Ingenieria Petolera

Review of Waterflooding Performance in Stratified Reservoirs
Dr. Noaman El-Khatib Professor of Petroleum Engineering Geoscience and Petroleum Engineering Department PETRONAS Technical University Summery Factors affecting oil recovery in waterflooding are reviewed. The recovery factor in waterflooding is the product of the displacement efficiency and the volumetric sweep efficiency. The differentmethods for the prediction of waterflooding Performance in Stratified Reservoirs are reviewed. The methods are grouped into two main categories depending on the degree of communication between the different layers. The method of Dykstra-Parsons for non-communicating reservoirs is outlined and its extensions are discussed. The models of Hiatt and Hearn for communicating reservoirs are reviewed andthe concept of pseudo-relative permeability functions is presented. The application of these models for systems with log-normal permeability distributions by Warren and Cosgrove is outlined. The analytical closed form solution of El-Khatib and the developed generalized correlation charts are presented. The effect of gravity crossflow and nonnewtonian fluids are presented. A model is developed forinclined stratified reservoirs. A dimensionless gravity number is found to characterize the effect of dip angle and density difference between the displacing and displaced fluid. The effects of the gravity number, mobility ratio and coefficient of permeability variation on the performance is investigated and discussed.
Key Words: Reservoir Engineering , Water flooding, Stratified Reservoirs,Immiscible Displacement, Mobility Ratio, Oil Recovery, Fractional Flow

Introduction Waterflooding is still the recovery process responsible for most of the oil production by secondary recovery. Water injected into the reservoir displaces almost all of the oil except the residual oil saturation from the portions of the reservoir contacted or swept by water The recovery factor in waterflooding isthe product of the displacement efficiency and the volumetric sweep efficiency. RF = ED . EVOL = ED . EA . EV …………………. (1) Where RF is the recovery factor, ED is the displacement efficiency, EVOL is the volumetric sweep efficiency, EA is the areal sweep efficiency, and EV is the vertical sweep efficiency. The displacement efficiency is the fraction of oil displaced from a contacted volume. Itdepends on the relative permeability characteristics of the rock as well as the viscosities of the displacing and displaced fluids. The ultimate recoverable oil pore volume by waterflooding is given by Sw = 1 – Swi –Sor which can be achieved in piston like displacement .Where, Swi and Sor are the end points of the relative permeability curves. The displacement efficiency at water breakthrough isobtained using the BuckleyLeverett frontal advance theory (Buckley and Leverett 1942). Welge used a grapgical method to determine the displacement efficiency at and after water breakthrough (Welge 1952). A tangent is drawn to the fractional flow curve ( fw vs. Sw ) from the point 1

corresponding to the initial water saturation .After water breakthrough, the displacement efficiency is obtained bydrawing a tangent to the curve with a slope equal to the reciprocal of the pore volume of water injected 1/ . The intersection of the tangent with the line of fw = 1 gives the average water saturation Swav as shown in Figure 1. The displacement efficiency is given by (Swav- Swi). It is equal to B at the time of water breakthrough and increases with the volume of water injected until it eventuallyreaches the ultimate value of (1- Swi – Sor) The fractional flow formula considering capillary and gravity terms, is given by (Pirson 1958)
1  1.127 fw  kkro A  Pc   .433 sin    o qt  x   k ro  w 1 k rw  o

………………….(2)

The fractional flow curve and hence the displacement efficiency depends on the oil/water viscosity ratio o/w. The volumetric sweep efficiency represents...