Near-well upscaling for two and three-phase flows

Near-well effects can have a strong impact on many subsurface flow processes. In oil production, because dissolved gas is released from the oil phase when the pressure falls below the bubble point, the detailed pressure field in the immediate vicinity of a production well can strongly impact gas (and thus oil) production. This effect is complicated by the interplay of fine-scale heterogeneity and multiphase flow physics and can be difficult to capture in coarse-grid simulations.;The new upscaling techniques are applied to a variety of heterogeneous reservoir models. Two different fluid models, specifically a typical black oil system and a heavy oil system, are considered. Extensive simulation results are presented for both two and three-phase flows. These results illustrate that the methods are able to accurately capture key near-well effects and to provide predictions for component production rates that are in close agreement with reference fine-scale results. The level of accuracy of the procedures is shown to be significantly higher than that of a standard approach which uses only upscaled single-phase flow parameters. The computational requirements for the methods depend mainly on the number of fine-grid cells in the local well models. For the examples considered in this thesis, speedups of about a factor of 35 relative to the reference fine-grid simulation model are typically achieved, though larger speedups can be readily obtained through use of smaller local well models or by selecting an optimized coarsening factor. An interpolation procedure is introduced which avoids the need for some upscaling computations. Use of this approach results in significantly more speedup if many coarse-scale simulations are performed.;Finally, the general approach is extended to enable the upscaling of unstructured fine-scale models to structured coarse-scale descriptions. The basic upscaling procedures applied for these computations are very similar to those used for upscaling structured models, though additional complexity arises because the simulation of highly detailed unstructured local well models, with resolution down to the scale of the wellbore, is required. Numerical results for oil-gas systems demonstrate that the method is able to provide coarse-scale results in close agreement with reference unstructured fine-scale solutions.;In this thesis, new upscaling (coarse-graining) procedures to capture such near-well effects in coarse-scale flow simulation models are developed and applied. The general methodology entails the use of preprocessing computations over near-well domains (referred to as local well models) for the determination of upscaled single-phase and multiphase near-well parameters. These parameters are computed by minimizing the mismatch between fine and coarse-scale flows over the local well model. Minimization is accomplished using a gradient-based optimization procedure, with gradients calculated through solution of adjoint equations. The boundary conditions applied on the local well model can impact the upscaled parameters, but these boundary conditions depend on the global flow and are not, therefore, known a priori. To circumvent this difficulty, an adaptive local-global procedure is applied. This entails performing a global coarse-scale simulation with initial estimates for well-block parameters. The resulting pressure and saturation fields are then interpolated onto the boundaries of the local well model to provide boundary conditions for the near-well upscaling computations. The overall upscaling methodology is developed first for oil-gas flows. The procedures are then extended to three-phase (oil-gas-water) systems.