# Quasi-analytical modelling of advective-diffusive transport in porous media

Verrall, Damien Paul (2015) Quasi-analytical modelling of advective-diffusive transport in porous media. PhD thesis, James Cook University.

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## Abstract

This thesis formulates mathematical modelling techniques to investigate groundwater contamination from a leaky saline pond situated above a freshwater aquifer. This problem has received little attention from researchers, but given the increasing prevalence of land based aquaculture, and the fact that saline ponds can be considered a proxy for other types of contaminated ponds, for example, tailings dams, it's a scenario that deserves more consideration. Unfortunately, it's also a problem that (currently) cannot be solved mathematically using analytical techniques. As such, it falls to numerical methods when a solution is required. However, although numerical methods will always give a solution, problems such as truncation error and numerical diffusion often cast doubt on the result. Therefore, this thesis will instead explore combined analytical/numerical techniques (or quasi-analytical techniques) as a potential alternative.

The major transport processes in groundwater contamination are advection and diffusion. These processes are coupled, with each affecting the evolution of the other through time. However, depending on the problem, often one of these processes can be ignored. This is the initial approach taken in this thesis. Given a leaky contaminated pond, separate quasi-analytical solutions are devised for the individual processes of advection and diffusion. These then form the basis of two additional quasi-analytical techniques, which solve for contaminant transport via combined advection-diffusion. Using the above techniques, mathematical experimentation also revealed general empirical equations which simplify the modelling of contaminant transport beneath leaky contaminated ponds.

Item ID: 43808 Thesis (PhD) advection; diffusion; flow; fluid dynamics; ground water pollution; groundwater contamination; liquid flow; mathematical modeling; mathematical modelling; porous; quasi-analytic function; quasi-analytical method; transport Publications arising from this thesis are available from the Related URLs field. The publications are:Verrall, D.P., Read, W.W., and Narayan, K.A. (2009) Predicting salt advection in groundwater from saline aquaculture ponds. Journal of Hydrology, 364 (3-4). pp. 201-206.Verrall, D.P., Read, W.W., and Narayan, K.A. (2009) Computational aspects of accurately modelling salt advection beneath aquaculture ponds. In: Proceedings of the 13th Biennial Computational Techniques and Applications Conference, CTAC-2006 (48), C1075-C1089. From: 13th Biennial Computational Techniques and Applications Conference (CTAC2006), 2-5 Jul 2006, Townsville, QLD, Australia.Verrall, D.P., and Read, W.W. (2012) Predicting diffusion in aquifers beneath saline ponds. Journal of Hydrology, 475. pp. 150-157. 19 May 2016 00:00 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified @ 34%04 EARTH SCIENCES > 0404 Geophysics > 040403 Geophysical Fluid Dynamics @ 33%09 ENGINEERING > 0905 Civil Engineering > 090509 Water Resources Engineering @ 33% 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 33%96 ENVIRONMENT > 9611 Physical and Chemical Conditions of Water > 961103 Physical and Chemical Conditions of Water in Fresh, Ground and Surface Water Environments (excl. Urban and @ 34%96 ENVIRONMENT > 9614 Soils > 961401 Coastal and Estuarine Soils @ 33% Total: 107 Last 12 Months: 2 More Statistics

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