Technical Papers
Jul 22, 2022

Single-Pipe Model of Oxygen Diffusion in Unsaturated Cement Pastes: Comprehensive Analysis of Surface, Knudsen, Bulk, Transition, and Water-Curtain Diffusion

Publication: Journal of Materials in Civil Engineering
Volume 34, Issue 10

Abstract

One of the most important factors affecting the durability of concrete structures is reinforcement corrosion, which is caused by oxygen concentration. Therefore, it is important to investigate oxygen diffusion in cement pastes. However, current research on oxygen diffusion models of unsaturated cement pastes has led to unclear conclusions. In this study, we propose a single-pipe oxygen diffusion model that considers five diffusion mechanisms: surface, Knudsen, transition, bulk, and water curtain. Further, a three-stage method is used to set up the model, and the division mode of this method is based on the mean free path (MFP) and the Mohycan model. The accuracy of the model is verified by comparing the calculated results with the experimental data. The proposed single-pipe model can be used to further analyze the durability degradation of reinforced concrete structures caused by steam, carbon dioxide, and other gases in the atmospheric environment.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

This project has been supported by the National Natural Science Foundation of China (No. 52108216), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 19KJB560004), the China Postdoctoral Science Foundation (Nos. 2019M661693 and 2021T140115), the Open Foundation of the State Key Laboratory of High Performance Civil Engineering Materials (No. 2021CEM004), the Natural Science Foundation of Shandong Province (No. 2019GSF110006), and the First-Class Discipline project funded by the Education Department of Shandong Province.

References

Abyaneh, S. D., H. S. Wong, and N. R. Buenfeld. 2013. “Modelling the diffusivity of mortar and concrete using a three-dimensional mesostructure with several aggregate shapes.” Comput. Mater. Sci. 78 (Oct): 63–73. https://doi.org/10.1016/j.commatsci.2013.05.024.
Androutsopoulos, G. P., and C. E. Salmas. 2000. “Tomography of macro-meso-pore structure based on mercury porosimetry hysteresis loop scanning—Part II: MP hysteresis loop scanning along the overall retraction line.” Chem. Eng. Commun. 181 (1): 137–177. https://doi.org/10.1080/00986440008912819.
Bajja, Z., W. Dridi, B. Larbi, and P. Le Bescop. 2015. “The validity of the formation factor concept from through-out diffusion tests on Portland cement mortars.” Cem. Concr. Compos. 63 (Oct): 76–83. https://doi.org/10.1016/j.cemconcomp.2015.07.014.
Berger, F., and I. Dékány. 2001. “Multilayer adsorption on solid surfaces: Calculation of layer thickness on the basis of the athermal parallel layer model.” J. Colloid Interface Sci. 243 (1): 37–45. https://doi.org/10.1006/jcis.2001.7741.
Boher, C., F. Frizon, S. Lorente, and F. Bart. 2013. “Influence of the pore network on hydrogen diffusion through blended cement pastes.” Cem. Concr. Compos. 37 (Mar): 30–36. https://doi.org/10.1016/j.cemconcomp.2012.12.009.
Boumaaza, M., B. Huet, G. Pham, P. Turcry, A. Aït-Mokhtar, and C. Gehlen. 2018. “A new test method to determine the gaseous oxygen diffusion coefficient of cement pastes as a function of hydration duration, microstructure, and relative humidity.” Mater. Struct. 51 (2): 1–17. https://doi.org/10.1617/s11527-018-1178-z.
Castellote, M., C. Alonso, C. Andrade, G. A. Chadbourn, and C. L. Page. 2001. “Oxygen and chloride diffusion in cement pastes as a validation of chloride diffusion coefficients obtained by steady-state migration tests.” Cem. Concr. Res. 31 (4): 621–625. https://doi.org/10.1016/S0008-8846(01)00469-0.
Chai, D., G. Yang, Z. Fan, and X. Li. 2019. “Gas transport in shale matrix coupling multilayer adsorption and pore confinement effect.” Chem. Eng. J. 370 (Aug): 1534–1549. https://doi.org/10.1016/j.cej.2019.03.276.
Chen, Y. D., and R. T. Yang. 1991. “Concentration dependence of surface diffusion and zeolitic diffusion.” AIChE J. 37 (10): 1579–1582. https://doi.org/10.1002/aic.690371015.
Choi, J. G., D. D. Do, and H. D. Do. 2001. “Surface diffusion of adsorbed molecules in porous media: Monolayer, multilayer, and capillary condensation regimes.” Ind. Eng. Chem. Res. 40 (19): 4005–4031. https://doi.org/10.1021/ie010195z.
Cussler, E. L. 2009. Diffusion: Mass transfer in fluid systems. Cambridge, UK: Cambridge University Press.
Czanderna, A. W. 1977. “Isosteric heat of adsorption of oxygen on silver.” J. Vac. Sci. Technol. 14 (1): 408–411. https://doi.org/10.1116/1.569243.
Fu, C., Y. Ling, and K. Wang. 2020. “An innovation study on chloride and oxygen diffusions in simulated interfacial transition zone of cementitious material.” Cem. Concr. Compos. 110 (Jul): 103585. https://doi.org/10.1016/j.cemconcomp.2020.103585.
Houst, Y. F., and F. H. Wittmann. 1994. “Influence of porosity and water content on the diffusivity of CO2 and O2 through hydrated cement paste.” Cem. Concr. Res. 24 (6): 1165–1176. https://doi.org/10.1016/0008-8846(94)90040-X.
Hu, Z., and E. F. Vansant. 1995. “Carbon molecular sieves produced from walnut shell.” Carbon 33 (5): 561–567. https://doi.org/10.1016/0008-6223(94)00141-L.
Hussain, R. R., and T. Ishida. 2010. “Development of numerical model for FEM computation of oxygen transport through porous media coupled with micro-cell corrosion model of steel in concrete structures.” Comput. Struct. 88 (9–10): 639–647. https://doi.org/10.1016/j.compstruc.2010.02.008.
Hussain, R. R., and T. Ishida. 2012. “Multivariable empirical analysis of coupled oxygen and moisture for potential and rate of quantitative corrosion in concrete.” J. Mater. Civ. Eng. 24 (7): 950–958. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000474.
Hwang, S.-T., and K. Kammermeyer. 1966. “Surface diffusion in microporous media.” Can. J. Chem. Eng. 44 (2): 82–89. https://doi.org/10.1002/cjce.5450440206.
Ibrahim, M., A. S. Al-Gahtani, M. Maslehuddin, and F. H. Dakhil. 1999. “Use of surface treatment materials to improve concrete durability.” J. Mater. Civ. Eng. 11 (1): 36–40. https://doi.org/10.1061/(ASCE)0899-1561(1999)11:1(36).
Isgor, O. B., and A. G. Razaqpur. 2004. “Finite element modeling of coupled heat transfer, moisture transport and carbonation processes in concrete structures.” Cem. Concr. Compos. 26 (1): 57–73. https://doi.org/10.1016/S0958-9465(02)00125-7.
Jiang, J., Y. Yuan, Q. Zeng, and T. Mo. 2013. “Relationship of moisture content with temperature and relative humidity in concrete.” Mag. Concr. Res. 65 (24): 1494–1496. https://doi.org/10.1680/macr.13.00211.
Jiang, Z., Y. Xi, X. Gu, Q. Huang, and W. Zhang. 2017. “Mesoscopic predictions of cement mortar diffusivity by analytical and numerical methods.” J. Mater. Civ. Eng. 29 (4): 04016256. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001805.
Kobayashi, K., and K. Shuttoh. 1991. “Oxygen diffusivity of various cementitious materials.” Cem. Concr. Res. 21 (2–3): 273–284. https://doi.org/10.1016/0008-8846(91)90009-7.
Krishna, R., and J. M. van Baten. 2012. “Investigating the validity of the Bosanquet formula for estimation of diffusivities in mesopores.” Chem. Eng. Sci. 69 (1): 684–688. https://doi.org/10.1016/j.ces.2011.11.026.
Li, N. 2002. “Active control of oxygen in molten lead–bismuth eutectic systems to prevent steel corrosion and coolant contamination.” J. Nucl. Mater. 300 (1): 73–81. https://doi.org/10.1016/S0022-3115(01)00713-9.
Liu, C., Z. Liu, and Y. Zhang. 2020. “A multi-scale framework for modelling effective gas diffusivity in dry cement paste: Combined effects of surface, Knudsen and molecular diffusion.” Cem. Concr. Res. 131 (May): 106035. https://doi.org/10.1016/j.cemconres.2020.106035.
May, H. B., I. Lauder, and R. Wollast. 1974. “Oxygen diffusion coefficients in alkali silicates.” J. Am. Ceram. Soc. 57 (5): 197–200. https://doi.org/10.1111/j.1151-2916.1974.tb10857.x.
Miao, Y., X. Li, J. Lee, Y. Zhou, K. Wu, Z. Sun, and S. Liu. 2018. “A new rate-decline analysis of shale gas reservoirs: Coupling the self-diffusion and surface diffusion characteristics.” J. Pet. Sci. Eng. 163 (Apr): 166–176. https://doi.org/10.1016/j.petrol.2017.12.097.
Ngala, V. T., and C. L. Page. 1997. “Effects of carbonation on pore structure and diffusional properties of hydrated cement pastes.” Cem. Concr. Res. 27 (7): 995–1007. https://doi.org/10.1016/S0008-8846(97)00102-6.
Pitre, L., M. D. Plimmer, F. Sparasci, and M. E. Himbert. 2019. “Determinations of the Boltzmann constant.” C. R. Phys. 20 (1–2): 129–139. https://doi.org/10.1016/j.crhy.2018.11.007.
Pollard, W., and R. D. Present. 1948. “On gaseous self-diffusion in long capillary tubes.” Phys. Rev. 73 (7): 762–774. https://doi.org/10.1103/PhysRev.73.762.
Raupach, M. 1996. “Investigations on the influence of oxygen on corrosion of steel in concrete—Part I.” Mater. Struct. 29 (3): 174–184. https://doi.org/10.1007/BF02486163.
Remick, R. R., and C. J. Geankoplis. 1974. “Ternary diffusion of gases in capillaries in the transition region between Knudsen and molecular diffusion.” Chem. Eng. Sci. 29 (6): 1447–1455. https://doi.org/10.1016/0009-2509(74)80169-7.
Ruther, W. E., and S. Greenberg. 1964. “Corrosion of steels and nickel alloys in superheated steam.” J. Electrochem. Soc. 111 (10): 1116–1121. https://doi.org/10.1149/1.2425932.
Satsuma, A., D. Yang, and K.-I. Shimizu. 2011. “Effect of acidity and pore diameter of zeolites on detection of base molecules by zeolite thick film sensor.” Microporous Mesoporous Mater. 141 (1–3): 20–25. https://doi.org/10.1016/j.micromeso.2009.12.002.
Schwiete, H. E., H. J. Bohme, and U. Ludwig. 1969. “Measuring gas diffusion for the valuation of open porosity on mortars and concretes.” Matér. Constr. 2 (1): 43–48. https://doi.org/10.1007/BF02473654.
Scrivener, K. L., A. K. Crumbie, and P. Laugesen. 2004. “The interfacial transition zone (ITZ) between cement paste and aggregate in concrete.” Interface Sci. 12 (4): 411–421. https://doi.org/10.1023/B:INTS.0000042339.92990.4c.
Sercombe, J., R. Vidal, C. Gallé, and F. Adenot. 2007. “Experimental study of gas diffusion in cement paste.” Cem. Concr. Res. 37 (4): 579–588. https://doi.org/10.1016/j.cemconres.2006.12.003.
Shafiq, N., and J. G. Cabrera. 2004. “Effects of initial curing condition on the fluid transport properties in OPC and fly ash blended cement concrete.” Cem. Concr. Compos. 26 (4): 381–387. https://doi.org/10.1016/S0958-9465(03)00033-7.
Sikora, P., M. Abd Elrahman, S. Y. Chung, K. Cendrowski, E. Mijowska, and D. Stephan. 2019. “Mechanical and microstructural properties of cement pastes containing carbon nanotubes and carbon nanotube-silica core-shell structures, exposed to elevated temperature.” Cem. Concr. Compos. 95 (Jan): 193–204. https://doi.org/10.1016/j.cemconcomp.2018.11.006.
Sladek, K. J., E. R. Gilliland, and R. F. Baddour. 1974. “Diffusion on surfaces. II. Correlation of diffusivities of physically and chemically adsorbed species.” Ind. Eng. Chem. Fundam. 13 (2): 100–105. https://doi.org/10.1021/i160050a002.
Sun, J., Z. Liu, and D. Cao. 2019. “A permeation model of shale gas in cylindrical-like kerogen pores at geological conditions.” Chem. Eng. Sci. 207 (Nov): 457–463. https://doi.org/10.1016/j.ces.2019.06.048.
Thorstenson, D. C., and D. W. Pollock. 1989. “Gas transport in unsaturated zones: Multicomponent systems and the adequacy of Fick’s laws.” Water Resour. Res. 25 (3): 477–507. https://doi.org/10.1029/WR025i003p00477.
Tittarelli, F. 2009. “Oxygen diffusion through hydrophobic cement-based materials.” Cem. Concr. Res. 39 (10): 924–928. https://doi.org/10.1016/j.cemconres.2009.06.021.
Tomadakis, M. M., and D. Rupani. 2007. “Diffusion controlled reaction rate, survival probability, and molecular trajectory characteristics in the bulk, transition and Knudsen regime.” Chem. Eng. J. 128 (1): 1–10. https://doi.org/10.1016/j.cej.2006.10.005.
Tomadakis, M. M., and S. V. Sotirchos. 1993. “Ordinary, transition, and Knudsen regime diffusion in random capillary structures.” Chem. Eng. Sci. 48 (19): 3323–3333. https://doi.org/10.1016/0009-2509(93)80149-K.
Vu, T. H., F. Frizon, and S. Lorente. 2009. “Architecture for gas transport through cementitious materials.” J. Phys. D: Appl. Phys. 42 (10): 105501. https://doi.org/10.1088/0022-3727/42/10/105501.
Wang, L., Z. Zeng, L. Zhang, L. Qiao, Y. Zhang, and Y. Lu. 2018. “A new boundary scheme for simulation of gas flow in kerogen pores with considering surface diffusion effect.” Physica A 495 (Apr): 180–190. https://doi.org/10.1016/j.physa.2017.12.028.
Wang, P., R. Mo, S. Li, J. Xu, Z. Jin, T. Zhao, and D. Wang. 2021a. “A chemo-damage-transport model for chloride ions diffusion in cement-based materials: Combined effects of sulfate attack and temperature.” Constr. Build. Mater. 288 (Jun): 123121. https://doi.org/10.1016/j.conbuildmat.2021.123121.
Wang, P., R. Mo, X. Zhou, J. Xu, Z. Jin, and T. Zhao. 2021b. “A chemo-thermo-damage-transport model for concrete subjected to combined chloride-sulfate attack considering the effect of calcium leaching.” Constr. Build. Mater. 306 (Nov): 124918. https://doi.org/10.1016/j.conbuildmat.2021.124918.
Wong, H. S., M. Zobel, N. R. Buenfeld, and R. W. Zimmerman. 2009. “Influence of the interfacial transition zone and microcracking on the diffusivity, permeability and sorptivity of cement-based materials after drying.” Mag. Concr. Res. 61 (8): 571–589. https://doi.org/10.1680/macr.2008.61.8.571.
Wu, K., Z. Chen, X. Li, C. Guo, and M. Wei. 2016a. “A model for multiple transport mechanisms through nanopores of shale gas reservoirs with real gas effect–adsorption-mechanic coupling.” Int. J. Heat Mass Transfer 93 (Feb): 408–426. https://doi.org/10.1016/j.ijheatmasstransfer.2015.10.003.
Wu, K., X. Li, C. Guo, C. Wang, and Z. Chen. 2016b. “A unified model for gas transfer in nanopores of shale-gas reservoirs: Coupling pore diffusion and surface diffusion.” SPE J. 21 (5): 1583–1611. https://doi.org/10.2118/2014-1921039-PA.
Wu, K., X. Li, C. Wang, W. Yu, and Z. Chen. 2015. “Model for surface diffusion of adsorbed gas in nanopores of shale gas reservoirs.” Ind. Eng. Chem. Res. 54 (12): 3225–3236. https://doi.org/10.1021/ie504030v.
Xu, J., and F. Li. 2018. “Meso-scale analysis of concrete chloride diffusion considering skins.” ACI Mater. J. 115 (4): 605–614. https://doi.org/10.14359/51702195.
Yang, F., J. Gu, L. Ye, Z. Zhang, G. Rao, Y. Liang, K. Wen, J. Zhao, J. B. Goodenough, and W. He. 2016. “Justifying the significance of Knudsen diffusion in solid oxide fuel cells.” Energy 95 (Jan): 242–246. https://doi.org/10.1016/j.energy.2015.12.022.
Yang, P., C. Shi, Z. Gong, and X. Tan. 2019. “Numerical study on water curtain system for fire evacuation in a long and narrow tunnel under construction.” Tunnell Underground Space Technol. 83 (Jan): 195–219. https://doi.org/10.1016/j.tust.2018.10.005.
Yu, S. W., and C. L. Page. 1991. “Diffusion in cementitious materials: 1. Comparative study of chloride and oxygen diffusion in hydrated cement pastes.” Cem. Concr. Res. 21 (4): 581–588. https://doi.org/10.1016/0008-8846(91)90109-U.
Yuan, W., Z. Pan, X. Li, Y. Yang, C. Zhao, L. D. Connell, S. Li, and J. He. 2014. “Experimental study and modelling of methane adsorption and diffusion in shale.” Fuel 117 (Jan): 509–519. https://doi.org/10.1016/j.fuel.2013.09.046.
Zalc, J. M., S. C. Reyes, and E. Iglesia. 2004. “The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures.” Chem. Eng. Sci. 59 (14): 2947–2960. https://doi.org/10.1016/j.ces.2004.04.028.
Zheng, J. 2013. “Effective medium approach for evaluating the oxygen diffusivity of concrete.” J. Mater. Civ. Eng. 25 (6): 711–717. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000569.
Zheng, J., J. Zhang, X. Zhou, and X. Wang. 2019. “Numerical method for predicting chloride diffusivity of mature cement paste.” J. Mater. Civ. Eng. 31 (6): 04019080. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002713.

Information & Authors

Information

Published In

Go to Journal of Materials in Civil Engineering
Journal of Materials in Civil Engineering
Volume 34Issue 10October 2022

History

Received: Mar 28, 2021
Accepted: Jan 31, 2022
Published online: Jul 22, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 22, 2022

Permissions

Request permissions for this article.

Authors

Affiliations

Postdoctoral Researcher, School of Materials Science and Engineering, Southeast Univ., Nanjing, Jiangsu 211189, China; Lecturer, College of Civil Engineering and Architecture, Jiangsu Univ. of Science and Technology, Zhenjiang, Jiangsu 212003, China. Email: [email protected]
Master’s Candidate, School of Civil Engineering, Qingdao Univ. of Technology, Qingdao, Shandong 266033, China. Email: [email protected]
Associate Professor, School of Civil Engineering, Qingdao Univ. of Technology, Qingdao, Shandong 266033, China (corresponding author). ORCID: https://orcid.org/0000-0002-6066-7734. Email: [email protected]
Guihua Wang [email protected]
Lecturer, School of Civil Engineering, Baicheng Normal Univ., Baicheng, Jilin 137000, China. Email: [email protected]
Professor, School of Materials Science and Engineering, Southeast Univ., Nanjing, Jiangsu 211189, China. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share