A novel methodology for synthesizing the wetting capillary pressure curve of rocks through sorptivity data

Capillary pressure as a function of moisture content is an essential element in the modelling of multiphase flow in porous media, such as rocks. The constitutive relationship predicting the capillary pressure as a function of fluid saturation in these materials has been the focus of many studies in the literature, as the direct experimental determination of the former is usually time-consuming and not quite straightforward, owing to the topologically complicated pore structure of rocks. In this paper, we perform a systematic analysis of the interrelation between capillary pressure curves (CPC)and the corresponding imbibition curves to evaluate the parameters influencing the entire diffusive process. The aim is the reconstruction of the wetting CPC from sorptivity test data through back analysis, within the framework of the Van Genuchten model. We perform numerical simulations with finite elements, using as input synthetic models of CPC with one, two and three degrees of freedom, the latter being the widely accepted Van Genuchten model. The effectiveness and the limitations of the different models used and the sensitivity of the imbibition curves to each degree of freedom are investigated and critically evaluated. The whole investigation is assisted by theoretical estimations of the sorptivity coefficient, as a function of the model parameters and the measured quantities. The results of our analysis provide not only a clarification of the aforementioned interrelation, but also a relatively simple procedure for reconstructing synthetically the wetting CPC.