Chemical dissolution of a porous medium by a reactive fluid

Abstract

Chemical dissolution of a two-dimensional porous medium by a reactive fluid which produces fractal patterns is studied. A new model is proposed that introduces a cumulative erosion process which broadens the branches of the cluster and gives structures very similar to the experimental ones. Diffusion-limited aggregation is a limiting case of this model. An interpretation of the evolution of the injection pressure with time which yields the fractal dimension is also presented, and agrees with the experimental results.PACS numbers: 47.70.Fw, 47.20.Hw It has been known for a long time that injection of a reactive fluid into a soluble porous medium yields very ramified dissolution patterns. In nature, the networks of caves in calcareous regions are macroscopic results of such processes. Acids are routinely injected into oilbearing rocks and similar patterns are thought to occur. At present, there is no clear understanding of the physical basis of the patterns formed by chemical dissolution processes.The physical phenomenon of the formation of dissolution patterns (DP) involves the flow of a liquid in a porous medium coupled with a chemical reaction. 1,2 Although qualitative ID models 3 have been proposed, there are no quantitative models for the actual DP observed. In this Letter, I present experimental results on a simple 2D system and develop a new model that provides a quantitative description of the DP.The essential idea of my experiments is to take advantage of the property of plaster of being slightly soluble in pure water. Thus I pumped water into the center of the model and observed a "breakdown" of the porous plaster medium (Fig. l). I used 2D radial geometries, 4 the sample consisting of a thin disk (thickness b = 1 mm and radius /?ext = 125 mm) of pure plaster held between two transparent plates. Plaster was made by mixing 10 parts of water with 11 parts of CaSO 4 0.5H 2 O. After setting, the medium was very homogeneous 5 and had a porosity of 60% porous and a permeability of 60 /xm 2 .Initially, the plaster was fully saturated (in chemical equilibrium) with water with a concentration in calcium sulphate co~ 13 mm. At time /=0, pure water (viscosity p. and concentration in calcium sulphate c =0) was injected at constant flow rate Q at the center of the disk, displacing the saturated water and subsequently dissolving some of the plaster. Good images of the final DP were obtained by injection of a low-melting-point alloy (Wood's metal) into the dried plaster sample. After cooling, the plaster was dissolved. Figure 1 shows three patterns obtained for different flow rates but same time. At low flow rate, the branches are broader and the number of ramifications decreases.At first glance, the 2D radial structures obtained are very similar to other experimental growth patterns asso-ciated with the model of diffusion-limited aggregation 6 (DLA): dielectric breakdown, 7 electrodeposited metal leaves, 8 viscous fingering, 9 or diffusion-limited polymerization. 10 This analogy can be understood by comparison with ...

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

“…The &point local slopes were calculated as the slope of a least-squares line fit to every 8 successive points. This protocol has been successfully applied to a wide range of fractal objects (Nittmann et al, 1985;Daccord et al, 1986;Daccord, 1987;Daccord and Lenormand, 1987). To extend these methods to 3 dimensions, we counted all the mass (pixels) inside spheres of various radii instead of disks.…”

Influence of Layering on the Formation and Growth of Solution Pipes

“…It is worth noting that in three dimensions, an analysis analogous to Equations (16)(17)(18)(19) would yield Da −1/3 scaling, thus the dependence on the dissolution rate is weaker in 3D.…”

“…In that context, it has also been studied experimentally [6,11] and numerically [12][13][14][15]. In the physics community, the interest toward these systems has been sparked by classical papers of Daccord and Lenormand, which analyzed the patterns formed in a dissolving plaster and related them to other pattern-forming systems, such as diffusion-limited aggregation [16,17]. In earth sciences, the understanding of the profound role that flow-focusing plays in karst development came with the pioneering works of Ewers [18], who has analyzed a number of analog models of karst formation made of sand or plaster of Paris.…”

Sculpting of Rocks by Reactive Fluids

“…Of particular geochemical relevance was the flow channeling experiments of Daccord (1987) and Daccord and LeNormand (1987) which might not, even today, have been fully explored in terms of their relevance for geomorphic patterns such as karsts.…”