Multiple-well invasion percolation

Abstract

When the invasion percolation model is applied as a simplified model for the displacement of a viscous fluid by a less viscous one, the distribution of displaced mass follows two distinct universality classes, depending on the criteria used to stop the displacement. Here we study the distribution of mass for this process, in the case where four extraction wells are placed around a single injection well in the middle of a square lattice. Our analysis considers the limit where the pressure of the extraction well Pe is zero; in other words, an extraction well is capped as soon as less viscous fluid reaches that extraction well. Our results show that, as expected, the probability of stopping the production with small amounts of displaced mass is greatly reduced. We also investigate whether or not creating extra extraction wells is an efficient strategy. We show that the probability of increasing the amount of displaced fluid by adding an extra extraction well depends on the total recovered mass obtained before adding this well. The results presented here could be relevant to determine efficient strategies in oil exploration.

Invasion Percolation With a Hardening Interface Under Gravity

“…Since then, the IP paradigm has been extensively used to describe different physical systems. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] In the present work, we modified the IP model to take into account the interfacial hardening of fluids. Before describing our model, we recall the standard IP.…”

Percolation of functionalized colloids on patterned substrates

“…Substrates patterned with space-dependent physicochemical properties have a strong influence on the equilibrium and dynamical properties of soft materials deposited or adsorbed on them. Examples of physical processes affected by the presence of patterns include wetting [1,2], crystal nucleation [3,4], phase separation [5], freezing [6,7], adsorption [8,9], sedimentation [10], and colloidal transport [11][12][13].…”

Nonequilibrium self-organization of colloidal particles on substrates: adsorption, relaxation, and annealing

“…Yet, the presence of a surface improves the control over aggregation [16,17,18,19,20,21,22,23]. For example, in the limit of irreversible binding, the assembled structures differ dramatically from the thermodynamic ones [24,25,26,27]. We also consider colloidal particles with limited valence, known as patchy colloids.…”