A More Accurate Water Influx Formula With Applications
Authors: Vogt J.P. , Wang B. 
Published: March 2010

Abstract
The widely, used step pressure formula for calculating water influx is approximate as it is normally employed in the material balance equation. This causes the material balance equation to give approximate results. A totally general, linear pressure formula is introduced that more accurately evaluates water influx and leads to the following advantages when used in the material balance equation:the original-gas-in-place or original-oil-inplace (OG/OOIP) and aquifer parameters can be determined earlier in a reservoir's life;OGIP/OOIP and equivalent aquifer parameters can be determined jar reservoirs with a variety of drive mechanisms - including an unsteady stale aquifer, a pal al1uifer, shale water influx, and rock compressibility without knowing what the actual drive mechanism is; andreservoir pressure can be predicted more accurately once the OGIP/OOIP and aquifer parameters are known.

Introduction
Material balance methods (e.g. Havlena-Odeh(1) or Tehrani(2) are important reservoir engineering tools for estimating OGIP/OOIP and aquifer parameters for partial water drive reservoirs. A material balance approach can also be used to predict reservoir pressure once OGIP/OOIP and aquifer parameters are known. The results from these procedures are, however, only as accurate as the water influx calculations for the reservoir.
Van Everdingen and Hurst(3) presented a formula that is commonly used to calculate water influx. In this paper, this formula will be called the step pressure (SP) formula because it approximates the aquifer inner boundary pressure as a step function in each time interval.
It is often believed that the SP formula is the most accurate one available. It will be shown, however, that when used for a small number of time steps (e, g. less than 20), which is usually the case when employing material balance methods, the SP formula underpredicts water influx. This is especially true for quick aquifers, such as the small or highly permeable aquifers that are often found along the Texas and Louisiana Gulf Coast. So, primarily, quick aquifers will be the ones discussed below.
A linear pressure (LP) formula will be derived. It is an exact expression for water influx when the aquifer inner boundary pressure is a series of straight line segments connecting the data points. In real reservoirs, where the aquifer inner boundary pressure is more nearly a series of straight line segments than step functions, the LP formula is more accurate than the SP expression.
It will be demonstrated by examples that replacing the SP with the LP formula in the material balance equation has a number of important engineering consequences. The material balance methods for finding OGIP/OOIP and aquifer parameters become more accurate and general. Further, a number of anomalies that occur when the SP formula is used are explained. Finally, reservoir pressure predictions become more accurate.
The Havlena-Odeh material balance method for finding OGIP/OOIP and aquifer parameters is discussed instead of the Tehrani technique. This is only because the Havlena-Odeh method is more widely used and is associated with a two-dimensional plot that is useful for illustrating material balance results.