Masters Degrees (Institute for Groundwater Studies (IGS))

Permanent URI for this collection

http://hdl.handle.net/11660/435

Browse

Browsing Masters Degrees (Institute for Groundwater Studies (IGS)) by Author "Atangana, Abdon"

Now showing 1 - 5 of 5
  • Thumbnail Image
    ItemOpen Access
    Development of a groundwater recharge model
    (University of the Free State, 2017-01) Spannenberg, Jescica M.; Atangana, Abdon
    English: Existing groundwater recharge estimation methods appear to mainly generate site specific groundwater recharge estimates. These methods fail to yield reliable recharge estimates on a regional scale. This is due to failure in accounting for the concepts of heterogeneity, viscoelasticity, and the memory effect. Accordingly, this study was aimed at developing a new approach to groundwater recharge estimation by means of taking these concepts into account. Literature proves that these concepts have been well accounted for in the field of fractional differentiation. This study’s methodological approach entailed obtaining an exact solution to a selected groundwater recharge equation by applying the Laplace and inverse Laplace transform. Upon doing an uncertainty analysis and statistical analysis of the parameters within the solution, it was found that storativity and drainage resistance both require accurate estimation when estimating recharge from the selected equation. Following this, the Caputo derivative, Caputo-Fabrizio derivative, and the Atangana-Baleanu derivative were applied and an exact solution was obtained for each derivative; and upon doing a numerical simulation for each of these solutions, the results depict the behaviour of a particular real world problem. It was concluded that groundwater recharge within a heterogeneous and viscoelastic geological formation is well described with the concept of fractional differentiation with the generalised Mittag-Leffler law or the Atangana-Baleanu fractional derivative. To add, recharge via elastic geological formations can be model via the Caputo and Caputo-Fabrizio derivatives. Furthermore, hydraulic head is assumed to be influenced by uncertain factors which are not accounted for in the general recharge equations. The Eton approach was thus applied, and reveals the uncertain function has a significant effect on hydraulic head distribution. Ultimately, this study concludes that a groundwater recharge model incorporating heterogeneity, viscoelasticity, the memory effect, and uncertainties, will generate a new and improved understanding to groundwater recharge investigations.
  • Thumbnail Image
    ItemOpen Access
    The investigation of groundwater transport in a geological formation: West Park Cemetery, Johannesburg, South Africa
    (University of the Free State, 2023) Vava, Bomkazi; Atangana, Abdon
    Groundwater is a source of fresh water for many people who live in communities with little surface water around the world. The major sectors of groundwater use are municipal; rural; agricultural irrigation; agricultural-livestock watering; industry and mining. The amount and quality of groundwater have nevertheless decreased because of anthropogenic activities, global climate change, and poor groundwater management. The use of fertilizers and pesticides, urban development, the dumping of household waste on the land, municipal waste discharge and laboratory waste disposal, the aquifer close to contaminated streams, mining operations, and the discharge of effluents with high concentrations of industrial chemicals and sludge on the land pose a concern on groundwater. Due to the migration of solutions from leachate to the soil, dumpsites are also regarded as important sources of groundwater pollution. Pollution from naturally existing toxins, such as arsenic or fluoride, should not be overlooked. Historically, contaminated drinking water has been known to be capable of transmitting dangerous chemicals and deadly diseases. In this thesis, we have considered contamination from cemeteries because they also contribute to contaminating groundwater, which spreads infectious diseases and dangerous substances. Many lives are lost because of the spread of some infectious diseases, resulting in a large number of burials that could pollute groundwater. The Johannesburg West Park Cemetery was selected as our case study location. We gathered a variety of data regarding the cemetery expect for water samples as the boreholes were dry. The collected data were subjected to numerous analyses, and a detailed presentation of the geological structure under the cemetery was made. A high rate of burials was seen between 2020 and 2022, primarily because of the spread of COVID-19. We presented evidence to support our claim that the crossover seen during the decay process cannot be replicated by the decay model with the classical derivative. To simulate the transition from fast decay to slow decay, a fractional model was utilized using a Mittag-Leffler function as the solution. The acquired results assisted us in choosing an appropriate mathematical formulation of the advection-dispersion equation, which was also numerically examined. Under certain hypotheses, we ran some numerical simulations utilizing the mass released within the geological formation as the beginning concentration. The cemetery's boreholes should be checked monthly to improve the environment, and additional boreholes should be dug to figure out the type of aquifer beneath the cemetery and the direction of flow since these details aren't currently known. This will help to ensure that the cemetery does not contaminate the environment, or the water supplies nearby.
  • Thumbnail Image
    ItemOpen Access
    Modelling reactive pollutant transport in ground water: the case of two species
    (University of the Free State, 2019-06) Hans Tah, Mbah; Atangana, Abdon
    The locations of a significant number of industrial facilities, landfills and almost all mineral ore bodies are characterised by high in situ stresses and fractures and fissures act as flow paths for fluids underground. Regional scale fracture systems that transport pollution from spatially isolated source locations can cause mixing of chemical pollutants from different source origins due to fracture- fracture flux across two or more intersecting fractures, hence reactive transport. Alerts of groundwater contamination in response to multicomponent pollution transport have been investigated using a mathematical model of the hydrodynamic response of incompressible fluids such as groundwater flow. Fundamental to the model is the conservation of mass associated with the applied source strength and the concentration velocity field redistributions after source has released pollution, assuming the formation is homogenous. Solute distribution depends on the formation porosity and generally, fluids travel faster in fractures than in sedimentary formations. Different variations of the deterministic advection dispersion equation have been employed to predict coupled transport/reactive processes by substitution of a reaction term (retardation factor, etc..) which accounts for the changing concentration of the solid face components through time due to chemical reaction. However, fractured aquifers are inherently heterogeneous due to interconnecting fractures. The results in a non-homogenous mathematical formulation which difficult to solve analytically. As a result, most research endeavours have tended to depend on numerical solutions, increasingly made possible through advanced computational power. Even though it is questionable to what extend numerical models of groundwater reactive transport can be useful in making accurate quantitative predictions, it is still possible for a reactive model to predict the outcome of a particular chemical representation in an aquifer. Nevertheless, the linear, non-homogenous advection dispersion equation can still be solved analytical using the Green’s function method. In this thesis, we show how the advection-dispersion transport equation can be extended to account for geochemical reaction processes in a heterogeneous media. For the hypothetical case study, the system was made of a homogenous and a non-homogenous sub-component. The study’s methodological approach involved coupling of the homogenous transport phase with the non- homogenous system. The solution of the homogenous equation is obtained using Laplace transform and the exact solution of the new non-homogenous equation is obtained analytically using Laplace transform and the Green’s Function method. Both sub-models were solved numerically using the Crank-Nicolson discretization scheme and their stability conditions also established. For the proposed fracture flow system, the linear non-homogenous model was able to approximate the contribution of reactive transport processes in the system. Chemical reactions can attenuate the spread of a contaminant plume due to processes such as sorption and precipitation. The model presented in this thesis was able to predict fate of each species within the system. Mass transfer during and after the reaction resulted in the depletion of one source with respect to another, which the model showed positive results in capturing. The thesis concludes with a chapter on chemical equilibria which is the basis of kinetic modelling and the understanding of the progress of chemical reactions.
  • Thumbnail Image
    ItemOpen Access
    A new method for modeling groundwater flow problems: fractional-stochastic modeling
    (University of the Free State, 2019-06) Mahantane, Mohau L.; Atangana, Abdon
    To date, groundwater flow problems are still increasingly becoming a great environmental concern worldwide. This is among some of the reasons that many researchers from various fields of science have focused much of their attention in formulating new mathematical equations and models that could be used to capture and understand the behavior of groundwater flow with respect to space and time. The main aim of this study was to develop a new concept for modeling groundwater flow problems. The approach involved coupling of differential operators with stochastic approach. Literature proves that each of these two concepts has shown a great success in modeling complex real-world problems. But we argued that differential equations with constant coefficient are not fit to capture complexities with statistical setting. Therefore, to solve such a problem in this study, we considered a classical one-dimensional advection-dispersion equation for describing transport in porous medium and then applied stochastic approach to convert groundwater velocity (v), retardation (R) and the dispersion (D) constant coefficients into probability distribution. The next step was to employ the concept of fractional differentiation where we substituted the time derivative with the time fractional differential operator. Thereafter, we applied the Caputo, Caputo-Fabrizio and the Atangana-Baleanu fractional operators and derived conditions under which the exact solution for each derivative can be obtained. We then suggested the numerical solutions using the newly established numerical scheme of the Adams-Bashforth in the case of the aforementioned three (3) different types of differential operators. By combining the two concepts, we developed a new method to capture groundwater flow problems that could not be possible to capture using differential operators or stochastic approach alone. This new approach is believed to be a future technique for modeling complex groundwater flow problems. After solving the new model numerically, the condition for stability was also tested using the Von Neumann stability analysis method. Lastly, we presented numerical simulations using a software package called MATLAB.
  • Thumbnail Image
    ItemOpen Access
    Stochastic groundwater flow models in confined and leaky aquifers
    (University of the Free State, 2019-06) Amakali, Sarti Rautia; Atangana, Abdon
    This dissertation proposes an application of stochastic modeling of groundwater flow in confined and leaky aquifers. We are estimating that aquifer parameters such as transmissivity, storativity and leakage factor vary, not constant, in space at different period especially in heterogeneous environment. Heterogeneous environment are known to be complex because of their uncertainty. Uncertainty referred in modeling includes errors in dataset, which might be bias or variance (under fitting/over fitting), low or not enough data, or unbalanced data, which all affect the model produced if not captured with appropriate model technique. The groundwater flow equation for confined and leaky aquifers derived by the latest version Atangana and Ramotsho, as well asAtangana and Mathobo, which all include scaling matrix of the soil, are considered and further modified to a new scheme of stochastic models for confined and leaky aquifer. We tried to achieve the capture statistical setting of aquifer parameters using the concept of stochastic modeling technique. The aquifer parameters are replaced by distribution for instance, Gaussian or normal distribution.Due to the complexity of the modified models, it is almost impossible to obtain the exact solution by using analytical solution, thus we opt to numerical analysis, in particular the Newton method used to derive the numerical solutions of the modified models. Detailed analysis of stability and convergences, we used method are presented for both models. Numerical simulations are depicted for different distributions.