Structural barriers to complete homogenization and wormholing in dissolving porous and fractured rocks

TL;DR

The paper addresses how dissolution patterns in porous and fractured rocks arise from the coupled effects of advection, diffusion, reaction, and the medium's intrinsic heterogeneity. It adapts a flow focusing profile as a unified diagnostic to compare three network models—regular pore networks, disordered pore networks, and discrete fracture networks—across a broad range of conditions. The main findings show that structural topology imposes a fundamental limit on homogenization, with regular networks capable of approaching uniform dissolution, while disordered networks and DFNs preserve residual flow focusing due to path-length and connectivity heterogeneity. These results have implications for upscaling reactive transport, suggesting that preserving network topology or using hybrid continuum-network models is essential to accurately predict injectivity, channeling, and wormhole formation at reservoir scales.

Abstract

Dissolution in porous media and fractured rocks alters both the chemical composition of the fluid and the physical properties of the solid. Depending on system conditions, reactive flow may enlarge pores uniformly, widen pre-existing channels, or trigger instabilities that form wormholes. The resulting pattern reflects feedbacks among advection, diffusion, surface reaction, and the initial heterogeneity of the medium. Porous and fractured media can exhibit distinct characteristics -- for example, the presence of large fractures can significantly alter the network topology and overall connectivity of the system. We quantify these differences with three network models -- a regular pore network, a disordered pore network, and a discrete fracture network -- evaluated with a unified metric: the flow focusing profile. This metric effectively captures evolution of flow paths across all systems: it reveals a focusing front that propagates from the inlet in the wormholing regime, a system-wide decrease in focusing during uniform dissolution, and the progressive enlargement of pre-existing flow paths in the channeling regime. The metric shows that uniform dissolution cannot eliminate heterogeneity resulting from the network topology. This structural heterogeneity -- rather than just pore-diameter or fracture-aperture variance -- sets a fundamental limit on flow homogenization and must be accounted for when upscaling dissolution kinetics from pore or fracture scale to the reservoir level.

Figures (9)

• Figure 1: (a) Example regular pore network realization (diamond lattice); edge width is proportional to the initial pore diameter. (b) Example disordered pore network realization (Delaunay lattice); edge width again reflects the initial pore diameter. (c) Example discrete fracture network; colors denote fracture families. (d) Graph representation of the same DFN, projected into two dimensions via principal component analysis. Edge width is kept constant, so color intensity corresponds to the local density of fracture segments.
• Figure 2: Evolution of the three network types and the flow focusing profile in the wormholing regime. (a) Regular pore network ($\textrm{Da}_\textrm{eff} = 0.2$, $\textrm{G} = 5$). (b) Disordered pore network ($\textrm{Da}_\textrm{eff} = 0.2$, $\textrm{G} = 5$). (c) Discrete fracture network ($\textrm{Da}_\textrm{eff} = 0.02$, $\textrm{G} = 5$) shown as a graph after a principal-component-analysis projection. In each case, edge width is proportional to the volumetric flow rate, with the same proportionality constant used for a given network type. For the DFN, only edges carrying more than 1% of the maximum flow rate in the system are plotted. In the flow focusing plots, the initial profile is shown by the black line, and profiles at later times ($T = 1.0, 2.0, 5.0,$ and $10.0$ for both pore networks; $T = 0.1, 0.2, 0.5,$ and $1.0$ for the fracture network) are shown by colored lines.
• Figure 3: Evolution of the regular pore network and the flow focusing profile in three dissolution regimes: (a) uniform ($\textrm{Da}_\textrm{eff} = 0.002$, $\textrm{G} = 5$), (b) channeling ($\textrm{Da}_\textrm{eff} = 0.02$, $\textrm{G} = 5$), and (c) wormholing ($\textrm{Da}_\textrm{eff} = 0.2$, $\textrm{G} = 5$). Edge width is proportional to the volumetric flow rate, with the same proportionality constant used in all panels. The plots show the initial flow focusing profile (black line) and profiles at times $T = 1.0, 2.0, 5.0,$ and $10.0$ (colored lines). The frame color denotes the dissolution regime: green for uniform, red for channeling, and blue for wormholing.
• Figure 4: Evolution of the flow focusing profile for the regular pore network across the ($\textrm{Da}_\textrm{eff}$, $\textrm{G}$) parameter space. (a) Mean profile value at successive time snapshots (solid lines). (b) Same data, with ensemble variability: the shaded band around each curve denotes the mean $\pm$ 1 standard deviation across all realizations. The plots show the initial flow focusing profile (black line) and profiles at times $T = 1.0, 2.0, 5.0,$ and $10.0$ (colored lines). The frame color denotes the dissolution regime: green for uniform, red for channeling, and blue for wormholing.
• Figure 5: Evolution of the disordered pore network and the flow focusing profile in three dissolution regimes: (a) uniform ($\textrm{Da}_\textrm{eff} = 0.002$, $\textrm{G} = 5$), (b) channeling ($\textrm{Da}_\textrm{eff} = 0.02$, $\textrm{G} = 5$), and (c) wormholing ($\textrm{Da}_\textrm{eff} = 0.2$, $\textrm{G} = 5$). Edge width is proportional to the volumetric flow rate, with the same proportionality constant used in all panels. The plots show the initial flow focusing profile (black line) and profiles at times $T = 1.0, 2.0, 5.0,$ and $10.0$ (colored lines). The frame color denotes the dissolution regime: green for uniform, red for channeling, and blue for wormholing.