Estimation of the Oil Reserves Requirement to Meet a Given Production Level—Mathematical Modeling

The problem of estimating annual oil reserves demand needed to maintain some given production level may be of real importance for big oil companies. The existing mathematical models of oil production permit the calculationor estimation of the daily or annual production from the reservoir of given dimensions with given properties. Nevertheless, the existing models do not answer many questions important for reservoir management, and, first of all, estimating the requirements in annual and total reserves increase. The authors developed an analytical model for predicting the reserves requirement to ensure a given production rate from a specific formation or region. The model is based on the data of annual rate of oil production measured in fractions of the field reserves. In modeling, we assumed as given the productive quality of reserves, that is, production rate from the unit of the proved reserves. As input function the so-called production deficit is considered, namely, a function describing the difference between the total annual planned production level and annual planned production from the already discovered fields. The model uses approximate continuous analytical description of discrete input data. Governing intergral equations of material balance relating the reserves requirement, production deficit, and productive quality of reserves are solved by application of the Laplace transformation. The solution permits calculation of the annual reserves increase to meet a given production rate specified by an analytical expression (polynomial or exponential) with 3–5 free parameters. The parameters are to be appraised from a prescribed production curve by a best-fit technique. Prediction horizon may be about 10 to 20 years.