Page 219 - Fundamentals of Enhanced Oil and Gas Recovery

CHAPTER SEVEN

Waterflooding

Mohammad Ali Ahmadi
Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB, Canada

7.1 INTRODUCTION

Darcy’s law governs reservoir flow, which is the fundamental flow equation for
fluids through a porous media in the steady state. The fractional flow equation
together with the derivation of solutions to predict the performance of displacing
water system started from Darcy equation. Many researchers have ventured into the
development of waterflooding designs to understand the performance of water injec-
tion. This has led to diverse quantitative approaches in analyzing waterflooding based
on different geometries [1].
According to literature, the most important advances in understanding multiphase
flow in porous media started back in the 1920s [2] and majorly in the 1940s [3].
Reservoirs have transition zones between water and oil phase; the true oil zone sees
the presence of connate water with respect to the true water zone, which is essentially
100% water. During production from a completed well, water production is from the
true water zone whereas only oil is produced from the true oil zone [7]. However, at
the transition zone, both oil and water are produced which is dependent on the satu-
ration of oil and water at that point. As time passes, the saturation becomes a multiple
valued function of the distance coordinate (x), solved by material balance consider-
ation. When the initial saturation in the flow system is uniform, a simple graphic
approach developed by Welge [4] can be used to determine the abrupt saturation front
without difficulty. Sheldon and Cardwell [5] solved the Buckley Leverett problem
with the method of characteristics.

7.2 DERIVATION OF CONTINUITY EQUATION FOR DISPLACEMENT
FRONT OF LINEAR DISPLACEMENT SYSTEM

Assume that the total flow rate is the same at all the medium cross-section.
Neglect capillary and gravitational forces may be acting. Let the oil be displaced by

Fundamentals of Enhanced Oil and Gas Recovery from Conventional and Unconventional Reservoirs. © 2018 Elsevier Inc.
DOI: https://doi.org/10.1016/B978-0-12-813027-8.00007-2 All rights reserved. 207