In recent years several authors have demonstrated that relative permeability hysteresis effects may be significant in the physically correct modelling of general gas injection processes and WAG processes in particular. Today simple hysteresis models are available in most simulators, but more recent and advanced models are still not standard tools. Especially when compositional simulation is needed the choice of hysteresis models is generally limited to very simple models.
In this work we have combined a compositional simulator with a calculation method for relative permeabilities developed for Water Alternating Gas (WAG) injection (Ref. 1). The model can roughly be categorised as an extension of the well known Killough hysteresis model from two to three phases. Hysteresis behaviour is implemented for the water and gas phases (wetting and non-wetting phases). The residual oil saturation (intermediate phase) is dependent on the trapped gas saturation if the Stone1 method is used for calculation of relative permeabilities for the oil phase.
The paper describes a few simplifications made to the model and its implementation in a compositional simulator. Special attention is given to compositional effects such as solution of gas components in the oil phase. We then present simulation results showing the impact of the hysteresis model on oil production, first for a synthetic model (5th SPE comparative solution project), then for a real North Sea oil reservoir with WAG as primary recovery mechanism. The model is found to give a more physically correct description of three phase flow than exisiting hysteresis models and will be an enhanced tool for history matching and simulation of production forecasts.
It has been shown by several independent sources (Ref. 2,3) that the classical methods for calculations of relative permeabilities do not apply to WAG injection. This is due to the complex flow pattern normally seen in this operation, where saturation increases and decreases repeatedly for the wetting and nonwetting phases (water and gas), and maybe even for the intermediate phase (oil). During the modelling of three-phase flow (oil, water and gas) the relative permeabilities are used as a parameter in the Darcy equation and in the mobility terms. Changes of the relative permeability may have a large influence on the simulation results.
Whereas two phase relative permeability curves are routinely measured in laboratories, measurements of three phase relative permeability curves are very difficult. It is therefore common to use correlations for estimation of these curves. The most well known correlations for calculating three phase oil relative permeability are the Stone I and the Stone II methods. However, a special case arises in the simulation of processes where the saturation is oscillating, such as the WAG process where injection normally is made in slugs. In this case trapping of the gas phase may occur, when injected water invades areas already swept by gas. This phenomenon leads to hysteresis in the shape of the relative permeability curves, since the space available for liquid movement in the rock decreases (due to the presence of immobile gas). In such cases not only the three-phase relative permeability, but also the hysteresis must be modelled.
Figure 1 shows a schematic representation of the WAG injection process with one injector at the left and one producer at the right. The WAG area is a 3 phase area where gas, oil and water are mobile. It is especially in this area that relative permeability and hysteresis effects will be important. However, all zones maybe affected as all mechanisms affect each other and interact.