Influence of aperture variability on dissolutional growth of fissures in Karst Formations

Abstract

Abstract. The influence of aperture variability on dissolutional growth of fissures is investigated on the basis of two-dimensional numerical simulations. The logarithm of the fissure aperture before dissolution begins is modeled as a Gaussian stationary isotropic random field. The initial phase of dissolutional growth is studied up to the time when turbulent flow first occurs at a point within the fissure (the breakthrough time). The breakthrough time in variable aperture fissures is smaller than that in uniform fissures and decreases as the coefficient of variation of the aperture field (cr//x) increases. In comparing uniform and variable aperture fissures in limestone, the breakthrough time with cr//x = 0.1 is about a factor of 2 smaller than that in a uniform fissure. The breakthrough time is reduced by about an order of magnitude with cr//x = 2.0. The mechanism leading to reduced breakthrough times is the focusing of flow into preferential flow channels which are enlarged at a faster rate than the surrounding regions of slower flow. Dissolution channels are narrower and more tortuous as cr//x increases. Investigations of the influence of reaction rate reveal that the influence of aperture variability is more pronounced in rapidly dissolving rock. In uniform fissures in rapidly dissolving minerals, breakthrough times are very long since water becomes saturated with respect to the mineral within a short distance of the entrance to the flow path. However, in variable aperture fissures, breakthrough occurs rapidly because of selective growth along preferential flow channels, which progressively capture larger fractions of the total flow. These results partly explain why conduits develop rapidly in gypsum, although previous one-dimensional studies suggest that conduit growth will not occur. IntroductionQuantitative modeling of the evolution of hydraulic conduits in karst formations is an area of active research. Initiation of conduits during the early evolution of karst is of particular interest because it is believed to be the slowest phase of cave development. In previous modeling studies, Dreybrodt [1990Dreybrodt [ , 1996, Palmer [1991], and Groves and Howard [1994a, b] observed that once turbulent flow is initiated, further dissolutional growth occurs at a relatively rapid rate. In these works the duration of the initial phase of karst evolution is quantified using the concept of "breakthrough time," which refers to the time at which turbulent flow is first encountered. As breakthrough is approached, the flow rate through the system increases rapidly, leading eventually to turbulent flow. After breakthrough occurs, conduits are expected to grow at a relatively rapid rate of a few millimeters a year [Dreybrodt, 1990[Dreybrodt, , 1996 Groves and Howard, 1994a, b]. Thus the occurrence of breakthrough ensures further development of caverns. The time required for the onset of turbulent flow typically depends on the length of the fissure, the hydraulic gradient, and the initial aperture. Typical breakthrough time...

Early-stage hypogene karstification in a mountain hydrologic system: A coupled thermohydrochemical model incorporating buoyant convection

“…Nevertheless, we note that our simulations provide several useful insights on mechanisms of early-stage speleogenesis. For instance, the dissolution growth patterns in the fracture plane do not show the formation of fingers and unstable growth by positive feedback, as noted in previous modeling studies of epigenic systems [e.g., Hanna and Rajaram, 1998;Siemers and Dreybrodt, 1998;Szymczak and Ladd, 2012]. Correspondingly, the generation of branch work patterns evident in fracture plane models of epigenic systems after Figure 17.…”

Alteration of fractures by precipitation and dissolution in gradient reaction environments: Computational results and stochastic analysis

“…In this regime a dissolution or precipitation front typically develops. The reaction front is often unstable in the dissolution case and leads to fingered dissolution channels, as documented in previous work on fractures [e.g., Hanna and Rajaram, 1998;Durham et al, 2001;Detwiler et al, 2003;Szymczak and Ladd, 2004;Detwiler and Rajaram, 2007]. Natural spatial variations in fracture apertures aid the initiation of unstable finger growth [Cheung and Rajaram, 2002].…”

“…Thus, the overall process of reactive alteration and its feedback on fluid flow and dissolved mineral transport can be modeled on the basis of quasi steady state flow and transport equations, coupled with a medium alteration equation. This approach has been used in the context of fracture alteration by Hanna and Rajaram [1998], Andre and Rajaram [2005], and Detwiler and Rajaram [2007].…”

Effect of mineral reactions on the hydraulic properties of unsaturated soils: Model development and application

“…Within the domain of reactive flow in unsaturated soils three main types of interfering instabilities occur: (i) reaction instabilities due to initial heterogeneities in the hydraulic properties with dissolution of wormholes and karst phenomena [1,[96][97][98][99][100][101][102][103][104][105], (ii) flow instabilities with moisture content fingering during the infiltration of a moisture front [106][107][108][109][110][111][112][113][114][115][116] and (iii) density instabilities due to local differences of solution densities [117][118][119][120][121][122][123][124]. However, the scope of this paper is not to investigate instability phenomena, but to propose a new approach that relates changes in mineral volumes and hydraulic properties.…”