DERIVATION OF HILLSLOPE LEAKAGE-DEPENDENT EQUATIONS MODELING GROUNDWATER FLOW IN THREE-AQUIFER SYSTEM WITHIN A SEDIMENTARY BASIN

Authors

  • S. A Sonloye Department of Physics, University of Maiduguri, P.M.B. 1069, Maiduguri, Borno State. Author
  • A Usman Department of Physics, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State. Author
  • L. E Agada Department of Physics, Yobe State University, Damaturu, Yobe State. Author
  • A.S. Oniku Department of Physics, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State. Author

Keywords:

Boussinesq, Aquifer, flow, three-aquifer, Leakage Groundwater, Hillslope

Abstract

This paper derived hillslope leakage-dependent equations that can be used to study groundwater flow dynamics in leaky sloping three-aquifer system within a sedimentary basin. This was done by the introduction of leakage term(s) and Darcy flux in Boussinesq context into the general groundwater continuity flow equations in each of the aquifers within the three-aquifer system. The derived equations have been shown to be capable of modeling groundwater flow not only in sloping three-aquifer system but also in horizontal three-aquifer system, where the slope angle is zero. These equations, when solved and used for simulations of groundwater flow in three-aquifer system, will be very useful to hydrogeologists in studying the leakage properties of aquifer-aquitard system which is very crucial in estimating long time yields of aquifers within a three-aquifer system. Also, extension of Boussinesq equation into three-aquifer system will help geoscientists to conduct detailed studies and have better understanding of the groundwater flow dynamics in such geological structures.

         Views | Downloads: 23 / 14

Downloads

Download data is not yet available.

References

Su N (2017). The fractional Boussinesq equation of groundwater flow and its applications. Journal of Hydrology 547 (2017) 403–412.

Darcy H (1856). Les FontainesPubliques De La Ville De Dijon. Dalmont, Paris.

Igbokwe M U, Amos U (2011). Fundamental Approach in Groundwater Flow and Solute Transport Modeling using the Finite Difference Method. J. Earth and Environmental Sciences, DrImram Dar (Ed.), ISBN: 978-953-307-468-9.

Boussinesq J (1877). Essaisur la theorie des eaux courantes(Test on the theory of running waters). Mem. Acad. Sci. Inst. Fr. 23 (1), 252–260.

Boussinesq J (1904). Recherches théori qu essurl’écoulement des nappesd’eauin filtréesdans le sol etsurdébit de sources. J. Math. Pure Appl. 10, 5–78.

Henderson, F M., Wooding RA. (1964), Overland flow and groundwater flow from a steady rainfall of finite duration, J. Geophys. Res.,69 (8), 1531–1540.

Abdellaoui B, Peral, Walias (2015). Some existence and regularity results for porous media and fast diffusion equations with a gradient term. Trans. Am. Math. Soc. 367, 4757–4791.

Telyakovskiy AS, Kurita S, Allen MB (2016). Polynomial-based approximate solutions to the Boussinesq equation near a well. Adv. Water Resour. 96, 68–73 (2016).

Alkahtani BST, Atangana, A (2016). Controlling the wave movement on the surfaceof shallow water with the Caputo-Fabrizio derivative with fractional order. Chaos, Solitons Fractals 89, 539–546.

Atangana A, Alkahtani BST (2016). New model of groundwater flowing within a confine aquifer: application of Caputo-Fabrizio derivative. Arab. J. Geosci. 9 (1),1–6.

Atangana A, Baleanu D (2016). New fractional derivatives with non-local and nonsingular kernel: theory and application to heat transfer model. Therm. Sci. 20 (2), 763–769. arXiv:1602.03408.

Djida JD, Area I, Atangana A (2016). New numerical scheme of Atangana-Baleanu fractional integral: an application to groundwater flow within leaky aquifer.arXiv:1610.08681.

Troch PA, Paniconi C, Van Loon E (2003). Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 1. Formulation and characteristic response, Water Resour. Res., 39(11), 1316, doi: 10.1029/2002WR001728.

Uchida T, Asano Y, Ohte N, Mizuyama T (2003). Seepage area and rate of bedrock groundwater discharge at a granitic un-channeled hillslope. Water Resour. Res. 39 (1), 1018. Doi:10.1029/2002WR001298.

Tromp-van M, Peters NE, McDonnell JJ (2007). Effect of bedrock permeability on subsurface storm flow and the water balance of a trenched hillslope at the Panola Mountain Research Watershed, Georgia, USA. Hydrol. Process. 21, 750–769.

Ebel BA, Loague K, Montgomery DR, Dietrich WE (2008). Physics-based continuous simulation of long-term near-surface hydrologic response for the Coos Bay experimental catchment. Water Resour. Res. 44, W07417. doi:10.1029/2007WR006442.

Graham CB, Woods RA, McDonnell, JJ (2010). Hillslope threshold response to rainfall: (1) A field based forensic approach. J. Hydrol. 393, 65–76.

Koussis AD, Smith ME, Akylas E, Tombrou M (1998). Groundwater drainage flow in a soil layer resting onan inclined leaky bed. Water Resour. Res. 34 (11), 2879–2887.

Broda S, Paniconi C, Larocque M (2008). Evaluation of the hillslope-storage Boussinesq model with leakage. In: Calibration and Reliability in Groundwater Modelling (Proceedings of ModelCARE 2007), IAHS Red Book, vol. 320. IAHS Press, Copenhagen, Denmark, pp. 182–187.

Baker M, Hemker K (2002). A Dupuit formulation for flow in layered, anisotropic aquifers. Elsevier Journal of Advances in Water Resources 25, pp 747-754.

Kruseman GP, DeRidder NA (1990). Analysis and evaluation of pumping test data. International Institute for Reclamation and Improvement, Wageningen, The Netherlands.

Downloads

Published

2022-12-01

How to Cite

DERIVATION OF HILLSLOPE LEAKAGE-DEPENDENT EQUATIONS MODELING GROUNDWATER FLOW IN THREE-AQUIFER SYSTEM WITHIN A SEDIMENTARY BASIN. (2022). The Transactions of the Nigerian Association of Mathematical Physics, 18, 63 –68. https://nampjournals.org.ng/index.php/tnamp/article/view/159

Share

Similar Articles

You may also start an advanced similarity search for this article.