Identified Models for Gas Storage Dynamics

Abstract

Abstract The classical approach to forecasting hydrocarbon reservoir behavior is through modeling. Traditional models are based on equations describing the physical behavior of the reservoir-plus-aquifer system; usually the parameters describing aquifer behavior are not known beforehand and are evaluated by a trial-and-error procedure based on the best fit of past reservoir performance. This approach leads to models that are intrinsically realistic, as they reflect the physical nature of the phenomena involved. A completely different approach, based on system theory techniques, is presented in this paper. This technique, called identification, consists of the determination of a mathematical model equivalent to the process under test, the word "equivalent" meaning that the process and the model show the same input/output behavior. As a consequence, an identified model of this type can be used to predict the response of an actual reservoir-plus-aquifer system to different inputs - i.e., to different production schedules. Case histories of the application of the identification technique to actual gas storage reservoirs are presented. Introduction As with many other aspects of the world, a gas reservoir can be considered a dynamical system interacting with an external environment by means of inputs and outputs. The exchanges between a reservoir and the rest of the world occur through wells and the measurable attributes at every well are given by the gas production rate and pressure. Thus, it is possible to consider the cumulative gas production of wells as inputs and the well pressures as outputs of this system. Note that when a water drive mechanism is present, the cumulative quantity of water which has entered the reservoir should be considered one of the system's inputs; however, this information is not usually available since wells are drilled where hydrocarbons, rather than water, are expected. In the selection of a suitable model for a reservoir, the choice between linear and nonlinear models must be made. In many cases, linear models are used because of their relative simplicity and of the general theory that has been developed for their treatment. No general theory can be found for nonlinear systems; this explains why clearly nonlinear systems have been studied, designed, built, tested, and operated using only the linear system theory. A gas reservoir, particularly when used for storage purposes, is virtually a linear system; therefore a model of this type is useful to describe its behavior accurately. Another choice regards the time invariance of the model. Gas reservoirs are time invariant; however, if an aquifer is present and no measurements of the cumulative amount of water which has entered the reservoir are available as a system input, the reservoir behavior will change with time and only a time-dependent model could be completely accurate. The selection of a time-invariant model can lead to a lack of accuracy, particularly for water-driven reservoirs when the first production years are considered; the aquifer contribution to time dependency becomes less important in subsequent years. This paper shows that the limits on the use of time-invariant models are no longer valid for reservoirs subjected to injection/production schedules and that models of this kind can be obtained inexpensively and accurately by means of identification procedures performed on the available system history. SPEJ P. 151^