Equations of thermohydrodynamic exchange among continuous media in karst and its environmental consequences
Main Article Content
Abstract
The engineering and environmental treatment of the problems of mass transport in karst aquifers (fluid flow, contaminant transport, assimilation, inertia, resilience, self purification capability, interaction among miscible and immiscible liquids among others is often complicated basically due to thermodynamic reasons. The mathematical treatment of those processes is commonly oversimplified. In turn it limits or reduces the appropriate solution of the problems and the sustainable environmental management of karst landscapes that, in cuba, comprises 65% of the emerged surface of the country. This paper describes an approach to the solution of the problem of mass exchange based on a thermodynamic model that accounts for the interaction among the sets of multiple spaces integrating the karst universe: solid matrix-porous-joints-caves.
Article Details
How to Cite
Molerio LeónL. (2020). Equations of thermohydrodynamic exchange among continuous media in karst and its environmental consequences. Cub@: Medio Ambiente Y Desarrollo, 13(24). Retrieved from https://cmad.ama.cu/index.php/cmad/article/view/162
Section
Original Article
References
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Barlow, P.M. & Moench, A.F. .1995. WTAQ- A computer program for calculating drawdowns and estimating hydraulic properties for confined and unconfined aquifers. USEPA, 78pp.
Bear,J.D.; Zaslavsky, I. & Irmay, S. .1968. Physical principles of water percolation and seepage. UNESCO, Arid Zone Research, XXIX, 465 pp, Paris.
Bibby, R. .1981. Mingling by displacement in dual porosity media. Geol. Jb. C 29 pp. 217-229
Borevskii, B.; B. Samsonov & L. Yazvin .1982. Metódica para la determinación de los parámetros de los acuíferos por datos de aforos .en ruso). Nedra, 328 pp, Moscú.
Boulton, N.S. & Streltsova, T.D. .1977a. Unsteady flow to a pumped well in a fissured water-bearing formation. Jour. Hydrol. 35pp. 257-269.
Boulton, N.S. & Streltsova, T.D. .1977b. Unsteady flow to a pumped well in a two-layered water-bearing formation. Jour. Hydrol. 35pp. 245-256.
Carnahan, C.L. .1976. Non-equilibrium thermodynamics of groundwater flow systemspp. symmetry properties of phenomenological coefficients and considerations of hydrodynamic dispersion. Jour. Hydrol. .31. 125-150
Duguid, J. O. & Lee, P.C.Y. .1977. Flow in fractured porous media. Water Resour. Res. 13 .3. 558-566
Herrera, I & B. Chen .1983. Delayed yield. An exact quasi-three dimensional model for free aquifers. Adv. Water Resourc. 6, March, pp. 54-48
Huyakorn, P. S.; Lester, B. H., & Mercer, J. W. .1983a. An efficient finite element technique for modeling transport in fractured porous media. 1. Single species transport. Water Resourc. Res. 19 .3. 841-854, June.
Huyakorn, P. S.; Lester, B. H., & Faust, Ch. R. .1983b. Finite element techniques for modeling groundwater flow in fractured aquifers. Water Resourc. Res. 19 .4. 1019-1035, August.
Illman, Walter A. .2006) Strong field evidence of directional permeability scale effect in fractured rock Journal of Hydrology 319 227–236
Illman, W.A., Neuman, S.P., 2003. Steady-state analyses of crosshole pneumatic injection tests in unsaturated fractured tuff. J. Hydrol. 281, 36–54.
Illman, W.A., Tartakovsky, D.M., 2005. Asymptotic analysis of three-dimensional pressure interference testspp. point source solution. Water Resour. Res. 41, W01002. doipp.10.1029/ 2004WR003431.
Jeffrey Yang, Y; Spencer, R.D.; T.M. Gates .1995. Analytical solutions for determination of non-steady state capture zones. GWMR, Winterpp. 101-106
Lee Chen-Chang, Cheng-Haw Lee, Hsin-Fu Yeh, Hung-I Lin .2010) Modeling spatial fracture intensity as a control on flow in fractured rock Environ Earth Sci. DOI 10.1007/s12665-010-0794-x
Long, J. C. S.; J. S. Remer; C. R. Wilson; P. A. Witherspoon .1982. Porous Media Equivalents for Networks of Discontinuous Fractures. Water Resour. Res. 18 .3. 645-658
Maasland, M. .1957. Soil anisotropy and land drainage. In/ J.N. Luthin, ed.pp. Drainage of Agricultural Lands. Amer. Soc. Agr. Madison, Wisconsin pp. 216-228.
March Delgado, C. & L.F. Molerio León .1987. A General Approach to An Algorithm For Groundwater Flow in Karstic Aquifers. Hydro- And Thermodynamical Considerations. Internatl. Symp. Groundwater Monitoring and Management, Dresden, GDR, 21pp.
McKenna SA, Reeves PC .2006. Fractured continuum approach to stochastic permeability modeling. Inpp. Stochastic modeling and geostatisticspp. principles, methods, and case studies, AAPG computer applications in geology, vol 3, 2nd edn. American Association of Petroleum Geologists, Tulsa, Okla, pp 173–186
Moench, A. F. .1984. Double porosity model for a fissured groundwater reservoir with fracture skin. Water Resour. Res. 20,.7.831-846
Molerio León, Leslie F..1984. El Efecto del Factor de Escala en la Interpretación del Campo de Propiedades Físicas de los Acuíferos Cársicos. XXVII Internatl. Geol. Congr., Moscú, Vol VII, Secc. 16,:468-469
Molerio León, Leslie F. .1985a. Dominios de flujo y jerarquización del espacio en acuíferos cársicos. Resumen. Simposio XLV Aniv. Soc. Espeleol. de Cuba: 44
Molerio León, L. F. .1985b. El Área Elemental Representativa .AER. para la evaluación de las propiedades físicas del carso. Modelo teórico. Resumen Simposio XLV Aniv. Soc. Espeleol. de Cuba: 45
Molerio León, Leslie F..1998. Mathematical Simulation of Karst Development. Internatl. Symp. Hydrology in the Humid Tropic Environment, Kingston, Jamaica, AIHS,:315-325
Molerio León, L.F. .2003. Modelo del desarrollo de cavernas y conductos cársicos. V Congreso Cubano de Geología y Minería. Memorias Geomin 2003, La Habana, Marzo 24-28 GQGC 09,: 84-91,
Molerio León, L.F. .2007. Thermo dynamical approach to cave development simulation .MTDC. in epigenetic karst. Geophysical Research Abstracts, Vol. 9, 01843, 2007, SRef-ID: 1607-7962/gra/EGU2007-A-01843, European Geosciences Union 2007
Molz FJ, Rajaram H, Lu S .2004. Stochastic fractal-based models of heterogeneity in subsurface hydrology: origins, applications, limitations, and future research questions. Rev Geophys. doi: 10.1029/2003RG000126
Narasimhan, T.N. .1982. Multidimensional numerical simulation of fluid flow in fractured porous media . Water Resour. Res. 18 .4. 1235-1247
Neuman, S.P., 2005. Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeology Journal 13 .1., 124–147.
Niemi, Auli, Kimmo Kontio, Auli Kuusela-Lahtinen 2000: Hydraulic characterization and upscaling of fracture networks based on multiple-scale well test data Water Resources Research, Vol. 36, No. 12, Pages 3481–3497, December
Odeh, A.S. .1965. Unsteady state behavior of natural fractured reservoirs. Soc. Petroleum Engineer Jour., 5 .1. 60-64
Pan Jian-Bang, Chen-Chang Lee, Cheng-Haw Lee, Hsin-Fu Yeh, Hung-I Lin .2010. Application of fracture network model with crack permeability tensor on flow and transport in fractured rock. Engineering Geology 116 166–177
Reeves, D.M., Benson, D.A., Meerschaert, M.M., 2008. Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation, Water Resource Research 44, W05404.
Snow DT .1969. Anisotropic permeability of fractured media. Water Resour Res 5:1273–1289
Streltsova-Adams, T.D. .1976a. Comments on "Analysis of pumping tests data from anisotropic unconfined aquifers considering delayed gravity response" by Shlomo P. Neumann. Water Resour. Res. 2 .1. : 113-114.
Streltsova-Adams, T.D. .1976b. Advances and uncertainties in the study of groundwater flow in fissured rocks. Adv. Groundwater Hydrol. Amer. Water Resourc. Ass. 48-56
Svensson, U., 2001a. A continuum representation of fracture networks. part I: Method and basic test cases, Journal of Hydrology 250, 170–186.
Svensson, U., 2001b. A continuum representation of fracture networks. part II: Application to the Aspo Hard Rock laboratory, Journal of Hydrology 250, 187–205.
Teutsch G, Sauter M .1991. Groundwater flow and transport processes in karst aquifers—scale effects, data provision and model validation. In: EPA/NWWA international symposium on environmental problems in Karst Terrains, Nashville
Theis, C.V. .1935. The relation between the lowering of the piezometric surface and the rate and duration of the discharge of a well using groundwater storage. Trans. Amer. Geoph. Union, .16. 519-524.
Warren, J. E. & Root, P. J. .1963. Behavior of natural fractured reservoirs. Soc. Pet. Eng. Jour. 9,: 245-255.
Wellman TP, Shapiro AM, Hill MC .2009. Effects of simplifying fracture network representation on inert chemical migration in fracture controlled aquifers. Water Resour Res 45:W01416
Wu,Y.S., Liu,H.H., Bodvarsson, G.S., 2004. A triple-continuum approach for modeling flow and transport processes in fractured rock. Journal of Containment Hydrology 73, 145–179.
Zyvoloski, G.A., Robinson, B.A., Viswanathan, H.S., 2008. Generalized dual porosity: a numerical method for representing spatially variable sub-grid scale processes. Advances in Water Resources 31, 535–544.
Barlow, P.M. & Moench, A.F. .1995. WTAQ- A computer program for calculating drawdowns and estimating hydraulic properties for confined and unconfined aquifers. USEPA, 78pp.
Bear,J.D.; Zaslavsky, I. & Irmay, S. .1968. Physical principles of water percolation and seepage. UNESCO, Arid Zone Research, XXIX, 465 pp, Paris.
Bibby, R. .1981. Mingling by displacement in dual porosity media. Geol. Jb. C 29 pp. 217-229
Borevskii, B.; B. Samsonov & L. Yazvin .1982. Metódica para la determinación de los parámetros de los acuíferos por datos de aforos .en ruso). Nedra, 328 pp, Moscú.
Boulton, N.S. & Streltsova, T.D. .1977a. Unsteady flow to a pumped well in a fissured water-bearing formation. Jour. Hydrol. 35pp. 257-269.
Boulton, N.S. & Streltsova, T.D. .1977b. Unsteady flow to a pumped well in a two-layered water-bearing formation. Jour. Hydrol. 35pp. 245-256.
Carnahan, C.L. .1976. Non-equilibrium thermodynamics of groundwater flow systemspp. symmetry properties of phenomenological coefficients and considerations of hydrodynamic dispersion. Jour. Hydrol. .31. 125-150
Duguid, J. O. & Lee, P.C.Y. .1977. Flow in fractured porous media. Water Resour. Res. 13 .3. 558-566
Herrera, I & B. Chen .1983. Delayed yield. An exact quasi-three dimensional model for free aquifers. Adv. Water Resourc. 6, March, pp. 54-48
Huyakorn, P. S.; Lester, B. H., & Mercer, J. W. .1983a. An efficient finite element technique for modeling transport in fractured porous media. 1. Single species transport. Water Resourc. Res. 19 .3. 841-854, June.
Huyakorn, P. S.; Lester, B. H., & Faust, Ch. R. .1983b. Finite element techniques for modeling groundwater flow in fractured aquifers. Water Resourc. Res. 19 .4. 1019-1035, August.
Illman, Walter A. .2006) Strong field evidence of directional permeability scale effect in fractured rock Journal of Hydrology 319 227–236
Illman, W.A., Neuman, S.P., 2003. Steady-state analyses of crosshole pneumatic injection tests in unsaturated fractured tuff. J. Hydrol. 281, 36–54.
Illman, W.A., Tartakovsky, D.M., 2005. Asymptotic analysis of three-dimensional pressure interference testspp. point source solution. Water Resour. Res. 41, W01002. doipp.10.1029/ 2004WR003431.
Jeffrey Yang, Y; Spencer, R.D.; T.M. Gates .1995. Analytical solutions for determination of non-steady state capture zones. GWMR, Winterpp. 101-106
Lee Chen-Chang, Cheng-Haw Lee, Hsin-Fu Yeh, Hung-I Lin .2010) Modeling spatial fracture intensity as a control on flow in fractured rock Environ Earth Sci. DOI 10.1007/s12665-010-0794-x
Long, J. C. S.; J. S. Remer; C. R. Wilson; P. A. Witherspoon .1982. Porous Media Equivalents for Networks of Discontinuous Fractures. Water Resour. Res. 18 .3. 645-658
Maasland, M. .1957. Soil anisotropy and land drainage. In/ J.N. Luthin, ed.pp. Drainage of Agricultural Lands. Amer. Soc. Agr. Madison, Wisconsin pp. 216-228.
March Delgado, C. & L.F. Molerio León .1987. A General Approach to An Algorithm For Groundwater Flow in Karstic Aquifers. Hydro- And Thermodynamical Considerations. Internatl. Symp. Groundwater Monitoring and Management, Dresden, GDR, 21pp.
McKenna SA, Reeves PC .2006. Fractured continuum approach to stochastic permeability modeling. Inpp. Stochastic modeling and geostatisticspp. principles, methods, and case studies, AAPG computer applications in geology, vol 3, 2nd edn. American Association of Petroleum Geologists, Tulsa, Okla, pp 173–186
Moench, A. F. .1984. Double porosity model for a fissured groundwater reservoir with fracture skin. Water Resour. Res. 20,.7.831-846
Molerio León, Leslie F..1984. El Efecto del Factor de Escala en la Interpretación del Campo de Propiedades Físicas de los Acuíferos Cársicos. XXVII Internatl. Geol. Congr., Moscú, Vol VII, Secc. 16,:468-469
Molerio León, Leslie F. .1985a. Dominios de flujo y jerarquización del espacio en acuíferos cársicos. Resumen. Simposio XLV Aniv. Soc. Espeleol. de Cuba: 44
Molerio León, L. F. .1985b. El Área Elemental Representativa .AER. para la evaluación de las propiedades físicas del carso. Modelo teórico. Resumen Simposio XLV Aniv. Soc. Espeleol. de Cuba: 45
Molerio León, Leslie F..1998. Mathematical Simulation of Karst Development. Internatl. Symp. Hydrology in the Humid Tropic Environment, Kingston, Jamaica, AIHS,:315-325
Molerio León, L.F. .2003. Modelo del desarrollo de cavernas y conductos cársicos. V Congreso Cubano de Geología y Minería. Memorias Geomin 2003, La Habana, Marzo 24-28 GQGC 09,: 84-91,
Molerio León, L.F. .2007. Thermo dynamical approach to cave development simulation .MTDC. in epigenetic karst. Geophysical Research Abstracts, Vol. 9, 01843, 2007, SRef-ID: 1607-7962/gra/EGU2007-A-01843, European Geosciences Union 2007
Molz FJ, Rajaram H, Lu S .2004. Stochastic fractal-based models of heterogeneity in subsurface hydrology: origins, applications, limitations, and future research questions. Rev Geophys. doi: 10.1029/2003RG000126
Narasimhan, T.N. .1982. Multidimensional numerical simulation of fluid flow in fractured porous media . Water Resour. Res. 18 .4. 1235-1247
Neuman, S.P., 2005. Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeology Journal 13 .1., 124–147.
Niemi, Auli, Kimmo Kontio, Auli Kuusela-Lahtinen 2000: Hydraulic characterization and upscaling of fracture networks based on multiple-scale well test data Water Resources Research, Vol. 36, No. 12, Pages 3481–3497, December
Odeh, A.S. .1965. Unsteady state behavior of natural fractured reservoirs. Soc. Petroleum Engineer Jour., 5 .1. 60-64
Pan Jian-Bang, Chen-Chang Lee, Cheng-Haw Lee, Hsin-Fu Yeh, Hung-I Lin .2010. Application of fracture network model with crack permeability tensor on flow and transport in fractured rock. Engineering Geology 116 166–177
Reeves, D.M., Benson, D.A., Meerschaert, M.M., 2008. Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation, Water Resource Research 44, W05404.
Snow DT .1969. Anisotropic permeability of fractured media. Water Resour Res 5:1273–1289
Streltsova-Adams, T.D. .1976a. Comments on "Analysis of pumping tests data from anisotropic unconfined aquifers considering delayed gravity response" by Shlomo P. Neumann. Water Resour. Res. 2 .1. : 113-114.
Streltsova-Adams, T.D. .1976b. Advances and uncertainties in the study of groundwater flow in fissured rocks. Adv. Groundwater Hydrol. Amer. Water Resourc. Ass. 48-56
Svensson, U., 2001a. A continuum representation of fracture networks. part I: Method and basic test cases, Journal of Hydrology 250, 170–186.
Svensson, U., 2001b. A continuum representation of fracture networks. part II: Application to the Aspo Hard Rock laboratory, Journal of Hydrology 250, 187–205.
Teutsch G, Sauter M .1991. Groundwater flow and transport processes in karst aquifers—scale effects, data provision and model validation. In: EPA/NWWA international symposium on environmental problems in Karst Terrains, Nashville
Theis, C.V. .1935. The relation between the lowering of the piezometric surface and the rate and duration of the discharge of a well using groundwater storage. Trans. Amer. Geoph. Union, .16. 519-524.
Warren, J. E. & Root, P. J. .1963. Behavior of natural fractured reservoirs. Soc. Pet. Eng. Jour. 9,: 245-255.
Wellman TP, Shapiro AM, Hill MC .2009. Effects of simplifying fracture network representation on inert chemical migration in fracture controlled aquifers. Water Resour Res 45:W01416
Wu,Y.S., Liu,H.H., Bodvarsson, G.S., 2004. A triple-continuum approach for modeling flow and transport processes in fractured rock. Journal of Containment Hydrology 73, 145–179.
Zyvoloski, G.A., Robinson, B.A., Viswanathan, H.S., 2008. Generalized dual porosity: a numerical method for representing spatially variable sub-grid scale processes. Advances in Water Resources 31, 535–544.