Invasion percolation with viscous forces

Physical Review E, 2000

We study an invasion percolation model for drainage where the disorder comes partly from capillary thresholds and partly from height differences in a rough self-affine landscape. As a function of the buoyancy, the geometry of the invaded clusters changes dramatically. Long-range correlations from the fracture topography induce a double cluster structure with strings and compact blobs. A characteristic length is introduced comparing the width of the capillary threshold distribution and gravity effects at the pore scale. We study electrical properties of percolating clusters. Current distributions along percolating clusters are shown to be multifractal and sensitive to the buoyancy.

Europhysics Letters (EPL), 1995

PACS. 47.55Mh -Flows through porous media. PACS. 47.55Kf -Multiphase and particle-laden flows.

Transport in Porous Media

We apply steady-state capillary-controlled upscaling in heterogeneous environments. A phase may fail to form a connected path across a given domain at capillary equilibrium. Moreover, even if a continuous saturation path exists, some regions of the domain may produce disconnected clusters that do not contribute to the overall connectivity of the system. In such cases, conventional upscaling processes might not be accurate since identification and removal of these isolated clusters are extremely important to the global connectivity of the system and the stability of the numerical solvers. In this study, we address the impact of percolation during capillary-controlled displacements in heterogeneous porous media and present a comprehensive investigation using random absolute permeability fields, for water-wet, oil-wet and mixed-wet systems, where J-function scaling is used to relate capillary pressure, porosity and absolute permeabilities in each grid cell. Important information is revealed about the average connectivity of the phases and trapping at the Darcy scale due to capillary forces. We show that in oil-wet and mixed-wet media, large-scale trapping of oil controlled by variations in local capillary pressure may be more significant than the local trapping, controlled by pore-scale displacement. Keywords Immiscible displacements • Capillary-driven flow • Large-scale percolation • Steady-state upscaling List of symbols A p Symmetric matrix used in percolation solver for a given phase A i j Cross-sectional area between two nodes (m 2) B Adjacent matrix of a simulation model B Hasan A. Nooruddin

Marine and Petroleum Geology, 2000

Experiments have been carried out to study the displacement of wetting fluids by immiscible non-wetting fluids in quasi-two-dimensional and three-dimensional granular porous media. These experiments included a systematic investigation of the effects of gravity acting on the density difference between the two fluids. The simple invasion percolation model provides a surprisingly realistic simulation of the slow fluid–fluid displacement process in

Energy, 2005

We have studied experimentally and numerically the displacement of a highly viscous wetting fluid by a non-wetting fluid with low viscosity in a random two-dimensional porous medium under stabilizing gravity. In situations where the magnitudes of the viscous-, capillary-and gravity forces are comparable, we observe a transition from a capillary fingering behavior to a viscous fingering behavior, when decreasing apparent gravity. In the former configuration, the vertical extension of the displacement front saturates; in the latter, thin branched fingers develop and rapidly reach breakthrough. From pressure measurements and picture analyzes, we experimentally determine the threshold for the instability, a value that we also predict using percolation theory. Percolation theory further allows us to predict that the vertical extension of the invasion fronts undergoing stable displacement scales as a power law of the generalized Bond number Bo à ¼ Bo À Ca, where Bo and Ca are the Bond and capillary numbers, respectively. Our experimental findings are compared to the results of a numerical modeling that takes local viscous forces into account. Theoretical, experimental and numerical approaches appear to be consistent. #

Journal of Fluid Mechanics, 1982

We consider capillary displacement of immiscible fluids in porous media in the limit of vanishing flow rate. The motion is represented as a stepwise Monte Carlo process on a finite two-dimensional random lattice, where a t each step the fluid interface moves through the lattice link where the displacing force is largest. The displacement process exhibits considerable fingering and trapping of displaced phase at all length scales, leading to high residual retention of the displaced phase. Many features of our results are well described by percolation-theory concepts. I n particular, we find a residual volume fraction of displaced phase which depends strongly on the sample size, but weakly or not a t all on the co-ordination number and microscopicsize distribution of the lattice elements.

Physica A: Statistical Mechanics and its Applications, 1993

Physica A: Statistical Mechanics and its Applications, 1992

The effects of gravity stabilization and destabilization on the slow displacement of a wetting fluid by a non-wetting fluid in two-dimensional and three-dimensional porous media have been investigated experimentally. The characteristic features of the resulting displacement patterns can be reproduced quite well by invasion percolation models with a spatial gradient added to the usual random threshold distribution. In the case of destabilized displacement the patterns can be described in terms of a string of blobs of size e that form a directed walk. The internal structure of the blobs is like that of an invasion percolation cluster (with trapping in the two-dimensional case). In the stabilized case the structure is like that of a fractal invasion percolation cluster on short length scales (lengths +[) and is uniform on longer lengths. The correlation length also describes the maximum hole diameter. The invasion front is a self-similar fractal on length scales shorter than 5 and flat on longer length scales. In both the experiments and the simulations the correlation length .$ is related to the Bond number (B,, the ratio between buoyancy and capillary forces) by .$ -1 BO[-y'(V+') where Y is the ordinary percolation correlation length exponent) in accord with the theoretical arguments of Wilkinson (Phys. Rev. A 30 (1984) 520; 34 (1986) 1380). 0378-4371/92/$05.00 @ 1992 -Elsevier Science Publishers B.V. AU rights reserved P. Meakin et al. I Gradient (dejstabilized invasion percolation 229

Physical Review Letters, 1992

Pressure fluctuations measured during slow drainage in a two-dimensional porous model exhibit sudden jumps that identify bursts where the invasion front proceeds abruptly. The pressure jump size distribution is observed to be exponential. The nonscaling dynamics created fractal fronts and invaded regions described by invasion percolation. A new modified invasion percolation algorithm includes invasion dynamics. A capacitive volume associated with each interface throat results in a crossover from powerlaw behavior to an exponential pressure jump distribution consistent with observations.

Scientific reports, 2017

Wettability is an important factor which controls the displacement of immiscible fluids in permeable media, with far reaching implications for storage of CO2 in deep saline aquifers, fuel cells, oil recovery, and for the remediation of oil contaminated soils. Considering the paradigmatic case of random piles of spherical beads, fluid front morphologies emerging during slow immiscible displacement are investigated in real time by X-ray micro-tomography and quantitatively compared with model predictions. Controlled by the wettability of the bead matrix two distinct displacement patterns are found. A compact front morphology emerges if the invading fluid wets the beads while a fingered morphology is found for non-wetting invading fluids, causing the residual amount of defending fluid to differ by one order of magnitude. The corresponding crossover between these two regimes in terms of the advancing contact angle is governed by an interplay of wettability and pore geometry and can be pr...