Interpretation of Water Saturation Above the Transitional Zone in Chalk Reservoirs
- Jens K. Larsen (Technical U. of Denmark) | Ida L. Fabricius (Technical U. of Denmark)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2004
- Document Type
- Journal Paper
- 155 - 163
- 2004. Society of Petroleum Engineers
- 5.6.1 Open hole/cased hole log analysis, 1.14 Casing and Cementing, 5.2 Reservoir Fluid Dynamics, 5.5.11 Formation Testing (e.g., Wireline, LWD), 5.1.5 Geologic Modeling, 5.1.8 Seismic Modelling, 4.3.4 Scale, 1.6.9 Coring, Fishing, 5.8.5 Oil Sand, Oil Shale, Bitumen, 5.5.2 Core Analysis, 5.6.2 Core Analysis, 5.3.1 Flow in Porous Media, 5.3.2 Multiphase Flow, 5.8.7 Carbonate Reservoir, 1.2.3 Rock properties
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The free water level (FWL) in chalk reservoirs in the North Sea may be hard to establish owing to strong influence from capillary forces and lack of pressure equilibrium across the reservoir. Even where wireline formation tester data on the FWL are available in one well, it is no straightforward task to predict the FWL in other parts of the field, where only conventional core analysis and logging data are available. It is thus difficult to predict the geometry of the hydrocarbon-bearing interval.
This paper offers a simple model which, in a given well, allows us to predict the location of the FWL from conventional core analysis and logging data if wireline formation tester data are available from another well.
Water saturation is averaged over the internal surface of the formation by applying Kozeny's equation, resulting in a pseudo water-film thickness (PWFT). The PWFT is larger than the equilibrium water-film thickness calculated from the augmented Young-Laplace equation because it includes water associated with grain contacts. The PWFT has a gradient with true vertical depth (TVD) that is related to the capillary pressure; this gradient is approximately the same for the wells investigated. Consequently, a unique relationship between the PWFT and the height above the FWL can be established, provided that the depth of the FWL is known from formation pressure data. The unique PWFT height above the FWL relationship can be used to establish the FWL in offset wells for which no reliable formation-pressure data exist. The estimation of the FWL in offset wells is inexpensive because it requires the use of log data and sufficient conventional core-analysis data only.
The model was tested on seven wells from the Gorm and Dan field in the North Sea and resulted in predictions of the FWL in the Dan field wells based on wireline formation tests in one Gorm field well.
The interplay between capillary pressure and phase saturation in chalk is not well established; traditional normalization methods of capillary pressure curves are not able to model capillary pressure behavior within chalk reservoirs.1-3 In North Sea chalk reservoirs, water saturations above the transitional zone vary frequently from values as low as 5% to those as high as 60% (Figs. 1a and 1b), depending on the capillary rock properties. Traditionally, the zone above the transitional zone is referred to as the irreducible zone because little or no water is produced. Experiments reveal that water saturations lower than those encountered in the irreducible zone can be obtained in the laboratory, provided that a sufficiently large difference in phase pressures is applied and sufficient experimental time is available. In fact, a water saturation close to zero can be obtained if a sufficiently high capillary pressure is applied and if the water phase remains continuous to provide an escape path for the water phase.
In a field in equilibrium, the difference in phase pressures is caused by the difference in hydrostatic pressure (which itself is caused by the difference in fluid density). The capillary pressure, defined as the difference in phase pressures for an oil/water system in equilibrium, can be calculated by Eq. 1, where h is the height above the FWL defined as the point at which the capillary pressure is zero.
Consequently, the largest difference in phase pressures will occur immediately below the top of the reservoir and gradually decrease downward to the FWL, provided that capillary continuity is sustained. We assume that the hydrocarbon and water phases are continuous throughout the reservoir column and that no effective lower limit exists for the water saturation. Therefore, the terms "irreducible zone" and "irreducible water saturation" (Swi) provide little meaning when interpreting the water saturation in chalk reservoirs. Throughout the paper, we will refer to the irreducible water saturation only while discussing or referring to traditional saturation models; otherwise, it should be assumed that no lower limit exists for the water saturation.
Before a reservoir is filled with hydrocarbon, the formation is saturated with formation brine. Under the assumption that the formation is initially water-wet, oil will displace the formation brine in a drainage process. Given sufficient height for an oil column, water will be displaced from the center of all pores and will cover only the surface of the mineral grains of the formation. Considering a drainage process in which the water has been displaced from all pore centers, it is thus reasonable to expect a relationship between water saturation and the internal surface area of the formation.
Wyllie and Rose4 proposed a relationship between permeability, porosity, and irreducible water saturation and proved it valid for some sandstone reservoirs. Timur5 suggested a generalized equation,
where A, X, and Y are constants. Several authors have proposed similar relationships;6-11 we refer to these kinds of models as water-film models because the volume of water is assumed to cover the surface of the rock in a thin water film. Wyllie and Rose's relationship, however, has not been tested on chalk. Moreover, there is no effective irreducible water saturation in chalk; consequently, we feel that establishing a relationship between the internal surface and the water saturation is a better approach.
Kozeny's equation expresses a relationship between the specific surface of a porous medium and its permeability and porosity.12
where S is the specific surface with respect to total volume. The specific surface with respect to porosity is given by
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