A numerical model of controlled bioinduced mineralization in a porous medium

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INTRODUCTION

We presents a numerical model of controlled bioinduced mineralization in a porous medium as a possible corrosion protection mechanism. Corrosion is a significant economic problem - recent reports evaluate the annual cost of metal corrosion as 3-4% of the gross domestic product (GDP), in both developed and developing countries. As an alternative corrosion control method, bioinduced deposition of protective mineral layers has been proposed [1]. Bioinduced precipitation has already been investigated for CO2 geological sequestration and soil improvement [2]. To our knowledge, though, no numerical study of biomineralization for corrosion protection has been published yet.

MICROBIALLY INFLUENCED CORROSION

Scheme of iron corrosion by Sulphate Reducing Bacteria (SRB) [3] Netto reaction: 4Fe +SO4

−2

+3HCO3+5H +1

→FeS +3FeCO3+4H2O

REACTIVE TRANSPORT

Our model includes three phases - solid, biofilm and mobile water, in the latter are dissolved the reactive elements involved in the precipitation and the

biosubstrate:

θ_w+θ_b+θ_s=1 (1)

where θw is the water content, θb is the biofilm content, and θs is the solid content. The reactive transport of solutes is described by:

∂θ_wC_i

∂t =∇⋅(Di∇Ci)−SS (2)

where Ci is the concentration, Di the diffusion coefficient and SS the source-sink term. The consumption of substrate in biofilm (such as SO4-2_{) is described} by the Monod term [4]:

R_b=−q θ_bX Cb Kb+Cb

(3) where q is the substrate utilization rate, X the concentration of bacteria, Cb concentration of substrate and Kb is the Monod constant. Change in porosity as a result of precipitation of solids such as FeS is described by:

∂θ_s ∂t =

M_s

ρ_s Rs (4)

where Ms is the molecular mass, ρs the density of the precipitate and Rs the precipitation rate.

MODEL VALIDATION

We validate the model with simple analytical solutions and against

experimental data. The image below shows a plastic container filled with sand and water, into which a steel rod has been inserted and incubated for several months. Concentration gradients of the corrosion products are clearly visible.

The container diameter is 3 cm, the steel rod has a diameter of 2 mm

OUTLOOK

Future development of the model includes multiple chemical species and reactions, multispecies biofilm that grows and detaches, varying coverage of solid grains by biofilms, and reactive solid phase. The predictive capacities of our model will be used to design experiments that will demonstrate the capacity to prevent corrosion in a porous medium by controlled bioinduced

mineralization. Developing biological corrosion protection is a first step in developing the future capacity to use Nature's constructive forces in assembling functioning structures.

REFERENCES

[1] Rongjun Zuo. Biolms: strategies for metal corrosion inhibition employing microorganisms. Applied Microbiology and Biotechnology , 76(6):1245 53, October 2007.

[2] A. Ebigbo, A. Phillips, R. Gerlach, R. Helmig, A. B. Cunningham, H. Class, and L. H. Spangler. Darcy-scale modeling of microbially induced carbonate mineral precipitation in sand columns. Water Resources Research , 48(7): W07519, July 2012.

[3] Dinh Thuy Hang. Microbiological study of the anaerobic corrosion of iron . PhD thesis, Universität Bremen, 2003.

[4] M. M. Al-Darbi, K Agha, and M R Islam. Comprehensive Modelling of the Pitting Biocorrosion of Steel. Canadian Journal of Chemical Engineering , 83 (October), 2005.

ACKNOWLEDGEMENTS

This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs, Agriculture and

Innovation. Other contributants are the Port of Rotterdam, Vopak and Deltares, to all of whom we express our gratitude.