Transfer Kinetics at the Aqueous/Non-Aqueous Phase Liquid Interface. A Statistical Mechanic Approach
Abstract
Many modeling efforts in the literature use a first-order, linear-driving-force model to represent the chemical dissolution process at the non-aqueous/aqueous phase liquid (NAPL/APL) interface. In other words, NAPL to APL phase flux is assumed to be equal to the difference between the solubility limit and the "bulk aqueous solution" concentrations times a mass transfer coefficient. Under such assumptions, a few questions are raised: where, in relation to a region of pure NAPL, does the "bulk aqueous solution" regime begin and how does it behave? The answers are assumed to be associated with an arbitrary, predetermined boundary layer, which separates the NAPL from the surrounding solution. The mass transfer rate is considered to be, primarily, limited by diffusion of the component through the boundary layer. In fact, compositional models of interphase mass transfer usually assume that a local equilibrium is reached between phases. Representing mass flux as a rate-limiting process is equivalent to assuming diffusion through a stationary boundary layer with an instantaneous local equilibrium and linear concentration profile. Some environmental researchers have enjoyed success explaining their data using chemical engineering-based correlations. Correlations are strongly dependent on the experimental conditions employed. A universally applicable theory for NAPL dissolution in natural systems does not exist. These correlations are usually expressed in terms of the modified Sherwood number as a function of Reynolds, Peclet, and Schmidt numbers. The Sherwood number may be interpreted as the ratio between the grain size and the thickness of the Nernst stagnant film. In the present study, we show that transfer kinetics at the NAPL/APL interface under equilibrium conditions disagree with approaches based on the Nernst stagnant film concept. It is unclear whether local equilibrium assumptions used in current models are suitable for all situations.A statistical mechanic framework has been chosen to study the transfer kinetic processes at the microscale level. The rationale for our approach is based on both the activation energy of transfer of an ion and its velocity across the NAPL/APL interface. There are four major energies controlling the interfacial NAPL dissolution kinetics: (de)solvation energy, interfacial tension energy, electrostatic energy, and thermal fluctuation energy. Transfer of an ion across the NAPL/APL interface is accelerated by the viscous forces which can be described using the averaged Langevin master equation. The resulting energies and viscous forces were combined using the Boltzmann probability distribution. Asymptotic time limits of the resulting kinetics lead to instantaneous local equilibrium conditions that contradict the Nernst equilibrium equation. The NAPL/APL interface is not an ideal one: it does not conserve energy and heat. In our case the interface is treated as a thin film or slush zone that alters the thermodynamic variables. Such added zone, between the two phases, is itself a phase, and, therefore, the equilibrium does not occur between two phases but rather three. All these findings led us to develop a new non-linearly coupled flow and transport system of equations which is able to account for specific chemical dissolution processes and precludes the need for empirical mass-transfer parameters. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.
- Publication:
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AGU Spring Meeting Abstracts
- Pub Date:
- May 2001
- Bibcode:
- 2001AGUSM...H51B02D
- Keywords:
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- 1829 Groundwater hydrology;
- 1831 Groundwater quality;
- 1832 Groundwater transport