Analysis of Relative Permeability Hysteresis Trends in Mixed-wet Porous Media Using
Authors: Dixit A.B. , McDougall S.R. , Sorbie K.S. 
Published: December 2007

Abstract
In crude oil/brine/rock systems, pore level displacements involving oil and brine are governed by the pore geometry, network topology and wettability of the system. The corresponding petrophysical parameters (e.g. Pc and Krw/Kro) are also strongly affected by these quantities. In recent years, network models have been widely employed to examine the consequences of topological and wettability alterations on petrophysical properties. Recently, we have developed a network model which takes into account wettability alterations after primary drainage. Additional pore level flow phenomena, such as film flow of the wetting phase, trapping of wetting and non-wetting fluids by snap-off and bypassing and variations in advancing/receding contact angles, were also included. The concept of an "effective contact angle", which takes into account the pore geometry as well as pore wettability has been introduced and a novel Regime based framework for wettability classification has been proposed using simulation results to analyse and explain experimental fundings on oil recovery (SPE/DOE 35451). The same modelling approach has also been used to explain the various types of relative permeability hysteresis which are observed in strongly and weakly water-wet systems (Regime IA) (SPE 37233).
The present study extends this previous work to mixed- wet systems (e.g. preserved/aged cores), where hysteresis trends between the secondary imbibition (SI) and secondary drainage (SD) oil/water relative permeability curves have been observed. However, "contradictory" trends have been seen by different workers and these fall into categories where, say, the oil SI relative permeability is either above or below the oil SD curve. A clear statement of the circumstances under which these various trends should be seen and the explanation of these trends has not yet appeared in the literature.
In this paper, we present network modelling results which reproduce, explain and reconcile most of the observed (apparently contradictory) experimental results on relative permeability hysteresis in mixed-wet systems. The effects upon hysteresis patterns of different imbibition mechanisms (snap-off and piston-like) in the water-wet and oil-wet regions of mixed-wet systems are examined using pore-scale network models. These processes may lie in different Regimes of the wettability Regime diagram. The hysteresis trends are analyzed using oil/water phase occupancy plots which highlight variations in the spanning and flowing oil/ water phase clusters during both imbibition and drainage processes. Simulation results suggest that a great deal of information can be obtained concerning displacement mechanisms in mixed- wet cores using laboratory secondary imbibition and secondary drainage relative permeability curves. Results also demonstrate that the various hysteresis trends reported in the literature appear contradictory mainly due to the fact that cores probably lie in different Regimes and/or are characterized by different displacement mechanisms.
In summary, experimental SI/SD relative permeability observations are explained and reconciled by identifying; (i) the Regime in which the wettability state is located; and (ii) the combination of pore-scale displacement mechanisms (viz. snap-off and piston-like) which are operating.
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