Spontaneous imbibition, the capillary-driven process of displacing the nonwetting phase by the wetting phase in porous media, is of great importance in oil/gas recovery from matrix blocks of fractured reservoirs. The question of how properly scaling up the recovery by counter-current spontaneous imbibition has been the subject of extensive research over decades, and numerous scaling equations have been proposed. As a convention, the scaling equations are usually defined analytically by relating the early time squared recovery to squared pore volume. We show this convention does not apply to common scaling practices and, if used, causes nontrivial scatter in the scaling plots. We explain that for three common scaling practices, where the recovery is normalized by (1) final recovery, (2) pore volume, or (3) initial oil/gas in place, this convention should be redefined accordingly. The main contribution is to emphasize that during the development of any scaling equation, its consistency with common applications should be considered. Such consistency has been historically neglected in literature works. Using this new insight, we consider the latest scaling published in the literature to present three different consistent scaling equations for three corresponding scaling situations. The new scaling equations, which are valid for both gas–liquid and liquid–liquid systems, incorporate all factors influencing the process and resolve all limitations of scaling groups published during past decades. These scaling equations are rewritten in terms of two physically meaningful dimensionless numbers, Da1/2/Ca (Da, Darcy number; Ca, capillary number), and validated against experimental data from the literature. This approach enables us to scale all data perfectly and represents all recovery curves by a single master curve. We further highlight the necessity of incorporation of directional permeability effects in scaling equations by defining the new concept of characteristic permeability.

Petrophysical rock typing in reservoir characterization is an important input for successful drilling, production, injection, reservoir studies and simulation. In this study petrophysical rock typing is divided into two major categories: 1) a petrophysical static rock type (PSRT): a collection of rocks having the same primary drainage capillary pressure curves or unique water saturation for a given height above the free water level, 2) a petrophysical dynamic rock type (PDRT): a set of rocks with a similar fluid flow behavior. It was shown that static and dynamic rock types do not necessarily overlap or share petrophysical properties, regardless of wettability. In addition, a new index is developed to define PDRTs via the Kozeny-Carman equation and Darcy's law. We also proposed a different index for delineation of PSRTs by combining the Young-Laplace capillary pressure expression and the Kozeny-Carman equation. These new indices were compared with the existing theoretical and empirical indices. Results showed that our indices are representatives of previously developed models which were also tested with mercury injection capillary pressure, water-oil primary drainage capillary pressure, and water-oil relative permeability data on core plugs from a highly heterogeneous carbonate reservoir in an Iranian oil field. This study enabled us to modify the conventional J-function to enhance its capability of normalizing capillary pressure data universally.

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Identification of hydraulic flow units (HFUs) is an important part of reservoir characterization. Rock samples within a given HFU are expected to have the same mean hydraulic radius. We show that the famous reservoir quality index‐flow zone indicator (RQI/FZI) technique and its recent modifications do not use the concept of mean hydraulic radius. Each predicted HFU by these methods may contain the samples with different pore structures, and further the rocks with similar structures may be distributed in more than one HFU. This makes the reservoir characterization very complicated and sometimes an erroneous process. An improved method, referred to as FZI star method (FZI*), is presented here using the base form of the Kozeny–Carmen (K–C) equation, opposed to RQI/FZI method which relies on the generalized form of the K–C equation, by proper consideration of the mean hydraulic radius concept. The presented method is verified using a large set of capillary pressure measurements.

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