Page 362 - Fundamentals of Reservoir Engineering

CHAPTER 9

NATURAL WATER INFLUX

9.1 INTRODUCTION

Natural water influx into both gas and oil reservoirs has been described previously
(Chapter 1, sec. 7, and Chapter 3, sec. 7) using the simple, time independent aquifer
material balance

W e = c W i (p i - p)

for calculating the amount of influx. In this equation

W i = initial volume of water in the aquifer and is therefore dependent upon
aquifer geometry
p i = initial aquifer/reservoir pressure

p = current reservoir pressure, which in this chapter will always be assumed to
be equal to the pressure at the original oil (or gas) water contact

c = total aquifer compressibility = c w + c f

The equation is simply a re-statement of the basic definition of compressibility and is
only applicable to very small aquifers. For large aquifers a mathematical model is
required which includes time dependence, to cater for the fact that it takes a finite time
for the aquifer to respond fully to a pressure change in the reservoir. Two such models
1
will be studied in this chapter: firstly, that of Hurst and van Everdingen and secondly,
2
the more recent, approximate method of Fetkovitch . These techniques will be applied
in the classical reservoir engineering manner of first building a model which will
adequately match the reservoir's production and pressure history when included in the
material balance equation (this is sometimes referred to as aquifer fitting) then, once a
satisfactory model has been built, using it to predict the future performance of the
reservoir, say, for a given offtake policy.

It should be appreciated that there are more uncertainties attached to this subject, in
reservoir engineering, than to any other. This is simply because one seldom drills wells
into an aquifer to gain the necessary information about the porosity, permeability,
thickness and fluid properties. Instead, these properties have frequently to be inferred
from what has been observed in the reservoir. Even more uncertain, however, is the
geometry and areal continuity of the aquifer itself. The reservoir engineer should
therefore consult both production and exploration geologists, concerning the latter,
rather than relying entirely upon his own judgement. Due to these inherent
uncertainties the aquifer fit obtained from history matching is seldom unique and the
aquifer model may require frequent updating as more production and pressure data
become available, as illustrated in exercise 9.2.