Modelling and Upscaling Unstable Miscible Displacement Processes: Characterisation of Physical Instabilities

The compositional simulations are required to model CO2 flooding are computationally expensive particularly for fine-gridded models that have high resolutions, and many components. Upscaling procedures can be used in the subsurface flow models to reduce the high computation requirements of the fine grid simulations and accurately model miscible CO2 flooding. However, the effects of physical instabilities are often not well represented and captured by the upscaling procedures. This paper presents an approach for upscaling of miscible displacements is presented which adequately represents physical instabilities such as viscous and heterogeneity induced fingering on coarser grids using pseudoisation techniques. The approach was applied to compositional numerical simulations of two-dimensional reservoir models with a focus on CO2 injection. Our approach is based on the pseudoisation of relative permeability and the application of transport coefficients to upscale viscous fingering and heterogeneity-induced channelling in a multi-contact miscible CO2 injection. Pseudo-relative permeability curves were computed using a pseudoisation technique and applied in combination with transport coefficients to upscale the behaviour of fine-scale miscible CO2 flood simulations to coarser scales. The accuracy of the results of the pseudoisation procedures were assessed by applying statistical analysis to compare them to the results of the fine grid simulations. It is observed from the results that the coarse models provide accurate predictions of the miscible displacement process and that the fingering regimes are adequately captured in the coarse models. The study presents a framework that can be employed to represent the dynamics of physical instabilities associated with miscible CO2 displacements in upscaled coarser grid reservoir models.

CFD Challenge: Solutions Using the Spectral Element Solver NEKTAR

Flow problems in cardiovascular mechanics involve complex geometries and pulsatile flow that may give rise to instabilities, especially in pathological cases. High-order methods are particularly suitable for resolving such unsteady phenomena whereas low-order methods may exhibit excessive dissipation and hence suppress any such physical instabilities. This, for example, is the case for certain type of cerebral aneurysms, see [1], for which we have demonstrated that shear layer instabilities may be triggered even at physiological flow rates, giving rise to audible frequencies in the range of 10Hz to 50 Hz. Similar phenomena may be present in stenotic arteries, where a jet type flow may develop that is also susceptible to temporal instabilities, especially during the decelerating systole.