Detailed Near-Well Darcy-Forchheimer Flow Modeling and Upscaling on Unstructured 3D Grids

Abstract

Abstract Computing well performance accurately is very important for reservoir management and optimization. Standard large-scale reservoir simulators, however, are not able to resolve detailed near-well physics such as the interaction between the local pressure gradient, reservoir heterogeneity, and well completion. This is because these effects occur on scales that are very small compared to typical simulation grid blocks. In this work, we describe a modeling procedure for representing the well and near-well region that is able to resolve flow down to the scale of the completion and perforations. Our computations involve single-phase flow simulations on unstructured 3D tetrahedral grids. The Darcy-Forchheimer equation is solved in order to include non-Darcy effects, which can be important in the near-well region where fluid velocities are high. The new modeling capability is applied to quantify the impact of completion type - open hole or perforated cased hole - on well productivity. Next, in order to capture these detailed effects in large-scale simulation models, a new upscaling procedure is developed and applied. The approach can be categorized as a local-global upscaling method which uses global coarse-scale simulations to provide key parameters for the local upscaling computations. An example for a case with significant non-Darcy effects demonstrates the high degree of accuracy achievable using this technique. Introduction Accurate well models are essential for reservoir and production engineering applications. In reservoir simulation, wells act as source terms, so the accuracy of the overall flow solution depends directly on well representations. Standard (default) well models, which couple the wellbore and wellblock using a well index, are valid for idealized cases. These models can lose accuracy for complex situations, however, as they evaluate the well index based ont he assumption of radial flow in the near-well region. Although a number of more general procedures for computing well index have been presented (e.g., Su (1995), Peaceman (1990), Wolfsteiner et al. (2003)), these techniques still contain a number of assumptions, are only approximate in the case of general reservoir heterogeneity, and do not attempt to resolve details down to the level of the completion. Our goals in this work are to generalize previous well treatments by introducing models that are resolved down to the scale of the wellbore, including details of the completions and non-Darcy flow effects, and to develop a procedure for upscaling these models for use in practical simulation studies.