Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-29T10:36:05.784Z Has data issue: false hasContentIssue false

Instability of the salinity profile during the evaporation of saline groundwater

Published online by Cambridge University Press:  16 October 2008

ANDREJ T. IL'ICHEV
Affiliation:
Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, 119991 Moscow, Russiailichev@mi.ras.ru
GEORGE G. TSYPKIN
Affiliation:
Institute for Problems in Mechanics, Russian Academy of Sciences, Av. Vernadskogo 101, 119420 Moscow, Russiatsypkin@ipmnet.ru
DAVID PRITCHARD
Affiliation:
Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotlanddtp@maths.strath.ac.uk
CHRIS N. RICHARDSON
Affiliation:
BP Institute for Multiphase Flow, University of Cambridge, Madingley Rise, Cambridge CB3 0EZ, UKchris@bpi.cam.ac.uk

Abstract

In this paper we investigate salt transport during the evaporation and upflow of saline groundwater. We describe a model in which a sharp evaporation–precipitation front separates regions of soil saturated with an air–vapour mixture and with saline water. We then consider two idealized problems. We first investigate equilibrium configurations of the freshwater system when the depth of the soil layer is finite, obtaining results for the location of the front and the upflow of water induced by the evaporation. We then develop a solution for a propagating front in a soil layer of infinite depth and investigate the gravitational stability of the salinity profile which develops below the front, obtaining marginal linear stability conditions in terms of a Rayleigh number and a dimensionless salt saturation parameter. Applying our findings to realistic parameter regimes, we predict that salt fingering is unlikely to occur in low-permeability soils, but is likely in high-permeability (sandy) soils under conditions of relatively low evaporative upflow.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Gowing, J. W., Konukcu, F. & Rose, D. A. 2006 Evaporative flux from a shallow watertable: the influence of a vapour–liquid phase transition. J. Hydrol. 321, 7789.Google Scholar
Hassanizadeh, S. M. & Leijnse, A. 1995 A non-linear theory of high-concentration-gradient dispersion in porous media. Adv. Wat. Res. 18 (4), 203215.Google Scholar
Hassanizadeh, S. M. & Leijnse, T. 1988 On the modelling of brine transport in porous media. Wat. Resour. Res. 24 (3), 321330.Google Scholar
Helmig, R. 1997 Multiphase Flow and Transport Processes in the Subsurface. Springer-Verlag.Google Scholar
Herbert, A. W., Jackson, C. P. & Lever, D. A. 1988 Coupled groundwater flow and solute transport with fluid density strongly dependent upon concentration. Wat. Resour. Res. 24 (10), 17811795.Google Scholar
Lide, D. R. 2001 CRC Handbook of Chemistry and Physics (82nd edn). CRC.Google Scholar
Phillips, O. M. 1991 Flow and Reactions in Permeable Rocks. Cambridge University Press.Google Scholar
Pieters, G. J. M. & van Duijn, C. J. 2006 Transient growth in linearly stable gravity-driven flow in porous media. Eur. J. Mech. B Fluids 25, 8394.Google Scholar
Rose, D. A., Konukcu, F. & Gowing, J. W. 2005 Effect of watertable depth on evaporation and salt accumulation from saline groundwater. Aust. J. Soil Res. 43, 565573.Google Scholar
Schofield, R. V. & Kirkby, M. J. 2003 Application of salinization indicators and initial development of potential global salinization scenario under climate change. Global Biogeochem. Cycles 17 (3), 1078.Google Scholar
Straughan, B. 1992 The Energy Method, Stability, and Nonlinear Convection. Springer.Google Scholar
Tsypkin, G. G. 2003a Accumulation and precipitation of salts during groundwater evaporation and flow. Fluid Dyn. 38, 900907. (Translated from Izvestiya Ross. Acad. Nauk, Mekh. Zhid. i Gaza 6, 8493.)Google Scholar
Tsypkin, G. G. 2003b Mathematical model of salt precipitation due to groundwater evaporation. Dokl. Phys. 48, 198201.Google Scholar
Tsypkin, G. G. & Brevdo, L. 1999 A phenomenological model of the increase in solute concentration in ground water due to evaporation. Transport Porous Media 37, 129151.Google Scholar
van Duijn, C. J., Peletier, L. A. & Schotting, R. J. 1998 Brine transport in porous media: self-similar solutions. Adv. Wat. Resour. 22 (3), 285297.Google Scholar
van Duijn, C. J., Wooding, R. A., Pieters, G. M. & van der Ploeg, A. 2002 Stability criteria for the boundary layer formed by throughflow at a horizontal surface of a porous medium. In Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere, ed. Raats, P. A. C., Smiles, D. & Wanrick, A. W.. Geophysical Monograph 129, American Geophysical Union.Google Scholar
Vukalovitch, M. P. 1955 Thermodynamic Properties of Water and Water Vapour. Mashgiz.Google Scholar
Wagner, W. & Pruss, A. 2002 The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31 (2), 387535.Google Scholar
Wooding, R. A. 1960 Rayleigh instability of a thermal boundary layer in flow through a porous medium. J. Fluid Mech. 9, 183192.Google Scholar
Wooding, R. A., Tyler, S. W. & White, I. 1997 Convection in groundwater below an evaporating salt lake. 1. Onset of instability. Wat. Resour. Res. 33 (6), 11991217.Google Scholar
Yakirevich, A., Berliner, P. & Sorek, S. 1997 A model for numerical simulating of evaporation from bare saline soil. Wat. Resour. Res. 33 (5), 10211033.Google Scholar
Yeo, A. 1999 Predicting the interaction between the effects of salinity and climate change on crop plants. Scientia Horticulturae 78, 159174.Google Scholar