Application of the x-Plot Technique to the Study of Water Influx in the Sidi El-Itayem Reservoir, Tunisia (includes associated paper 17548 )
Authors: Ershaghi I. , Handy L.L. , Hamdi M. 
Published: December 2007

Summary.
The x-plot technique is extended and a relationship is developedbetween water throughput and water cut by use of field performance data. This relationship allows the estimation of water that has invaded thedrainage area of a well, a group of wells, or a field under water injectionor natural water influx. Applications to a simulated waterflood, an actualwaterflood in Long Beach, CA, and the water influx in the Sidi El-Itayemreservoir in Tunisia are discussed.

Introduction
The x-plot technique introduced by Ershaghi and Omoregie and Ershaghi and Abdassah is a convenientmethod for representing oilfield performance historyunder water injection or natural water drive. The procedureis a linearization of water cut vs. recovery plot, allowingextrapolation to higher cuts. From the relationship one
(1)
may also derive a field composite relative-permeability-ratiocurve. Flood pot test data are often used to derive a relationshipbetween water throughput and water cut. This approachrequires the availability of core material representativeof reservoir properties. Additionally, such core-derived correlations, which are based on laboratory relative-permeabilitycurves, may not be extrapolated to actual field conditionsbecause of layering and permeability variations that affectthe field composite relative permeabilities. Our experimentation with Eq. 1 in which both a reservoirsimulation approach and actual field performance datawere used shows that one may obtain a fair estimate ofthe cumulative water throughput at any high water cut from the slope of the x-plot. This paper describes the proposed technique and itsapplication to the Sidi El-Itayem reservoir in Tunisia, which is under a strong water drive.

Method Description
The x-plot procedure requires plotting × ln(1/fw − 1) − 1/fw vs. fractional recovery. In the absence of layeringeffects and remedial profile corrections, a linear plot isobtained for cut values above 50%. The formation of astraight line indicates that the performance is beingcontrolled by the relative-permeability-ratio characteristicsof the reservoir. If the oil recovery is expressed in terms of the fractionof oil in place(Eq. 1), then rn and n may be used to obtaina field relative-permeability-ratio curve. The amount of water throughput at any fw from thefrontal advance equation may be expressed as
(2)
In practice, Eq. 2 requires a fieldwide relative-permeability-ratio curve. With a simple transformation of Eq. 1 and the derivationshown in Ref. 1 for dfw/dSw, we have developed a procedure toobtain estimates of water through-put from the slope of the x-plot. If we express oil recovery in terms of actual volumes produced, Eq. 1 can be written as x--m'N +n', where m'=1/(Nm) and n'= -n/m. From Ref. 1,
(3)
and b=1/[m(1 − Swi)]. Therefore, with the definitionfor m',
=
=
Now the water throughput in terms of actual volume canbe estimated from
(4)
where m' is in 1/vol.

Application to Waterflood
Application of Eq. 4 to both a simulated and an actualwaterflood is demonstrated here.
JPT
P. 1127^