Gravity‐destabilized nonwetting phase invasion in macroheterogeneous porous media: Near‐pore‐scale macro modified invasion percolation simulation of experiments

Abstract

Abstract. We r½conccptualiz½ "macro" modified invasion pcrcolation (MMIP) at the near pore (NP) scale and apply it to simulate the nonwetting phase invasion experiments of Glass e! al. [2000] conducted in macroheterogeneous porous media. For experiments where viscous forces were nonnegligible, we redefine the total pore filling pressure to include viscous losses within the invading phase as well as the viscous influence to decrease randomness imposed by capillary forces at the front. NP MMIP exhibits the complex invasion order s½½n experimentally with characteristic alternations between periods of gravity-stabilized and d½stabilizcd invasion growth controlled by capillary barriers. The breaching of these barriers and subsequent pore-scale fingering of the nonwetting phase is represented extremely well, as is the saturation field evolution and total volume invaded. IntroductionRecent experiments presented by Glass et al.[2000], henceforth referred to as GCP, have demonstrated the complexity of the gravity-destabilized nonwetting invasion process in macroheterogeneous porous media and suggested the difficulty of attempting simulation using standard porous continuum approaches. These experiments show a characteristic alternation between gravity-stabilized and destabilized invasion growth controlled by the sequential capillary barriers (CBs) within the heterogeneous field. The final nonwetting invasion structure existed as a set of macroscopic pools connected by pore-scale fingers. Viscous forces were shown to increase the number of fingers, their width, and the height of pools above CBs. The experiments also documented unsteady pulsation behind the invasion front; however, the pulsation did not significantly influence the maximum extent of the invasion structure.In an accompanying analysis, GCP also developed length scales that describe pool height, finger width, and pulsation. Each of these length scales required conceptualization at the pore scale to predict experimental behavior. To avoid the problems of porous continuum simulation, a "structural" growth model was proposed at the macroscale that would assemble these length scales to build the nonwetting phase migration pathway directly, its geometry of fingers and pools, and the locations of pulsation within a complex heterogeneous formation. Such an approach is underpinned by the physics of the pore-scale behavior and is a more abstracted or upscaled version of macromodified invasion percolation (MMIP) developed and applied originally by Glass et al. [1993, 1995] to the gravity-destabilized, dense nonaqueous phase liquid (DNAPL) migration problem.The development of such modeling approaches is in its infancy compared to conventional porous continuum conceptualizations of reality. Here we continue to lay a foundation for MMIP by first reconceptualizing it generally in a form that encompasses the near pore (NP) scale and then comparing NP MMIP simulations to the laboratory experiments presented by GCP. Our initial NP MMIP simulations of the experiments show seve...

The effect of spontaneous gas expansion and mobilization on the aqueous-phase concentrations above a dense non-aqueous phase liquid pool

“…Local displacement pressures (P D ) were assigned to each block by randomly selecting P c values from the cumulative distribution function defined by Eq. (6) [34], and using parameter values previously reported for this sand [22] (Table 2). These local displacement pressures were then used to calculate local entry pressures using Eq.…”

“…The inability of continuum-based numerical models such as this to simulate the processes that control the unstable flow of non-wetting fluids in porous media has been previously recognized [12,15,18,29]. Therefore, the expansion to adjacent grid blocks within the model, as well as the fragmentation and mobilization of gas clusters, was simulated using macroscopic invasion percolation (IP) techniques [20,[30][31][32][33][34], with modifications for IP in a gravity gradient [33,35] and migration and fragmentation of the invading gas phase [19][20][21]. Macroscopic IP is a modified form of IP [36].…”

“…However, macroscopic IP differs from traditional IP in that sites represent a sub-region of the porous medium, and sites can be occupied by multiple fluids. An approach using local capillary pressure-saturation relationships at each grid block [30,31,33], rather than a single characteristic pore radius [20,32,34], was used to model the occupation of a site by multiple fluids and to allow simulation of the pressurization of the gas phase within an invaded block due to multi-component partitioning.…”

In Situ Thermal Remediation of DNAPL Source Zones

“…The MIP model is a modified form of the invasion percolation (IP) technique which has been used extensively to model fluid displacement processes in the subsurface (Glass et al, 2001;Kueper & McWhorter, 1992). IP and MIP techniques use invasion and drainage thresholds to control the fluid movement, however whereas IP represents the porous medium by a network of sites and bonds, MIP models the domain with sites only.…”

“…In searching for connections, only blocks sharing faces were considered (coordination number of 4). Each cluster was examined individually and assessed for expansion or mobilization, following the rules outlined by Glass et al (2001) and Li & Yortsos (1995). The three processes are shown in Figure 4.26, where the hatched squares represent gas-occupied blocks while white squares are fully water saturated grid blocks (adapted from Wagner et al (1997).…”