Analysis of Three-Phase Relative Permeability Hysteresis Data
In a previous article, David Element of ECL Technology Ltd (david.element@ecltechnology.com) described how a number of hysteresis features had been identified in a new dataset of three-phase WAG relative permeability measurements [1]. In this article he provides some further conclusions from a DTI SHARP project which compared the match of two relative permeability hysteresis models with this measured data.
Recent published investigations have considered relative permeability hysteresis for immiscible three-phase processes, and a number of new hysteresis models have been proposed. The models include trapping of gas and reduction of water relative permeability in the presence of trapped gas (e.g. models of Skauge [2], Blunt [3] and Egermann [4]). In an immiscible three-phase situation multiple cycling of gas increases gas trapping, leading to lower gas relative permeabilities, higher oil relative permeabilities and lower residual oil saturations. These effects are generally beneficial to WAG projects, so there may be considerable benefit in being able to model the processes involved adequately.
Data from secondary and tertiary WAG floods in water-wet Berea core have been analysed, attempting a quantitative comparison of the models proposed by Skauge and Blunt. Calculated relative permeabilities were compared to the water and gas relative permeabilities measured in the laboratory study. In order to match the measured residual saturations, it was necessary to adjust both hysteresis models. Each model uses Land’s empirical equation to calculate trapped saturations, and here the models were extended to allow the Land trapping parameter to vary between floods.
Even with simplified inputs, the Blunt and Skauge hysteresis calculations require a significant number of input values. More than 20 separate data items needed to be specified. With a set of suitable input parameters, both the Skauge and Blunt models compute water and gas end point relative permeabilities which are broadly consistent with the data measured in the two WAG sequences in the laboratory hysteresis study (see Figures 1 and 2). The Blunt model does not include any reduction in gas relative permeability in the presence of water, and therefore it predicts a wider range of gas relative permeabilities than the Skauge model.
Figure 1: Gas Relative Permeability End-Points, Showing General Agreement Between Calculated and Measured Values
Figure 2: Water Relative Permeability End-Points, Showing General Agreement Between Calculated and Measured Values
Both models show a progressive reduction in oil relative permeability through successive WAG cycles (Figure 3). In [2], oil relative permeability calculations use the Stone I formulation, and in [3] the Saturation-Weighted formulation. In practice the calculation of oil relative permeability can be defined quite independently of the choice of hysteresis model. The shortcomings of some three-phase oil relative permeability models were discussed in a previous IOR newsletter article. In these WAG floods, the oil relative permeabilities calculated with the Stone I model were up to four orders of magnitude higher than using other models, due to known shortcomings of this model.
Figure 3: Oil Relative Permeability Reduced Through Successive WAG Cycles. Shortcomings of the Stone I Model Give Higher Relative Permeabilities than other Three-Phase Oil Relative Permeability Models
Although both models are able to match the laboratory hysteresis data, the Skauge hysteresis model offers several advantages over Blunt’s model:
- Skauge’s model includes more hysteresis features, particularly reduction in gas relative permeability due to presence of mobile water
- Skauge’s equations requires less relative permeability input data than Blunt’s,
- the Skauge model is available in a commercial simulator.
The main drawback of the Skauge model is the absence of any water-trapping – which implies that for each gas flood the residual water saturation equals the irreducible water saturation. The laboratory dataset indicates that water is trapped by gas. The model proposed by Blunt can include water-trapping, and a similar water-trapping model could presumably be included in the Skauge model.
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, presented at SPE International Improved Oil Recovery Conference (IIORC), 20-21 October 2003, Kuala Lumpur, Malaysia.
- Skauge, A. and Larsen, J.A.: “Three-phase relative permeability and trapped gas measurements related to WAG processes”. Society of Core Analysts, 1994.
- 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.
- 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