Institute for Groundwater Studies (IGS)
http://hdl.handle.net/11660/103
2021-06-22T14:36:19ZCharacterisation of the deep aquifers of South Africa - the Karoo Supergroup and Table Mountain Group
http://hdl.handle.net/11660/10374
Characterisation of the deep aquifers of South Africa - the Karoo Supergroup and Table Mountain Group
Makiwane, Nwabisa
Abstract not available
2019-06-01T00:00:00ZStochastic groundwater flow models in confined and leaky aquifers
http://hdl.handle.net/11660/10373
Stochastic groundwater flow models in confined and leaky aquifers
Amakali, Sarti Rautia
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.
2019-06-01T00:00:00ZModelling reactive pollutant transport in ground water: the case of two species
http://hdl.handle.net/11660/10372
Modelling reactive pollutant transport in ground water: the case of two species
Hans Tah, Mbah
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.
2019-06-01T00:00:00ZA new method for modeling groundwater flow problems: fractional-stochastic modeling
http://hdl.handle.net/11660/10371
A new method for modeling groundwater flow problems: fractional-stochastic modeling
Mahantane, Mohau L.
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.
2019-06-01T00:00:00Z