Thermodynamically consistent transport coefficients for upscaling of compositional processes

Compositional simulation of oil reservoirs is necessary for accurate representation of the physics associated with near-miscible gas injection processes. Performing the simulations using the fine-scale geocellular model is computationally expensive; as a result, reliable upscaling methods for compositional flow are needed. Compared with black-oil models, the interactions between the thermodynamic phase behavior and the sub-grid heterogeneities that are associated with compositional displacements pose significant additional challenges to upscaling. We introduce a new framework to upscale multi-component, multi-phase compositional displacements with special attention to accurate representation of the fine-scale phase behavior on the coarse grid. We use a mass-conservative formulation and introduce an upscaled molar mobility for each phase. These upscaled flow functions account for the sub-scale absolute and relative permeability variations, as well as, compressibility effects. They also correct -somewhat- for numerical dispersion effects at the coarse-grid level. The upscaling of the thermodynamic phase behavior is performed as follows. We assume that instantaneous thermodynamical equilibrium is valid at the fine-scale, and we derive coarse-scale equations, in which the thermodynamic phase behavior is not necessarily at equilibrium. Deviation from local equilibrium may be due to different bypassing mechanisms, such as fingering and channelling. As a result, the fugacity of a component in the two phases may not be equal at the coarse scale, and this deviation is quantified by the coarse-scale thermodynamic functions. We demonstrate that these upscaled functions can be interpreted as a transformation of the equilibrium phase space on the fine scale to a modified region of similar shape, but with tilted tie-lines. We then describe how to convert non-equilibrium coarse-scale behavior into the widely used transport coefficients (alpha-factors). The proposed methodology is applied to various challenging gas injection problems. We compare our upscaling method with standard upcaling techniques for compositional simulation, and we show improvements, both in terms of accuracy and computational efficiency, of the new approach.