Amir Paster

A particle number conserving Lagrangian method for mixing‐driven reactive transport

The purely Lagrangian algorithm for chemical reactions introduced by Benson and Meerschaert (2008) suffers from a low-concentration resolution problem. We alleviate the problem by redefining the probabilistic collision/reaction (birth/death) stochastic process as a mass-reduction operation. Theoretically, this corresponds to replacing an on/off particle with a large number of “subparticles” and tracking the number fraction. The new particle reaction process maintains the original particle numbers but adjusts each particles mass upon reaction. Several simulations show the veracity as well as the gains in low-concentration resolution offered by the algorithm. We also compare the results to those obtained by a traditional finite difference model with suitably defined initial condition, demonstrating that the Lagrangian models match these.

Communication: A full solution of the annihilation reaction A + B → ∅ based on time-subordination

The connection between the governing equations of chemical reaction and the underlying stochastic processes of particle collision and transformation have been developed previously along two end-member conditions: perfectly mixed and maximally diffusion-limited. The complete governing equation recognizes that in the perfectly mixed case, the particle (i.e., molecular or macro-particle) number state evolution is markovian, but that spatial self-organization of reactants decreases the probability of reactant pairs finding themselves co-located. This decreased probability manifests itself as a subordination of the clock time: as reactant concentrations become spatially variable (unmixed), the time required for reactants to find each other increases and the random operational time that particles spend in the active reaction process is less than the clock time. For example, in the system A + B → [empty-set], a simple approximate calculation for the return time of a brownian motion to a moving boundary allows a calculation of the operational time density, and the total solution is a subordination integral of the perfectly-mixed solution with a modified inverse gaussian subordinator. The system transitions from the well-mixed solution to the asymptotic diffusion-limited solution that decays as t(-d∕4) in d-dimensions.

Prediction of Remediation of a Heterogeneous Aquifer: A Case Study.

Contaminant plumes whose characteristic length is smaller than the horizontal integral scale of the hydraulic conductivity, K, are abundant in shallow, phreatic aquifers. In such cases, the aquifer can be regarded as layered, with K being only a function of the vertical coordinate. The heterogeneity of K has a critical role upon the efficiency of remediation of such sites, for example, by Pump and Treat schemes. The expected efficiency is a random variable, with uncertainty. Quantifying this uncertainty can be of great importance to decision making. In this study, we focus on a case study in the coastal aquifer of Israel and compare two different approaches for constructing realizations of K: continuous and indicator. We observe a significant difference between the constructed realizations, which results in a considerable difference in the predicted remediation efficiency and its uncertainty. Furthermore, we study the effect of conditioning the realizations by a rather limited number of K data points. We find that the conditioning results in a major reduction of the uncertainty. In addition, we compare the results of the transport model to a simplified semi-analytical solution that is based on assuming radial flow. We find a good agreement with the three-dimensional numerical model. This result illustrates that the simplified solution can be used for prediction of the remediation efficiency when the flow at the plume vicinity can be regarded as radial.

An improved scheme for a Robin boundary condition in discrete-time random walk algorithms

Abstract Random Walk (RW) is a common numerical tool for modeling the Advection–Diffusion equation. In this work, we develop an improved scheme for incorporating a heterogeneous reaction (i.e., a Robin boundary condition) in a discrete-time RW model. In addition, we apply the approach in two test cases. We compare the improved scheme with the classical as well as with analytical and other numerical solution. We show that the new scheme can reduce the computational error significantly, relative to the first order scheme. This reduction comes at no additional computational cost.

Applying short-duration pulses as a mean to enhance volatile organic compounds removal by air sparging

Application of short-duration pulses of high air pressure, to an air sparging system for groundwater remediation, was tested in a two-dimensional laboratory setup. It was hypothesized that this injection mode, termed boxcar, can enhance the remediation efficiency due to the larger ZOI and enhanced mixing which results from the pressure pulses. To test this hypothesis, flow and transport experiments were performed. Results confirm that cyclically applying short-duration pressure pulses may enhance contaminant cleanup. Comparing the boxcar to conventional continuous air-injection shows up to a three-fold increase in the single well radius of influence, dependent on the intensity of the short-duration pressure-pulses. The cleanup efficiency of Toluene from the water was 95% higher than that achieved under continuous injection with the same average conditions. This improvement was attributed to the larger zone of influence and higher average air permeability achieved in the boxcar mode, relative to continuous sparging. Mixing enhancement resultant from recurring pressure pulses was suggested as one of the mechanisms which enhance the contaminant cleanup. The application of a boxcar mode in an existing, multiwell, air sparging setup can be relatively straightforward: it requires the installation of an on-off valve in each of the injection-wells and a central control system. Then, turning off some of the wells, for a short-duration, result in a stepwise increase in injection pressure in the rest of the wells. It is hoped that this work will stimulate the additional required research and ultimately a field scale application of this new injection mode.Application of short-duration pulses of high air pressure, to an air sparging system for groundwater remediation, was tested in a two-dimensional laboratory setup. It was hypothesized that this injection mode, termed boxcar, can enhance the remediation efficiency due to the larger ZOI and enhanced mixing which results from the pressure pulses. To test this hypothesis, flow and transport experiments were performed. Results confirm that cyclically applying short-duration pressure pulses may enhance contaminant cleanup. Comparing the boxcar to conventional continuous air-injection shows up to a three-fold increase in the single well radius of influence, dependent on the intensity of the short-duration pressure-pulses. The cleanup efficiency of Toluene from the water was 95% higher than that achieved under continuous injection with the same average conditions. This improvement was attributed to the larger zone of influence and higher average air permeability achieved in the boxcar mode, relative to continuous sparging. Mixing enhancement resultant from recurring pressure pulses was suggested as one of the mechanisms which enhance the contaminant cleanup. The application of a boxcar mode in an existing, multiwell, air sparging setup can be relatively straightforward: it requires the installation of an on-off valve in each of the injection-wells and a central control system. Then, turning off some of the wells, for a short-duration, result in a stepwise increase in injection pressure in the rest of the wells. It is hoped that this work will stimulate the additional required research and ultimately a field scale application of this new injection mode.