A Simplified Approach to Water Influx Calculations-Finite Aquifer Systems
Authors: Fetkovich M.J. 
Published: December 2007

This approach to water influx calculations offers a useful and flexible method of forecasting and analyzing the performance of water drive reservoirs. The separation of the water influx problem into a rate equation and a material balance equation, not requiring superposition, makes the concepts and calculations quite simple and easy to apply.

Introduction
All gas and oil reservoirs are associated to varying extents with formation waters. The inclusion of the effects of expansion or invasion of this water into oil and gas reservoirs has taken many forms, from recognizing the effects of the expansion of the connote water within the gas or oil reservoir itself, to calculating water influx or efflux across a boundary (with the boundary usually being that of an oil or gas reservoir). There are four currently popular methods used for calculating water influx into reservoirs. They are:
Schilthuis, steady state Hurst Simplified, unsteady state Resistance or Influence Function, unsteadystate van Everdingen-Hurst Radial, unsteady state The first three methods have proved useful for predicting water drive performance after sufficient predicting water drive performance after sufficient historical data have been obtained to fix the necessary influx constants.
With what some consider to be disappointing results, the van Everdingen-Hurst Radial method is often used with geological and core data when little or no performance history is available. It has also been used to predict reservoir performance after enough historical data have been accumulated to develop values of the influx constants, tD and C. In an attempt to include geometries other than radial, derivations for both limited and infinite systems have been made to cover linear spherical, elliptical, thick-sand, and wedge-shaped reservoir-aquifer models. The many rigorous geometrical representations that have been developed cannot readily handle the effect of interference between reservoirs. Electric analyzer studies of the Smackover Limestone aquifer in Arkansas by Bruce, of the Woodbine aquifer in East Texas by Rumble et al., and of the Ellenberger in West Texas by Moore and Truby have shown that reservoirs sharing a common aquifer can severely interfere with each other, and that, for individual reservoirs in a common aquifer, water drive performance calculations that do not consider interference performance calculations that do not consider interference can be greatly in error. Mortada developed a mathematical method with which to handle interference in a basically infinite radial aquifer system. The method has been applied to field cases. Coats concluded from his own study that, "In predicting the pressure-volume behavior of gas reservoirs situated on the common aquifer the effect of interference from other reservoirs on the common aquifer must be accounted for." Another aquifer problem more recently presented in the literature is that of flank water injection for pressure maintenance, either to initiate or to pressure maintenance, either to initiate or to supplement edge-water influx. A case history shows that we need to be able to study the effects of injecting water into the aquifer instead of merely including it in the hydrocarbon material balance equation.
JPT
P. 814