Saltwater intrusion simulation in heterogeneous aquifer using lattice Boltzmann method

This study develops a saltwater intrusion simulation model using a lattice Boltzmann method (LBM) in a two-dimensional coastal confined aquifer. The saltwater intrusion is described by density-dependent groundwater flow and mass transport equations, where a freshwater-saltwater mixing zone is considered. The problem is formulated in terms of hydraulic head instead of pressure, which is recommended in those cases where static pressures dominate to reduce computational cost. The aquifer heterogeneity is explicitly a function of the speed of sound, relaxation parameter and time steps in the LBM. This study explores the equivalent squared sound speed to deal with the spatial-temporal heterogeneity arising from the inhomogeneous hydraulic conductivity and fluid density to update the equilibrium distribution functions in each time step. The Henry problem and its variants are used to demonstrate the LBM applicability to solve the saltwater intrusion problem. The inverse relationship between the time step and diffusion coefficient results in a very small time step for the groundwater flow problem due to the high hydraulic diffusion coefficient. The study demonstrates the ease of implementing the LBM to different salt concentration boundary conditions at the seaside and shows that the isochlors distributions are significantly different. Due to doubts regarding the validity of the Henry problem to test variable-density flows, numerical simulation of freshwater injection into a sediment saturated with saltwater have been carried out, showing the capability of the LBM to represent strong buoyancy effects. Some examples with correlated and uncorrelated random hydraulic conductivity (K) distributions show reasonable flow fields and isochlors distributions. It was found in the Henry problem that completely random heterogeneity in K is insignificant in changing the scale of the saltwater intrusion from that predicted using the mean K value. However, the correlated K field may have significant impact on the saltwater intrusion, resulting different from that obtained by the mean K field

Simulating the influences of groundwater on regional geomorphology using a distributed, dynamic, landscape evolution modelling platform

A dynamic landscape evolution modelling platform (CLiDE) is presented that allows a variety of Earth system interactions to be explored under differing environmental forcing factors. Representation of distributed surface and subsurface hydrology within CLiDE is suited to simulation at sub-annual to centennial time-scales. In this study the hydrological components of CLiDE are evaluated against analytical solutions and recorded datasets. The impact of differing groundwater regimes on sediment discharge is examined for a simple, idealised catchment, Sediment discharge is found to be a function of the evolving catchment morphology. Application of CLiDE to the upper Eden Valley catchment, UK, suggests the addition of baseflow-return from groundwater into the fluvial system modifies the total catchment sediment discharge and the spatio-temporal distribution of sediment fluxes during storm events. The occurrence of a storm following a period of appreciable antecedent rainfall is found to increase simulated sediment fluxes

Lattice Boltzmann modeling for mass transport equations in porous media

The aim of this dissertation is to extend the lattice Boltzmann method (LBM) to cope with parameter heterogeneity and anisotropy in mass transport equations in porous media, as well as investigating the stability and accuracy. Although the LBM is a well known and effective numerical method to solve fluid flows, LBM has not been extensively applied to mass transport equations in porous medium flow yet, and only a few works can be found on improving LBM to cope with mass transport equations other than the diffusion and advection-diffusion equations. One of the reasons why LBM has not been extensively used is because it is not clearly understood how LBM solve mass transport equations. We first focus on investigating what type of partial differential equation (PDE) the LBM recovers. The recovery procedure is carried out in detail up to third order accuracy and including the effect of forcing terms. Once the recovered PDE is known, LBM can be tailored to solve targeted mass transport equations. In order to improve the accuracy of LBM, the analysis is based on the lattice Boltzmann equation with a two-relaxation-time collision operator. Regarding the stability of LBM, the von Neumann stability analysis is used and linear stability boundaries are found under different scenarios. By an appropriate selection of the equilibrium distribution functions (EDF) and forcing terms, LBM is able to cope with parameter heterogeneity and anisotropy in mass transport equations in porous media. The relaxation times offer some degrees of freedom that allows LBM to improve the accuracy without decreasing computational efficiency. For validation purposes LBM has been implemented to simulate saltwater intrusion in the Henry problem and modified versions, and the results are in good agreement with available analytical solutions and numerical solutions obtained by other methods

Macroscopic cellular automata for groundwater modelling: A first approach

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Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Flow and transport in saturated and unsaturated fractured porous media: Development of particle-based modeling approaches

Das Ziel der vorliegenden Arbeit ist die Entwicklung von partikelbasierenden Strömungs- und Transportmodellen zur Charakterisierung von kleinskaligen Strömungsprozessen in gesättigten und ungesättigten Poren- und Kluftsystemen. Aufgrund der unzureichenden Prozessbeschreibung von ungesättigter Strömung in Doppelkontinuummodellen mittels der Richardsgleichung und van Genuchten Parametern werden innovative Methoden präsentiert um die zugrunde liegenden hochdynamischen Strömungs- und Transportprozesse zu erfassen. Die Simulation von Strömung und Transport in ungesättigten geklüfteten Aquiferen bildet immer noch ein höchst anspruchsvolles Aufgabenfeld aufgrund von skalenübergreifenden Diskontinuitäten, welche oftmals die Definition eines globalen repräsentativen Einheitsvolumens nicht zulassen. Des Weiteren können die hydraulischen Eigenschaften und potentiellen Parameterräume von geklüfteten Aquiferen oftmals nur durch integrale Ansätze, wie z.B. Pump- und Slugtests, Zeitreihenanalysen von Quellschüttungen und Tracertests ermittelt werden. Doppelkontinuummodelle bieten hierfür einen ausgewogenen Ansatz hinsichtlich der erforderlichen Felddaten und der resultierenden prädiktiven Modellqualität. Der erste Teil dieser Arbeit evaluiert den Doppelkontinuumansatz, welcher die Simulation von Strömung mittels der Richardsgleichung und van Genuchten Parametern in zwei, durch einen linearen Austauschterm gekoppelten, Kontinua ermöglicht. Ganglinien von Karstquellen weisen eine charakteristischen steilen Abfall nach Niederschlagsereignissen auf, der durch das Modell erfolgreich reproduziert werden kann. Das Röhrensystem bildet die hydraulische Brücke zur Karstquelle und nimmt potentialabhängige Wassermengen des geklüfteten Matrixsystems auf. Um die Simulation von schneller Grundwasserinfiltration durch das Röhrenkontinuum innerhalb der ungesättigten Zone zu vermeiden wurde die entsprechende Randbedingung an die untere Grenze des Kontinuums gesetzt. Ein genereller Nachteil des Doppelkontinuumsansatz ist die potentielle Mehrdeutigkeit von Modellergebnissen. Der duale Parameterraum in Kombination mit schwierig zu ermittelnden Parametern, führt zur Existenz von mehr als einem kalibrierten Modell, wie durch mehrdimensionale Sensitivitätsanalysen aufgezeigt wird.  Insbesondere in Karstaquiferen bilden Diskontinuitäten, wie z.B. Lösungsdolinen, Klüfte und Störungssysteme, bevorzugte hydraulische Elemente für schnelle vertikale Grundwasserneubildungsprozesse, die oftmals nicht durch volumeneffektive Modellansätze erfasst werden können. Der Hauptteil dieser Arbeit befasst sich daher mit der Entwicklung von zwei Smoothed Particle Hydrodynamics (SPH) Modellen um ein adäquates numerisches Werkzeug zur partikelbasierenden Simulation von kleinskaligen Strömungen mit freien Oberflächen und Transportprozessen bereitzustellen. SPH Modelle ermöglichen eine Eulersche Beschreibung eines Strömungsfelds auf Basis der Navier-Stokes Gleichung und Partikelbewegung mittels klassischer Newtonscher Mechanik. Der gitterlose Modellansatz ermöglicht flexible Simulationen von hochdynamischen Phasengrenzen in ungesättigten Klüften und Porenräumen. Das erste SPH Modell wird eingesetzt um durch Oberflächenspannung dominierte Tropfen- und Filmströmungen auf glatten und rauhen Kluftoberflächen zu simulieren. Charakteristische dimensionslose Kennzahlen werden über einen weiten Bereich von Benetzungswinkeln und Reynoldszahlen bestimmt. Modellergebnisse weisen einen hervorragende Übereinstimmung mit dimensionslosen Skalierungsfunktionen auf und kritische Kontaktwinkel folgen der zu erwartenden Entnetzungsdynamik. Die Entstehung von adsorbierten Filmen auf trockenen Oberflächen wird für einen breiten Parameterraum bestimmt. Des Weiteren wird der Einfluss von befeuchteten Oberflächen auf die Geschwindigkeitszunahme von Tropfenströmung aufgezeigt und so die Bedeutung der Koexistenz verschiedener Strömungsmodi gezeigt. Der Effekt von Oberflächenrauhigkeit auf Tropfenströmung wird für verschiedene Rauhigkeiten ermittelt und eine deutliche Geschwindigkeitsabnahme demonstriert. Um die makroskopische Kontinuumsbeschreibung der Navier-Stokes Gleichung und atomistische Effekte eines klassischen Partikelsystems der statistischen Mechanik zu kombinieren wurde ein zweites mesoskopisches SPH Modell entwickelt. Diese neue Diskretisation der vollständig gekoppelten Landau-Lifshitz-Navier-Stokes und Advektions- Diffusionsgleichung ermöglicht die Simulation von Strömung und Transport bei gleichzeitiger Berücksichtigung von Fluktuationsdynamiken, welche sich korrekt der Systemskala anpassen. Die Verbindung von klassischer Fickscher Diffusion und thermodynamischen Fluktuationen wird hierbei durch einen effektiven Diffusionskoeffizienten beschrieben. Numerische Experimente zeigen die Präzision des Modells. Grenzflächen zwischen zwei Fluiden unterschiedlicher Konzentration weisen eine korrekte Wellenzahldivergenz entsprechend aktuellen Laborergebnissen auf

An integrated modelling approach for assessing the effect of multiscale complexity on groundwater source yields

A new multi-scale groundwater modelling methodology is presented to simulate pumped water levels in abstraction boreholes within regional groundwater models, providing a robust tool for assessing the sustainable yield of supply boreholes and improving our understanding of groundwater availability during drought. A 3D borehole-scale model, which solves the Darcy-Forchheimer equation in cylindrical co-ordinates to simulate both linear and non-linear radial flow to a borehole in a heterogeneous aquifer, is embedded within a Cartesian grid, using a hybrid radial-Cartesian finite difference method. The local-scale model is coupled to a regional groundwater model, ZOOMQ3D, using the OpenMI model linkage software, providing a flexible and efficient tool for assessing the behaviour of a groundwater source within its regional hydrogeological context during historic droughts and under climate change. The advantages of the new method are demonstrated through application to a Chalk supply borehole in the UK

Pore-to-continuum Multiscale Modeling of Two-phase Flow in Porous Media

Abstract Pore-scale network modeling using 3D X-ray computed tomographic images (digital rock technology) has become integral to both research and commercial simulations in recent years. While this technology provides tremendous insight into pore-scale behavior, computational methods for integrating the results into practical, continuum-scale models remain fairly primitive. The general approach is to run pore-scale models and continuum models sequentially, where macroscopic parameters are simulated using the pore-scale models and then used in the continuum models as if they have been obtained from laboratory experiments. While a sequential coupling approach is appealing in some cases, an inability to run the two models concurrently (exchanging parameters and boundary conditions in real numerical time) will prevent using pore-scale image-based modeling to its full potential. In this work, an algorithm for direct coupling of a dynamic pore-network model for multiphase flow with a traditional continuum-scale simulator is presented. The ability to run the two models concurrently is made possible by a novel dynamic pore-network model that allows simultaneous injection of immiscible fluids under either transient or steady-state conditions. The dynamic network algorithm can simulate both drainage and imbibition. Consequently, the network algorithm can be used to model a complete time-dependent injection process that comprises a steady-state relative permeability test, and also allows for coupling to a continuum model via exchange of information between the two models. Results also include the sensitivity analysis of relative permeability to pore-level physics and simulation algorithms. A concurrent multiscale modeling approach is presented. It allows the pore-scale properties to evolve naturally during the simulated reservoir time step and provide a unique method for reconciling the dramatically different time and length scales across the coupled models. The model is tested for examples associated with oil production and groundwater transport in which relative permeability depends on flowrate, thus demonstrating a situation that cannot be modeled using a traditional approach. This work is significant because it represents a fundamental change in the way we might obtain continuum-scale parameters in a reservoir simulation