Pore-scale prediction of the effective mass diffusivity of heterogeneous shale structure using the lattice Boltzmann method

Shale is a kind of heterogeneous porous medium consisting of organic matter (OM), inorganic matter (IM), and interparticle pores. A modified lattice Boltzmann model is developed at the pore-scale to accurately predict the effective mass diffusivity of the heterogeneous shale structure by fully considering the multicomponent and irregular morphological features. The model is validated by the classic empirical formulas and numerical results of the shale with regular IM and OM skeletons. The effects of average gain diameter, irregular structural morphology, porosity, OM volume fraction, and OM diffusivity on the effective mass diffusivity are investigated. The effect of average gain diameter can be ignored. The Nield formula is capable of predicting the effective mass diffusivity of a random OM structure. The formula of Comiti and Renaud can be extended to predict the effective mass diffusivity of a random IM structure by modifying the empirical coefficient to 1.6. The effective mass diffusivity of the heterogeneous shale structure with random OM and IM is between that of pure IM and OM. This effective mass diffusivity increases with the increment of porosity, OM volume fraction, and OM diffusivity. A general empirical formula is proposed to calculate the effective mass diffusivity effectively and conveniently.