Development of a groundwater recharge model

Abstract

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.

Afrikaans: Bestaande grondwater herlaai beraming metodes blyk om hoofsaaklik, op ‘n klein skaal, gebied spesifieke beramings te lewer. As gevolg van dit is hierdie metodes nie betroubaar op 'n plaaslike skaal nie. Dit kan toegeskryf word daartoe dat konsepte soos heterogeniteit, visco-elastiese eienskappe, en die geheue effek nie in ag geneem word nie. Hierdie studie is daarop gemik om 'n nuwe grondwater herlaai beraming metode aan te skaf waar die bogenoemde konsepte in ag geneem word. Literatuur bewys dat hierdie konsepte goed erken word in die veld van fraksionele differensiasie. Hierdie studie se metodologiese benadering het ingesluit om 'n presiese oplossing te vind vir 'n geselekteerde grondwater herlaai vergelyking, deur die Laplace-transform en inverse Laplace-transform toe te pas. Met die uitvoer van ‘n onsekerheid ontleding en statistiese ontleding van die parameters in die oplossing dui daarop dat die bergingsvermoë en dreinering weerstand beide 'n akkurate beraming vereis wanneer die herlaai beraam word met die geselekteerde vergelyking. Daarna was die Caputo afgeleide, Caputo-Fabrizio afgeleide, en die Atangana- Baleanu afgeleide toegepas om ‘n presiese oplossing te kry vir elke afgeleide. Die numeriese simulasie resultate vir elke oplossing wys dat die gedrag van 'n bepaalde werklike probleem uitgebeeld word. Daar was tot die gevolgtrekking gekom dat grondwater herlaai vir 'n heterogene en visco-elastiese geologiese formasie goed beskryf word met die konsep van fraksionele differensiasie deur die Mittag-Leffler wet of die Atangana-Baleanu fraksionele afgeleide. Dit was ook aanvaar dat herlaai in 'n elastiese geologiese formasie deur die Caputo en Caputo-Fabrizio afgeleide beraam kan word. Verder is dit aanvaar dat hidrouliese kop beïnvloed word deur onseker faktore wat nie in ag geneem word in algemene herlaai vergelykings nie. Die Eton benadering was dus toegepas, en wys dat die onsekere funksie 'n beduidende uitwerking op hidrouliese kop verspreiding het. Laastens, hierdie studie dui daarop dat 'n grondwater herlaai model wat heterogeniteit, visco-elastiese eienskappe, die geheue effek, en onsekerhede inkorporeer en in ag neem vir 'n nuwe en verbeterde begrip tot grondwater herlaai ondersoeke.