Dynamic capillary pressure analysis of tight sandstone based on digital rock model

Yixin Cao, Mingming Tang, Qian Zhang, Jiafan Tang, Shuangfang Lu

Abstract view|284|times       PDF download|46|times


In recent studies, dynamic capillary pressure has shown significant impacts on the flow behaviors in porous media under transient flow condition. However, the effect of dynamic capillary pressure effect on tight sandstone is still not very clear. Since lattice Boltzmann method (LBM) is a very promising and widely used method in analyzing flow behaviors, therefore, a two-phase D3Q27 LBM model is adopted in this paper to simulate the flow behaviors and analyze the dynamic capillary pressure effect in tight sandstone. Moreover, a new pore segmentation method for tight sandstone base on U-net deep learning model is implemented in this study to improve the pore boundary qualities of pore space, which is crucial for two-phase LBM simulation of tight sandstone. A total of 3800 3D sub-volume data sets extracted from computed tomography data of 19 tight sandstone samples are selected as ground truth data to train the network and segment the pore space afterward. The simulation results based on the segmented digital rock model, show that nonwetting phase fluid prefer the path with lower dynamic capillary pressure in the seepage process before breaking through the porous model. Furthermore, the increase of injection rate causes the saturation changes more quickly, injection rate also shows apparent positive correlation relationship with capillary pressure, which implies that dynamic capillary pressure effect also exists in tight sandstone, and LBM based two-phase flow simulation could be used to quantitatively analyze such effect in tight sandstone.

Cited as: Cao, Y., Tang, M., Zhang, Q., Tang, J., Lu, S. Dynamic capillary pressure analysis of tight sandstone based on digital rock model. Capillarity, 2020, 3(2): 28-35, doi: 10.46690/capi.2020.02.02.


Dynamic capillary pressure; digital rock model; U-net; lattice Boltzmann method

Full Text:



Abidoye, L.K., Das, D.B. Scale dependent dynamic capillary pressure effect for two-phase flow in porous media. Adv. Water Resour. 2014, 74: 212-230.

Alexandra, R., Dubravka, P., Wu, K., et al. 3D pore system reconstruction using nano-scale 2D SEM images and pore size distribution analysis for intermediate rank coal matrix. Fuel 2020, 275: 117934.

Andrew, M., Bijeljic, B., Blunt, M.J. New frontiers in exper-imental geoscience: X-ray microcomputed tomography and fluid flow. Microsc. Anal. 2014, 28(2): 4-7.

Blunt, M.J., Jackson, M.D., Piri, M., et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 2002, 25(8-12): 1069-1089.

Bottero, S., Hassanizadeh, S.M., Kleingeld, P.J., et al. Nonequilibrium capillarity effects in two-phase flow through porous media at different scales. Water Resour. Res. 2011, 47(10): W10505.

Cai, J., Perfect, E., Cheng, C.L., et al. Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures. Langmuir 2014, 30(18): 5142-5151.

Cekmer, O., Um, S., Mench, M.M. A combined path-percolation-Lattice-Boltzmann model applied to multi-phase mass transfer in porous media. Int. J. Heat Mass Transf. 2016, 93: 257-272.

Chen, C., Lu, S., Li, J., et al. Digital core modeling construction of different lithofacies shale: A case study of dongying depression. Geoscience 2017, 31(5): 1069-1078. (in Chinese)

Chen, S., Chen, H., Martnez, D., et al. Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys. Rev. Lett. 1991, 67(27): 3776-3779.

Chen, X., Qu, X., Xu, S., et al. Dissolution pores in shale and their influence on reservoir quality in Damintun Depression, Bohai Bay Basin, East China: Insights from SEM images, N2 adsorption and fluid-rock interaction experiments. Mar. Pet. Geol. 2020, 117: 104394.

Choi, C., Lee, Y., Song, J., et al. Equivalent pore channel model for fluid flow in rock based on microscale X-ray CT imaging. Materials 2020, 13(11): 2619.

Curtis, M.E., Sondergeld, C.H., Ambrose, R.J., et al. Microstructural investigation of gas shales in 2D and 3D using nano-meterscale resolution imaging. AAPG Bull. 2012, 96(4): 665-677.

Dahle, H.K., Celia, M.A., Hassanizadeh, S.M. Bundle-of-tubes model for calculating dynamic effects in the capillary-pressure-saturation relationship. Transp. Porous Media 2005, 58(1-2): 5-22.

Das, D.B., Hanspal, N.S., Nassehi, V. Analysis of hydro-dynamic conditions in adjacent free and heterogeneous porous flow domains. Hydrol. Process. 2005, 19(14): 2775-2799.

Diamantopoulos, E., Durner, W., Harter, T. Prediction of capillary air-liquid interfacial area vs. saturation function from relationship between capillary pressure and water saturation. Adv. Water Resour. 2016, 97: 219-223.

Goral, J., Andrew, M., Olson, T., et al. Correlative core-to pore-scale imaging of shales. Mar. Pet. Geol. 2020, 111: 886-904.

Hassanizadeh, S.M., Celia, M.A., Dahle, H.K. Dynamic effects in the capillary pressure saturation relationship and their impacts on unsaturated flow. Vadose Zone J. 2002, 1(1): 38-57.

Kang, D., Yang, E., Yun, T. Stokes-Brinkman flow simulation based on 3-D µ -CT images of porous rock using grayscale pore voxel permeability. Water Resour. Res. 2019, 55(5): 4448-4464.

Kunz, P., Zarikos, I.M., Karadimitriou, N.K., et al. Study of multi-phase flow in porous media: Comparison of SPH simulation with micro-model experiments. Transp. Porous Media 2016, 114(2): 581-600.

Landry, C.J., Karpyn, Z.T., Ayala, O. Relative permeability of homogenous-wet and mixed-wet porous media as determined by pore-scale lattice Boltzmann modeling. Water Resour. Res. 2014, 50(5): 3672-3689.

LeCun, Y., Bengio, Y., Hinton, G. Deep learning. Nature 2015, 521(7553): 436-444.

Li, J., Ho, M.T., Wu, L., et al. On the unintentional rarefaction effect in LBM modeling of intrinsic permeability. Adv. Geo-Energy Res. 2018a, 2(4): 404-409.

Li, J., Wang, Z., Wei, J., et al. The numerical simulation of the shale gas fluid-structure interaction based on the digital rock and LBM. Scientia Sinica (Technologica) 2018b, 48(5): 499-509. (in Chinese)

Li, M., Guo, Y., Li, Z., et al. Pore-throat combination types and gas-water relative permeability responses of tight gas sandstone reservoirs in the Zizhou area of east Ordos Basin, China. Acta Geol. Sin.-Engl. Ed. 2019, 93(3): 622-636.

Liu, H., Yang, Y., Wang, F., et al. Micro pore and throat characteristics and origin of tight sandstone reservoirs: A case study of the Triassic Chang 6 and Chang 8 members in Longdong area, Ordos Basin, NW China. Pet. Explor. Dev. 2018, 45(2): 239-250.

Liu, K., Ostadhassan, M. Multi-scale fractal analysis of pores in shale rocks. J. Appl. Geophys. 2017, 140: 1-10.

Li, Y., Li, H., Cai, J., et al. The dynamic effect in capillary pressure during the displacement process in ultra-low permeability sandstone reservoirs. Capillarity 2018c, 1(2): 11-18.

Loucks, R.G., Reed, R.M., Ruppel, S.C., et al. Morphology, genesis, and distribution of nanometer-scale pores in siliceous mudstone of the Mississippian Barnett shale. J. Sediment. Res. 2009, 79(12): 848-861.

Niasar, V.J., Hassanizadeh, S.M., Dahle, H.K. Non-equilibrium effects in capillarity and interfacial area in two-phase flow: Dynamic pore-network modelling. J. Fluid Mech. 2010, 655: 38-71.

Qu, Y., Sun, W., Tao, R., et al. Pore-throat structure and fractal characteristics of tight sandstones in Yanchang Formation, Ordos Basin. Mar. Pet. Geol. 2020, 120: 104573.

Raeini, A.Q., Bijeljic, B., Blunt, M.J. Numerical modelling of sub-pore scale events in two-phase flow through porous media. Transp. Porous Media 2014, 101(2): 191-213.

Ronneberger, O., Fischer, P., Brox, T. U-net: Convolutional networks for biomedical image segmentation. Paper Presented at 18th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), Munich, Germary, 5-9 October, 2015.

Shaina, K., Hesham, E., Carlos, T., et al. Assessing the utility of FIB-SEM images for shale digital rock physics. Adv. Water Resour. 2016, 95: 302-316.

Shan, C., Zhao, W., Wang, F., et al. Nanoscale pore structure heterogeneity and its quantitative characterization in Chang7 lacustrine shale of the southeastern Ordos Basin, China. J. Pet. Sci. Eng. 2020, 187: 106754.

Shou, Y., Zhao, Z., Zhou, X. Sensitivity analysis of segmen-tation techniques and voxel resolution on rock physical properties by X-ray imaging. J. Struct. Geol. 2020, 133: 103978.

Sukop, M.C., Thorne, D.T. Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. New York, Springer, 2006.

Tang, M., Lu, S., Zhan, H., et al. The effects of a microscale fracture on dynamic capillary pressure of two-phase flow in porous media. Adv. Water Resour. 2018, 113: 272-284.

Tang, M., Zhan, H., Lu, S., et al. Pore-scale CO2 displacement simulation based on the three fluid phase lattice Boltzmann method. Energy Fuels 2019a, 33: 10039-10055.

Tang, M., Zhan, H., Ma, H., et al. Upscaling of dynamic capillary pressure of two-phase flow in sandstone. Water Resour. Res. 2019b, 55(4): 426-443.

Tang, M., Zhao, H., Ma, H., et al. Study on CO2 huff-n-puff of horizontal wells in continental tight oil reservoirs. Fuel 2017, 188: 140-154.

Tartakovsky, A.M., Meakin, P. Pore scale modeling of immiscible and miscible flows using smoothed particle hydrodynamics. Adv. Water Resour. 2006, 29: 1464-1478.

Tavanaei, A., Salehi, S. Pore, throat, and grain detection for rock sem images using digitalwatershed image segmentation algorithm. J. Porous Media 2015, 18(5): 507-518.

Wang, H., Yuan, X., Liang, H., et al. A brief review of the phase-field-based lattice Boltzmann method for multiphase flows. Capillarity 2019, 2(3): 33-52.

Wang, P., Qiang, Y., Yang, X., et al. Double attention 3D-UNet for lung nodule segmentation. Computer Engineering 2020, 2020: 1-10. (in Chinese)

Xiang, Y., Zhao, Y., Dong, J. Remote sensing image mining area change detection based on improved UNet siamese network. Journal of China Coal Society 2019, 44(12): 3773-3780. (in Chinese)

Xu, D., Li, H., Zhou, L., et al. Model of automatic identifica-tion of diabetic macular edema via convolutional neural networks UNet. Recent Advances in Ophthalmology 2020, 40(4): 357-361. (in Chinese)

Xu, J., Jin, G., Zhu, T. Segmentation of rock images based on U-net. Industrial Control Computer 2018, 31(4): 98-99.

(in Chinese) Zhang, G., Zhang, Y., Xu, A., et al. Microflow effects on the hydraulic aperture of single rough fractures. Adv. Geo-Energy Res. 2019, 3(1): 104-114.

Zhao, J., Wang, P., Zhang, Y. Influence of CO2 injection on the pore size distribution and petrophysical properties of tight sandstone cores using nuclear magnetic resonance. Energy Sci. Eng. 2020, 8(7): 2286-2296.

Zhu, G., Li, A. Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities. Adv. Geo-Energy Res. 2020, 4(1): 86-98.

Zhu, R., Jin, X., Wang, X., et al. Multi-scale digital rock evaluation on complex reservior. Earth Science 2018, 43(5): 1773-1782. (in Chinese)


  • There are currently no refbacks.

Copyright (c) 2020 The Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright ©2018. All Rights Reserved