The significant oil reserves related to karst reservoirs in Brazilian pre-salt field adds new frontiers to the development of upscaling procedures to reduce time on numerical simulations. This work aims to represent karst reservoirs in reservoir simulators based on special connections between matrix and karst mediums, both modeled in different grid domains of a single porosity flow model. This representation intends to provide a good relationship between accuracy and simulation time.
The concept follows the Embedded Discrete Fracture Model (EDFM) developed by Moinfar, 2013; however, this work extends the approach for karst reservoirs (Embedded Discrete Karst Model - EDKM) by adding a representative volume through grid blocks to represent karst geometries and porosity. For the extension of EDFM approach in a karst reservoir, we adapt the methodology to four stages: (a) construction of a single porosity model with two grid domains, (b) geomodeling of karst and matrix properties for the corresponding grid domain, (c) application of special connections through the conventional reservoir simulator to represent the transmissibility between matrix and karst medium, (d) calculation of transmissibility between karst and matrix medium.
For a proper validation, we applied the EDKM methodology in a carbonate reservoir with mega-karst structures, which consists of non-well-connected enlarged conduits and above 300 mm of aperture. The reference model was a refined grid with karst features explicitly combined with matrix facies, including coquinas interbedded with mudstones and shales. The grid block of the reference model measures approximately 10 × 10 × 1 meters. For the simulation model, the matrix grid domain has a grid block size of approximately 100 × 100 × 5 meters. The karst grid domain had the same block size as the refined grid. Flow in the individual karst grid domain or matrix grid domain is governed by Darcy's equation, implicitly solved by simulator. However, the transmissibility for the special connections between karst and matrix blocks is calculated as a function of open area to flow, matrix permeability and block center distance. The matrix properties were upscaled through conventional analytical methods. The results show that EDKM had a considerable performance regarding a dynamic matching response with reference model, within a reduced simulation time while maintaining a higher dynamic resolution in the karst grid domain without using an unconstructed grid.
This work aims to contribute to the extension of EDFM approach for karst reservoirs, which can be applied to commercial finite-difference reservoir simulators and it presents itself as a solution to reduce simulation time without disregarding the explicit representation of karst features in structured grids.