Compositional upscaling for individual models and ensembles of realizations [electronic resource]
Keywords: Energy Resources Engineering.

Compositional flow simulation can be very demanding computationally because it can involve complex physics and many unknowns. This issue is of particular concern in certain applications, such as optimization and uncertainty quantification, where multiple simulations are required. This motivates the development of upscaling procedures, in which coarse-scale parameters and functions that capture subgrid effects are computed. The goals of this work are the development of a compositional upscaling methodology and its use for both single models and ensembles of geological realizations. In the first part of this study, a global compositional upscaling procedure is implemented to enable efficient flow simulation for a specific geological model. The coarse-scale transmissibilities are computed from a global fine-scale single-phase pressure solution, and the upscaled relative permeabilities and alpha-factors (which appear in the coarse-scale representation of component fluxes) are calculated from a global fine-scale compositional simulation. A new procedure for improving accuracy, which entails coarse-scale iteration, is applied. In addition, near-well upscaling is incorporated to compute coarse-scale well-block and near-well parameters. Numerical results for heterogeneous two- and three-dimensional models demonstrate that the overall upscaling technique provides accurate coarse results. These results are shown to be much more accurate than those using 'standard' approaches in which only single-phase parameters (transmissibilities and well indices) are upscaled. We also demonstrate that the upscaled models are robust, in that they continue to provide accurate results even when well bottom-hole pressures vary substantially from the values used in the upscaling computations. This capability should enable the upscaled models to be used for well control optimization. The global compositional upscaling procedure is then incorporated into an ensemble level upscaling (EnLU) framework, which enables efficient uncertainty quantification for compositional problems. In EnLU, global upscaling is applied for only a few selected realizations. For 90% or more of the realizations, upscaled functions are assigned statistically based on quickly-computed flow and permeability attributes. A sequential Gaussian co-simulation procedure is implemented to provide coarse models that honor the spatial correlation structure of the upscaled functions. The resulting EnLU procedure is applied for multiple realizations of two-dimensional models, involving both Gaussian and channelized permeability fields. Results demonstrate that EnLU provides results for flow statistics (e.g., P10, P50 and P90 for phase and component production rates) that are in close agreement with reference fine-scale results. Less accuracy is observed in realization-by-realization comparisons, though the models are still much more accurate than those generated using standard coarsening approaches. To achieve higher efficiency (at the expense of some accuracy), a local-global upscaling procedure for compositional problems is developed. With this approach, global single-phase upscaling is still used to compute the upscaled transmissibilities and well indices, but the upscaled relative permeabilities and alpha-factors are calculated from local (rather than global) fine-scale compositional simulations. The pressure boundary conditions required for the local upscaling are estimated from an initial global coarse-scale compositional simulation. An attribute-based approach, which enables efficient assignment of upscaled relative permeabilities and alpha-factors, is introduced. Numerical results show that the local-global upscaling method, with or without the attribute-based assignment of upscaled functions, provides more accurate coarse results than standard methods. Although the accuracy is not as high as that using global compositional upscaling, substantial computational savings relative to the global approach are achieved.