Assessment of Three-Phase Relative Permeability Models Using Laboratory Hysteresis Data

Abstract

Gas injection techniques, 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. This paper presents the analysis of a detailed laboratory study, designed to provide data for verifying hysteresis models for such simulations. 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. A reduction in gas mobility tends to improve gas sweep and incremental recovery for WAG based IOR schemes. Three-phase hysteresis models have recently been developed to include these hysteresis effects. 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. A carefully planned laboratory study investigated secondary and tertiary immiscible 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. Analysis of the experimental data shows that hysteresis models should include the following features: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, with potential for the fractional flow to vary with trapped gas saturation;Variation in Land trapping factor between hysteresis cycles. This study confirms the need for three-phase hysteresis models. Although published models may include some of the observed hysteresis effects, no model includes them all. Introduction Reservoir engineering calculations frequently require consideration of co-existing oil, gas and water phases. In the case of immiscible hydrocarbon gas WAG flooding, these considerations include the displacement of oil by simultaneous gas-water flow. These displacement processes are usually assessed using numerical simulation. Although the permeability of reservoir rock typically depends on the interstitial pore geometry, the relative permeability depends on factors such as wettability, spreading characteristics and the fluid distribution in the pore space. There is usually more than one way a given fraction of the pore space can be occupied by each fluid phase and so it is possible for different relative permeability values to be measured for the same fluid saturation. The sequence of saturation changes will, therefore, affect fluid distribution and the relative permeability. Historically, hysteresis effects have been included in numerical simulations using empirical models based on two-phase flow [1,2]. Recent investigations have considered hysteresis for more complex three-phase processes and a number of new models have been proposed for inclusion in commercial simulation packages [3,4,5].

Pore-scale Simulation of Water Alternate Gas Injection

“…We will use the network model to predict three experimental datasets: Oak (1990), Egermann et al (2000) and Element et al (2003) before using the model to predict trends in behavior with wettability.…”

“…Comparison of measured (Egermann et al, 2000) and tracked saturation paths. Element et al (2003) performed WAG experiments on water-wet Berea sandstone cores. The contact angles and spreading conditions of the experimental system were not measured.…”

“…This again confirms the hysteresis trends observed and predicted for the previous two experiments. During both the first and second water injection Element et al (2003) σ gw (mN/m) 67 σ go (mN/m) 19 σ ow (mN/m) 48 θ r gw (degrees) 4.4-16.9 θ r go (degrees) 0 θ r ow (degrees) 0-20 θ a gw (degrees) 16.9-33.7 θ a go (degrees) 0 θ a ow (degrees) 20-40 Figure 14. Comparison of measured (Element et al, 2003) and tracked saturation paths.…”

“…Although the saturation of the gas phase may not be affected significantly, this causes disconnection of continuous gas clusters, reducing the gas phase relative permeability. It has been observed that continued cycles of gas/water injection lead to progressively lower gas relative permeability and additional oil recovery in both micromodel and core experiments (Egermann et al, 2000;Sohrabi et al, 2000;Element et al, 2003;Feng et al, 2004van Dijke et al, 2004. However, most reservoirs are mixed-or oil-wet where gas is not necessarily the most non-wetting phase.…”

“…Furthermore, most of the widely used empirical correlations are developed with an assumption that the rock is strongly water-wet (Blunt, 2000). This is why empirical equations fail to predict three-phase relative permeabilities accurately for non-water-wet conditions (Element et al, 2003). Skauge and Larsen (1994) proposed a relative permeability hysteresis model for WAG processes and validated it with experimental data.…”