Groundwater flow analytical and numerical solutions
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Date
2021
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UMT Lahore
Abstract
Groundwater flow models which can be used to determine the aquifer hydraulics of an artificially recharged aquifer of Windhoek in Namibia are investigated. The geology of this aquifer is very complex and heterogeneous, due to the presence of various and randomly distributed fractures and faults as well as the variations in the mineral composition of the water-bearing pure quartzite and micaceous quartzite. Water storage occurs within these rocks and fractures, causing the aquifer to be categorized as a double porosity type aquifer. The flow of the injected water within the Windhoek aquifer has been analyzed using the Forchheimer and Darcy’s law equations. In this study the flow was evaluated in one dimension. Therefore, to replicate the flow of water within a double porosity aquifer, various types of differential operators were applied to these flow equations. Consequently, two distinct models were developed. The first one is based on the classical differentiation as it does not consider the heterogeneity of the geological formations; hence the Laplace transform operator has been utilized to derive the exact solution to this effect. The second model is based on the nonlocal differential operator which has the ability to incorporate the effect of long-range dependency that is expressing memory effect into the mathematical formulation. Therefore, the approximate solution in this case has been derived using numerical methods such as the Adams-Bashforth and the Newton polynomial (Atangana-Seda) schemes. The classical numerical simulations depicted a normal flow when the fractional order was equal to 1; and this defines a flow within a homogeneous medium. Whereas, the model developed using fractional derivative depicted two flow scenarios namely the fast flow and the slow flow; observed when the fractional order was smaller and closer to 1 respectively. Thus, the fast flow has been attributed to the flow within the pure quartzite where the permeability and porosity are considered very high. Moreover, the slow flow has been attributed to the flow occurring in the micaceous quartzite; which has less permeability and low porosity due to less degree of fracturing and increasing mica content in the rock.