Inversion of the lattice network wettability subjected to the capillary pressure of the entire flooding cycle: Hamiltonian Monte Carlo posterior sampling and prediction of the relative permeability

We developed a new method for predicting accurately the imbibition oil/water relative permeabilities for carbonates using pore network modelling. The proposed method uses Hamiltonian dynamics for the stochastic inversion of the pore-network model parameters, which are conditioned only to the capillary pressure. We applied our method to three carbonate rock samples of different rock types. Carbonate rock samples are particularly challenging because of their wettability and the various orders of variation in the pore-size distribution. We found that micro- and submicron-porosity had larger advancing contact angles than larger pore sizes. This better explains the gentle curvature of the imbibition water relative permeability, compared with the customary assumed mixed-wet large wettability model. Our results showed that, when inferring wettability for pore-network models, the oil residual saturation, minimum and maximum capillary pressure during drainage and imbibition were particularly important. Additionally, we showed that the average contact angles and the contact angles measured outside porous media cannot sufficiently characterise the wettability in pore-network models. This work is important because it provides guidelines for interpreting more complicated pore-network models. (C) 2016 Elsevier B.V. All rights reserved.