistical analyses are then presented.

CRUDE OIL RESERVES APPRECIATION MODEL
A model is proposed which assumes that the instantaneous increase in IPR is proportional to the reserves remaining to be proved. It is obvious that such a simple model does not contain all the factors affecting changes in the IPR estimate. In addition, it is inappropriate to use this model as a description of an individual field because factors other than those accounted for by the model mould generally predominate changes in the IPR estimate. An example of predominate changes in the IPR estimate. An example of such a factor is the specific waterflood response of an individual field.
As stated in the Introduction, the model represents an attempt to describe changes in the IPR estimate by discovery year aggregated over all U.S. fields. It is shown in the remainder of the paper that the model adequately meets the objectives for which it is designed. A prime reason for this success is the availability of adequate data for model evaluation. While it may be easy to propose more comprehensive models, it is difficult to provide suitable data for evaluation. Without such data more comprehensive models are useless.
The development of the present model follows.