Abstract
This paper examines the ground-water flow problem associated with the injection and recovery of certain corrosive fluids into mineral bearing rock. The aim is to dissolve the minerals in situ, and then recover them in solution. In general, it is not possible to recover all the injected fluid, which is of concern economically and environmentally. However, a new strategy is proposed here, that allows all the leaching fluid to be recovered. A mathematical model of the situation is solved approximately using an asymptotic solution, and exactly using a boundary integral approach. Solutions are shown for two-dimensional flow, which is of some practical interest as it is achievable in old mine tunnels, for example.
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References
R. W. Bartlett, Solution Mining. Philadelphia: Gordon and Breach (1992) 276pp.
J. E. Pahlman, Evaluation of the potential for in situ leach mining of domestic manganese ores. In: S. A. Swan and K. R. Coyne (eds.), In Situ Recovery of Minerals II. New York: Engineering Foundation (1994) 299-321.
S. Kubo, Development of gold ore leaching method by iodine. In: S. A. Swan and K.R. Coyne (eds.), In Situ Recovery of Minerals II. New York: Engineering Foundation (1994) 405-431.
G. Pantelis and A. I. M. Ritchie, Rate-limiting factors in dump leaching of pyritic ores. Appl. Math. Modelling 16 (1992) 553-560.
J. W. Crockett, Permitting and closure of an in situ minerals recovery operation: an attorney's perspective. In: S. A. Swan and K. R. Coyne (eds.), In Situ Recovery of Minerals II. New York: Engineering Foundation (1994) 21-43.
D. R. Tweeton, J. C. Hanson, M. J. Friedel and L. J. Dahl, Field tests of geophysical methods for monitoring the flow pattern of leach solution. In: S.A. Swan and K. R. Coyne (eds.), In Situ Recovery of Minerals II. New York: Engineering Foundation (1994) 179-199.
R. D. Schmidt, D. Barley and M. J. Friedel, Dynamic influences on hydraulic conductivity during in situ copper leaching. In: S. A. Swan and K. R. Coyne (eds.), In Situ Recovery of Minerals II. New York: Engineering Foundation (1994) 259-286.
E. Aharonov, J. A. Whitehead, P. B. Kelemen and M. Spiegelman, Channeling instability of upwelling melt in the mantle. J. Geophys. Res. 100,no B10 (1995) 20, 433-20, 450.
G. Lapidus, Mathematical modelling of metal leaching in nonporous minerals. Chem. Eng. Sci. 47 (1992) 1933-1941.
J. N. Dewynne, A. C. Fowler and P. S. Hagan, Multiple reaction fronts in the oxidation-reduction of iron-rich uranium ores. SIAM J. Appl. Math. 53 (1993) 971-989.
L. K. Forbes, Progress toward a mining strategy based on mineral leaching with secondary recovery. Appl. Math. Modelling 20 (1996) 16-25.
M. K. Hubbert, The Theory of Ground-water Motion and Related Papers. New York: Hafner (1969) 310pp.
A. Verruijt, Theory of Groundwater Flow. London: MacMillan (1970) 190pp.
O. D. L. Stack, Groundwater Mechanics. New Jersey: Prentice Hall (1989) 732pp.
J. Bear, Dynamics of Fluids in Porous Media. New York: American Elsevier (1972) 764pp.
M. Muskat, The Physical Principles of Oil Production. New York: McGraw-Hill (1949) 922pp.
S.K. Lucas, J. R. Blake and A. Kucera, A boundary-integral method applied to water coning in oil reservoirs. J. Austral. Math. Soc. Ser. B 32 (1991) 261-283.
S. K. Lucas and A. Kucera, A boundary integral method applied to the 3D water coning problem. Phys. Fluids 8 (1996) 3008-3022.
H. Zhang and G. C. Hocking, Withdrawal of layered fluid through a line sink in a porous medium. J. Austral. Math. Soc. Ser. B 38 (1996) 240-254.
H. Zhang, G. C. Hocking and D. A. Barry, An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium. J. Austral. Math. Soc. Ser. B 39 (1997) 271-279.
H. Zhang and G. C. Hocking, Axisymmetric flow in an oil reservoir of finite depth caused by a point sink above an oil-water interface. J. Eng. Math. 32 (1997) 365-376.
C.-T. Tan and G. M. Homsy, Viscous fingering with permeability heterogeneity. Phys. Fluids A 4 (1992) 1099-1101.
M. B. Butts and K. H. Jensen, Effective parameters for multiphase flow in layered soils. J. Hydrology 183 (1996) 101-116.
M. J. Martinez and D. F. Mctigue, A boundary integral method for steady flow in unsaturated porous media. Int. J. Numer. Analytical Meth. in Geomechanics 16 (1992) 581-601.
L. K. Forbes, A. M. Watts and G. A. Chandler, Flow fields associated with in situ mineral leaching. J. Austral. Math. Soc. Ser. B 36 (1994) 133-151.
L. M. Milne-Thomson, Theoretical Hydro dynamics, 5th edition. London: MacMillan (1968) 743pp.
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Forbes, L.K., McCue, S.W. Optimal fluid injection strategies for in situ mineral leaching in two-dimensions. Journal of Engineering Mathematics 36, 185–206 (1999). https://doi.org/10.1023/A:1004406311441
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DOI: https://doi.org/10.1023/A:1004406311441