WaterSubject

At present, the almost universal practice in the oil industry is to use empirical models to predict three-phase flow properties, such as capillary pressure and relative permeability, that are extrapolations from two-phase measurements. However, the three-phase relative permeability is known to be a function of two saturations and the displacement path, indicating that a finite number of measurements is unlikely to reproduce the full range of behavior. One simplifying hypothesis is to propose that the relative permeability is a unique function of the flowing (non-trapped) fluid saturation . Hence relative permeability could be predicted from a single displacement experiment if the trapped saturation were known.

Land developed an empirical expression in the context of two-phase flow that relates trapped non-wetting phase saturation to the initial and maximum non-wetting phase saturations in the system. This model embodies the idea that the maximum non-wetting phase saturation determines the amount of trapping.

Using data from Prudhoe Bay sandstone core samples, Jerauld suggested that pore structure may also play an important role in determining the trapped gas saturation. He showed that the trapped gas saturation decreases with increasing porosity for sandstones. He proposed that lower porosity samples have larger pore–throat aspect ratios which in turn results in more snap-off displacements disconnecting gas clusters. Jerauld also suggested that the total hydrocarbon (oil and gas) trapped in a three-phase system would be up to 20% greater than the water-flood residual oil saturation during two-phase flow. He concluded that unless the system is strongly water-wet, the trapped gas and residual oil saturations should be approximately independent since they are not necessarily competing to occupy the same pores.

Blunt developed a three-phase trapping model by extending two-phase model to three-phase systems. He assumed that the total trapped hydrocarbon saturation in a strongly water-wet system can be estimated by using a similar approach to Land. According to this model, the total trapped hydrocarbon saturation in a three-phase system should be the same as the trapped non-wetting phase saturation in a two-phase flow.

Kralik et al. studied a comprehensive set of experimental data obtained from an oil-wet sandstone reservoir. They suggested that gas trapping not only depends on its own saturation but also on wettability and the relative amounts of the other two phases. It was shown that in oil-wet reservoirs the trapped gas saturation can be significantly lower in the presence of water, since gas may become the intermediate-wet phase which inhibits water to gas snap-off displacements during water invasion. This explanation is similar to that for two-phase systems in which residual oil saturation is lower for intermediate-wet systems than water-wet systems.

At present, despite the work described above, there is no robust model to predict trapping in three-phase flow for a complete range of displacement paths and wettabilities. In this work, we apply pore-network modeling as a tool to estimate the trapped hydrocarbon saturation in Berea sandstone. We will compute the trapped oil and gas saturations separately and relate them to the initial gas saturation and wettability of the system for a particular saturation path (gas injection followed by water injection). The advantage of this approach is that situations outside the range of displacements studied experimentally can be explored, and, from an analysis of displacement processes and fluid configurations, the trends in behavior can be given a physical explanation. The properties of the Berea network, with analytical computations of the threshold displacement pressures and transport properties have already been discussed in the literature. We are not going to present all these equations here in this paper; however two- and three-phase fluid configurations and the relevant displacement mechanisms do deserve a brief introduction.