Slow invasion of a nonwetting fluid from multiple inlet sources in a thin porous layer

Abstract

We numerically study the process of quasistatic invasion of a nonwetting fluid in 2D and 3D porous layers from multiple inlet injection sources and show that a porous layer acts as a two-phase filter as a result of the repeated convergence of flow paths: The probability for a pore at the outlet to be a breakthrough point is significantly lower than the fraction of active injection points at the inlet owing to the merging within the porous layer of liquid paths originating from different inlet injection points. The study of the breakthrough point statistics indicates that the number of breakthrough points diminishes with the system thickness and that the behavior of thin layers, defined here as systems of typical thicknesses of less than 15 lattice spacing units (≈15 pore or grain mean sizes), is distinct from thicker layers. For thicker systems, it is found that the probability of an outlet pore to be a breakthrough pore scales as l(1-d) where l is the system thickness and d is the space dimensionality, whereas, a power law behavior is not obtained with a thin system. Other properties, such as the invading phase occupancy profiles are studied. We also described a kinetic algorithm that allowed us to compute the occurrence times of breakthrough points. The distribution of these times is markedly different in 2D and in 3D.

Liquid Invasion from Multiple Inlet Sources and Optimal Gas Access in a Two-Layer Thin Porous Medium

“…In fact, the numerical results for a network of size N x × N x × N x show that the number of breakthrough points is one with a probability P 1 , two with probability P 2 and three with probability P 3 (see Fig. 7b in Ceballos et al (2011)) with P 1 + P 2 + P 3 ≈ 1 provided that N x is not too small. Hence, the probability of having more than three breakthrough points is negligible.…”

“…As shown in Ceballos and Prat (2010), the surface density of breakthrough points is then consistent with the observations. The impact of this boundary condition was then studied in detail in Ceballos et al (2011) and Ceballos and Prat (2013). We are not aware of previous works in the context of IP theory where the IP variants considered in Ceballos and Prat (2010) and Ceballos et al (2011) were studied.…”

“…In this section, we recall some of the results presented in Ceballos et al (2011) and Ceballos and Prat (2013) which are useful for the present study. These results were obtained using a simple cubic pore network.…”

“…We used the simultaneous IP algorithm referred to as the sequential algorithm in Ceballos et al (2011). The algorithm can be summarized as follows:…”

“…This problem was studied in previous publications (i.e., Ceballos and Prat 2010;Ceballos et al 2011;Ceballos and Prat 2013). However, the system was formed only by the coarse layer without the fine layer.…”