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II Problem and Objectives

[] The problem to be discussed in this article is the question of whether or not there exists a mesoscopic length scale with new constitutive laws intermediate between the microscopic pore scale and the macroscopic sample size L. [] Recent capillary desaturation experiments in [11, 5] seem to hint towards the possible existence of a mesoscopic length scale. [] Existing theories do not explain or predict capillary desaturation curves or spatiotemporal changes of nonpercolating residual saturations. [] Direct upscaling from pore to sample scale may be difficult or impossible, because mesoscopic nonpercolating clusters and their interaction become important [12, 13, 14].

[] The theoretical importance of nonpercolating trappedclusters (ganglia) on macroscopic scales (Darcy scale and larger) was emphasized already in [15]. [] It was thoroughly analyzed in [16] and [17]. [] The results of this analysis led to the proposal of a generalized macroscopic theory [18] predicting hysteresis [19], recovering the traditional theory [20] and highlighting the role of interfacial areas in [21]. [] Experimental evidence for the possible importance of a mesoscopic scale seems to have been found in recent experimental advances allowing in situ monitoring of immiscible displacement processes using fast X-ray computed microtomography [5]. [] Theoretical evidence for the importance of clusters on macroscopic scales was found in [22] for immiscible fluids in hydrostatic equilibrium, in [23] for raising and/or rotating closed columns, in [24] for Buckley-Leverett shocks, in [25] for McWhorter-Sunada flows and capillarity driven horizontal redistribution (Philip-problem), in [26] for saturation overshoot, and in [27] for multistep outflow experiments. [] Recent drainage and imbibition experiments with pore scale imaging performed by [11] confirm that the dynamics is nonlocal and that capillary action at menisci is percolating over some mesoscopic distance. [] These experimental observations and theoretical advances all seem to hint towards a mesoscopic cluster scale, that might be defined via the nonpercolating clusters and their interaction with each other.

[] The main objectives of this paper are:

  1. to study the process dependence of capillary desaturation curves and the dependence on the desaturation protocol,

  2. to introduce new capillary saturation curves for oil injection based on traditional two-phase flow theory,

  3. to propose new capillary saturation experiments with oil injection instead of water injection,

  4. to introduce a new relation between capillary desaturation curves and the product of relative permeabilities with normalized capillary pressure functions that seems to have remained unnoticed so far,

  5. to show that the plateau saturation in capillary desaturation curves is not given as the residual oil saturation SOr (defined in eq. (25b) below), but can be either 1-SWi (where the irreducible water saturation SWi is defined in eq. (25a) below) or any saturation below 1-Sz where Sz is defined as the zero PcimbSz=0 on the capillary pressure curve for secondary imbibition, and

  6. to quantify the large variation of breakpoints in capillary desaturation curves within the traditional two-phase flow theory.