The hysterisis phenomenon affects the flow behaviour in various occasions. In particular, during the WAG process the cyclic injections of wetting and non-wetting (water and gas) fluids cause the appearance of the hysterisis phenomena. In this work, to access the magnitude of the hysterisis phenomena on the flow in porous media we performed experimental tests and analytical studies. We measured for different formations the relative permeabilities in the imbibition and drainage cycle, using oil and water. We monitored the rates and pressures at the inlet and outlet points of the rock sample and also the internal saturation evolution. These data permitted to obtain the fractional flow curve for the associated imbibition and drainage processes. We then performed a flow test, which result, could be compared with different mathematical approaches proposed in the literature to take into account the effect of hysterisis on flow in porous media. There are in the literature different proposals to calculate the flow in porous media honouring the hysteretic flow. We used three semi-analytical and one numerical method to describe the experimental test. At the end, a comparison between the results obtained is presented.


The hysterisis phenomena in flow in porous media manifest itself in different occasions. In the oil exploitation we could mention the cyclic injection of gas and water for the WAG process, in the ascending and descending of the water cone, in the gas injection and production of storage aquifers, in the miscellar flooding process where an oil bank is displaced by water(1)(2)(3)(4)(5)(6). In hydrology the ascending and descending of the water table in the vadoze zone presents a hysterisis phenomena (7).

Different rocks and fluids present different degrees of hysterisis. It is believed that this phenomena depends on, besides fluid properties, morphological and topological aspects of porous media (8).

Normally the hysterisis manifests itself in different petrophysical properties. The more frequently cited in the literature are the capillary pressure, fractional flow curves and relative permeabilities.

The first drainage presents a very pronounced hysterisis. In oil fields, normally the first drainage occurs in the secondary oil migration and is not present in the exploitation stage. For this reason we will not consider it in this article and only periods after the first imbibition and secondary drainage will be considered.

In our paper we will focus mainly on the two-phase relative permeabilities, and its derived fractional flow curve. The main reason for not measuring capillary hysterisis is the fact that semi-analytical models based on hyperbolic equation based on mass conservation do not consider the capillary pressure. Also, the literature shows that this is an acceptable simplification.

For our two-phase system there is some controversy about the behaviour of different curves.

Our experimental results confirm, what is usually acceptable, that the hysterisis effect is important only on the non-wetting phase permeability and the imbibition permeability is greater than the drainage (3)(9)(10)(11). We measured the relative permeability in a steady-state process and calculated and compared experimental tests with one numerical and three semi-analytical methods (12)(13)(14)(15)(10)(11)(16)(17(18).

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