A novel 3D green element method to simulate counter-current spontaneous imbibition considering the effect of gravity

This paper firstly proposes a novel three-dimensional (3D) Green element method (GEM). We have proven it by theoretical error analysis that, the novel GEM with the third-order accuracy, has good convergence and stability, which are the advantages that previous GEMs do not have. This novel method is used to numerically simulate 3D core's counter-current imbibition process with gravity effect, and 1D, 2D and 3D models are implemented to depict good convergence and accuracy of proposed method. Compared with finite difference method (FDM) used by many previous studies, the novel method has the same advantage as previous GEMs, that it requires less elements to achieve a good agreement between simulation results and experiment data. Moreover, specific gravity effect is analyzed, and three typical stages of gravity effect are divided. In summary, the novel 3D GEM and corresponding 3D simulator are effective to simulate counter-current imbibition of the real 3D core considering the effect of gravity.