Burst dynamics during drainage displacements in porous media: Simulations and experiments

– We investigate the burst dynamics during drainage going from low to high injection rate at various fluid viscosities. The bursts are identified as pressure drops in the pressure signal across the system. We find that the statistical distribution of pressure drops scales according to other systems exhibiting self-organized criticality. The pressure signal was calculated by a network model that properly simulates drainage displacements. We compare our results with corresponding experiments. Since the early 1980s physicists have paid attention to the complex phenomena observed when one fluid displaces another fluid in porous media. The papers that have appeared in the literature mostly refer to the rich variety of displacement structures that is observed due to different fluid properties like flow rate, viscosity, interfacial tension, and wettability. The major displacement structures have been found to resemble structures generated by geometrical models like invasion percolation (IP) [1, 2, 3], DLA [4, 5, 6, 7], and anti-DLA [5, 8]. Only a few authors [9, 10, 11] have addressed the interplay between the displacement structures and the evolution of the fluid pressure. In slow drainage when non-wetting fluid displaces slowly wetting fluid in porous media, the pressure evolves according to Haines jumps [9, 12, 13]. The displacement is controlled solely by the pressure difference between the two fluids across a meniscus (the capillary pressure), and the non-wetting fluid invades the porous medium in a series of bursts accompanied by sudden negative pressure drops. The purpose of this paper is to study the dynamics of the fluid pressure during drainage going from low to high displacement rates. To do so, we examine the statistical properties of the sudden negative pressure drops due to the bursts. We find that for a wide range of displacement rates and fluid viscosities, the pressure drops act in analogy to theoretical predictions of systems exhibiting self-organized criticality [14], like IP. Even at high injection rates, where Typeset using EURO-TEX 2 EUROPHYSICS LETTERS 315 320 325 330 335 340 345 t (s) 190