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Analytical Solutions for Solute Transport from two-point Sources along Porous Media Flow with Spatial Dispersity involving Flexible Boundary Inputs, initial Distributions and Zero-order Productions | ||
| Pollution | ||
| دوره 8، شماره 4، مهر 2022، صفحه 1398-1417 اصل مقاله (1.44 M) | ||
| نوع مقاله: Original Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/poll.2022.339642.1398 | ||
| نویسندگان | ||
| Thomas Tjock-Mbaga* 1؛ Patrice Ele Abiama1، 2؛ Jean Marie Ema'a Ema'a3؛ Germain Hubert Ben-Bolie1 | ||
| 1Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Cameroon | ||
| 2Nuclear Technology Section, Energy Research Laboratory, Institute of Geological and Mining Research, Yaounde, Cameroon | ||
| 3Higher Teacher Training College, Department of physics, University of Bertoua, P.O. Box 652, Cameroun | ||
| چکیده | ||
| This study derives an analytical solution of a one-dimensional (1-D) Advection-Dispersion Equation (ADE) for solute transport with two contaminant sources incorporating the source term. Groundwater velocity is considered as a linear function of space while the dispersion as a nth power of velocity and analytical solutions are obtained for , and . The solution is derived using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). Analytical solutions are compared with numerical solutions obtained in MATLAB pedpe solver and are found to be in good agreement. The obtained solutions are illustrated for linear combination of exponential input distribution and its particular cases. The dispersion coefficient and temporal variation of the source term on the solute distribution are demonstrated graphically for the set of input data based on similar data available in the literature. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public for such problem. | ||
| کلیدواژهها | ||
| Advection, Dispersion؛ Groundwater؛ Analytical solution؛ Two sources | ||
| مراجع | ||
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Almeida, A. R. and Cotta, R. M. (1995). Integral transform methodology for convection-diffusion problems in petroleum reservoir engineering. Int. J. Heat Mass Transfer, 38(18); 3359-3367. Bharati, V. K., Singh, V. P., Sanskrityayn, A. and Kumar, N. (2017). Analytical solution of advection diffusion equation with spatially dependent dispersivity. J. Eng. Mech., 143(11); 1–11. Bharati, V. K., Singh, V. P., Sanskrityayn, A. and Kumar, N. (2018). Analytical solutions for solute transport from varying pulse source along porous media flow with spatial dispersivity in fractal & Euclidean framework. Eur. J. Mech. B Fluids, 72; 410–421. Bharati, V. K., Singh, V. P., Sanskrityayn, A. and Kumar, N. (2019). Analytical solution for solute transport from a pulse point source along a medium having concave/convex spatial dispersivity within fractal and Euclidean framework. J. Earth Syst. Sci., 128(203). Carntrell, K. J., Serne, R. J. and Last, G. V. (2003). Hanford contaminant distribution coefficient database and users guide. U.S. department of Energy under contract DE-AC06-76RL01830, Pacific Northwest National laboratory Richland Washington 99352. PNNL-13895 Rev. 1. Chaudhary, M., Kumar, Thakur, C. and Kumar Singh, M. (2020). Analysis of 1-D pollutant transport in semi-infinite groundwater reservoir. Environmental Earth Sciences (2020) 79(24). Chen, J. S., Chen, J. T., Liu, C. W., Liang, C. P. and Lin, C. W. (2011). Analytical solutions to two-dimensional advection–dispersion equation in cylindrical coordinates in finite domain subject to first- and third-type inlet boundary conditions. J. Hydrol., 405; 522-531. Chen, J. S. and Liu, C. W. (2011). Generalized analytical solution for advection-dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition. Hydrol. Earth Syst. Sci., 15(8); 2471-2479. Chen, J. S., Liang, J. P., Chang, C. H. and Ming-Hsien (2019). Wan simulating three-dimensional plume migration of a radionuclide decay chain through groundwater. Energies, 2019 12(3740). Cotta, R. M. (1993). Integral Transforms in Computational Heat and Fluid Flow. CRC Press, Boca Raton, FL. Cotta, R. M. and Mikhailov, M. D. (1997). Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computations. Wiley-Interscience, New York (1997). Crank, J. (1975). The Mathematics of Diffusion. Oxford Univ. Press London, 2nd ed. Freeze, R. A. and Cherry, J. A. (1979). Groundwater, Prentice Hall, Englewood Cliffs, NJ. ICRP. Compendium of Dose Coefficients based on ICRP Publication 60; ICRPP ublication: Ottawa, ON, Canada, 2012. Kumar, A. and Yadav, R. R. (2014). One-dimensional solute transport for uniform and varying pulse type input point source through heterogeneous medium. Environmental technology. Kumar, R., Chatterjee, A., Singh, M. K. and Singh, V. P. (2019). Study of solute dispersion with source/sink impact in semi-infinite porous medium. Pollution, 6(1); 87-98. Liu, C., Ball, W. P. and Ellis, J. H. (1998). An analytical solution to one-dimensional solute advection-dispersion equation in multi-layer porous media. Transp. Porous Media, 30; 25-43. Liu, C., Szecsody, J. E., Zachara, J. M. and Ball, W. P. (2000). Use of the generalized integral transform method for solving equations of solute transport in porous media. Adv. Water Resour., 23; 483–492. Manger, G. E. (1963). Porosity and bulk density of sedimentary rocks. U.S. Atomic Energy Commission USGPO, Washington, D.C. Mazarheti, M. Samani, J. M. V. and Samani, H. M. V. (2013). Analytical solution to one-dimensional advection-diffusion equation with several point sources through arbitrary time-dependent emission rate patterns. J. Agr. Sci. Tech., 15; 1231-1245. Moranda, A., Cianci, R. and Paladino, O. (2018). Analytical solutions of one-dimensional contaminant transport in soils with source production-decay. Soil Syst., 2018, 2(40). Ozisik, M. N. (1980). Heat Conduction. Wiley, New York. Ozisik, M. N. (1993). Heat Conduction. John Wiley and Sons Inc., New York. Pang, L., Hunt, B., 2001. Solutions and verification of a scale-dependent dispersion model. J. Contam. Hydrol., 53 (12); 2139. Park, E. and Zhan, H. (2001). Analytical solution of contaminant transport from one-, two-, and three-dimensional sources in a finite-thickness aquifer. J. Contam. Hydrol., 53; 41-61. Pérez, Guerrero, J. S., Pimentel, L. C. G., Skaggs, T. H. and van Genuchten, M. Th. (2009). Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique. Int. J. Heat Mass Transfer, 52(1314); 3297–3304. Pérez, Guerrero, J. S. and Skaggs, T. H. (2010). Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients. J. Hydrol., 390 (2010) 5765. Paladino, O., Moranda, A., Massabò, M. and Robbins, G. A. (2018). Analytical Solutions of Three-Dimensional Contaminant Transport Models with Exponential Source Decay. Groundwater, 2018 56; 6–108.. Sanskrityayn, A. and Kumar, N. (2016). Analytical solution of advection-diffusion equation in heterogeneous infinite medium using Green’s function method. J. Earth Syst Sci., 125(8); 1713-1723. Sanskrityayn, A., Suk, H. and Kumar, N. (2017). Analytical solutions for solute transport in groundwater and riverine flow using Green’s Function Method and pertinent coordinate transformation method. J. Hydrol., 2017, 547; 517–533. Sanskrityayn, A., Singh, V. P., Bharati, V. K. and Kumar, N. (2018). Analytical solution of two-dimensional advection-dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method. Environ. Fluid Mech., 18; 739–757. Serrano, S. E. (1992). The form of the dispersion equation under recharge and variable velocity, and its analytical solution. Water Resour. Res., 28(7); 1801-1808. Sim, Y. and Chrysikopoulos, C. V. (1996). One-dimensional virus transport in porous media with time-dependent inactivation rate coefficients. Water Resour. Res., 32(8); 2607–2611. Singh, M. K. and Kumari, P. (2014). Contaminant concentration prediction along unsteady groundwater flow. In: Basu SK, Kumar N (eds) Modelling and simulation of diffusive processes. Springer, Cham, 257–275. Singh, M. K. and Das, P. (2015). Scale dependent solute dispersion with linear isotherm in heterogeneous medium. J. Hydrol., 520; 289–299. Skaggs, T. H. and Leij, F. J. (2002). Solute Transport: Theoretical Background. In J. H., Dane, C. G. Topp (Eds), Method of soil analysis, Part 4 Physical methods, SSSA Books series, 5; 1353-1380, SSSA Madison, WI (Chapter 6.3). Skaggs, T. H., Jarvis, N. J., Pontedeiro, E. M., van Genuchten, M. Th. and Cotta, R. M. (2007). Analytical advection-dispersion model for transport ant plant uptake of contaminants in the root zone. Vardose Zone J., 6(1). Su, N., Sander, G. C., Liu, F. and Anh, Barry, D. A. (2005). Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity. Applied Mathematical Modelling, 29(9); 852–870. Suk, H. (2013). Developing semi-analytical solutions for multispecies transport coupled with a sequential first-order reaction network under variable flow velocities and dispersion coefficients. Water Resour. Research, 49; 3044–3048. Thakur, C. K., Chaudhary, M., van der Zee S. E. A. T. M. and Singh, M. K. (2019). Two-dimensional solute transport with exponential initial concentration distribution and varying flow velocity. Pollution, 5(4); 721-737. Van Genuchten, M. Th. (1981). Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay. J. Hydrol., 49(3-4); 213-233. Van Genuchten, M. Th. and Alves, W. J. (1982). Analytical solutions of the one-dimensional convective-dispersive solute transport equation. U S Dept. Ag. Tech. Bull. N°. 1661; 1-51. Van Genuchten, M. Th. (1985). Convective-dispersive transport of solutes involved in sequential first-order decay reactions. Comput. Geosci., 11; 129–147. Yadav, R. R. and Kumar, L. K. (2019). Solute transport for pulse type input point source along temporally and spatially dependent flow. Pollution, 5(1); 53-70, Winter 2019. Yates, S. R. (1992). An analytical solution for one-dimensional transport in porous media with an experimental dispersion function. Water Resources Research, .28(8); 2149-2154. Yu, C., Zhou, M., Ma, J., Cai, X. and Fang, D. (2019). Application of the homotopy analysis method to multispecies reactive transport equations with general initial conditions. Hydrogeology Journal, https://doi.org/10.1007/s10040-019-01948-7. Zhan, H., Wen, Z., Huang, G. and Sun, D. (2009). Analytical solution of two dimensional solute transports in an aquifer-aquitard system. J. Contaminant Hydrol., 107; 162-174. Zoppou, C. and Knight, J. H. (1997). Analytical solutions for advection and advection diffusion equation with spatially variable coefficients. Journal of Hydraulic Engineering, 123; 144-148. | ||
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