Multiphase flow involving saturation oscillations should be modeled with history-dependent, relative permeability functions. Earlier approaches have been based on two-phase flow. The main assumptions have been that the imbibition process is reversible. Moreover, scanning curves were developed only for saturations between some extreme values.

Several tertiary oil recovery processes have shown cycle-dependent hysteresis for relative permeability. When saturation oscillations occur during three-phase flow such as water alternating gas (WAG), the two-phase hysteresis models will generally not be able to describe relative permeabilities obtained from corefloods. For three-phase flow, local hysteresis effects may also be important. New relative permeability representations that account for local hysteresis effects are presented.

Hysteresis models for both wetting and nonwetting phase permeabilities have been developed. The new models account for reduced mobility and irreversible hysteresis loops during three phase flow. The models depend on the initial saturation at the start of the given process. An algorithm is presented for implementing the nonwetting phase hysteresis model in a numerical simulator. The new three-phase models use experimental wetting and nonwetting relative permeabilities as input, and knowledge of relations between maximum nonwetting saturation and trapped nonwetting saturation.


Characteristic parameters describing multiphase flow in porous media are process dependent. In particular, relative permeabilities are considered to be dependent on saturation and saturation history. This latter dependency is described in the literature as relative permeability hysteresis. The number of phases present in porous media is important when discussing hysteresis. The problem of hysteresis increases significantly when moving from two-phase to three-phase flow systems. On a macroscopic scale, the number of process paths increases from two-phase flow to three-phase flow. In addition, the saturation path within the ternary diagram is not predefined in three-phase systems. For the two-phase case, the only unknown part of the saturation trajectory is the endpoint, as compared with three-phase flow, for which the whole saturation trajectory is initially unknown.

On the microscopic scale, displacement sequences that can occur in three-phase systems are not seen in two-phase systems. These include double-displacement mechanisms and the spreading behavior of the intermediate wetting phase. Depending on the equilibrium spreading coefficient, one or two phases can be distributed as films in the porous medium.

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