Properties of concentration waves in presence of nonlinear sorption, precipitation/dissolution, and homogeneous reactions: 1. Fundamentals

Abstract

Properties of concentration waves of solutes affected by nonlinear sorption, precipitation/ dissolution and homogeneous reactions in the mobile and stationary phases are established when the number of phases is constant. These properties essentially depend on the structure of a stoichiometric matrix which describes the chemical interactions. A reduction procedure of the stoichiometric matrix gives the number of waves or peaks together with their propagation velocities, and the retardation factors of species at trace levels. The location of the peaks and their broadening behavior due to the nonlinear equilibria are estimated. The number of waves and the properties of suitable linear combinations of concentrations provide a method for discriminating among rival interaction mechanisms irrespective of the equilibrium constants. This cannot be done using conventional methods based on the comparison between numerical simulations and experimental curves. Bryant et al., 1986] are devoted to the consequences of the set of elementary interactions (homogeneous reactions, adsorption and/or exchange reactions, precipitation, dissolution, degassing processes, etc.) on the structure and properties of the corresponding breakthrough curves (BTC).Predicting qualitative properties of BTCs or elucidating the main features of an interaction mechanism from experimental BTCs can be performed using numerical computer codes. Unfortunately, these calculations can be time consuming and they require that the interaction parameters (i.e., equilibrium constants, kinetic constants, etc.) be known.There is thus a need for some general properties relating the structure (i.e., shape, number, and existence of waves or peaks) of the BTCs to the structure of the solid-fluid interaction mechanism. These properties should be as independent as possible of the interaction parameters, and they should help one both to discriminate among rival mecHanisms and to estimate the sensitivity of the shape of the BTCs to physicochemical parameters. This first of two papers describes the underlying concepts used to achieve this goal. We begin by reviewing the concept used for the formulation of a speciation problem, and by defining a general "reduction procedure" which is the key point in the method described in this work. Subsequently, the solute transport model is presented assuming instantaneous equilibrium in a nondispersive steady flow. Finally, this model is used to derive the general properties of the BTCs resulting from a given solid-fluid interaction mechanism. In paper 2 [Schweich et al., this issue] these theoretical properties are compared with BTCs calculated with the computer code IMPACT, which allows one to simulate BTCs for any type of interaction, whether it be homogeneous or heterogeneous. ASSUMPTIONSTo focus our attention on the consequences of physicochemical interactions it will be assumed that water flows at a constant velocity and that the porous medium is isothermal. The behavior of reactive species will be accounted for by a "phenomenologic...

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