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Register a new userInstabilities in the dissolution of a porous matrix
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A reactive fluid dissolving the surrounding rock matrix can trigger an instability in the dissolution front, leading to spontaneous formation of pronounced channels or wormholes. Theoretical investigations of this instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. In this paper we show that this is not the only possible dissolutional instability in porous rocks; there is another instability that operates instantaneously on any initial porosity field, including an entirely uniform one. The relative importance of the two mechanisms depends on the ratio of the porosity increase to the initial porosity. We show that the inlet instability is likely to be important in limestone formations where the initial porosity is small and there is the possibility of a large increase in permeability. In quartz-rich sandstones, where the proportion of easily soluble material (e.g. carbonate cements) is small, the instability in the steady-state equations is dominant.
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The dissolution of porous materials in a flow field shapes the morphologies of many geologic landscapes. Identifying the dissolution front, the interface between the reactive and the unreactive regions in a dissolving medium, is a prerequisite for studying dissolution kinetics. Despite its fundamental importance, the dynamics of a dissolution front in an evolving natural microstructure has never been reported. Here we show an unexpected spontaneous migration of the dissolution front against the pressure gradient of a flow field. This retraction stems from the infiltration instability induced surface generation, which can lead to a reactive surface dramatically greater than the ex situ geometric surface. The results are supported by a very good agreement between observations made with real time X-ray imaging and simulations based on static images of a rock determined by nanoCT. They both show that the in situ specific surface area of natural porous media is dependent on the flow field and reflects a balancing between surface generation and destruction. The reported dynamics challenge many long-held understanding of water-rock interactions and shed light on reconciling the discrepancies between field and laboratory measurements of reaction kinetics.
Chemical reactions can accelerate, slow down or even be at the very origin of the development of dissolution-driven convection in partially miscible stratifications, when they impact the density profile in the host fluid phase. We numerically analyze the dynamics of this reactive convective dissolution in the fully developed non-linear regime for a phase A dissolving into a host layer containing a dissolved reactant B. We show that for a general A+B$rightarrow$C reaction in solution, the dynamics vary with the Rayleigh numbers of the chemical species, i.e. with the nature of the chemicals in the host phase. Depending on whether the reaction slows down, accelerates or is at the origin of the development of convection, the spatial distributions of species A, B or C, the dissolution flux and the reaction rate are different. We show that chemical reactions enhance the steady-state flux as they consume A and can induce more intense convection than in the absence of reactions. This result is important in the context of CO$_2$ geological sequestration where quantifying the storage rate of CO$_2$ dissolving into the host oil or aqueous phase is crucial to assess the efficiency and the safety of the project.
It is generally accepted that melt extraction from the mantle at mid-ocean ridges (MORs) is concentrated in narrow regions of elevated melt fraction called channels. Two feedback mechanisms have been proposed to explain why these channels grow by linear instability: shear flow of partially molten mantle and reactive flow of the ascending magma. These two mechanisms have been studied extensively, in isolation from each other, through theory and laboratory experiments as well as field and geophysical observations. Here, we develop a consistent theory that accounts for both proposed mechanisms and allows us to weigh their relative contributions. We show that interaction of the two feedback mechanisms is insignificant and that the total linear growth rate of channels is well-approximated by summing their independent growth rates. Furthermore, we explain how their competition is governed by the orientation of channels with respect to gravity and mantle shear. By itself, analysis of the reaction-infiltration instability predicts the formation of tube-shaped channels. We show that with the addition of even a small amount of extension in the horizontal, the combined instability favours tabular channels, consistent with the observed morphology of dunite bodies in ophiolites. We apply the new theory to MORs by calculating the accumulated growth and rotation of channels along streamlines of the solid flow. We show that reactive flow is the dominant mechanism deep beneath the ridge axis, where the most unstable orientation of high-porosity channels is sub-vertical. Channels are then rotated by the solid flow away from the vertical. The contribution of the shear-driven instability is confined to the margins of the melting region. Within the limitations of our study, the shear-driven feedback is not responsible for significant melt focusing or for shallowly dipping seismic anisotropy [abridged].
When reactive fluids flow through a dissolving porous medium, conductive channels form, leading to fluid breakthrough. This phenomenon is important in geologic carbon storage, where the dissolution of CO2 in water increases the acidity and produce microstructures significantly different from those in an intact reservoir. We demonstrate the controlling mechanism for the dissolution patterns in natural porous materials. This was done using numerical simulations based on high resolution digital models of North Sea chalk. We tested three model scenarios, and found that aqueous CO2 dissolve porous media homogeneously, leading to large breakthrough porosity. In contrast, CO2-free solution develops elongated convective channels in porous media, known as wormholes, and resulting in small breakthrough porosity. We further show that a homogeneous dissolution pattern appears because the sample size is smaller than the theoretical size of a developing wormhole. The result indicates that the presence of dissolved CO2 expands the reactive subvolume of a porous medium, and thus enhances the geochemical alteration of reservoir structures and might undermine the sealing integrity of caprocks when minerals dissolve.
Multi-phase reactive transport processes are ubiquitous in igneous systems. A challenging aspect of modelling igneous phenomena is that they range from solid-dominated porous to liquid-dominated suspension flows and therefore entail a wide spectrum of rheological conditions, flow speeds, and length scales. Most previous models have been restricted to the two-phase limits of porous melt transport in deforming, partially molten rock and crystal settling in convecting magma bodies. The goal of this paper is to develop a framework that can capture igneous system from source to surface at all phase proportions including not only rock and melt but also an exsolved volatile phase. Here, we derive an n-phase reactive transport model building on the concepts of Mixture Theory, along with principles of Rational Thermodynamics and procedures of Non-equilibrium Thermodynamics. Our model operates at the macroscopic system scale and requires constitutive relations for fluxes within and transfers between phases, which are the processes that together give rise to reactive transport phenomena. We introduce a phase- and process-wise symmetrical formulation for fluxes and transfers of entropy, mass, momentum, and volume, and propose phenomenological coefficient closures that determine how fluxes and transfers respond to mechanical and thermodynamic forces. Finally, we demonstrate that the known limits of two-phase porous and suspension flow emerge as special cases of our general model and discuss some ramifications for modelling pertinent two- and three-phase flow problems in igneous systems.
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