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Slow and Fast Transport in Heap Leaching of Precious Metals

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Abstract

Heap leaching of precious metals from low-grade ores is modeled using the slow and fast zone concept of liquid movement in porous media (Kartha and Srivastava Transport in Porous Media 75, 227–247, 2008). The heap is conceptualized as a porous medium with the pores filled by liquid and/or air. The liquid phase is further divided into three zones—immobile, slow moving, and fast moving, with only the immobile and slow-moving liquids interacting with the solid particles. The conceptual model is applied to simulate two- dimensional leaching of a shallow gold ore heap. Temporal evolution of gold concentration in the solid and the liquid phases are analyzed to ascertain the effect of several parameters on the leaching process. Sensitivity analyses are performed with respect to the irrigation rate, the equilibrium sorption coefficient, and the fractional volume of the slow-moving liquid. For a constant volume of the leaching solution and for the same duration of leaching, the metal extraction is higher when a larger number of irrigation cycles are used. The metal extraction is found to be smaller for higher values of the sorption coefficient.

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Abbreviations

Ω :

Volume of an individual finite-difference cell and/or arbitrary porous medium [M0L3T0]

α im :

Solute mass transfer rate between slow and immobile liquid [M0L0T−1]

α sf :

Solute mass transfer rate between slow and fast liquid [M0L0T−1]

α*:

van-Genuchten’s parameter [M0L−1T0]

ε :

Porosity of the media [M0L0T0]

λ :

van-Genuchten’s parameter in computing permeability in Eq. (5) [M0L0T0]

Δx :

Spatial step size for finite-difference scheme [M0L1T0]

Δt :

Temporal step size for finite-difference scheme [ML−1T−1]

ρ m :

Mass of gold per unit volume of porous medium [ML−3T0]

ρ b :

Bulk density of the porous medium [ML−3T0]

ρ l :

Density of liquid [ML−3T0]

σ fs :

Saturation of the fast-moving liquid [M0L0T0]

σim :

Immobile liquid saturation in the porous medium [M0L0T0]

σ sl :

Saturation of the slow-moving liquid [M0L0T0]

σ sle :

Effective slow liquid saturation in the porous medium [M0L0T0]

A :

Area of cross section used in divergence theorem for integration [M0L2T0]

C fs :

Solute concentration in fast-moving liquid [M0L0T0]

C im :

Solute concentration in immobile liquid [M0L0T0]

C sl :

Solute concentration in slow-moving liquid [M0L0T0]

C 0 :

Solute concentration in the inflow liquid [M0L0T0]

\({D^{\ast}_{\rm f}}\) :

Dispersion coefficient in fast liquid [M0L2T]

\({D^{\ast}_{{\rm sl}}}\) :

Dispersion coefficient in slow liquid [M0L2T]

F im :

Instantaneous sorption fraction in immobile zone [M0L0T0]

F sl :

Instantaneous sorption fraction in slow liquid [M0L0T0]

K im :

Immobile equilibrium sorption coefficient [M−1L3T0]

K sl :

Equilibrium sorption coefficient in the slow liquid [M−1L3T0]

L :

Characteristic length of column [M0LT0]

M Au :

Mass of gold in porous medium [ML0T0]

P l :

Liquid pressure in the column [ML−1T−2]

Ṡ fs :

Liquid source term in the fast zone [ML−3T−1]

Ṡ sl :

Liquid source term in the slow zone [ML−3T−1]

S im1 :

Instantaneously sorbed solute concentration from immobile liquid [M0L0T0]

S im2 :

Rate-limited sorbed solute concentration from immobile liquid [M0L0T0]

S sl1 :

Instantaneously sorbed solute concentration from slow liquid [M0L0T0]

S sl2 :

Rate-limited sorbed solute concentration from slow liquid [M0L0T0]

T 0 :

Duration of input contaminant pulse at the top of the column [M0L0T]

d :

Dispersivity [M0LT0]

f :

Fraction of sorption site available for slow-moving liquid [M0L0T0]

ĝ :

Acceleration due to gravity vector [M0LT−2]

k rls :

Relative permeability for slow liquid [M0L0T0]

k im :

Sorption rate in the immobile liquid [M0L0T−1]

k sl :

Sorption rate in the slow liquid [M0L0T−1]

k ps :

Slow permeability in the liquid zone [M0L2T0]

k s :

Intrinsic permeability of the ore [M0L2T0]

̂n :

Unit outward normal vector [M0LT0]

q :

Irrigation application rate [M0LT−1]

\({{\vec{u}}_{\rm l}}\) :

Darcy discharge or Darcy velocity [M0LT−1]

\({{\vec{u}}_{{\rm fs}}}\) :

Fast component of Darcy discharge [M0LT−1]

\({{\vec{u}}_{{\rm sl}}}\) :

Slow component of Darcy discharge [M0LT−1]

t :

Time variable [M0L0T]

References

  • Bartlett R.W.: Simulation of ore heap leaching using deterministic models. Hydrometallurgy 29(1–3), 231–260 (1992)

    Article  Google Scholar 

  • Bartlett R.W.: Metal extraction from ores by heap leaching. Metall. Mater. Trans. 28, 529–545 (1997)

    Article  Google Scholar 

  • Bartlett R.W.: Solution Mining—Leaching and Fluid Recovery of Metals, 2nd edn. Taylor and Francis, New York (1998)

    Google Scholar 

  • Bear J.: Dynamics of Fluids in Porous Media. American Elsevier Publishing Company Inc., New York (1972)

    Google Scholar 

  • Bear J., Cheng A.H.D.: Modeling Groundwater Flow and Contaminant Transport. Springer, Dordrecht (2010)

    Book  Google Scholar 

  • Bedient, P.B., Rifai, H.S., Newell, C.J.: Ground Water Contamination—Transport and Remediation, 2nd edn. Prentice Hall PTR, Upper saddle River (1999)

  • Box J.C., Prosser A.P.: A general model for the reaction of several minerals and several reagents in heap and dump leaching. Hydrometallurgy 16, 77–92 (1986)

    Article  Google Scholar 

  • Brusseau M.L., Jessup R.E., Rao P.S.C.: Modeling the transport of solutes influenced by multiprocess nonequilibrium. Water Resour. Res. 25(9), 1971–1988 (1989)

    Article  Google Scholar 

  • Cariaga E., Concha F., Sepulveda M.: Flow through porous media with applications to heap leaching of copper ores. Chem. Eng. J. 111(2-3), 151–165 (2005)

    Article  Google Scholar 

  • Cross M., Bennett C.R., Croft T.N., McBride D., Gebhardt J.E.: Computational modeling of reactive multi-phase flows in porous media: Applications to metals extraction and environmental recovery processes. Miner. Eng. 19, 1098–1108 (2006)

    Article  Google Scholar 

  • de Andrade Lima L.R.P.: A mathematical model for isothermal heap and column leaching. Braz. J. Chem. Eng. 21(3), 435–447 (2004)

    Article  Google Scholar 

  • Decker D.L., Tyler S.W.: Evaluation of flow and solute transport parameters for heap leach recovery materials. J. Environ. Qual. 28, 543–555 (1999)

    Article  Google Scholar 

  • Decker D.L., Simunek J., Tyler S.W., Papelis C., Logsdon M.J.: Variably saturated reactive transport of arsenic in heap-leach facililties. Vadose Zone J. 5, 430–444 (2006)

    Article  Google Scholar 

  • Fitts C.R.: Groundwater Science. Academic Press, Elsevier, London, UK (2002)

    Google Scholar 

  • Galla, V.: Investigating unsaturated flow for heap leach materials in large diameter columns. M.S. Dissertation, University of Nevada. Proquest Information and Learning Company, Document ID 1436369881 (2007)

  • Goltz M.N., Roberts P.V.: Interpreting organic solute transport data from a field experiment using physical non-equilibrium models. J. Contam. Hydrol. 1, 77–93 (1986)

    Article  Google Scholar 

  • Kartha, S.A.: Non-ideal flow and transport in heap leaching of precious metals. Ph.D Dissertation, Indian Institute of Technology, Kanpur (2007)

  • Kartha S.A.: Non-ideal solute transport model on heap leaching of oxide copper ores. Int. J. Earth Sci. Eng. 4(06 SPL), 451–458 (2011)

    Google Scholar 

  • Kartha S.A., Srivastava R.: Effect of slow and fast moving liquid zones on solute transport in porous media. Trans. Porous Media 75, 227–247 (2008)

    Google Scholar 

  • Marsden, J.O., House, I.C.: The Chemistry of Gold Extraction, 2nd edn. SME, Littleton (2006)

  • Mclaughlin J., Agar G.E.: Development and application of a first order rate equation for modeling the dissolution of gold in cyanide solution. Miner. Eng. 4(12), 1305–1314 (1991)

    Article  Google Scholar 

  • Orr S.: Enhanced heap leaching—part 1: insights. Min. Eng. 54(9), 49–56 (2002)

    Google Scholar 

  • Orr S., Vesselinov V.: Enhanced heap leaching—part-2: applications. Min. Eng. 54(10), 33–38 (2002)

    Google Scholar 

  • Peng S.: Characterization of solute transport parameters in leach ore: inverse modeling based on column experiments. Front. Earth Sci. China 3(2), 208–213 (2009)

    Article  Google Scholar 

  • Roman R.J., Benner B.R., Becker G.W.: Diffusion model for heap leaching and its application to scale-up. Soc. Min. Eng. AIME Trans. 256, 247–252 (1974)

    Google Scholar 

  • Sánchez-Chacón A.E., Lapidus G.T.: Model for heap leaching of gold ores by cyanidation. Hydrometallurgy 44, 1–20 (1997)

    Article  Google Scholar 

  • Šimŭnek, J., Köhne, J.M., Kodešová, R., Šejna, M.: Simulating nonequilibrium movement of water, solutes, and particles using HYDRUS: a review of recent applications. Soil Water Res. 3(special issue 1), S42–S51 (2008)

    Google Scholar 

  • Suarez D.L., Šimŭnek J.: UNSATCHEM: unsaturated water and solute transport model with equilibrium and kinetic chemistry. Soil Sci. Soc. Am. J. 61, 1633–1646 (1997)

    Article  Google Scholar 

  • van Genuchten M.Th.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898 (1980)

    Article  Google Scholar 

  • Vetter K.J.: Electrochemical Kinetics—Theoretical and Experimental Aspects. Academic press, New York (1967)

    Google Scholar 

  • Wadsworth M.E., Zhu X., Thompson J.S., Pereira C.J.: Gold dissolution and activation in cyanide solution: kinetics and mechanism. Hydrometallurgy 57, 1–11 (2000)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Suresh A. Kartha

  2. Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Rajesh Srivastava

Authors
  1. Suresh A. Kartha
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  2. Rajesh Srivastava
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Correspondence to Suresh A. Kartha.

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Kartha, S.A., Srivastava, R. Slow and Fast Transport in Heap Leaching of Precious Metals. Transp Porous Med 94, 707–727 (2012). https://doi.org/10.1007/s11242-012-0020-2

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