Yao, G.; Bliss, K. M.; Crimi, M.; Fowler, K. R.; Clark-Stone, J.; Li, W.; Evans, P. J. Radial basis function simulation of slow-release permanganate for groundwater remediation via oxidation. (English) Zbl 1382.76252 J. Comput. Appl. Math. 307, 235-247 (2016). Summary: An emerging strategy for remediation of contaminated groundwater is the use of permanganate cylinders for contaminant oxidation. The cylinders, which are only a few inches in diameter, can be placed in wells or pushed directly into the subsurface. This work focuses on the modeling and simulation of the reactive process to better understand the design of a group of cylinders for large scale contaminated sites. The underlying model is a coupled system of nonlinear partial differential equations accounting for advection, dispersion, and reactive transport for a contaminant and the permanganate in two spatial dimensions. Radial Basis Functions collocation method is used to simulate different spatial arrangements of the cylinders to understand the behavior of the system and gain insight into designing a remediation strategy for a large-scale contaminated region. Since the radial basis function collocation method is a meshless method, the locations of the cylinders are not tied to a numerical grid, making it an attractive choice for determining optimal placement. Our focus is to (1) identify a domain of influence measuring the effectiveness of the injected cylinders, (2) understand the placement for multiple cylinders required to effectively clean-up a given domain, and (3) determine a protocol for injecting multiple cylinders over time. We provide numerical results showing that domain of influence is a way to measure the effectiveness of installed cylinders. Domain of influence of one through three sources are simulated. Placement of two cylinders for an area of \(13ft\) by \(3ft\) and three sources for an area of \(26ft\) by \(6ft\) are sufficient to clean the contaminant within a reasonable time period. The average concentrations of oxidant and contaminant are simulated for the cases of a third cylinder is installed at different time and locations. MSC: 76S05 Flows in porous media; filtration; seepage 76V05 Reaction effects in flows Keywords:radial basis function; contaminant; reactive transport; chemical oxidation Software:HYDROGEOCHEM PDFBibTeX XMLCite \textit{G. Yao} et al., J. Comput. Appl. Math. 307, 235--247 (2016; Zbl 1382.76252) Full Text: DOI References: [1] Lee, E. S.; Schwartz, F. W., Characteristics and applications of controlled-release \(KMnO_4\) for groundwater remediation, Chemosphere, 66, 11, 2058-2066 (2007) [2] Christenson, M. D.; Kambhu, A.; Comfort, S. D., Using slow-release permanganate candles to remove TCE from a low permeable aquifer at a former landfill, Chemosphere, 89, 6, 680-687 (2012) [3] Kambhu, A.; Comfort, S.; Chokejaroenrat, C., Developing slow-release persulfate candles to treat BTEX contaminated groundwater, Chemosphere, 89, 6, 656-664 (2012) [4] Kang, N.; Hua, I.; Suresh, P.; Rao, C., Production and characterization of encapsulated potassium permanganate for sustained release as an in situ oxidant, Ind. Eng. Chem. Res., 43, 17, 5187-5193 (2004) [5] Rauscher, L.; Sakulthaew, C.; Comfort, S., Using slow-release permanganate candles to remediate PAH-contaminated water, J. Hazard Mater., 241-242, 441-449 (2012) [6] Ross, C.; Murdoch, L. C.; Freedman, D. L., Characteristics of potassium permanganate encapsulated in polymer, J. Environ. Eng., 131, 8, 1203-1211 (2005) [7] Brady, P. V.; Bethke, C. M., Beyond the Kd approach, Ground Water, 38, 321-322 (2000) [8] Lichtner, P. C., Contiuum model for simultaneous chemical reactions and mass transport in hydrothermal systems, Geochem. Cosmochem. Acta, 49, 779-800 (1985) [9] Gharasoo, M.; Centler, F.; Regnier, P.; Harms, H.; Thullner, M., A reactive transport modelling approach to simulate biogeochemical processes in pore structures with pore-scale heterogeneities, Environ. Modell. Softw., 30, 102-114 (2012) [10] Steefel, C. I.; Lasaga, A. C., A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems, Amer. J. Sci., 294, 529-592 (1994) [11] Yeh, G. T.; Tripathi, V. S., A critical evaluation of recent developments in hydrogeochemical transport models of reactive multi-chemical components, Water Resour. Res., 25, 93-108 (1989) [12] Wolf, G., Slow release permanganate cylinders for sustainable in situ chemical oxidation: Development of a conceptual design tool (2013), Clarkson University: Clarkson University Potsdam, NY, (M.S. Thesis) [13] Slaugh, E., Design tool for slow-release oxidant cylinders (2015), Clarkson University: Clarkson University Potsdam, NY, (Unpublished Honors Undergraduate Thesis) [14] Kansa, E. J., Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics. 2. Solutions to parabolic, hyperbolic and elliptic partial-differential equations, Comput. Math. Appl., 19, 147-161 (1990) · Zbl 0850.76048 [15] Zerroukat, M.; Power, H.; Chen, C. S., A numerical method for heat transfer problems using collocation and radial basis functions, Internat. J. Numer. Methods Engrg., 42, 1263-1278 (1998) · Zbl 0907.65095 [16] Sarler, B.; Gobin, D.; Goyeau, B.; Perko, J.; Power, H., Natural convection in porous media-dual reciprocity boundary element method solution of the Darcy model, Int. J. Numer. Methods Fluids, 33, 279-312 (2000) · Zbl 0972.76071 [17] Sarler, B., A radial basis function collocation approach in computational fluid dynamics, Comput. Model. Eng. Sci., 7, 185-193 (2005) · Zbl 1189.76380 [18] Tolstykh, A. I.; Shirobokov, D. A., On using radial basis functions in a “finite difference” mode with applications to elasticity problems, Comput. Mech., 33, 68-79 (2003) · Zbl 1063.74104 [19] Wen, P. H.; Chen, C. S., The method of particular solutions for solving scalar wave equations, Int. J. Numer. Methods Biomed. Eng., 26, 1878-1889 (2010) · Zbl 1208.65153 [20] Rocca, La; Power, H., Free mesh radial basis function collocation approach for the numerical solution of system of multi-ion electrolytes, Internat. J. Numer. Methods Engrg., 64, 13, 1699-1734 (2005) · Zbl 1113.76419 [21] Li, J.; Chen, C. S.; Peppery, D.; Chen, Y., Mesh-free method for groundwater modeling, (International Series on Advances in Boundary Elements (2002)) · Zbl 1086.76562 [22] Alhuri, Y.; Ouazar, D.; Taik, A., Comparison between local and global Mesh-free methods for Ground-Water modeling, IJCSI Int. J. Comput. Sci. Issues, 8, 2 (2011) [23] Chantasiriwan, S., Performance of Multiquadric collocation method in solving lid-driven cavity flow problem with low Reynolds number, Comput. Model. Eng. Sci., 15, 137-146 (2006) [24] Sarra, Scott A., A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains, Appl. Math. Comput., 218, 19, 9853-9865 (2012) · Zbl 1245.65144 [25] Yao, Guangming; Yu, Zeyun, A localized meshless approach for modeling spatial-temporal calcium dynamics in ventricular myocytes, Int. J. Numer. Methods Biomed. Eng., 28, 2, 187-204 (2012) · Zbl 1243.92038 [26] Lee, E. S.; Schwartz, F. W., Characterization and optimization of long-term controlled release system for groundwater remediation: a generalized modeling approach, Chemosphere, 69, 2, 247-253 (2007) [27] Roseman, T. J.; Higuchi, W. I., Release of medroxyprogesterone acetate from a silicone polymer, J. Pharm. Sci., 59, 3, 353-357 (1970) [28] Fasshauer, G. E., Solving partial differential equations by collocation with radial basis functions, (Mehaute, A. L.; Rabut, C.; Schumaker, L. L., Surface Fitting and Multiresolution Methods (1997)), 131-138 · Zbl 0938.65140 [29] Fasshauer, G. E.; Zhang, J. G., On choosing optimal shape parameters for RBF approximation, Numer. Algorithms, 45, 345-368 (2007) · Zbl 1127.65009 [30] Huang, C.-S.; Lee, C. F.; Cheng, A. H.-D., Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method, Eng. Anal. Bound. Elem., 31, 7, 614-623 (2007) · Zbl 1195.65176 [31] Wang, J. G.; Liu, G. R., On the optimal shape parameters of radial basis functions used for 2-d meshless methods, Comput. Methods Appl. Mech. Engrg., 191, 2611-2630 (2002) · Zbl 1065.74074 [32] Wertz, J.; Kansa, E. J.; Ling, L., The role of the multiquadric shape parameters in solving elliptic partial differential equations, Comput. Math. Appl., 51, 8, 1335-1348 (2006) · Zbl 1146.65078 [33] Courant, R.; Friedrichs, K.; Lewy, H., On the partial difference equations of mathematical physics, IBM J. Res. Dev., 11, 2, 215-234 (1967) · Zbl 0145.40402 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.