Guidelines for Numerically Modeling Co- and Counter-current Spontaneous Imbibition

We present guidelines for accurately simulating both co- and counter-current spontaneous imbibition (SI) phenomenon in 1D systems. We first consider several cases for this study, which involve strongly water-wet, weakly water-wet and mixed-wet wettability states, to simulate co- and counter-current SI in an oil-water system. We create two separate 1D models on a numerical simulator to simulate and obtain saturation profiles for the different cases. We then match simulation results with saturation profiles obtained through the capillary dominated flow semi-analytical solution proposed by Schmid et al. (Water Resour Res 47(2), 2011, SPE J 21:2-308, 2016). The numerical study evaluates the effect of model orientation and co-ordinate system on the saturation profiles. Moreover, we perform grid sensitivity analysis to choose the optimal number of grid cells, as well as the optimal time steps for the model. We find that capturing 0.25% of core volume in each grid cell is sufficient to numerically model an SI experiment within the acceptable margin of error of 5%. Simulations are performed for 23 different cases based on the SI mode, wettability and mobility ratios. The simulation results in saturation profiles have a mean absolute percentage error from the profile obtained from the semi-analytical solution between 0.14 and 5.41% for counter-current SI for the different wettability states. For most wettability states for the co-current SI, however, we do not get a close match, indicating that the semi-analytical solution does not hold for co-current SI. The paper lists some useful guidelines for simulating SI phenomenon, such as selecting the optimum number of grid cells for the SI model and accounting for capillary backpressure, which could be extended to be applied for simulating coreflooding experiments. This paper also discusses current limitations of the semi-analytical solution. These calibration and sensitivity studies can significantly improve the accuracy of the simulation results.