Particle tracking simulations for reactive transport

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We study the effect of incomplete mixing on the slow-down of a kinetic bi-molecular reaction A+B->P. We have developed a numerical method, namely a Monte-Carlo “particle tracking” approach, where particles simulate concentration fields. The particles move erratically by random walk (modeling diffusion/dispersion) and react with each other. Reactions happen at a certain probability, proportional to the reaction rate constant and the particles co-location probability. We are currently working on generalizing the approach to cases where advection is variable. The simplest problem at hand in that context is shear flow, with some preliminary results already obtained. In the near future, we hope to be able to apply the particle tracking approach to flow at pore scale, where advection is highly variable and is playing a very important role in stretching and mixing. One of the final goals of this research is to enable us to solve reactive transport in Darcy scale, which is an important problem in the hydrological community.  (In collaboration with Prof. David Benson).

Movie of Particle Reactions in 1-D

Movie of Particle Reactions in 2-D

                       

                               Zero Flow                                                        Pure Shear Flow

Salinization of a pumping well

Many freshwater aquifers have saltwater bodies in their deeper part. Such saltwater bodies may be a result of various processes, the most well-known of which is seawater intrusion. Studying the physical processes in the transition zone between fresh and saline waters in the aquifer is important since it can help in reducing risk of salinization of pumping wells. Specifically, we study the effect of pumping from a well whose screen is submerged into the transition zone. Typically, wells are screened only against freshwater bearing strata, and the pump is installed close to the water table. However, if the screen of a production well extends below the freshwater body, and the well is screened against the transition layer between the two bodies, or even against the saltwater, the question is whether saline or brackish water will be pumped when the well is operated. It seems this problem has never been tested by scientific tools in the past. A preliminary lab experiment and a preliminary numerical model revealed that the well screen may have an important role in the physical process of mixing. The flow through the fine mesh of the screen results in head loss. The head difference between the outside and the inside of the screen results in a ‘jump’ in the elevation of saltwater. This jump forces the freshwater outside the screen to flow through the screen slots in thin filaments into the saltwater, leading to enhanced mixing and step-function concentration profile. (In collaboration with Ricky Villareal, PhD candidate).

Fractional calculus in applied hydrology

We study anomalous kinetics associated with incomplete mixing for a bimolecular irreversible kinetic reaction where the underlying transport of reactants is governed by a fractional (non-Fickian) dispersion equation. We demonstrated that at late times incomplete mixing effects dominate and the decay of reactants follows a fundamentally different scaling comparing to the idealized well mixed case. We study the role that the initial correlation structure of the distribution of reactants plays on the late time scalings. This research was done in collaboration Prof. Natalie Kleinfelter Domelle.