Retreat to advance: self-blocking enables efficient mineral replacement

Abstract

Mineral replacement reactions under advective flow often suffer from severe spatial inefficiency: dissolution causes the flow to self-focus into a few dominant wormholes that bypass the surrounding matrix, leaving most of the rock unreplaced. Here we show -- through two-dimensional pore-network simulations -- that replacement can be effective in two regimes. The first arises when the precipitation rate significantly exceeds the dissolution rate, leading to in situ replacement in which a uniform front of the secondary mineral advances through the matrix. The second, exploratory mode, occurs when the system repeatedly self-blocks and re-routes. In this regime, each channel lives only long enough to deliver reactant a short distance ahead of the front before its tip is cemented by the product phase; pressure re-routes through an adjacent corridor, and the cycle begins anew. Over time the replacement front advances as a mosaic of overlapping micro-fronts, distributing the secondary mineral almost uniformly. We derive design criteria for achieving exploratory-mode behaviour and discuss implications for both natural and engineered reactive-infiltration systems.

Figures (4)

• Figure 1: Four distinct replacement regimes: (a) dissolution-dominated: wormholing creates a high-permeability conduit that breaks through to the outlet, confining replacement to the immediate vicinity of the channel; (b) balanced dissolution–precipitation: wormholes are periodically blocked by precipitate, forcing the flow to re-route and carve new paths; (c) in situ replacement: precipitation is much faster than dissolution, thus the dissolved material gets immediately precipitated, leading to the in situ replacement of the primary mineral with the secondary phase; (d) precipitation-dominated: rapid product accumulation completely clogs the network and halts the reaction front.
• Figure 2: Morphological phase diagram of dissolution-precipitation patterns as a function of $\mathrm{Fo}$ and $\Gamma$ ($\mathrm{Da}=0.5$, $\varphi_0=0.04$). The simulations are carried out on a grid of $200\times 200$ randomly distributed nodes, continuing until either a continuous fluid pathway develops (breakthrough) or the system becomes completely sealed by mineral precipitation (clogging). Upper panel: pore diameter maps. Pores that are heavily overgrown, $d \leq d_0/10$, are marked in red; intermediate pores, $d_0/10 < d \leq d_0$, are yellow; pores larger than $d_0$, $d_0 < d \leq 2d_0$, are grey; pores creating dissolution pattern, $d > 2d_0$, are marked in black. Lower panel: mineral content maps. Colours indicate mineral compositions of the grains: mineral A is shown in blue, mineral E in red, and mixtures of the two appear in shades of purple; pore space (not occupied by grains) is yellow. Adapted from Budek2025.
• Figure 3: (a–c): Snapshots of system evolution in the exploratory regime ($\mathrm{Fo}=1, \Gamma = 0.75, \mathrm{Da}=0.5, \varphi_0=0.04$). The simulation uses a network of $400\times 400$ randomly distributed nodes. (a) Mineral map: mineral A (blue), mineral E (red), mixtures (purple); pore space (yellow). (b–c) Concentration fields of species B and C, respectively. Only a small subset of channels conveys solute deeper into the system. (d) Relative permeability $K/K_0$, as a function of time (in injected pore volumes) for the same run.
• Figure 4: (a) Schematic morphologies in $\mathrm{Fo}$–$\Gamma$ space. The regime boundaries are approximate; their locations depend on the initial porosity $\varphi_0$, the Damköhler number $\mathrm{Da}$ and the size of the system. (b) Volume of the precipitated mineral $V_{\text{E}}^{\text{final}}$, normalised by the initial volume of the primary mineral $V_{\text{A}}^0$, as a function of $\mathrm{Fo}$ for $\mathrm{Da} = 0.5$, $\varphi_0 = 0.04$ and $\Gamma=0.6$, $1.0$, $1.1$ and $1.2$. The statistics are averaged over $40$ realizations on $100\times100$ random-node grids, with each simulation terminated at either clogging or breakthrough.