Effects of Hydrodynamic Pressure Interference on Reservoir Performance, Buffalo Lake D-3 Pool
Authors: Paxman D.S. , Havlena D. 
Published: December 2007

Abstract
Articles in the literature have presented theoretical methods of solving the material balance equation (MBE) for partial water drive reservoirs. The theory and application of solving MBE by the straight line concept was an extension of the original idea presented by van Everdingen et al. In these solutions, the effects of hydrodynamic pressure interference from other pools located in the same aquifer were not considered. Mortada, Robinson and other authors investigated interference between pools, but unfortunately for the practicing reservoir engineer none of them published a complete factual field study of such an interference phenomenon. The present investigation examines qualitatively the physical effects of interference on the solution of the MBE, and particularly the effects of interference on a pool discovered some time after a reduction of its reservoir pressure had already occurred. It is emphasized that this particular solution may well surpass the limits of applicability of the MBE. This concept has no precedent (to the best of our knowledge) in the petroleum engineering literature, and therefore the contribution of this paper is in the physical definition and use of the interrelated physical parameters and the qualitative correlation of all the many necessary conditions imposed on the successful solution of the MBE. It is not expected that the basic assumptions or solutions are unique or that they will be entirely free of dispute. However, realizing these limitations, it is hoped that a practical method has been presented which will allow the handling of similar reservoir problems. Of subordinate importance is a re-emphasis of the simplicity of applying the constant terminal rate method and the superposition theorem for predicting pressures within the aquifer. The application uses the straight-line method approach for an explicit evaluation of the unknown parameters of the aquifer. Once these unknown parameters are determined (i.e., after obtaining a satisfactory match with the available pressure-production history), pressure performance for any future rate can be simply predicted using a desk calculator.

Introduction
The effects of hydrodynamic pressure interference between pools producing from a common aquifer have been described in general terms in the literature. The present study presents a field example of an interference problem and the solution of the expanded material balance equation (EMBE) while accounting for such effects. As pointed out by Mortada, the rate of propagation of the pressure decline can be such as to significantly reduce the pressure many miles from the producing pool. In his paper he referred to the Woodbine formation in East Texas where a dozen or more pools draw on that horizon for water drive. A similar situation also exists in Alberta, Canada, where many Devonian (Leduc) D-3 reef pools are developed on a common water bearing platform stratigraphically identified as the Cooking Lake formation (Fig. 2). A unique situation which complicates the simple interference problem occurs when the pool to be evaluated is discovered some time subsequent to a drop in its initial pressure due to interference from other pools (p (discovery) less than p i). The application of material balance principles to such a pool therefore requires adjustments of its pressure performance history to account for the effects of interference, not only during its exploitation life, but also before its discovery. Furthermore, because of the inherent limitations of the EMBE, heuristic criteria must be used to adequately describe such a complicated physical phenomenon. Independent principles such as geology, geophysics or even logic must be used to relate the material balance solutions. Such a non-mathematical approach admittedly renders the answers open to some question; however, realizing these limitations, the acceptability of such a semi-quantitative solution should not be impaired by the unknown exactness of the final results.

Theory

EMBE With Interference Term
In a reservoir which suffers from hydrodynamic interference, the measured, instantaneous, effective pressure drops are numerically greater than those caused by the net withdrawals from that particular field alone.
JPT
P. 23ˆ