The complex physics of multiphase flow in porous media are usually modeled at the field scale using Darcy-type formulations. The key descriptors of such models are the relative permeabilities to each of the flowing phases. It is well known that, whenever the fluid saturations undergo a cyclic process, relative permeabilities display hysteresis effects.

In this paper we investigate hysteresis in the relative permeability of the hydrocarbon phase in a two-phase system. We propose a new model of trapping and waterflood relative permeability, which is applicable for the entire range of rock wettability conditions. The proposed formulation overcomes some of the limitations of existing trapping and relative permeability models. The new model is validated by means of pore-network simulation of primary drainage and waterflooding. We study the dependence of trapped (residual) hydrocarbon saturation and waterflood relative permeability on several fluid/rock properties, most notably the wettability and the initial water saturation.

The relevance of relative permeability hysteresis is then evaluated for modeling geological CO2 sequestration processes. Here we concentrate on CO2 injection in saline aquifers. In this setting, the CO2 is the nonwetting phase, and trapping of the CO2 is an essential mechanism after the injection phase, during the lateral and upward migration of the CO2 plume. We demonstrate the importance of accounting for CO2 trapping in the relative permeability model for predicting the distribution and mobility of CO2 in the formation. We conclude that a proper treatment of the nonwetting phase trapping leads to a higher estimate of the amount of CO2 that it is safe to inject.


Hysteresis refers to irreversibility or path dependence. In multiphase flow, it manifests itself through the dependence of relative permeabilities and capillary pressures on the saturation path and saturation history. From the point of view of pore-scale processes, hysteresis has at least two sources:

  1. contact angle hysteresis; and

  2. trapping of the nonwetting phase.

The first step in characterizing relative permeability hysteresis is the ability to capture the amount of oil that is trapped during any displacement sequence. Indeed, a trapping model is the crux of any hysteresis model: it determines the endpoint saturation of the hydrocarbon relative permeability curve during waterflooding.

Extensive experimental and theoretical work has focused on the mechanisms that control trapping during multiphase flow in porous media.[1–3] Of particular interest to us is the influence of wettability on the residual hydrocarbon saturation. Early experiments in uniformly wetted systems suggested that waterflood efficiency decreases with increasing oil-wet characteristics.[4, 5] These experiments were performed on cores whose wettability was altered artificially, and the results need to be interpreted carefully for two reasons: (1) reservoirs do not have uniform wettability, and the fraction of oil-wet pores is a function of the topology of the porous medium and initial water saturation,[6] and (2) the core-flood experiments were not performed for a long enough time, and not enough porevolumes were injected to drain the remaining oil films to achieve ultimate residual oil saturation. Other core-flood experiments, in which many pore volumes were injected, the observed trapped/residual saturation did not follow a monotonic trend as a function of wettability, and was actually lowest for intermediate-wet to oil-wet rocks.[7–9] Jadhunandan and Morrow[10] performed a comprehensive experimental study of the effects of wettability on water-flood recovery, showing that maximum oil recovery was achieved at intermediate-wet conditions.

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