Use of Permanent Resistivity and Transient-Pressure Measurement for Time-Lapse Saturation Mapping
- M. Charara (Schlumberger Riboud Product Center) | Y. Manin (Schlumberger Riboud Product Center) | C. Bacquet (Exxon Mobil Corp.) | J.P. Delhomme (Schlumberger Riboud Product Center)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2002
- Document Type
- Journal Paper
- 472 - 479
- 2002. Society of Petroleum Engineers
- 5.8.7 Carbonate Reservoir, 3.3 Well & Reservoir Surveillance and Monitoring, 5.4.1 Waterflooding, 5.3.4 Reduction of Residual Oil Saturation, 4.1.5 Processing Equipment, 5.6.4 Drillstem/Well Testing, 5.1 Reservoir Characterisation, 5.1.7 Seismic Processing and Interpretation, 4.1.2 Separation and Treating, 1.14 Casing and Cementing
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Optimization of hydrocarbon recovery requires information on the space and time behavior of the saturation of various fluids present in the reservoir. This is particularly true for oil fields under secondary recovery such as waterflooding, where an even reservoir sweep or zones of bypassed oil can be assessed by a proper description of the waterfront advance. Recently, permanent downhole electrodes have been deployed successfully in oil wells.
This technology allows the time variation of the electrode potentials to be interpreted in terms of changes in saturation within the formation. However, the depth of investigation of such measurements is limited. Time-lapse pressure transient is an independent source of information with a greater depth of investigation and, therefore, it provides an adequate complement to the permanent resistivity array measurement.
In this paper, we propose to use pressure buildup from repeated shut-in in association with the electrical measurements. After recalling analytical analogies in both types of measurements, we propose a quick-look method for interpreting the time-lapse pressure transients. We then compare the physical and practical advantages of each type of measurement and the domain of application of the two measurements with respect to fluid and reservoir properties. Finally, we propose an example showing the benefit obtained by coupling the two techniques.
Innovative applications of waterflood monitoring using arrays of electrodes permanently installed behind casing have been published recently.1,2 Interpreting the measurement acquired by such installation in reservoirs under waterflooding leads to a real-time description of the water front as it moves away from the injection well(s) toward a producer or observation well. In most cases, the depth of investigation of this type of measurement (although approximately two orders of magnitude larger than that of conventional saturation logging) does not cover the distance between the injector and the producer.
In the following paper, we propose to use pressure transients generated during repeated buildup periods to predict (in a timelapse manner) the waterfront positions, even at large distances from the observation point. After introducing the concept, we present a quick-look analysis method based on an analytical formulation for a single-layer reservoir. The extension of the technique to multilayer systems is then evaluated as a function of the connectivity between layers.
Finally, we show how the results obtained from the pressuretransient analysis can supplement those obtained with a permanent electrode array. The relative advantages and limitations of both approaches, as a function of fluid and reservoir types, are notably discussed in detail.
Time-Lapse Electrode Array Measurements
The principle of electrode array measurement (Fig. 1) consists in using, in turn, each electrode as a low-frequency current source while monitoring voltage at the other electrodes. The spatial resistivity distribution at the time of each acquisition can be inferred from a mathematical inversion of those potentials. Among factors affecting the depth of investigation of such a system, the contrast in resistivity between the oil and water zones plays a key role.
After water is injected into an oil reservoir, a water front is created, and the reservoir can be divided into two regions: Region 1, where only the connate water is present (Sw=Swc), and Region 2, situated behind the front and characterized by a water saturation equal to (1-Sor).
For the case of a sharp front in an infinite homogeneous reservoir, the distance from the producer well to the water front can be related, through a simple analytical formula, to a single voltage measurement. In practice, this value is recorded at a monitoring electrode cemented along an electrically insulated portion of the casing when a given electrical DC current is injected at another electrode cemented some distance away along the same casing.
The current injection electrode acts as a point source, and the front plane separating oil and water zones defines two half-spaces, with electrical properties (the formation resistivity) varying laterally at the front location. The classical reflection-transmission concept thus can be applied to locate the linear discontinuity in an otherwise infinite medium. The electrical problem can be solved by using the image theory3: the second half-space of resistivity ?2 at a distance L(t) from the point source located in the first halfspace of resistivity ?1 will act as a mirror of the point source weighted by the resistivity contrast between the two media. As a consequence, the potential at a distance s from the point source will be the sum of the contributions of both the source and its image:
where I=the intensity of the injected current.
The resistivity in Region 2, flooded by water, is given by Archie's law, ?2=aRw/fm (1-Sor)n, and the resistivity in Region 1, where Sw=Swc is ?1=aRw/fmSwcn.
Usually, one introduces be=?2-?1/?2+?1, which is a direct function of the contrast in resistivity between the two zones.
For a gradational contact, the calculations are less straightforward; the saturation curve has to be discretized into 1D slices of constant saturation where Archie's law applies and the electrical problem has a pseudoanalytical solution, based on the Hankel transform that can be used to compute the potential at the monitoring electrode. Nevertheless, numerical inversion techniques can be used to locate the front.
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