A Similarity Solution for Imbibition Process and its Adaptation in Finite Difference Simulation of Fractured Reservoirs

The imbibition process due to capillary force is an important mechanism that controls fluid flow between the two domains, matrix and fracture, in naturally or hydraulically fractured reservoirs. Many simulation studies have been done in the past decades to understand the multi-phase flow in the tight and shale formation. Although significant advances have been made in large-scale modeling for both unconventional and conventional fields, the imbibition processes in the fractured reservoirs remains underestimated in numerical simulation, that limits confidence in long-term field production predictions. In the meanwhile, to simulate the near-fracture imbibition process, traditionally very-fine simulation grids have to be applied so that the physical phenomena of small-length scale could be captured. However, this leads to expensive computation cost to simulate full-field models with a large number of fractures. To improve numerical efficiency in field-scale modeling, we propose a similarity solution for the imbibition process that can be incorporated into the traditional finite difference formulation with coarse grid cells. The semi-analytical similarity solutions are validated by comparing with numerical simulation results with fine-scale grids. The comparison clearly indicates that the proposed algorithm accurately represents the flow behaviors in complex fracture models. Furthermore, we adopt the semi-analytical study to hydraulic fracture models using Embedded Discrete Fracture Model (Lee et al., 2001) in our numerical studies at different scales to represent hydraulic fractures that are interconnected. We demonstrate: 1) the imbibition is critical in determining flow behavior in a capillary force dominant model, 2) conventional EDFM has its limitation in capturing sub-cell flow behaviors near fractures, 3) combining the proposed similarity solution and EDFM, we can accurately represent the multi-phase flow near fractures with coarser grids, and 4) it is straightforward to adapt the similarity solution concept in finite-difference simulations for fractured reservoirs