SPE 119132 Multiscale Mimetic Solvers for Efficient Streamline Simulation of Fractured Reservoirs

Advances in reservoir characterization and modeling have given the industry improved ability to build detailed geological models of petroleum reservoirs. These models are characterized by complex shapes and structures with discontinuous material properties that span many orders of magnitude. Models that represent fractures explicitly as volumetric objects pose a particular challenge to standard simulation technology with regard to accuracy and computational efficiency. We present a new simulation approach based on streamlines in combination with a new multiscale mimetic pressure solver with improved capabilities for complex fractured reservoirs. The multiscale solver approximates the flux as a linear combination of numerically computed basis functions defined over a coarsened simulation grid consisting of collections of cells from the geological model. Here, we use a mimetic multipoint flux approximation to compute the multiscale basis functions. This method has limited sensitivity to grid distortions. The multiscale technology is very robust with respect to fine-scale models containing geological objects such as fractures and fracture corridors. The methodology is very flexible in the choice of the coarse grids introduced to reduce the computational cost of each pressure solve. This can have a large impact on iterative modeling workflows. Introduction Modern reservoir characterization methods and 3D geological modeling are leading the industry to routinely build very large and detailed geological models. These models currently may range in size from 10 to 100 million grid cells and are growing. This has resulted in a steadily increasing gap between flow simulation capability and the desire to build geologic-scale reservoir simulation models. In addition to sheer size, strong heterogeneity in the geological models may create computational problems. Geological models may use very small cells, have highly contrasting reservoir properties, and often have a lower proportion of active cells, which are widely distributed, thereby producing extremely complex hydraulic connectivity. Traditional finitedifference simulators were not designed to handle such models efficiently. This is particularly true for fractured reservoirs, which are very difficult to manage and to optimize recovery for; see BockelRebelle et al. (2005). About 60% of the world’s conventional oil reserves and almost half of its gas reserves are contained in carbonate reservoirs, which tend to be more naturally fractured than sandstone reservoirs. To improve recovery factors, it is essential to have a thorough understanding of the depletion and displacement processes. Fractured reservoirs are complex geological structures in which fluids are stored in matrix blocks and flow occurs in the fractures. It is recognized that state-of-theart simulation methods based upon dual-porosity descriptions may not be able to deliver sufficient resolution of the complex flow patterns that may develop when a fractured reservoir is produced. Several approaches (e.g., Matthäi et al. 2007) have therefore been taken to accurately describe fracture-fault systems on a grid-block scale, e.g., based upon complex gridding schemes in which fractures are represented explicitly either as volumetric grid cells or as lower-dimensional objects at the cell faces. The performance of current finite-difference simulators can drop significantly when detailed descriptions and complex matrix-fracture transport processes are introduced. Traditional reservoir-modeling workflows have been deterministic, with a single “best effort” description of the reservoir and little or no quantitative evaluation of uncertainty in the data and its impact on predictions. More recently, geoscientists have taken advantage of increased computing power to generate many realizations to capture uncertainty in the static geological model. Discriminating between these multiple realizations requires dynamic simulation. In the case of reservoirs where there is a substantial production history, each of the realizations must be simulated and the predicted reservoir response statistically compared with history; the realizations giving the closest match may then be selected