Application of the x-Plot Technique to the Study of Water Influx in the Sidi El-Itayem Reservoir, Tunisia (includes associated paper 17548 )
- I. Ershaghi (U. of Southern California) | L.L. Handy (U. of Southern California) | M. Hamdi (U. of Southern California)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- September 1987
- Document Type
- Journal Paper
- 1,127 - 1,136
- 1987. Society of Petroleum Engineers
- 1.6.9 Coring, Fishing, 4.1.5 Processing Equipment, 5.5 Reservoir Simulation, 5.5.2 Core Analysis, 5.8.7 Carbonate Reservoir, 4.1.2 Separation and Treating, 6.5.2 Water use, produced water discharge and disposal, 5.4.1 Waterflooding, 5.1.2 Faults and Fracture Characterisation
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Summary. The x-plot technique is extended and a relationship is developed between water throughput and water cut by use of field performance data. This relationship allows the estimation of water that has invaded the drainage area of a well, a group of wells, or a field under water injection or natural water influx. Applications to a simulated waterflood, an actual waterflood in Long Beach, CA, and the water influx in the Sidi El-Itayem reservoir in Tunisia are discussed.
The x-plot technique introduced by Ershaghi and Omoregie and Ershaghi and Abdassah is a convenient method for representing oilfield performance history under water injection or natural water drive. The procedure is a linearization of water cut vs. recovery plot, allowing extrapolation to higher cuts. From the relationship one
may also derive a field composite relative-permeability-ratio curve. Flood pot test data are often used to derive a relationship between water throughput and water cut. This approach requires the availability of core material representative of reservoir properties. Additionally, such core-derived correlations, which are based on laboratory relative-permeability curves, may not be extrapolated to actual field conditions because of layering and permeability variations that affect the field composite relative permeabilities. Our experimentation with Eq. 1 in which both a reservoir simulation approach and actual field performance data were used shows that one may obtain a fair estimate of the cumulative water throughput at any high water cut from the slope of the x-plot. This paper describes the proposed technique and its application to the Sidi El-Itayem reservoir in Tunisia, which is under a strong water drive.
The x-plot procedure requires plotting x ln(1/fw - 1) - 1/ fw vs. fractional recovery. In the absence of layering effects and remedial profile corrections, a linear plot is obtained for cut values above 50%. The formation of a straight line indicates that the performance is being controlled by the relative-permeability-ratio characteristics of the reservoir. If the oil recovery is expressed in terms of the fraction of oil in place(Eq. 1), then rn and n may be used to obtain a field relative-permeability-ratio curve. The amount of water throughput at any fw from the frontal advance equation may be expressed as
In practice, Eq. 2 requires a fieldwide relative-permeability-ratio curve. With a simple transformation of Eq. 1 and the derivation shown in Ref. 1 for dfw/dSw, we have developed a procedure to obtain 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,
and b=1/[m(1 - Swi)]. Therefore, with the definition for m',
Now the water throughput in terms of actual volume can be estimated from
where m' is in 1/vol.
Application to Waterflood
Application of Eq. 4 to both a simulated and an actual waterflood is demonstrated here.
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