Mesoscale and hybrid models of fluid flow and solute transport

Reviews in Mineralogy and Geochemistry

Volumn 80, Issue 1, 2015, Pages 433-459

  Mehmani, Yashar ^a   Balhoff, Matthew T ^b  

^a STANFORD UNIVERSITY   (United States)

^b The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84948683245     PISSN: 15296466     EISSN: None     Source Type: Book Series    
DOI: 10.2138/rmg.2015.80.13     Document Type: Article

References (145)

1. Acharya RC, Van Dijke MIJ, Leijnse A, Van der Zee SEATM, Sorbie KS (2004) Upscaling of tracer transport including convection and Brownian motion using a 3D network model. Dev Water Sci 55:115-125.
2. Acharya RC, Van der Zee SEATM, Leijnse A (2005) Transport modeling of nonlinearly adsorbing solutes in physically heterogeneous pore networks. Water Resour Res 41:W02020, doi: 10.1029/2004WR003500
3. Acharya RC, Van Dijke MIJ, Sorbie KS, Van der Zee SEATM, Leijnse A (2007a) Quantification of longitudinal dispersion by upscaling Brownian motion of tracer displacement in a 3D pore-scale network model. Adv Water Resour 30:199-213
4. Acharya RC, Van der Zee SEATM, Leijnse A (2007b) Approaches for modeling longitudinal dispersion in pore-networks. Adv Water Resour 30:261-272
5. Al-Gharbi MS, Blunt MJ (2005) Dynamic network modeling of two-phase drainage in porous media. Phys Rev E 71:016308
6. Algive L, Bekri S, Vizika O (2010) Pore-network modeling dedicated to the determination of the petrophysical-property changes in the presence of reactive fluid. SPE J 15:618-633
7. Algive L, Békri S, Nader FH, Lerat O, Vizika O (2012) Impact of diagenetic alterations on the petrophysical and multiphase flow properties of carbonate rocks using a reactive pore network modeling approach. Oil Gas Sci Technol 67:147-160
8. Alvarado V, Davis HT, Scriven LE (1997) Effects of pore-level reaction on dispersion in porous media. Chem Eng Sci 52:2865-2881
9. Arbogast T, Cowsar LC, Wheeler MF, Yotov I (2000) Mixed finite element methods on nonmatching multiblock grids. SIAM J Numer Anal 37:1295-1315
10. Bakke S, Øren PE (1997) 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J 2:136-149
11. Balhoff MT (2005) Modeling the flow of non-Newtonian fluids in packed beds at the pore scale. PhD dissertation, Louisiana State University
12. Battiato I, Tartakovsky DM (2011) Applicability regimes for macroscopic models of reactive transport in porous media. J Contam Hydrol 120:18-26
13. Balhoff MT, Wheeler MF (2009) A predictive pore-scale model for non-Darcy flow in porous media. SPE J 14:579-587
14. Balhoff MT, Thompson KE, Hjortsø M (2007) Coupling pore-scale networks to continuum-scale models of porous media. Comput Geosci 33:393-410
15. Balhoff MT, Thomas SG, Wheeler MF (2008) Mortar coupling and upscaling of pore-scale models. Computat Geosci 12:15-27
16. Battiato I, Tartakovsky DM, Tartakovsky AM, Scheibe T (2009) On breakdown of macroscopic models of mixing-controlled heterogeneous reactions in porous media. Adv Water Resour 32:1664-1673
17. Battiato I, Tartakovsky DM, Tartakovsky AM, Scheibe TD (2011) Hybrid models of reactive transport in porous and fractured media. Adv Water Resour 34:1140-1150
18. Benson DA, Meerschaert MM (2008) Simulation of chemical reaction via particle tracking: Diffusion-limited versus thermodynamic rate-limited regimes. Water Resour Res 44, no. 12, doi: 10.1029/2008WR007111
19. Berkowitz B, Ewing RP (1998) Percolation theory and network modeling applications in soil physics. Surv Geophys 19:23-72
20. Berkowitz B, Naumann C, Smith L (1994) Mass transfer at fracture intersections: An evaluation of mixing models. Water Resour Res 30:1765-1773
21. Bernardi C, Maday Y, Patera AT (1994) A new nonconforming approach to domain decomposition: the mortar element method. In: Brezis H, Lions JL (eds) Nonlinear Partial Differential Equations and their Applications. Collège de France Seminar. Vol. XI. Harlow, Longman Scientific & Technical. (Pitman Research Notes in Mathematics Series 299)
22. Bijeljic B, Blunt MJ (2006) A Physically-Based Description of Dispersion in Porous Media. In: SPE Annual Tech Conf and Exhibition. Society of Petroleum Engineers, SPE-102869-MS
23. Bijeljic B, Blunt MJ (2007) Pore-scale modeling of transverse dispersion in porous media. Water Resour Res 43:W12S11, doi: 10.1029/2006WR005700
24. Bijeljic B, Muggeridge AH, Blunt MJ (2004) Pore-scale modeling of longitudinal dispersion. Water Resour Res 40:W11501, doi: 10.1029/2004WR003567
25. Blunt MJ (2001) Flow in porous media-pore-network models and multiphase flow. Curr Opin Colloid In 6:197-207
26. Boso F, Battiato I (2013) Homogenizability conditions for multicomponent reactive transport. Adv Water Resour 62:254-265
27. Bruderer C, Bernabé Y (2001) Network modeling of dispersion: Transition from Taylor dispersion in homogeneous networks to mechanical dispersion in very heterogeneous ones. Water Resour Res 37:897-908
28. Bryant SL, Blunt MJ (1992) Prediction of relative permeability in simple porous media. Phys Rev A 46:2004-2011, doi: http://dx.doi.org/10.1103/PhysRevA.46.2004
29. Bryant SL, Mellor DW, Cade CA (1993a) Physically representative network models of transport in porous media. AIChE J 39:387-396
30. Bryant SL, Cade CA, Mellor DW (1993b) Permeability prediction from geologic models. AAPG Bull 77:1338-1350
31. Bryntesson LM (2002) Pore network modelling of the behaviour of a solute in chromatography media: transient and steady-state diffusion properties. J Chromatogr A 945:103-115
32. Celia MA, Reeves PC, Ferrand LA (1995) Recent advances in pore scale models for multiphase flow in porous media. Rev Geophys 33, S2:1049-1057
33. Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30:329-364
34. Chen L, Kang Q, Robinson BA, He YL, Tao WQ (2013) Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems. Phys Rev E 87:043306
35. Chen L, Kang Q, Tang Q, Robinson BA, He YL, Tao WQ (2014) Pore-scale simulation of multicomponent multiphase reactive transport with dissolution and precipitation. arXiv preprint arXiv:1410.3464
36. Chu J, Engquist B, Prodanovič M, Tsai R (2012) A multiscale method coupling network and continuum models in porous media I: Steady-state single phase flow. Multiscale Model Simul 10:515-549
37. Chu J, Engquist B, Prodanovič M, Tsai R (2013) A multiscale method coupling network and continuum models in porous media II-Single- and two-phase flows. In: Advances in Applied Mathematics, Modeling, and Computational Science, Springer, p 161-185
38. Coelho D, Thovert JF, Adler PM (1997) Geometrical and transport properties of random packings of spheres and aspherical particles. Phys Rev E 55, doi: http://dx.doi.org/10.1103/PhysRevE.55.1959
39. de Arcangelis L, Koplik J, Redner S, Wilkinson D (1986) Hydrodynamic dispersion in network models of porous media. Phys Rev Lett 57:996
40. Dentz M, Le Borgne T, Englert A, Bijeljic B (2011) Mixing, spreading and reaction in heterogeneous media: A brief review. J Contam Hydrol 120:1-17
41. Dong H, Blunt MJ (2009) Pore-network extraction from micro-computerized-tomography images. Phys Rev E 80:036307
42. Edwards DA, Shapiro M, Brenner H, Shapira M (1991) Dispersion of inert solutes in spatially periodic, two-dimensional model porous media. Transport Porous Med 6:337-358
43. Ellis JS, Ebrahimi A, Bazylak A (2011) Characterization of a Two-Phase Pore-Scale Network Model of Supercritical Carbon Dioxide Transport Within Brine-Filled Porous Media. In: ASME 2011 5th International Conference on Energy Sustainability, p 1307-1314
44. Fatt I (1956a) The network model of porous media I. Capillary pressure characteristics. Trans Am I Min Met Eng 207:144-159
45. Fatt I (1956b) The network model of porous media. 2. Dynamic properties of a single size tube network. Trans Am I Min Met Eng 207:160-163
46. Fatt I (1956c) The network model of porous media III. Dynamic properties of networks with tube radius distribution. Trans Am I Min Eng 207:164-181
47. Finney JL (1968) Random packings and the structure of the liquid state. University of London (United Kingdom), PhD dissertation
48. Fischer U, Celia MA (1999) Prediction of relative and absolute permeabilities for gas and water from soil water retention curves using a pore-scale network model. Water Resour Res 35:1089-1100
49. Ganis B, Juntunen M, Pencheva G, Wheeler MF, Yotov I (2012) A Global Jacobian Method for Simultaneous Solution of Mortar and Subdomain Variables in Nonlinear Porous Media Flow. ICES REPORT 12-46, The Institute for Computational Engineering and Sciences, The University of Texas at Austin
50. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340-2361
51. Hoefner ML, Fogler HS (1988) Pore evolution and channel formation during flow and reaction in porous media. AIChE J 34:45-54
52. Iltis GC, Armstrong RT, Jansik DP, Wood BD, Wildenschild D (2011) Imaging biofilm architecture within porous media using synchrotron-based X-ray computed microtomography. Water Resour Res 47:W02601, doi: 10.1029/2010WR009410
53. Jha RK, Bryant SL, Lake LW (2011) Effect of diffusion on dispersion. SPE J 16:65-77
54. Joekar-Niasar V (2010) The immischibles: Capillarity effects in porous media, pore-network modeling. Geologica Ultraiectina 318
55. Joekar-Niasar V, Hassanizadeh SM, Dahle HK (2010) Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling. J Fluid Mech 655:38-71
56. Johnson J, Brown S, Stockman H (2006) Fluid flow and mixing in rough-walled fracture intersections. J Geophys Res: Solid Earth 111:B12206, doi: 10.1029/2005JB004087
57. 2 sequestration. Transport Porous Med 82:197-213
58. Karadimitriou NK, Hassanizadeh SM (2012) A review of micromodels and their use in two-phase flow studies. Vadose Zone J 11, doi:10.2136/vzj2011.0072.
59. Kechagia PE, Tsimpanogiannis IN, Yortsos YC, Lichtner PC (2002) On the upscaling of reaction-transport processes in porous media with fast or finite kinetics. Chem Eng Sci 57:2565-2577
60. Kim D, Lindquist WB (2012) Dependence of pore-to-core up-scaled reaction rate on flow rate in porous media. Transport Porous Med 94:555-569
61. 2-saturated brine flow in sandstone aquifers. Water Resour Res 47:W01505, doi: 10.1029/2010WR009472
62. Koplik J, Lasseter TJ (1985) Two-phase flow in random network models of porous media. Soc Petrol Eng J 25:89-100
63. Koplik, J, Redner S, Wilkinson D (1988) Transport and dispersion in random networks with percolation disorder. Phys Rev A 37:2619-2636
64. Li L, Peters CA, Celia MA (2006) Upscaling geochemical reaction rates using pore-scale network modeling. Adv Water Resour 29:1351-1370
65. Li L, Peters CA, Celia MA (2007a) Applicability of averaged concentrations in determining geochemical reaction rates in heterogeneous porous media. Am J Sci 307:1146-1166
66. Li L, Peters CA, Celia MA (2007b) Effects of mineral spatial distribution on reaction rates in porous media. Water Resour Res 43:W01419, doi: 10.1029/2005WR004848
67. Li L, Steefel CI, Yang L (2008) Scale dependence of mineral dissolution rates within single pores and fractures. Geochim Cosmochim Acta 72:360-377
68. Lindquist WB, Lee SM, Coker DA, Jones KW, Spanne P (1996) Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J Geophys Res: Solid Earth 101(B4):8297-8310
69. Lindquist WB, Venkatarangan A (1999) Investigating 3D geometry of porous media from high resolution images. Phys Chem Earth Pt A 24:593-599
70. Lopez X, Valvatne PH, Blunt MJ (2003) Predictive network modeling of single-phase non-Newtonian flow in porous media. J Colloid Interface Sci 264:256-265
71. Lu C, Yortsos YC (2005) Dynamics of forward filtration combustion at the pore-network level. AIChE J 51:1279-1296
72. Maier RS, Kroll DM, Bernard RS, Howington SE, Peters JF, Davis HT (2000) Pore-scale simulation of dispersion. Phys Fluids 12:2065-2079
73. Maier RS, Kroll DM, Bernard RS, Howington SE, Peters JF, Davis HT (2003) Hydrodynamic dispersion in confined packed beds. Phys Fluids 15:3795-3815
74. Martins AA, Laranjeira PE, Braga CH, Mata TM (2009) Modeling of transport phenomena in porous media using network models. In: Progress in Porous Media Research, ISBN:978-1-60692-435-8
75. Meakin P, Tartakovsky AM (2009) Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev Geophys 47: RG3002, doi: 10.1029/2008RG000263
76. Mehmani Y (2014) Modeling of single-phase flow and solute transport across scales. PhD dissertation, University of Texas at Austin
77. Mehmani Y, Balhoff MT (2014) Bridging from pore to continuum: A hybrid mortar domain decomposition framework for subsurface flow and transport. Multiscale Model Simul 12:667-693
78. Mehmani A, Prodanovič M (2014a) The effect of microporosity on transport properties in porous media. Adv Water Resour 63:104-119
79. Mehmani A, Prodanovič M (2014b) The application of sorption hysteresis in nano-petrophysics using multiscale multiphysics network models. Int J Coal Geol 128:96-108
80. Mehmani Y, Sun T, Balhoff MT, Eichhubl P, Bryant SL (2012) Multiblock pore-scale modeling and upscaling of reactive transport: application to carbon sequestration. Transport Porous Med 95:305-326
81. Mehmani A, Prodanovič M, Javadpour F (2013) Multiscale, multiphysics network modeling of shale matrix gas flows. Transport Porous Med 99:377-390
82. Mehmani Y, Oostrom M, Balhoff MT (2014) A streamline splitting pore-network approach for computationally inexpensive and accurate simulation of transport in porous media. Water Resour Res 50:2488-2517
83. Moebius F, Or D (2014) Inertial forces affect fluid front displacement dynamics in a pore-throat network model. Phys Rev E 90:023019
84. Mohanty KK, Davis HT, Scriven LE (1987) Physics of oil entrapment in water-wet rock. SPE Reservoir Eng 2:113-128
85. Molins S (2015) Reactive interfaces in direct numerical simulation of pore scale processes. Rev Mineral Geochem 80:461-481
86. Molins S, Trebotich D, Steefel CI, Shen C (2012) An investigation of the effect of pore scale flow on average geochemical reaction rates using direct numerical simulation. Water Resour Res 48:W03527, doi: 10.1029/2011WR011404
87. Molins S, Trebotich D, Yang L, Ajo-Franklin JB, Ligocki TJ, Shen C, Steefel CI (2014) Pore-scale controls on calcite dissolution rates from flow-through laboratory and numerical experiments. Env Sci Tech 48:7453-7460, doi:10.1021/es5013438
88. Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543-574
89. Mostaghimi P, Bijeljic B, Blunt MJ (2012) Simulation of flow and dispersion on pore-space images. In: SPE Annual Technical Conference and Exhibition, Italy. SPE 135261
90. Nogues JP, Fitts JP, Celia MA, Peters CA (2013) Permeability evolution due to dissolution and precipitation of carbonates using reactive transport modeling in pore networks. Water Resour Res 49:6006-6021
91. Noiriel C, Bernard D, Gouze P, Thibault X (2005) Hydraulic properties and microgeometry evolution accompanying limestone dissolution by acidic water. Oil Gas Sci Tech 60:177-192
92. Noiriel C (2015) Resolving time-dependent evolution of pore-scale structure, permeability and reactivity using X-ray microtomography. Rev Mineral Geochem 80:247-285
93. Oostrom M, Mehmani Y, Romero-Gomez P, Tang Y, Liu H, Yoon H, Kang Q, Joekar-Niasar V, Balhoff MT, Dewers T, Tartakovsky GD, Leist EA, Hess NJ, Perkins WA, Rakowski CL, Richmond MC, Serkowski JA, Werth CJ, Valocchi AJ, Wietsma TW, Zhang C (2014) Pore-scale and continuum simulations of solute transport micromodel benchmark experiments. Comput Geosci 1-23, doi 10.1007/s10596-014-9424-0
94. Øren PE, Bakke S, Arntzen OJ (1998) Extending predictive capabilities to network models." SPE J 3:324-336. SPE 38880
95. Øren PE, Bakke S (2002) Process based reconstruction of sandstones and prediction of transport properties. Transport Porous Med 46:311-343
96. Ovaysi S, Piri M (2011) Pore-scale modeling of dispersion in disordered porous media. J Contam Hydrol 124:68-81
97. Park YJ, Lee KK (1999) Analytical solutions for solute transfer characteristics at continuous fracture junctions. Water Resour Res 35:1531-1537
98. Park YJ, Lee KK, Berkowitz B (2001a) Effects of junction transfer characteristics on transport in fracture networks. Water Resour Res 37:909-923
99. Park YJ, Dreuzy JR, Lee KK, Berkowitz B (2001b) Transport and intersection mixing in random fracture networks with power law length distributions. Water Resour Res 37:2493-2501
100. Parmigiani A, Huber C, Bachmann O, Chopard B (2011) Pore-scale mass and reactant transport in multiphase porous media flows. J Fluid Mech 686:40-76, doi:10.1017/jfm.2011.268
101. Patzek TW (2001) Verification of a complete pore network simulator of drainage and imbibition. SPE J 6:144-156. SPE-71310-PA
102. Payatakes AC, Ng KM, Flumerfelt RW (1980) Oil ganglion dynamics during immiscible displacement: Model formulation. AIChE J 26:430-443
103. Peszynska M, Wheeler MF, Yotov I (2002) Mortar upscaling for multiphase flow in porous media. Computat Geosci 6:73-100
104. Picard G, Frey K (2007) Method for modeling transport of particles in realistic porous networks: Application to the computation of NMR flow propagators. Phys Rev E 75:066311
105. Piri M, Blunt MJ (2005) Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. I. Model description. Phys Rev E 71:026301
106. Prodanovič M, Lindquist WB, Seright RS (2006) Porous structure and fluid partitioning in polyethylene cores from 3D X-ray microtomographic imaging. J Colloid Interface Sci 298:282-297
107. Prodanovič M, Mehmani A, Sheppard AP (2014) Imaged-based multiscale network modelling of microporosity in carbonates. Geological Society, London, Special Publications 406: SP406-9
108. Raoof A, Nick HM, Hassanizadeh SM, Spiers CJ (2013) PoreFlow: A complex pore-network model for simulation of reactive transport in variably saturated porous media. Comput Geosci 61:160-174
109. Rhodes ME, Blunt MJ (2006) An exact particle tracking algorithm for advective-dispersive transport in networks with complete mixing at nodes. Water Resour Res 42:W04501, doi: 10.1029/2005WR004504
110. Rhodes ME, Bijeljic B, Blunt MJ (2009) A rigorous pore-to-field-scale simulation method for single-phase flow based on continuous-time random walks. SPE J 14:88-94
111. Roubinet D, Tartakovsky DM (2013) Hybrid modeling of heterogeneous geochemical reactions in fractured porous media. Water Resour Res 49:7945-7956
112. Sahimi M, Hughes BD, Scriven LE, Davis HT (1986) Dispersion in flow through porous media-I. Onephase flow. Chem Eng Sci 41:2103-2122
113. Scheibe TD, Tartakovsky AM, Tartakovsky DM, Redden GD, Meakin P (2007) Hybrid numerical methods for multiscale simulations of subsurface biogeochemical processes. J Phys: Conf Ser 78:012063. IOP Publishing. Doi:10.1088/1742-6596/78/1/012063
114. Scheibe TD, Murphy EM, Chen X, Rice AK, Carroll KC, Palmer BJ, Tartakovsky AM, Battiato I, Wood BD (2015) An analysis platform for multiscale hydrogeologic modeling with emphasis on hybrid multiscale methods. Groundwater 53:38-56
115. Sheng Q, Thompson KE (2013) Dynamic coupling of pore-scale and reservoir-scale models for multiphase flow. Water Resour Res 49:5973-5988
116. Sheppard AP, Sok RM, Averdunk H, Robins VB, Ghous A (2006) Analysis of rock microstructure using high-resolution X-ray tomography. In: Proceedings of the International Symposium of the Society of Core Analysts, Trondheim, Norway. SCA2006-26
117. Silin D, Patzek T (2006) Pore space morphology analysis using maximal inscribed spheres. Physica A 371:336-360
118. Sorbie KS, Clifford PJ (1991) The inclusion of molecular diffusion effects in the network modelling of hydrodynamic dispersion in porous media. Chem Eng Sci 46:2525-2542
119. Steefel CI, MacQuarrie KTB (1996) Approaches to modeling of reactive transport in porous media. Rev Mineral Geochem 34:85-129
120. Steefel CI, DePaolo DJ, Lichtner PC (2005) Reactive transport modeling: An essential tool and a new research approach for the Earth sciences. Earth Planet Sci Lett 240:539-558
121. 2 injection and sequestration. Rev Mineral Geochem 77:259-303
122. Stehfest H (1970) Algorithm 368: Numerical inversion of Laplace transforms [D5]. Commun ACM 13:47-49
123. Suchomel BJ, Chen BM, Allen MB (1998a) Macroscale properties of porous media from a network model of biofilm processes. Transport Porous Med 31:39-66
124. Suchomel BJ, Chen BM, Allen MB (1998b) Network model of flow, transport and biofilm effects in porous media. Transport Porous Med 30:1-23
125. Sun T, Mehmani Y, Bhagmane J, Balhoff MT (2012a) Pore to continuum upscaling of permeability in heterogeneous porous media using mortars. Int J Oil Gas Coal Tech 5:249-266
126. Sun T, Mehmani Y, Balhoff MT (2012b) Hybrid multiscale modeling through direct substitution of porescale models into near-well reservoir simulators. Energy & Fuels 26:5828-5836
127. Tartakovsky AM, Tartakovsky DM, Scheibe TD, Meakin P (2008a) Hybrid simulations of reaction-diffusion systems in porous media. SIAM J Sci Comp 30:2799-2816
128. Tartakovsky AM, Redden G, Lichtner PC, Scheibe TD, Meakin P (2008b) Mixing-induced precipitation: Experimental study and multiscale numerical analysis. Water Resour Res 44:W06S04 doi: 10.1029/2006WR005725
129. Tartakovsky AM, Tartakovsky DM, Meakin P (2008c) Stochastic Langevin model for flow and transport in porous media. Phys Rev Lett 101:044502
130. Thane CG (2006) Geometry and topology of model sediments and their influence on sediment properties, Thesis, University of Texas at Austin
131. Thauvin F, Mohanty KK (1998) Network modeling of non-Darcy flow through porous media. Transp Porous Med 31:19-37
132. Thompson KE, Willson CS, White CD, Nyman S, Bhattacharya JP, Reed AH (2008) Application of a new grain-based reconstruction algorithm to microtomography images for quantitative characterization and flow modeling. No. NRL/JA/7430-07-13. Naval Research Lab Stennis Space Center Ms Marine Geoacoustics Div
133. Thovert JF, Salles J, Adler PM (1993) Computerized characterization of the geometry of real porous media: their discretization, analysis and interpretation. J Microsc 170:65-79
134. Tomin P, Lunati I (2013) Hybrid Multiscale Finite Volume method for two-phase flow in porous media. J Comput Phys 250:293-307
135. Trebotich D, Adams MF, Molins S, Steefel CI, Shen C (2014) High resolution simulation of pore scale reactive transport processes associated with carbon sequestration. Comput Sci Eng, 10.1109/MCSE.2014.77
136. van Milligen BP, Bons PD (2014) Simplified numerical model for clarifying scaling behavior in the intermediate dispersion regime in homogeneous porous media. Comput Phys Comm 185:3291-3301. Doi:10.1016/j.cpc.2014.09.006
137. Varloteaux C, Békri S, Adler PM (2013) Pore network modelling to determine the transport properties in presence of a reactive fluid: From pore to reservoir scale. Adv Water Resour 53:87-100
138. Vogel HJ (2000) A numerical experiment on pore size, pore connectivity, water retention, permeability, and solute transport using network models. Eur J Soil Sci 51:99-105
139. Wendt JF (2009) Computational Fluid Dynamics. Third Edition, Springer, Berlin
140. Werth CJ, Zhang C, Brusseau ML, Oostrom M, Baumann T (2010) A review of non-invasive imaging methods and applications in contaminant hydrogeology research. J Contam Hydrol 113:1-24
141. Wildenschild D, Sheppard AP (2013) X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems. Adv Water Resour 51:217-246
142. Yang X, Scheibe TD, Richmond MC, Perkins WA, Vogt SJ, Codd SL, Seymour JD, McKinley MI (2013) Direct numerical simulation of pore-scale flow in a bead pack: Comparison with magnetic resonance imaging observations. Adv Water Resour 54:228-241
143. Yoon H, Valocchi AJ, Werth CJ, Dewers T (2012) Pore-scale simulation of mixing-induced calcium carbonate precipitation and dissolution in a microfluidic pore network. Water Resour Res 48:W02524 doi: 10.1029/2011WR011192
144. Yoon H, Kang Q, Valocchi A (2015) Lattice Boltzmann-based approaches for pore-scale reactive transport. Rev Mineral Geochem 80:393-431
145. Zaretskiy Y, Geiger S, Sorbie K, Förster M (2010) Efficient flow and transport simulations in reconstructed 3D pore geometries. Adv Water Resour 33:1508-1516