CWEEE  Vol.3 No.1 , January 2014
A New Space-Time CE/SE Numerical Tracking of Contaminant Transport in Fractured Stratified Geologic Profiles

To date, efficient numerical simulation of contaminant transport in geologic porous media is challenged by parametric jumps resulting from stratification and the use of ideal initial/boundary conditions. Thus, to resolve some contaminant hydrology problems, this work presents the development of the Space-Time Conservation Element/Solution Element (CE/SE) scheme for advection-dispersion-reaction a-d-r transport in geologic media. The CE/SE method derives from the native form of Gauss conservation law. Therefore, it is able to effectively handle non-trivial discontinuities that may exist within the problem domain. In freshwater aquifer, stratification and other parametric jumps are examples of such discontinuity. To simulate the Nigerian experience of nitrate pollution of freshwater aquifers; the a-d-r contaminant transport model is herein solved under a time periodic nitrate fertilizer loading condition on farmlands. Results show that this approach is able to recover the well-known field pattern of nitrate profiles under farmlands. Cyclic loading impacts more on the dispersivity of an aquifer. Hence, dispersion coefficient modulates the response of aquifers to loading frequency. However, aquifers with conductivity less than 10-6 m/day are almost insensitive to periodic loads. The CE/SE method is able to sense slight (i.e. order of 10-3) variation in hydrological parameters. Also, CE/SE computes contaminant concentration and its flux simultaneously. Thus, it facilitates a better understanding of some reported phenomena such as contaminant accumulation and localized reverse transport at the interface between fracture and matrix in geologic medium. Clearly, CE/SE is an efficient and admissible tool into the family of numerical methods available for tracking contaminant transport in porous media.

Cite this paper: Fashanu, T. and Olunloyo, V. (2014) A New Space-Time CE/SE Numerical Tracking of Contaminant Transport in Fractured Stratified Geologic Profiles. Computational Water, Energy, and Environmental Engineering, 3, 8-21. doi: 10.4236/cweee.2014.31002.

[1]   X. Wang, S. Chang and P. C. Jorgenson, “Accuracy Study of Space-Time CE/SE Methods for Computational Aero-Acoustic Problems involving Shock Waves,” Proceedings of the 38th Aerospace Sciences Meeting & Exhibition, Reno, 10-13 January 2000, AIAA2000-0865.

[2]   Y. Chen and L. J. Durlofsky, “An Adaptive Local-Global up Scaling for General Flow Scenario in Heterogeneous Formations,” Transport in Porous Media, Vol. 62, No. 2, 2006, pp. 157-185.

[3]   A. El-Zein, J. P. Carter and W. Airey, “Three-Dimensional Finite Elements for the Analysis of Soil Contamination Using a Multiple-Porosity Approach,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 30, No. 7, 2006, pp. 577-597.

[4]   R. J. LeVeque, “Numerical Methods for Conservation Laws, Lecture in Mathematics Series,” Birkhauser Verlag, Basel, 1992.

[5]   D. De Cogan and A. De Cogan, “Applied Numerical Modeling for Engineers,” Oxford University Press, New York, 1997.

[6]   J. F. Botha and J. P. Verwey, “Aquifer Test Data and Numerical Models,” In: T. F. Russell, Ed., Computational Methods in Water Resources IX, Elsevier, New York, 1992, pp. 459-466.

[7]   S. A. Sadrnejad, A. Ghasemzadeh, A. S. Ghoreishian and G. H. Montazeri, “A Control Volume Based Finite Element Method for Simulating Incompressible Two-Phase Flow in Heterogeneous Porous Media and Its Application to Reservoir Engineering,” Petroleum Science, Vol. 9, No. 4, 2012, pp. 485-497.

[8]   A. El-Zein, J. Carter and D. Airey, “Multiple-Porosity Contaminant Transport by Finite-Element Method,” International Journal of Geomechanics, Vol. 5, No. 1, 2005, pp. 24-34.

[9]   I. Herera, “Localized Adjoint Method: Topics for Further Research and Some Contributions,” In: T. F. Russell, Ed., Computational Methods in Water Resources IX, Elsevier, New York, 1992, pp. 3-17.

[10]   G. Matheron and G. De Marsily, “Is Transport in Porous Media Always Diffusive? A Counter Example,” Water Resources Research, Vol. 16, No. 5, 1980, pp. 901-917.

[11]   M. Xiang and Z. Nicholas, “A Stochastic Mixed Finite Element Heterogeneous Multi-Scale Method for Flow in Porous Media,” Journal of Computational Physics, Vol. 230, No. 12, 2011, pp. 4696-4722.

[12]   M. Ibaraki and E. A. Sudiky, “Colloids-Facilitated Contaminant Transport in Discretely Fractured Porous Media, 1. Numerical Formulation and Sensitivity Analysis,” Water Resources Research, Vol. 31, No. 12, 1995, pp. 29452960.

[13]   S. C. Chang, “The Method of Space-Time Conservation Element and Solution Element, a New Approach for Solving the Navier-Stokes and Euler Equations,” Journal of Computational Physics, Vol. 119, No. 2, 1995, pp. 295-324.

[14]   S. C. Chang, X. Wang and C. Chow, “The Space-Time Conservation Element and Solution Element Method: A New High Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws,” Journal of Computational Physics, Vol. 156, No. 1, 1999, pp. 89136.

[15]   E. A. Sudiky and E. O. Frind, “Contaminant Transport in Fractured Porous Media: Analytical Solution for a System of Parallel Fractures,” Water Resources Research, Vol. 18, No. 6, 1982, pp. 1634-1642.

[16]   K. Hutter and V. O. S. Olunloyo, “On the Distribution of Stress and Velocity in an Ice Strip, Which Is Partly Sliding over and Partly Adhering to Its Bed, by Using a Newtonian Viscous Approximation,” Proceeding Royal Society London, Vol. 373, No. 1754, 1980, pp. 385-403.

[17]   R. J. LeVeque, “A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms,” Journal of Scientific Computing, Vol. 48, No. 1-3, 2011, pp. 209-226.

[18]   L. Leonard, “Simple High-Accuracy Resolution Program for Convective Modeling of Discontinuities,” International Journal of Numerical Methods in Fluids, Vol. 8, No. 10, 1988, pp. 1291-1318.

[19]   P. Grindrod, “The Theory and Applications of Reaction Diffusion Equations: Patterns and Waves,” Oxford Applied Mathematics and Computing Series, Clarendon Press, Oxford, 1996.

[20]   S. Mallick and S. Banerji, “Nitrate Pollution of Groundwater as a Result of Agricultural Development in Indogangan Plain, India,” Quality of Groundwater; Proceedings of International Symposium Noordwijkerhunt, Netherlands, 23-28 March 1981, pp. 17-38.

[21]   J. Noorisand and M. Mehran, “An Upstream Finite Element Method for Solution of Transient Transport Equation in Porous Media,” Water Resources Research, Vol. 18, No. 3, 1982, pp. 588-596.

[22]   V. O. S. Olunloyo, O. Ibidapo-Obe and T. A. Fashanu, “An Image Processing Approach for the Characterization of Hazardous Agricultural Waste Transport in Multilayered Soils and Aquifers,” Proceedings 4th World Congress of Computers in Agriculture and Natural Resources, Orlando, 24-26 July 2006, pp. 717-726.