Menisci in a Diamond-Shaped Capillary

This paper presents a closed form analytical solution to the augmented Young-Laplace equation for the meniscus profile in a capillary formed between four equal-sized tangent cylinders centered on the vertices of a square. The solution is valid for a large class of disjoining pressure isotherms and contact angles.     

Pore-scale network model for drainage-dominated three-phase flow in porous media

Drainage displacements in three-phase flow under strongly wetting conditions are completely described by a simple generalisation of well understood two-phase drainage mechanisms. As in two-phase flow, the sequence of throat invasions in three-phase flow is determined by fluid connectivity and threshold capillary pressure for the invading interface. Flow through wetting and intermediate spreading films is important in determining fluid recoveries and the progress of the displacement in three-phase flow. Viscous pressure drops associated with flow through films give rise to multiple filling and emptying of pores. A three-phase, two-dimensional network model based on the pore-scale fluid distributions and displacement mechanisms reported by Øren et al. and which accounts for flow through both wetting and intermediate fluid films is shown to correctly predict all the important characteristics of three-phase flow observed in glass micromodel experiments.     

Percolation Effects of Grain Contacts in Partially Saturated Sandstones: Deviations from Archie’s Law

We study the resistivity index of Fontainebleau and Bentheimer sandstones at ambient conditions down to low water saturations both experimentally and numerically. Numerical simulations are in good agreement with experimental measurements of capillary drainage resistivity index by the porous plate method down to water saturations as low as S _w = 10 %. Fontainebleau sandstone exhibits a percolating network of grain contacts, while the higher porosity Bentheimer sandstone does not. We show that this difference in the topological connection of conductive films at low water saturations is responsible for the non-Archie behaviour of Fontainebleau sandstone. Furthermore, it is necessary to attribute a grain contact conductivity to the grain contacts in Fontainebleau sandstone to reconcile experiment and numerical simulation. Conductive films organised as pendular rings around grain contacts are not able to explain this result.     

Effect of Network Topology on Relative Permeability

We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res. 105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.     

Invasion Percolation on Correlated and Elongated Lattices: Implications for the Interpretation of Residual Saturations in Rock Cores

The invasion percolation model is used to investigate the effect of correlated heterogeneity on capillary dominated displacements in porous media. The breakthrough and residual saturations are shown to be strongly influenced by the correlations. Correlated heterogeneity leads to lower residual saturations than those observed in random systems and the scatter commonly observed in laboratory core measurements of the residual saturations can be attributed to the presence of such heterogeneity at the pore scale. Invasion percolation computations on elongated lattices, those with a geometry of L ^d–1 × nL where n denotes the aspect ratio, show that residual saturations for systems with correlated heterogeneity exhibit a strong dependence on aspect ratio. This effect is not considered by experimentalists who advocate the use of long (high aspect ratio) cores in order to overcome end-effects in experiments on shorter cores. A new scaling law is proposed for the residual saturations in elongated systems with correlated heterogeneity, and is confirmed by numerical simulations.     

Volume Conservation of the Intermediate Phase in Three-Phase Pore-Network Models

Quasi-static rule-based network models used to calculate capillary dominated multi-phase transport properties in porous media employ equilibrium fluid saturation distributions which assume that pores are fully filled with a single bulk fluid with other fluids present only as wetting and/or spreading films. We show that for drainage dominated three-phase displacements in which a non-wetting fluid (gas) displaces a trapped intermediate fluid (residual oil) in the presence of a mobile wetting fluid (water) this assumption distorts the dynamics of three-phase displacements and results in significant volume errors for the intermediate fluid and erroneous calculations of intermediate fluid residual saturations, relative permeabilities and recoveries. The volume errors are associated with the double drainage mechanism which is responsible for the mobilization of waterflood residual oil. A simple modification of the double drainage mechanism is proposed which allows the presence of a relatively small number of partially filled pores and removes the oil volume errors.     

Effect of network topology on two-phase imbibition relative permeability

In a previous study Arns et al. (2004, Transport Porous Media 55, 21–46) we considered the role of topology on drainage relative permeability curves computed using network models derived from a suite of tomographic images of Fontainebleau sandstone. The present study extends the analysis to more complex imbibition displacements where the non-wetting fluid can be disconnected by snap-off as a result of swelling of wetting films in the corners of pores and throats. In contrast to the findings for drainage displacements which showed that relative permeabilities are significantly affected by network topology, the present study shows that the effect of topology on imbibition relative permeabilities depends on the level of snap-off. For strongly wetting conditions where snap-off dominates the displacement the effect of network topology is significantly smaller than for weakly wet conditions where snap-off is suppressed. For contact angles sufficiently large to completely suppress snap-off, the effect of topology on imbibition relative permeabilities is similar to that for drainage displacements. The findings are valid for random networks and for networks displaying short-range pore–throat and longer range spatial correlations.