Abstract
3D printing technology offers an innovative approach to manufacture rock samples with controlled properties. However, in this process, pore structure is one of the major concerns when printing similar specimens to natural rocks. The purpose of this study was to lay out an optimal post-processing of 3D-printed samples that can facilitate replicating natural rocks with similar microstructure characteristics. In this study, four cylindrical rocks were manufactured without designed porosity by 3D printing using gypsum powder as the main component. Various types of infiltrants (Colorbond® and Surehold®) and coating conditions (SmoothOn® and WBAE®) were used after completing the printing process of binder jetting. Mercury injection porosimetry was then used to investigate their petrophysical properties including porosity and pore throat size distribution. Multifractal theory was applied to understand the heterogeneity of pore throat distribution within the 3D-printed samples on different pore size intervals. The results showed that 3D-printed rocks have a clustered and negative skewness of pore throat size distributions. The majority of pore sizes are micropores, while a small portion can be categorized under nanopore size category. Multifractal analysis results found a homogeneous distribution of micropores but a heterogeneous distribution of nanopores. Comparing four different samples, it was found that infiltrants could mainly affect the heterogeneous distribution of nanopores more than the micropores, whereas coating does not impact pore structure significantly. In comparison with pore multifractal characteristics of common types of natural rocks, 3D-printed rocks exhibited a higher heterogeneity of pore size distribution.
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Anovitz, L.M., Freiburg, J.T., Wasbrough, M., Mildner, D.F., Littrell, K.C., Pipich, V., Ilavsky, J.: The effects of burial diagenesis on multiscale porosity in the St. Peter Sandstone: an imaging, small-angle, and ultra-small-angle neutron scattering analysis. Mar. Pet. Geol. 92, 352–371 (2017)
Bird, N., Díaz, M.C., Saa, A., Tarquis, A.M.: Fractal and multifractal analysis of pore-scale images of soil. J. Hydrol. 322, 211–219 (2006)
Brady, B.H., Brown, E.T.: Rock mechanics: for underground mining. Springer Science & Business Media, Berlin (2013)
Caniego, F., Martı́, M., San José, F.: Rényi dimensions of soil pore size distribution. Geoderma 112, 205–216 (2003)
Chen, Y., Joffre, D., Avitabile, P.: Underwater dynamic response at limited points expanded to full-field strain response. J. Vib. Acoust. 140, 051016 (2018)
Choi, H.-H., Kim, E.-H., Park, H.-Y., Cho, G.-H., Jung, Y.-G., Zhang, J.: Application of dual coating process and 3D printing technology in sand mold fabrication. Surf. Coat. Technol. 332, 522–526 (2017)
Clarkson, C.R., Solano, N., Bustin, R.M., Bustin, A., Chalmers, G., He, L., Melnichenko, Y.B., Radliński, A., Blach, T.P.: Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion. Fuel 103, 606–616 (2013)
Costa, A.: Permeability-porosity relationship: A reexamination of the Kozeny–Carman equation based on a fractal pore-space geometry assumption. Geophys. Res. Lett. 33, L02318 (2006)
Daigle, H., Johnson, A., Thomas, B.: Determining fractal dimension from nuclear magnetic resonance data in rocks with internal magnetic field gradients. Geophysics 79, D425–D431 (2014)
Ding, P., Di, B., Wang, D., Wei, J., Li, X.: P and S wave anisotropy in fractured media: experimental research using synthetic samples. J. Appl. Geophys. 109, 1–6 (2014)
Dullien, F.A.: Porous Media: Fluid Transport and Pore Structure. Academic Press, Cambridge (2012)
Feder, J.: Fractals. Springer Science & Business Media, New York (2013)
Fereshtenejad, S., Song, J.-J.: Fundamental study on applicability of powder-based 3D printer for physical modeling in rock mechanics. Rock Mech. Rock Eng. 49, 2065–2074 (2016)
Giesche, H.: Mercury porosimetry: a general (practical) overview. Part. Part. Syst. Charact. 23, 9–19 (2006)
Giffin, S., Littke, R., Klaver, J., Urai, J.: Application of BIB–SEM technology to characterize macropore morphology in coal. Int. J. Coal Geol. 114, 85–95 (2013)
Gong, L., Fu, X., Gao, S., Zhao, P., Luo, Q., Zeng, L., Yue, W., Zhang, B., Liu, B.: Characterization and prediction of complex natural fractures in the tight conglomerate reservoirs: a fractal method. Energies 11, 2311 (2018)
Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346 (1983)
Guo, Z., Du, D., Liu, F., et al.: Coating process of multi-material composite sand mold 3D printing. China Foundry. 14, 498–505 (2017)
Hansen, J., Skjeltorp, A.: Fractal pore space and rock permeability implications. Phys. Rev. B. 38, 2635 (1988)
Head, D., Vanorio, T.: Effects of changes in rock microstructures on permeability: 3-D printing investigation. Geophys. Res. Lett. 43, 7494–7502 (2016)
Hodder, K.J., Nychka, J.A., Chalaturnyk, R.J.: Process limitations of 3D printing model rock. Prog. Addit. Manuf. 3(3), 173–182 (2018)
Hou, Q., Li, H., Fan, J., Ju, Y., Wang, T., Li, X., Wu, Y.: Structure and coalbed methane occurrence in tectonically deformed coals. Sci. China Earth Sci. 55, 1755–1763 (2012)
Ishutov, S., Hasiuk, F.J., Fullmer, S.M., Buono, A.S., Gray, J.N., Harding, C.: Resurrection of a reservoir sandstone from tomographic data using three-dimensional printing. AAPG Bull. 101, 1425–1443 (2017)
Ishutov, S., Hasiuk, F.J., Harding, C., Gray, J.N.: 3D printing sandstone porosity models. Interpretation. 3, SX49–SX61 (2015)
Ishutov, S., Jobe, T.D., Zhang, S., Gonzalez, M., Agar, S.M., Hasiuk, F.J., Watson, F., Geiger, S., Mackay, E., Chalaturnyk, R.: Three-dimensional printing for geoscience: fundamental research, education, and applications for the petroleum industry. AAPG Bull. 102, 1–26 (2018)
Jiang, C., Zhao, G.-F., Zhu, J., Zhao, Y.-X., Shen, L.: Investigation of dynamic crack coalescence using a gypsum-like 3D printing material. Rock Mech. Rock Eng. 49, 3983–3998 (2016)
Katz, A., Thompson, A.: Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett. 54, 1325 (1985)
Khatibi, S., Ostadhassan, M., Tuschel, D., Gentzis, T., Bubach, B., Carvajal-Ortiz, H.: Raman spectroscopy to study thermal maturity and elastic modulus of kerogen. Int. J. Coal Geol. 185, 103–118 (2018)
Knabe, R., Wang, Y., et al.: Permeability characterization on tight gas samples using pore pressure oscillation method. Petrophysics 52, 437–443 (2011)
Kong, L., Ostadhassan, M., Li, C., Tamimi, N.: Rock physics and geomechanics of 3-D printed rocks. In: ARMA-2017-0776. American Rock Mechanics Association, ARMA (2017)
Kong, L., Ostadhassan, M., Li, C., Tamimi, N.: Can 3-D printed gypsum samples replicate natural rocks? An experimental study. Rock Mech. Rock Eng. (2018a). https://doi.org/10.1007/s00603-018-1520-3
Kong, L., Ostadhassan, M., Li, C., Tamimi, N.: Pore characterization of 3D-printed gypsum rocks: a comprehensive approach. J. Mater. Sci. 53, 5063–5078 (2018b). https://doi.org/10.1007/s10853-017-1953-1
Kunchala, P., Kappagantula, K.: 3D printing high density ceramics using binder jetting with nanoparticle densifiers. Mater, Des (2018)
Lai, J., Wang, G.: Fractal analysis of tight gas sandstones using high-pressure mercury intrusion techniques. J. Nat. Gas Sci. Eng. 24, 185–196 (2015)
Li, B., Liu, R., Jiang, Y.: A multiple fractal model for estimating permeability of dual-porosity media. J. Hydrol. 540, 659–669 (2016a)
Li, B.-L.: Fractal Dimensions. Wiley, Hoboken (2002)
Li, C., Ostadhassan, M., Gentzis, T., Kong, L., Carvajal-Ortiz, H., Bubach, B.: Nanomechanical characterization of organic matter in the Bakken formation by microscopy-based method. Mar. Pet. Geol. 96, 128–138 (2018a)
Li, C., Ostadhassan, M., Guo, S., Gentzis, T., Kong, L.: Application of PeakForce tapping mode of atomic force microscope to characterize nanomechanical properties of organic matter of the Bakken Shale. Fuel 233, 894–910 (2018b)
Li, W., Liu, H., Song, X.: Multifractal analysis of Hg pore size distributions of tectonically deformed coals. Int. J. Coal Geol. 144, 138–152 (2015)
Li, W., Wang, C., Shi, Z., Wei, Y., Zhou, H., Deng, K.: The description of shale reservoir pore structure based on method of moments estimation. PLoS ONE 11, e0151631 (2016b)
Ling, K., He, J., Pei, P., Wang, S., Ni, X., et al.: Comparisons of Biot’s coefficients of Bakken core samples measured by three methods. In: 50th US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association (2016)
Liu, K., Ostadhassan, M.: Quantification of the microstructures of Bakken shale reservoirs using multi-fractal and lacunarity analysis. J. Nat. Gas Sci. Eng. 39, 62–71 (2017)
Liu, K., Ostadhassan, M., Kong, L.: Fractal and Multifractal Characteristics of Pore Throats in the Bakken Shale. Transp. Porous Media 1–20 (2018)
Liu, K., Ostadhassan, M., Kong, L., et al.: Pore structure heterogeneity in middle Bakken formation. In: 51st US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association (2017)
Lopes, R., Betrouni, N.: Fractal and multifractal analysis: a review. Med. Image Anal. 13, 634–649 (2009)
Loucks, R.G., Reed, R.M., Ruppel, S.C., Hammes, U.: Spectrum of pore types and networks in mudrocks and a descriptive classification for matrix-related mudrock pores. AAPG Bull. 96, 1071–1098 (2012)
Malik, S., Smith, L., Sharman, J., Holt, E.M., Rigby, S.P.: Pore structural characterization of fuel cell layers using integrated mercury porosimetry and computerized X-ray tomography. Ind. Eng. Chem. Res. 55, 10850–10859 (2016)
Mandelbrot, B.B.: The Fractal Geometry of Nature. WH Freeman, New York (1983)
Martínez, F.S.J., Martín, M., Caniego, F., Tuller, M., Guber, A., Pachepsky, Y., García-Gutiérrez, C.: Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures. Geoderma 156, 32–42 (2010)
Mendoza, F., Verboven, P., Ho, Q.T., Kerckhofs, G., Wevers, M., Nicolaï, B.: Multifractal properties of pore-size distribution in apple tissue using X-ray imaging. J. Food Eng. 99, 206–215 (2010)
Muller, J.: Characterization of pore space in chalk by multifractal analysis. J. Hydrol. 187, 215–222 (1996)
Nabawy, B.S., Géraud, Y., Rochette, P., Bur, N.: Pore-throat characterization in highly porous and permeable sandstones. AAPG Bull. 93, 719–739 (2009)
Nasseri, M., Rao, K., Ramamurthy, T.: Anisotropic strength and deformational behavior of Himalayan schists. Int. J. Rock Mech. Min. Sci. 40, 3–23 (2003)
Oropallo, W., Piegl, L.A.: Ten challenges in 3D printing. Eng. Comput. 32, 135–148 (2016)
Ostadhassan, M., Liu, K., Li, C., Khatibi, S.: Fine Scale Characterization of Shale Reservoirs: Methods and Challenges. Springer, New York (2018)
Ostadhassan, M., Zeng, Z., Zamiran, S., et al.: Geomechanical modeling of an anisotropic formation-Bakken case study. In: 46th US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association (2012)
Pittman, E.D.: Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone (1). AAPG Bull. 76, 191–198 (1992)
Primkulov, B., Chalaturnyk, J., Chalaturnyk, R., Zambrano Narvaez, G.: 3D Printed sandstone strength: curing of furfuryl alcohol resin-based sandstones. 3D Print. Addit. Manuf. 4, 149–156 (2017)
Ramamurthy, T.: Strength and modulus responses of anisotropic rocks. Compr. Rock Eng. 1, 313–329 (1993)
Riedi, R.H., Crouse, M.S., Ribeiro, V.J., Baraniuk, R.G.: A multifractal wavelet model with application to network traffic. IEEE Trans. Inf. Theory 45, 992–1018 (1999)
Saidi, F., Bernabé, Y., Reuschlé, T.: Uniaxial compression of synthetic, poorly consolidated granular rock with a bimodal grain-size distribution. Rock Mech. Rock Eng. 38, 129–144 (2005)
Schön, J.H.: Physical Properties of Rocks: Fundamentals and Principles of Petrophysics. Elsevier, Amsterdam (2015)
Shen, Z., Sheng, J.J., et al.: Experimental study of asphaltene aggregation during CO2 and CH4 injection in shale oil reservoirs. In: SPE Improved Oil Recovery Conference. Society of Petroleum Engineers (2016)
Squelch, A.: 3D printing rocks for geo-educational, technical, and hobbyist pursuits. Geosphere 14, 360–366 (2018)
Stumpf, M., Travitzky, N., Greil, P., Fey, T.: Sol-gel infiltration of complex cellular indirect 3D printed alumina. J. Eur. Ceram. Soc. 38, 3603–3609 (2018)
Suzuki, A., Watanabe, N., Li, K., Horne, R.N.: Fracture network created by 3-D printer and its validation using CT images. Water Resour. Res. 53, 6330–6339 (2017)
Taha, I., Abdellatif, M., Dietz, P.: Infiltration and coating of rapid prototyping parts. Adv. Eng. Mater. 7, 91–96 (2005)
Tian, W., Han, N.: Preliminary research on mechanical properties of 3D printed rock structures. Geotech. Test. J. 40, 483–493 (2017)
Tien, Y.M., Tsao, P.F.: Preparation and mechanical properties of artificial transversely isotropic rock. Int. J. Rock Mech. Min. Sci. 37, 1001–1012 (2000)
Tillotson, P., Sothcott, J., Best, A.I., Chapman, M., Li, X.-Y.: Experimental verification of the fracture density and shear-wave splitting relationship using synthetic silica cemented sandstones with a controlled fracture geometry. Geophys. Prospect. 60, 516–525 (2012)
Vázquez, E.V., Ferreiro, J.P., Miranda, J., González, A.P.: Multifractal analysis of pore size distributions as affected by simulated rainfall. Vadose Zone J. 7, 500–511 (2008)
Vogler, D., Walsh, S.D., Bayer, P., Amann, F.: Comparison of surface properties in natural and artificially generated fractures in a crystalline rock. Rock Mech. Rock Eng. 50, 2891–2909 (2017)
Wang, H., Rabiei, M., Lei, G., Wang, S., et al.: A novel granular profile control agent for steam flooding: synthesis and evaluation. In: SPE Western Regional Meeting. Society of Petroleum Engineers (2017)
Wang, L., Fu, Y., Li, J., Sima, L., Wu, Q., Jin, W., Wang, T.: Mineral and pore structure characteristics of gas shale in Longmaxi formation: a case study of Jiaoshiba gas field in the southern Sichuan Basin. China. Arab. J. Geosci. 9, 733 (2016)
Wang, L., Zhao, N., Sima, L., Meng, F., Guo, Y.: Pore structure characterization of the tight reservoir: a systematic integration of mercury injection and nuclear magnetic resonance. Energy Fuels 32, 7471–7484 (2018a)
Wang, X., Hou, J., Song, S., Wang, D., Gong, L., Ma, K., Liu, Y., Li, Y., Yan, L.: Combining pressure-controlled porosimetry and rate-controlled porosimetry to investigate the fractal characteristics of full-range pores in tight oil reservoirs. J. Pet. Sci. Eng. 171, 353–361 (2018b)
Wang, Z.: Seismic anisotropy in sedimentary rocks, part 2: laboratory data. Geophysics 67, 1423–1440 (2002a)
Wang, Z.: Seismic anisotropy in sedimentary rocks, part 1: a single-plug laboratory method. Geophysics 67, 1415–1422 (2002b)
Wardlaw, N.C., Taylor, R.: Mercury capillary pressure curves and the intepretation of pore structure and capillary behaviour in reservoir rocks. Bull. Can. Pet. Geol. 24, 225–262 (1976)
Webb, P.A.: An introduction to the physical characterization of materials by mercury intrusion porosimetry with emphasis on reduction and presentation of experimental data. Micromeritics Instrum, Corp Norcross Ga (2001)
Wong, P., Howard, J., Lin, J.-S.: Surface roughening and the fractal nature of rocks. Phys. Rev. Lett. 57, 637 (1986)
Xiong, F., Jiang, Z., Li, P., Wang, X., Bi, H., Li, Y., Wang, Z., Amooie, M.A., Soltanian, M.R., Moortgat, J.: Pore structure of transitional shales in the Ordos Basin, NW China: effects of composition on gas storage capacity. Fuel 206, 504–515 (2017)
Zhang, Y., Lebedev, M., Al-Yaseri, A., Yu, H., Xu, X., Sarmadivaleh, M., Barifcani, A., Iglauer, S.: Nanoscale rock mechanical property changes in heterogeneous coal after water adsorption. Fuel 218, 23–32 (2018)
Zhao, P., Wang, Z., Sun, Z., Cai, J., Wang, L.: Investigation on the pore structure and multifractal characteristics of tight oil reservoirs using NMR measurements: permian Lucaogou Formation in Jimusaer Sag, Junggar Basin. Mar. Pet. Geol. 86, 1067–1081 (2017a)
Zhao, Y., Zhu, G., Dong, Y., Danesh, N.N., Chen, Z., Zhang, T.: Comparison of low-field NMR and microfocus X-ray computed tomography in fractal characterization of pores in artificial cores. Fuel 210, 217–226 (2017b)
Zhou, S., Liu, D., Cai, Y., Yao, Y.: Fractal characterization of pore–fracture in low-rank coals using a low-field NMR relaxation method. Fuel 181, 218–226 (2016)
Acknowledgements
The author greatly appreciates the American Association of Petroleum Geologists Foundation for awarding the 2017 Grand-in-aid. Co-author, Dr. Bo Liu, is supported by University Nursing Program for Young Scholars with Creative Talents in Heilongjianng Province (UNPYSCT-2015077).
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Kong, L., Ostadhassan, M., Liu, B. et al. Multifractal Characteristics of MIP-Based Pore Size Distribution of 3D-Printed Powder-Based Rocks: A Study of Post-Processing Effect. Transp Porous Med 129, 599–618 (2019). https://doi.org/10.1007/s11242-018-1152-9
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DOI: https://doi.org/10.1007/s11242-018-1152-9