Verification of a Dynamic Scaling for the Pair Correlation Function during the Slow Drainage of a Porous Medium

Abstract

In this Letter we give experimental grounding for the remarkable observation made by Furuberg et al. [Phys. Rev. Lett. 61, 2117 (1988)PRLTAO0031-900710.1103/PhysRevLett.61.2117] of an unusual dynamic scaling for the pair correlation function N(r,t) during the slow drainage of a porous medium. Those authors use an invasion percolation algorithm to show numerically that the probability of invasion of a pore at a distance r away and after a time t from the invasion of another pore scales as N(r,t)∝r^{-1}f(r^{D}/t), where D is the fractal dimension of the invading cluster and the function f(u)∝u^{1.4}, for u≪1 and f(u)∝u^{-0.6}, for u≫1. Our experimental setup allows us to have full access to the spatiotemporal evolution of the invasion, which is used to directly verify this scaling. Additionally, we connect two important theoretical contributions from the literature to explain the functional dependency of N(r,t) and the scaling exponent for the short-time regime (t≪r^{D}). A new theoretical argument is developed to explain the long-time regime exponent (t≫r^{D}).

Phase transitions and correlations in fracture processes where disorder and stress compete

“…This matches the exponent for invasion percolation dynamics [24]. Recently, this spatiotemporal scaling was observed experimentally for two-phase flow in a porous medium during slow drainage [47] where the exponent a was found ranging between 1.4 and 1.73. For the power law in the small-argument limit, we obtain the exponent b = 0.47 ± 0.06, which is different from 0.68 obtained by Furuberg et al…”

Intermittent Dynamics of Slow Drainage Experiments in Porous Media: Characterization Under Different Boundary Conditions

“…Next we move on to the analysis of the power spectral density of the pressure signals. The analysis presented here includes and extends the work initiated in Moura et al [24].…”

“…The topic of multiphase flow in porous media has received widespread attention by the scientific community in the past decades [1][2][3][4][5][6][7][8][9][10][11]. In addition to its inherent physical interest (pattern formation [12][13][14][15][16][17][18], intermittent dynamics [3,[19][20][21][22][23][24], collective phenomena [25][26][27][28][29], etc. ), the topic naturally receives focus due to its immediate industrial and environmental applications.…”

“…Another interesting aspect of this problem is the fact that the dynamics of fluids in porous media very frequently presents intermittent behavior [3,19,23,24,53], with long intervals of stagnation followed by short intervals of strong activity in an irregular aperiodic fashion [56][57][58]. Intermittent behavior has been observed in various physical, biological, and economical systems [20,[59][60][61][62][63][64][65][66][67][68][69][70][71].…”

Connectivity enhancement due to film flow in porous media

“…The study of the basic mechanisms behind fluid flow in porous media has received considerable attention from the scientific community in the past decades [1][2][3][4][5][6][7][8][9][10]. The theme is of importance not only because of its inherent physical interest (pattern formation [11][12][13][14][15][16][17], intermittent dynamics [2,[18][19][20][21][22][23][24], collective phenomena [25][26][27][28][29], etc.) but also because of direct environmental applications and economical aspects.…”