×

A control volume finite element method for adaptive mesh simulation of flow in heap leaching. (English) Zbl 1359.76188

Summary: Accurate determination of fluid flow within heap leaching is crucial for understanding and improving performance of the process. Numerical methods have the potential to assist by modelling the process and studying the transport phenomena within the porous medium. This paper presents an adaptive mesh numerical scheme to solve for unsaturated incompressible flow in porous media with applications to heap leaching. The governing equations are Darcy’s law and the conservation of mass. An implicit pressure explicit saturation method is used to decouple the pressure and saturation equations. Pressure is discretized using a control volume (CV) finite element method, while for saturation a node-centred CV method is employed. The scheme is equipped with dynamic anisotropic mesh adaptivity to update the mesh resolution as the leaching solution infiltrates through the heap. This allows for high-fidelity modelling of multiscale features within the flow. The method is verified against the Buckley-Leverett problem where a quasi-analytical solution is available. It is applied for two-phase flow of air and leaching solution in a simplified two-dimensional heap geometry. We compare the accuracy and CPU efficiency of an adaptive mesh against a static mesh and demonstrate the potential to achieve high spatial accuracy at low computational cost through the use of anisotropic mesh adaptivity.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Software:

Fluidity
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Bear J (1998) Dynamics of fluids in porous media. Elsevier, New York · Zbl 1191.76001
[2] Aziz K, Settari A (1979) Petroleum reservoir simulation. Applied Science Publishers, London
[3] van Zyl DJA, Hutchison IPG, Kiel JE (1988) Introduction to evaluation, design, and operation of precious metal heap leaching projects. Society of Mining Engineers, Littleton
[4] Gupta A, Yan D (2006) Mineral processing design and operation: an introduction. Elsevier Science
[5] Weiss NL (1985) Mineral processing handbook. Society of Mining Engineers of AIME, New York
[6] Hills RG, Porro I, Hudson DB, Wierenga PJ (1989) Modeling one-dimensional infiltration into very dry soils: 1. Model development and evaluation. Water Resour Res 25(6):1259-1269 · doi:10.1029/WR025i006p01259
[7] Kirkland MR, Hills RG, Wierenga PJ (1992) Algorithms for solving Richards’ equation for variably saturated soils. Water Resour Res 28(8):2049-2058 · doi:10.1029/92WR00802
[8] Pan L, Warrick AW, Wierenga PJ (1996) Finite element methods for modeling water flow in variably saturated porous media: numerical oscillation and mass-distributed schemes. Water Resour Res 32(6):1883-1889 · doi:10.1029/96WR00753
[9] Munoz J, Rengifo P, Vauclin M (1997) Acid leaching of copper in a saturated porous material: parameter identification and experimental validation of a two-dimensional transport model. J Contam Hydrol 27(1):1-24 · doi:10.1016/S0169-7722(96)00050-2
[10] McBride D, Gebhardt JE, Cross M (2012) A comprehensive gold oxide heap leach model: development and validation. Hydrometallurgy 113-114:98-108 · doi:10.1016/j.hydromet.2011.12.003
[11] Cariaga E, Concha F, Sepúlveda M (2005) Flow through porous media with applications to heap leaching of copper ores. Chem Eng J 111(2):151-165 · Zbl 1173.76333 · doi:10.1016/j.cej.2005.02.019
[12] Bennett CR, McBride D, Cross M, Gebhardt JE (2012) A comprehensive model for copper sulphide heap leaching: Part 1 basic formulation and validation through column test simulation. Hydrometallurgy 127-128:150-161 · doi:10.1016/j.hydromet.2012.08.004
[13] Croft TN, Pericleous K, Cross M (1995) Physica: a multi-physics environment for complex flow processes. In: Taylor C et al (eds) Numerical methods laminar and turbulent flow’95, pp 1269-1280
[14] Bennett CR, Cross M, Croft TN, Uhrie JL, Green CR, Gebhardt JE (2003) A comprehensive copper stockpile leach model: background and model formulation. In: Hydrometallurgy 2003: 5th international symposium honoring Professor Ian M. Ritchie, leaching and solution purification, pp 315-328
[15] Wu A, Liu J, Yin S, Wang H (2010) Analysis of coupled flow-reaction with heat transfer in heap bioleaching processes. Appl Math Mech 31(12):1473-1480 · Zbl 1205.35234 · doi:10.1007/s10483-010-1377-7
[16] Leahy MJ, Schwarz MP (2009) Modelling jarosite precipitation in isothermal chalcopyrite bioleaching columns. Hydrometallurgy 98(1):181-191 · doi:10.1016/j.hydromet.2009.04.017
[17] McBride D, Cross M, Croft N, Bennett CR, Gebhardt JE (2006) Computational modelling of variably saturated flow in porous media with complex three-dimensional geometries. Int J Numer Methods Fluids 50(9):1085-1117 · Zbl 1138.76438 · doi:10.1002/fld.1087
[18] Pain CC, Umpleby AP, De Oliveira CRE, Goddard AJH (2001) Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Comput Methods Appl Mech Eng 190(29):3771-3796 · Zbl 1008.76041 · doi:10.1016/S0045-7825(00)00294-2
[19] Piggott MD, Gorman GJ, Pain CC, Allison PA, Candy AS, Martin BT, Wells MR (2008) A new computational framework for multi-scale ocean modelling based on adapting unstructured meshes. Int J Numer Methods Fluids 56(8):1003-1015 · Zbl 1220.76045 · doi:10.1002/fld.1663
[20] AMCG (2012) Fluidity manual. Department of Earth Science and Engineering, Imperial College London, London
[21] Davies DR, Wilson CR, Kramer SC (2011) Fluidity: a fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics. Geochem Geophys Geosyst 12(6):Q06001 · doi:10.1029/2011GC003551
[22] Pain CC, Mansoorzadeh S, De Oliveira CRE, Goddard AJ (2001) Numerical modelling of gas solid fluidized beds using the two-fluid approach. Int J Numer Methods Fluids 36(1):91-124 · Zbl 0991.76087 · doi:10.1002/fld.132
[23] Buckley SE, Leverett MC (1942) Mechanism of fluid displacement in sands. Trans AIME 146(1337):107-116 · doi:10.2118/942107-G
[24] Mostaghimi P, Blunt MJ, Bijeljic B (2013) Computations of absolute permeability on micro-CT images. Math Geosci 45(1):103-125 · doi:10.1007/s11004-012-9431-4
[25] Carman PC (1937) Fluid flow through granular beds. Trans Inst Chem Eng 15:150-166
[26] Garcia X, Akanji LT, Blunt MJ, Matthai SK, Latham JP (2009) Numerical study of the effects of particle shape and polydispersity on permeability. Phys Rev E 80(2):021304 · doi:10.1103/PhysRevE.80.021304
[27] Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Hydrology papers. Colorado State University, Fort Collins
[28] Ilankoon IMSK, Neethling SJ (2012) Hysteresis in unsaturated flow in packed beds and heaps. Miner Eng 35:1-8 · doi:10.1016/j.mineng.2012.05.007
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.