Scale-up of pore-level relative permeability from micro- to macro-scale

Scaling up relative permeability curves of wetting and nonwetting phase of drainage and imbibition processes from pore scale to macro scale is a challenge. A new method for scaling up relative permeability from micro- to macro-scale is proposed based on electrical analogy of multiphase fluid flow at pore scale. The method is validated against four synthetic porous media generated using homogeneous and heterogeneous grain size distributions, each of which were cut into eight sub-segments. Single-phase and two-phase flow properties were calculated for the main blocks and the subsequent sub-segments using random network modelling technique. Then, the subsegments were randomly distributed in space to reconstruct the main blocks and the proposed scale-up method was employed to calculate the relative permeability curves of the reconstructed blocks. Results were compared to the ones obtained directly from the network model of the original blocks and show good agreement between the calculated and scaled-up relative permeability curves of primary drainage and secondary imbibition. Furthermore, the model was tested on real media. Eight network models were extracted from pore size distribution of core samples obtained from the Green River basin located in the Mesaverde Formation. Flow properties obtained from the network models were validated against experimental data and good agreement was observed. These network models show a higher level of heterogeneity at micro-scale. Then, the scale-up methods were employed in order to reconstruct the macro-scale sample and predict its properties. Scale-up methods successfully predict the single-phase and two-phase flow properties of the sample.