Ekkehard Holzbecher

Modelling the removal of p-TSA (para-toluenesulfonamide) during rapid sand filtration used for drinking water treatment.

A finite element model was set-up to determine degradation rate constants for p-TSA during rapid sand filtration (RSF). Data used for the model originated from a column experiment carried out in the filter hall of a drinking water treatment plant in Berlin (Germany). Aerated abstracted groundwater was passed through a 1.6m long column-shaped experimental sand filter applying infiltration rates from 2 to 6mh(-1). Model results were fitted to measured profiles and breakthrough curves of p-TSA for different infiltration rates using both first-order reaction kinetics and Michaelis-Menten kinetics. Both approaches showed that degradation rates varied both in space and time. Higher degradation rates were observed in the upper part of the column, probably related to higher microbial activity in this zone. Measured and simulated breakthrough curves revealed an adaption phase with lower degradation rates after infiltration rates were changed, followed by an adapted phase with more elevated degradation rates. Irrespective of the mathematical approach and the infiltration rate, degradation rates were very high, probably owing to the fact that filter sands have been in operation for decades, receiving high p-TSA concentrations with the raw water.

A novel modeling approach using arbitrary Lagrangian-Eulerian (ALE) method for the flow simulation in unconfined aquifers

The problem of groundwater flow in an unconfined aquifer, formulated as a free-surface problem, is solved numerically through a new approach by employing the arbitrary Lagrangian-Eulerian (ALE) method. The domain of interest is three dimensional or a two dimensional vertical cross-section of a phreatic zone of an aquifer, where the groundwater table is the upper boundary that is allowed to move. The ALE method allows capturing the location of the free-surface by transforming the moving domain to a fixed reference domain through arbitrary forced boundary conditions. The results of the verification runs of this new approach agree well with the known analytical solutions for aquifer characterization tests. Beside the comprehensive and accurate evaluation of the groundwater flow in the tested cases, the approach is also suitable for modeling complex situations. The implementation of our method for selected cases is illustrated by means of practically relevant examples. Steady state unconfined groundwater flow simulation.Tracking free-surface using arbitrary Lagrangian-Eulerian (ALE) method.Good agreement with classic analytical solutions.Flexible application for single borehole pumping and injection model set-ups.

An environmentally sound new method for groundwater lowering

Here we propose a novel method for groundwater lowering which can be applied at construction sites, for aquifer remediation measures or in open mining. In contrast to current and traditional techniques dewatering is achieved without water conveyance. Environmental problems above the ground surface with pumped water can be avoided. We introduce the concept and field experiments, before presenting modeling work.

Generalizing the concept of retardation factors

ABSTRACT In multi-phase environments, for example in porous media, and particularly in groundwater and in sediments, the spatial and temporal distribution of a chemical or biological species is usually described by a set of multiple coupled differential equations. Under the conditions that an isotherm exists, the set of equations can be simplified to a single equation. The most well-known application of such a procedure in a fluid-solid system leads to the equation for retarded transport with the retardation factor R. As a generalization of this mathematical concept, factors Rdecay, Radv and Rdiff are introduced, which for general situations appear as factors in the single differential equation. The Peclet and Damkoehler numbers depend on these generalized retardation factors. They may also have an effect on the steady state solution - in contrast to the classical retardation factor R. Due to the reduction to a single equation, analytical and numerical tools that are well established for single-phase environments can be utilized. As an example for the application of the presented approach, the case of aquatic sediments is presented, for which the generalized concept allows to study solute transport considering processes like compaction, bioirrigation and bioturbation in addition to the common fluid phase processes.

The Henry-Saltwater Intrusion Benchmark – Alternatives in Multiphysics Formulations and Solution Strategies

In a classical paper Henry set up a conceptual model for simulating saltwater intrusion into coastal aquifers. Up to now the problem has been taken up by software developers and modellers as a benchmark for codes simulating coupled flow and transport in porous media. The Henry test case has been treated using different numerical methods based on various formulations of differential equations. We compare several of these approaches using multiphysics software. We model the problem using Finite Elements, utilizing the primitive variables and the streamfunction approach, both with and without using the Oberbeck-Boussinesq assumption. We compare directly coupled solvers with segregated solver strategies. Changing finite element orders and mesh refinement, we find that models based on the streamfunction converge 2-4 times faster than runs based on primitive variables. Concerning the solution strategy, we find an advantage of Picard iterations compared to monolithic Newton iterations.

Virus removal vs. subsurface water velocity during slow sand filtration

In an attempt to obtain a conservative estimate of virus removal during slow sand and river bank filtration, a somatic phage was isolated with slow decay and poor adsorption to coarse sand. We continuously fed a phage suspension to a 7-m infiltration path and measured the phage removal. In a second set of experiments, we fed the phage suspension to 1-m long columns run at different pore water velocities. Using the data obtained, a mathematical model was constructed describing removal vs. pore water velocity (PWV), assuming different statistical distributions of the adsorption coefficient λ. The bimodal distribution best fit the results for PWVs higher than 1 m/d. It predicted a removal of approximately 4 log10 after 50 days infiltration at 1 m/d. At PWVs below 1 m/d the model underestimated removal. Sand-bound phages dissociated slowly into the liquid phase, with a detachment constant kdet of 2.6 × 10⁻⁵. This low kdet suggests that river bank filtration plants should be intermittently operated when viral overload is suspected, e.g. during flooding events or at high water-marks in rivers, in order for viruses to become soil-associated during the periods of standstill. Resuming filtration will allow only a very slow virus release from the soil.

Analytical Solution for Well Design with Respect to Discharge Ratio

For a well in the vicinity of a surface water body, a formula is developed that relates the share of bank filtrate on total pumpage, that is, the discharge ratio, on one side, to basic well and aquifer characteristics on the other. The application of the formula is demonstrated for solving the inverse problem: for an aimed discharge ratio, well characteristics (pumping rate, distance to shore) can be determined. Other useful applications of the formula are outlined.

Modeling Pathways and Stages of CO2 Storage

The storage of CO 2 in deep geological formations can be partitioned in three stages: diffusion, early and late convection. Convection emerges as a phenomenon of coupled flow and transport in porous media. For the characterization of the three stages we use numerical experiments with perturbations of a reference homogeneous situation. We explore the effect of different type and size of perturbations. The simulations show that the onset of the convection state depends strongly not only on the perturbations, but also on settings of the numerical method. Moreover it is found that the early convection state may consist of several peaks and is thus more complex than in the idealized simple concept of a single peak. For the late convection stage the decrease of the total mass transfer into the system is generally confirmed, within uncertainty margins.

Multiphysics Modelling of the Mandel- Cryer Effect

In porous medium studies the Mandel-Cryer effect is known, describing non-monotonic pore-water pressure evolution in response to loading or to changed stress conditions. In a 2D poro-elastic model we couple the pore water hydraulics with mechanics (HM). The Mandel-Cryer effect is identified in parts of the model region that are far from the drainage boundary. At parts of the loaded boundary an even more complex pressure evolution is revealed. Variations of the Biot-parameter as the coupling parameter clearly indicate the relevance of the two-way coupling between the involved physical regimes. Hence the Mandel-Cryer effect is a typical result of multi-physical coupling.

Dual-Screened Vertical Circulation Wells for Groundwater Lowering in Unconfined Aquifers.

A new type of vertical circulation well (VCW) is used for groundwater dewatering at construction sites. This type of VCW consists of an abstraction screen in the upper part and an injection screen in the lower part of a borehole, whereby drawdown is achieved without net withdrawal of groundwater from the aquifer. The objective of this study is to evaluate the operation of such wells including the identification of relevant factors and parameters based on field data of a test site and comprehensive numerical simulations. The numerical model is able to delineate the drawdown of groundwater table, defined as free-surface, by coupling the arbitrary Lagrangian-Eulerian algorithm with the groundwater flow equation. Model validation is achieved by comparing the field observations with the model results. Eventually, the influences of selected well operation and aquifer parameters on drawdown and on the groundwater flow field are investigated by means of parameter sensitivity analysis. The results show that the drawdown is proportional to the flow rate, inversely proportional to the aquifer conductivity, and almost independent of the aquifer anisotropy in the direct vicinity of the well. The position of the abstraction screen has a stronger effect on drawdown than the position of the injection screen. The streamline pattern depends strongly on the separation length of the screens and on the aquifer anisotropy, but not on the flow rate and the horizontal hydraulic conductivity.