Sharp Fronts within Geochemical Transport Problems
- PDF / 1,063,291 Bytes
- 10 Pages / 414.72 x 648 pts Page_size
- 37 Downloads / 165 Views
SHARP FRONTS WITHIN GEOCHEMICAL TRANSPORT PROBLEMS
PETER GRINDROD Intera Information Technologies, Chiltern House, 45 Station Road, Henley-on-Thames, Oxfordshire RG9 1AT, UK ABSTRACT We consider some reactive geochemical transport problems in groundwater systems. When incoming fluid is in disequilibrium with the mineralogy sharp transition fronts may develop. We show that this is a generic property for a class of systems where the timescales associated with reaction and diffusion phenomena are much shorter than those associated with advective transport. Such multiple timescale problems are relevant to a variety of processes in natural systems: mathematically methods of singular perturbation theory reduce the dimension of the problems to be solved locally. Furthermore we consider how spatial heterogeneous mineralogy can impact upon the propagation of sharp geochemical fronts. We develop an asymptotic approach in which we solve equations for the evolving geometry of the front and indicate how the non-smooth perturbations due to natural heterogeneity of the mineralogy on underlying ground water flow field are balanced against the smoothing effect of diffusion/dispersive processes. Fronts are curvature damped, and the results here indicate the generic nature of separate front propagation within both model (idealized) and natural (heterogeneous) geochemical systems. INTRODUCTION In this paper we shall consider the evolution of sharp geochemical fronts within saturated subsurface media. We focus on two major facets of their existence and behaviour: the characterization of geochemical waves as a sequence of transition fronts, each propagating at its own characteristic speed; and the development of non-planar fronts in response to natural heterogeneity in the underlying fluid flow field. Geochemical fronts occur in a variety of natural situations. For example, a host rock may be initially iron rich, abundant in pyrite, producing a strongly reducing environment, with incoming oxygenated water reacting with the pyrite yielding a sharp transition or 'front' between the reducing zone and the rust coloured oxidized rock. Behind such a front oxygen is abundant in solution, transported principally via advection due to groundwater flow; with the oxidization of pyrite taking place within a thin, reactive, transition layer located at the front itself. In nature geochemical transition layers are not only sharp but also irregular in shape. This is principally because the underlying groundwater velocity field is heterogeneous due to the variable permeability of the distributed microcracks, cracks, and fissures: consequently, oxygen is supplied to the evolving front unevenly, according to its position with respect to the relative size and direction of local flow field. In this paper we consider a generic class of flux-driven problems arising when the disMat. Res. Soc. Symp. Proc. Vol. 353 0 1995 Materials Research Society
132
tribution of solute species with incoming groundwater is in geochemical disequilibrium with the host medium.
Data Loading...
