Numerical Simulation of Solute Transport Instantaneously Injected in a Single Rock Fracture System: Inclusion of a Nonli
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NUMERICAL SIMULATION OF SOLUTE TRANSPORT INSTANTANEOUSLY INJECTED IN A SINGLE ROCK FRACTURE SYSTEM: INCLUSION OF A NONLINEAR SORPTION TERM YOKO FUJIKAWA AND M. FUKUI Research Reactor Institute, Kyoto University, Kumatori-Cho, Sennan-Gun, Osaka, 590-04, Japan ABSTRACT The effect of nonlinear Freundlich sorption isotherm on the transport of sorptive solute in a system of fracture and porous matrix was investigated through numerical simulation. To solve a set of partial differential equations of solute transport with nonlinear term, use of the Laplace transform Galerkin (LTG) technique was investigated. It was shown that the LTG method could be applied successfully to solve quasi-linearized transport equation. Sensitivity analysis showed that nonlinear sorption in porous matrix with order less than 1 increased the skewness of the breakthrough curve. The fitting of experimental effluent data using a transport model with nonlinear isotherms was also conducted. INTRODUCTION Radionuclide transport in fractured rocks is one of the fundamental processes of nuclide migration from underground radioactive waste repository. Safety of the geological disposal is governed by rock- radionuclide interactions that retard the nuclide migration toward the biosphere. Brusseau .3 classified the subsurface mass transport into the "ideal" and "nonideal" one. Similarly, in a dual porosity media we consider an "ideal" transport such as that takes place in fractures arranged regularly in homogeneous porous matrix and is representable by mathematical models which can be solved analytically 10,15,16,1,20,22 As opposed to "ideal" transport, we may consider a "nonideal" transport which takes place under various nonideality factors ,4,6,7,8,11,13,18,19,21. Since the analytical solution of "nonideality" transport models are generally not available, numerical simulation techniques have been developed to deal with nonideal transport. Fujikawa and Fukui 10 reported that the breakthrough curves (BTCs) obtained by delta-type flux fluid injection of radioactive cesium into a rock fracture could be fitted by the "ideal" transport model for linearly sorbing solute. There was, however, slight but definite discrepancy between the theoretical and experimental BTCs which suggested the relevance of some nonideality factors. One of the factors which may be operable in producing the discrepancy is the nonlinear Freundlich -type sorption of cesium of order 0.5627 observed in a batch experiment 26 , as well as the spatial heterogeneity in sorptivity of the rock 26 and velocity dependent dispersivity 8. General effect of sorption nonlinearity on BTC is known relatively well 2,17. Freundlich isotherm with n < 1 causes the larger retardation for smaller concentration while causing smaller retardation for higher concentration. Therefore, for a pulsed input, a steeper front, longer tailing, smaller peak of BTC develops. It should be noted, however, that above knowledge concerns the effect of sorption nonlinearity in homogeneous media and the effect of sorption nonlinear
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