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A 3D lattice Boltzmann model is developed and used to calculate the water and gas permeabilities of model cement pastes at different degrees of water saturation. In addition to permeable micron-sized capillary pores and impermeable solid inclusions, the lattice Boltzmann model comprises weakly-permeable nano-porous calcium silicate hydrate (C-S-H).The multi-scale problem is addressed by using an effective media approach based on the idea of partial bounce-back. The model cement paste microstructures are generated with the platform µic. The critical parameters, C-S-H density and capillary porosity, are taken from 1 H nuclear magnetic resonance relaxation analysis. The distribution of water and air is defined according to the Kelvin-Laplace law. It is found that when the capillary porosity is completely saturated with a fluid (either water or gas), the calculated intrinsic permeability is in good agreement with measurements of gas permeability on dried samples (10 -17 -10 -16 m 2 ).However, as the water saturation is reduced, the calculated apparent water permeability decreases and spans the full range of experimentally measured values (10 -16 -10 -22 m 2 ). It is concluded that the degree of capillary water saturation is the major cause for variation in experimental permeability measurements. It is further concluded that the role of the weaklypermeable C-S-H, omitted in earlier modelling studies, is critical for determining the permeability at low capillary saturation. Keywords

The paper shows that it is possible to combine the free energy lattice Boltzmann approach to multi-phase modelling of fluids involving both liquid and vapour with the partial bounce back lattice Boltzmann approach to modelling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce back approach, an effective media parameter or bounce back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (grey nodes) and solids (black nodes). The use of the wetting potential combined with the bounce back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid / material systems. Results for phase separation, permeability, contact angle and wicking in grey media are shown. Sorption is explored in small sections of model multi-scale porous systems to demonstrate two-step desorption, sorption hysteresis and the ink-bottle effect.

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