Multiscale Integration for Karst-Reservoir Flow-Simulation Models

Abstract

Summary The significant oil reserves related to karst reservoirs in a Brazilian presalt field add new frontiers to the development of upscaling procedures to reduce time for numerical simulations. This work aims to represent karst reservoirs in reservoir simulators using special connections between matrix medium and karst medium, each 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 Li and Lee (2008) and later extended by Moinfar et al. (2014); however, this work extends the approach for karst reservoirs [embedded discrete-karst model (EDKM)] by adding a representative volume through gridblocks to represent karst geometries and porosity. For the extension of the EDFM approach in a karst reservoir, we adapt the methodology to four stages: construction of a single-porosity model with two grid domains; geomodeling of karst and matrix properties, each for the corresponding grid domain; application of special connections through the conventional reservoir simulator to represent the transmissibility between the matrix and the karst medium; and calculation of transmissibility between the matrix and the karst medium. For a proper verification, we applied the EDKM methodology in a carbonate reservoir with megakarst structures, which consists of nonwell-connected enlarged conduits and greater than 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 gridblock of the reference model measures approximately 10 × 10 × 1 m. For the simulation model, the matrix-grid domain has a gridblock size of approximately 100 × 100 × 5 m. 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 a 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 scaled up through conventional analytical methods. The results show that EDKM had a considerable performance regarding a dynamic matching response with the 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 the EDFM approach for karst reservoirs, which can be applied to commercial finite-difference reservoir simulators. This could be a solution to reduce simulation time without disregarding the explicit representation of karst features in structured grids.