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Assessment of Three-Phase Relative Permeability Models Using Laboratory Hysteresis Data
David Element
Analysis of laboratory three-phase WAG data has identified a number of hysteresis features which should be incorporated into three-phase models [1]. A comparison with published hysteresis models has identified shortcomings in these models. David Element (david.element@ecltechnology.com) of ECL Technology reports on work undertaken as part of the DTI’s SHARP programme.
Background
Gas injection projects, such as WAG, frequently require consideration of co-existing oil, gas and water phases and the impact of saturation cycles as water and gas slugs move through the reservoir. These processes may be assessed using numerical simulations.
Historically, hysteresis effects were represented by empirical models based on two-phase flow. The two-phase models are characterised by trapping of the non wetting phase and permeability reduction when the saturation change direction is reversed. Subsequent saturation changes are considered to be reversible with no further permeability reduction [2,3].
A number of studies have reported evidence for hysteresis in gas relative permeabilities in WAG flooding, leading to lower gas mobilities than predicted by conventional two-phase models. Any reduction in gas mobility would improve gas sweep and incremental recovery for WAG based IOR schemes.
Several three-phase hysteresis models have been proposed to include these hysteresis effects [4,5,6]. The models include trapping of gas and reduction of water relative permeability in the presence of trapped gas. In these models, saturation changes can be irreversible, and relative permeability may decrease with each change in direction in saturation.
Figure 1: Ternary diagram for a water-wet core (flooding sequence started with a waterflood - tertiary WAG process) (Click image for larger view)
Laboratory Studies
A carefully planned laboratory study investigated secondary and tertiary WAG floods in both water-wet and intermediate-wet Berea cores, giving four separate sets of experimental data (a total of over 30 individual floods). For each flood, in-situ saturation profiles, mass balance and pressure drop data were measured. The in-situ saturation data ensures that laboratory artefacts (such as capillary end effects) do not influence conclusions.
Figure 2: End point gas relative permeabilities for a sequence of floods in water-wet core. (Click image for larger view)
Analysis of Data
The data from these experiments has been analysed, with a view to providing a qualitative assessment of the various three-phase hysteresis models. A number of analysis approaches were adopted:
- Ternary diagrams to investigate three-phase saturation trajectories;
- Evaluation of end point gas and water relative permeability values;
- Estimation of gas relative permeability curves from in-situ saturations and pressure drop measurements;
- Computation of in-situ gas and liquid fractional flows;
- Cross plots of initial gas saturation versus trapped gas saturation, comparing with the Land correlation.
Conclusions
Analysis of the experimental data has identified several features that must be included in any three-phase hysteresis model:
- Irreversibility of hysteresis cycles;
- Potential for the reduction in the residual oil saturation with trapping of gas by water;
- Reduction in both water and gas permeability;
- Variation in fractional flow with trapped gas saturation;
- Variation in Land trapping factor between hysteresis cycles.
This study confirms the need for three-phase hysteresis models. The two-phase models of Carlson or Killough do not adequately describe secondary and tertiary gas injection processes. The three-phase models of Skauge, Blunt and Egermann include most (but not all) of the observed hysteresis effects, but could presumably be extended to include all of the effects.
References
- Element, D.J., Jayasekera, A.J., Masters, J.H.K., Sargent, N.C., “Assessment of Three-Phase Relative Permeability Models Using Laboratory Hysteresis Data”, SPE 84903, to be presented at SPE International Improved Oil Recovery Conference (IIORC), 20-21 October 2003, Kuala Lumpur, Malaysia.
- Carlson, F.M.: “Simulation of Relative Permeability Hysteresis to the Non Wetting Phase”. SPE 10157, Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, San Antonio, 5-7 October 1981.
- Killough, J.E.: “Reservoir Simulation with History Dependent Saturation Functions”. SPE 5106
- Skauge, A. and Larsen, J.A.: “Three-phase relative permeability and trapped gas measurements related to WAG processes”. Society of Core Analysts, 1994.
- Egermann, P., Vizika, O., Dallet, L., Requin, C. and Sonier, F. “Hysteresis in Three-Phase Flow: Experiments, Modelling and Reservoir Simulation”. IEA Meeting, Edinburgh 2000.
- Blunt, M.J. “An Empirical Model for Three-phase Relative Permeability”. SPE 56474, Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Houston, 3-6 October 1999.
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