HR: 1340h
AN: NG33C-0190    [Abstracts]
TI: A Network Model of Channel Competition in Geochemical Flows
AU: * Szymczak, P
EM: piotrek@fuw.edu.pl
AF: Institute of Theoretical Physics, Warsaw University, Hoza 69, Warsaw, PL00-681 Poland
AU: Ladd, A J
EM: ladd@che.ufl.edu
AF: Department of Chemical Engineering, University of Florida, PO Box 116005, Gainesville, FL 32611-6005
AB: Dissolution in porous media introduces a positive feedback between fluid transport and chemical reactions at the mineral surfaces leading to the formation of pronounced wormhole-like channels [1]. As the dissolution proceeds, the channels interact and compete for the flow; eventually the growth of the shorter ones ceases. Thus the number of channels decreases with time while the characteristic distance between them increases, which leads to a scale-invariant power-law distribution of channel lengths. We present several resistor network models of the evolution of dissolving channels and explore them using computer simulation and theoretical methods such as a theory of branched growth [2]. First, the simplest case of two competing channels is considered, and the conditions under which one of them captures the flow from the other are explored. Next, the case of N competing channels is analyzed and the numerical results for N ~ 10³ are presented. The results are compared with pore-scale simulations of fracture dissolution using the microscopic, three-dimensional numerical model developed in [3]. It is seen that despite their simplicity, the resistor models retain the essential features of the nonlinear interaction between the channels. [1] P. Ortoleva, J. Chadam, E. Merino, and A. Sen, Geochemical Self Organisation II: The Reactive-Infiltration Instability, Am. J. Sci., 287, 1008, 1987 [2] T.C. Halsey, M. Leibig, Theory of Branched Growth, Phys. Rev. A, 46, 7793, 1992 [3] P. Szymczak, A. J. C. Ladd, Microscopic Simulations of Fracture Dissolution, Geophys. Res. Lett., 31, L23606, doi:10.1029/2004GL021297, 2004
DE: 1832 Groundwater transport
DE: 4460 Pattern formation
DE: 4475 Scaling: spatial and temporal (1872, 3270, 4277)
DE: 4485 Self-organization
DE: 5104 Fracture and flow
SC: Nonlinear Geophysics [NG]
MN: Fall Meeting 2005