Scaling equation for counter current imbibition in the presence of gravity forces considering initial water saturation and SCAL properties

Imbibition is an important mechanism in naturally fractured reservoirs. Despite the previous studies on the scaling groups introduced to characterize the imbibition process, a general scaling relation covering the existing situations such as gravity force, SCAL properties and initial water saturation, is missing. This paper has investigated the effects of different reservoir conditions on the imbibition behaviors in naturally fractured reservoirs. In particular, by performing realistic numerical simulation, the impact of parameters such as matrix block pressure, permeability, porosity, matrix block dimensions and initial water saturation were analyzed. A modified scaling equation based on the work of Mirzaei-Paiaman (2015) that considers the mentioned parameters was introduced. In addition, a new parameter named as normalized area was defined which shows the scaling efficiency of a scaling group. By calculating the normalized area factor, the performance of the introduced scaling equation was compared with the previously introduced scaling equations in different models with diverse conditions. The results showed an improvement accuracy on the imbibition scaling with the proposed scaling group in this study.