Water-Drive Gas Reservoirs: Influence of Pulse-Testing on the Indetermination Pulse-Testing on the Indetermination Range of Reserve Estimates

For water-drive gas reservoirs, the accuracy of reserve estimates that are based on past history depends upon the practical possibility of applying to the reservoir, for long periods of time, pulsed rates of large amplitude.

Introduction

Estimating the reserves of a water-drive gas reservoir from its past production history leads to results that are intrinsically affected by some indetermination. The indetermination range, which can be greatly widened by errors in past performance data, becomes especially important when the reservoir has been produced at a fairly constant rate. produced at a fairly constant rate. Following a suggestion made by Muskat, this paper investigates the possibility of narrowing the paper investigates the possibility of narrowing the reserves indetermination range by depleting a gas reservoir, at the very beginning of its life, with a "squarewave" production rate program. The effects of frequency, shape, amplitude and number of cycles of the square-wave production program upon the range of indetermination have been program upon the range of indetermination have been investigated with reference to a hypothetical gas reservoir. Practical limitations were given due consideration.

Theoretical Considerations

A gas reservoir-aquifer ensemble is a nonlinear system whose canonical equations are known and whose internal structure (gas reserves value, aquifer geometry and spatial distribution of aquifer characteristics, h, k) can be ascertained through direct measurements only within large limits of error. This is especially true for the aquifer, for which the sources of information are usually limited to some peripheral wells that produce water. The reservoir-aquifer system is therefore a "black box". It is known that for a black box the principle of indetermination holds: accordingly, the number of different internal structures that can account for the same external behavior (i.e., the same response to an external stimulus) is infinite. As a consequence, it is impossible to ascertain the internal structure of a reservoir-aquifer system (its initial gas reserves value in particular) from the reservoir past performance. The fact that a unique solution of the problem cannot be found is only of theoretical interest. From a practical point of view, it is important to evaluate the practical point of view, it is important to evaluate the range of indetermination encompassing the initial gas reserves value as determined from the reservoir past performance. It is known that this range can be very performance. It is known that this range can be very large when the past performance data are affected by experimental errors, even of modest size. It must be pointed out that the reservoir-aquifer systems are subjected to a special constraint. Contrary to other physical systems that the information theory deals with, the reservoir-aquifer systems cannot be subjected more than once to a predetermined type of external stimulus, as it is impracticable to restore them to initial conditions; for example, their frequency-response characteristics cannot be determined. A theoretical analysis of the problem shows that a square-wave stimulus is the most suitable one to determine the transfer function (that is, the external behavior) of a system subjected to the kind of constraint noted in the preceding paragraph.

JPT

P. 1521

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