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Register a new userEnhanced steady-state dissolution flux in reactive convective dissolution
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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.
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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.
Dissolution fingers (or wormholes) are formed during the dissolution of a porous rock as a result of nonlinear feedbacks between the flow, transport and chemical reactions at pore surfaces. We analyze the shapes and growth velocities of such fingers within the thin-front approximation, in which the reaction is assumed to take place instantaneously with the reactants fully consumed at the dissolution front. We concentrate on the case when the main flow is driven by the constant pressure gradient far from the finger, and the permeability contrast between the inside and the outside of the finger is finite. Using Ivantsov ansatz and conformal transformations we find the family of steadily translating fingers characterized by a parabolic shape. We derive the reactant concentration field and the pressure field inside and outside of the fingers and show that the flow within them is uniform. The advancement velocity of the finger is shown to be inversely proportional to its radius of curvature in the small P{e}clet number limit and constant for large P{e}clet numbers.
Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle -- a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape results from the interplay between interface motion and the natural convective flows driven by the descent of relatively heavy solute. Previous investigations suggest these structures to be associated with shock-formation in the underlying evolution equations, with the regularizing Gibbs-Thomson effect required for finite tip curvature. Here, we find a class of exact solutions that act as attractors for the shape dynamics in two and three dimensions. Intriguingly, the solutions exhibit large but finite tip curvature without any regularization, and they agree remarkably well with experimental measurements. The relationship between the dimensions of the initial shape and the final state of dissolution may offer a principle for estimating the age and environmental conditions of geological structures.
A reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. Although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. In previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. Here we describe a more general linear stability analysis, including axial diffusion, transport limited dissolution, non-linear kinetics, and a finite length system.
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.
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