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Understanding the processes involved in the transport of dissolved gas plumes in groundwater aquifers is essential for comprehending the effect that these transport processes can have on site characterization and remedial design applications. Previous laboratory and field studies have indicated that dissolved gas transport in groundwater can be greatly affected by the presence of even small amounts of trapped gas in the pore space of an aquifer. Recently, Fry et al. (1995) reported an increase in retardation factors R (where R=pore water velocity/dissolved gas velocity) for dissolved oxygen with increasing amounts of trapped gas. Fry showed that the retardation factor for a dissolved gas can be predicted using a relationship between the dimensionless Henry's Law constant for the dissolved gas, the volumetric gas content (i.e., the fraction of the total volume occupied by trapped gas), and the volumetric water content (i.e., the fraction of total volume occupied by water). In their experiments, Fry et al. (1995) found this relationship in an equilibrium model accurately predicted observed retardation factors for dissolved oxygen when the volumetric gas content was small, but underpredicted retardation factors for larger volumetric gas contents. Also, predicted breakthrough curves for dissolved oxygen obtained by incorporating this relationship into the advection-dispersion equation did not match the shape of experimentally observed breakthrough curves. The experimental curves were asymmetrical with long tails indicating that the local equilibrium assumption is inaccurate and suggesting that mass transfer of oxygen between the aqueous and trapped gas phases is diffusion limited. In an effort to gain further understanding of this process, a kinetic model was developed for dissolved gas transport that includes a diffusion type expression for the rate of gas transfer between the mobile aqueous and trapped gas phases. The model was tested in a series of transport experiments conducted in sand packed columns with varying amounts and composition of trapped gas. The kinetic model was found to better fit the shape of dissolved oxygen breakthrough and elution curves than the equilibrium model of Fry et al. (1995). This model was then extended to the case of two-dimensions to simulate dissolved gas transport in the presence of trapped gas under conditions that approximate injection and extraction wells used to distribute dissolved gases in an aquifer (e.g. to promote in situ bioremediation processes or to perform a dissolved gas tracer test). We then compared these predicted concentrations with measured concentrations obtained in a series of dissolved gas transport experiments in a large-scale physical aquifer model using two dissolved gases (oxygen and hydrogen) with very different physical properties. The model could accurately fit the development and movement of these plumes providing that key parameters, the amount of trapped gas and the effective mass transfer coefficient, were adjusted between the injection and drift stages. / Graduation date: 1997

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New upwind kinetic-difference schemes have been developed for flows with nonequilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Application of a directionally-split Courant-Isaacson-Rees (CIR) scheme at the Boltzmann level results in a flux-vector splitting scheme at the Euler level and is called Kinetic Flux-Vector Splitting (KFVS). Extension to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing non-equilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van-Leer and Roe for quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, 'viscous flow over a cone at zero angle-of-attack, and shock-induced combustion/detonation in a premixed hydrogen-air mixture. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe. A new approach toward the development of a genuinely multi-dimensional Riemann solver is also presented. The scheme is based on the same kinetic theory considerations used in the development of the KF VS scheme. The work has been motivated by the recent progress on multi-dimensional upwind schemes by the groups at the University of Michigan and the Von Karman Institute. These researchers have developed effective upwind schemes for the multi-dimensional linear advection equation using a cell-vertex fluctuation-splitting approach on unstructured grids of triangles or tetrahedra. They have made preliminary applications to the Euler equations using several wave decomposition models of the flux derivative. The issue of the appropriate wave model does not appear to be adequately resolved. The approach taken in the present work is to apply these new multi-dimensional upwind schemes for the scalar advection equation at the Boltzmann level. The resulting Euler schemes are obtained as moments of the fluctuations in the Maxwellian distribution function. The development is significantly more complicated than standard (dimensionally-split) kinetic schemes in that the Boltzmann discretization depends upon the direction of the molecular velocities which must be accounted for in the limits of integration in velocity space. The theoretical issues have been solved through analytic quadrature and Euler schemes have been developed. For this formulation it was not necessary to prescribe any explicit wave decomposition model. Encouraging preliminary results have been obtained for perfect gases on uniform Cartesian meshes with first-order spatial accuracy. Results are presented for a 29° shock reflection, a 45° shear discontinuity, and Mach 3 flow over a step. Finally, methods for obtaining accurate gas-dynamic simulations in the continuum transition regime are considered. In particular, large departures from translational equilibrium are modeled using algorithms based on the Burnett equations instead of the Navier-Stokes equations. Here, the same continuum formulation of the governing equations is retained, but new constitutive relations based on higher-order Chapman-Enskog theory are introduced. Both a rotational relaxation model and a bulk-viscosity model have been considered for simulating rotational non-equilibrium. Results are presented for hypersonic normal shock calculations in argon and diatomic nitrogen and comparisons are made with Direct Simulation Monte Carlo (DSMC) results. The present work closely follows that of the group at Stanford, however, the use of upwind schemes and the bulk-viscosity model represent new contributions. / Ph. D.

The abstract kinetic equation Tψ’=-Aψ is studied with partial range boundary conditions in two geometries, in the half space x≥0 and on a finite interval [0, r]. T and A are abstract self-adjoint operators in a complex Hilbert space. In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in the case of slab geometry T is a bounded injection and A is a bounded Fredholm operator with a finite dimensional negative part. Existence and uniqueness theory is developed for both models. Results are illustrated on relevant physical examples. / Ph. D.

This thesis examines the transient response of a packed bed heat regenerator when heated from an initial uniform bed temperature. Very large (1700 K) temperature differences were studied as well as the effect of simultaneous chemical reaction in the gas phase. First the effects of temperature on physical and transport properties were studied in detail in the absence of a reaction. Models with compressible flow were compared with conventional models with constant properties and incompressible flow. Several measures of the regenerator's response to a step change in inlet gas temperature were calculated to characterize the spread of the temperature front. Variances of the spatial derivative of the gas temperature profile and the time derivative of the product gas temperature were used to evaluate thermal efficiency. The effects of an exothermic homogeneous gas phase reaction in the regenerator process were also studied. Several simple kinetic schemes and inlet conditions were simulated and the profiles of reaction rate and conversion as well as temperature were analyzed. / Graduation date: 1993

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