A new model for groundwater transport in dual media
| dc.contributor.advisor | Atangana, Abdon | |
| dc.contributor.author | Deyi, Mpafane | |
| dc.date.accessioned | 2021-03-23T08:47:03Z | |
| dc.date.available | 2021-03-23T08:47:03Z | |
| dc.date.issued | 2020-01 | |
| dc.description.abstract | The concept of differentiation has been the most used mathematical concept to express change of physical problems in time and space. The concept has been used in many disciplines in the last decades, for instance, in groundwater pollution problems. The movement of pollution within the subsurface have been a worry among researchers, as such has serious impact on health since many people of different background rely of subsurface water for commercial and domestic use. One of the breakout of the groundwater pollution is perhaps the Love Canal scenario that led to the loss of many lives of human beings and animals. A Mathematical models that take into account the dispersion advection was introduced, used and modified with the aim to better depict such movement. However, this model and its modified versions were not able to replicate the anomalous movement of pollution as they were constructed with assumption that the geological formation is homogeneous. Another limitation of such models is to assume that the dispersion and advection coefficients are constant within and across the aquifer. However, it is worth noting that a mathematical model will accurately replicate the observed facts, if and only, the conversion from observation to mathematical formulas has taken into account of the main parameters of the real world problem. Additionally and more importantly, the advection dispersion equation does not provide us with transaction from matrix soil to fracture or the reverse. Neglection of such aspect could lead to incomplete and inaccurate model. Finally, the effect of variation of fracture aperture are not included into the mathematical model. Therefore such model can’t really be used for aquifers with complex system. In this thesis, an attempt to solve and extend the limitations of the classical advection dispersion equation is initiated. The new proposed model takes into account the transition of movement from matrix to fracture, this help to obtain a new mathematical model with variable dispersion and advection. The numerical simulations obtained from this model using classical differentiation with variable dispersion and advection let no doubt to believe that the variation of dispersion and advection coefficient play a crucial role to depict the effect of change in fracture aperture size. Beside, this new step forward, to capture the effect of elasticity of the geological formation, the well-known Caputo-Fabrizio fractional derivative was utilised to extend the classical model. Also to include the effect of fracture, a differential operator based on power law kernel was used to extend the classical advection dispersion equation with variable coefficient. Finally the Atangana-Baleanu differential operators was used to build a model with cross-over property. For each case a new numerical scheme was used to solve the model and numerical simulations were performed for different values of fractional orders and variable coefficients. This new model will open new doors of investigations toward modeling the movement of subsurface water. Additionally, a new software better than FeFlow could be constructed. | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11660/10970 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | University of the Free State | en_ZA |
| dc.rights.holder | University of the Free State | en_ZA |
| dc.subject | Thesis (Ph.D. (Geohydrology))--University of the Free State, 2020 | en_ZA |
| dc.subject | Diffusion | en_ZA |
| dc.subject | Fracture | en_ZA |
| dc.subject | Matrix dispersion | en_ZA |
| dc.subject | Cross-over | en_ZA |
| dc.subject | Power law | en_ZA |
| dc.subject | Fractional differentiation | en_ZA |
| dc.title | A new model for groundwater transport in dual media | en_ZA |
| dc.type | Thesis | en_ZA |