Fast Upscaling of Polymer Flood Simulations Using Fractional Flow and Scaled Mobilities

We introduce a pseudoisation method to upscale polymer flooding in order to capture the flow behaviour of fine scale models. This method is also designed to improve the predictability of pressure profiles during this process. This method controls the numerical dispersion of coarse grid models so that we are able to reproduce the flow behaviour of the fine scale model. To upscale polymer flooding, three levels of analysis are required such that we need to honour (a) the fractional flow solution, (b) the water and oil mobility and (c) appropriate upscaling of single phase flow. The outcome from this analysis is that a single pseudo relative permeability set that honours the modification that polymer applies to water viscosity modification without explicitly changing it. The shape of relative permeability can be chosen to honour the fractional flow solution of the fine scale using the analytical solution. This can result in a monotonic pseudo relative permeability set and we call it the Fractional-Flow method. To capture the pressure profile as well, individual relative permeability curves must be chosen appropriately for each phase to ensure the correct total mobility. For polymer flooding, changes to the water relative permeability included the changes to water viscosity implicitly thus avoiding the need for inclusion of a polymer solute. We call this type of upscaling as Fractional-Flow-Mobility control method. Numerical solution of the upscaled models, obtained using this method, were validated against fine scale models for 1D homogenous model and as well as 3D models with randomly distributed permeability for various geological realisations. The recovery factor and water cut matched the fine scale model very well. The pressure profile was reasonably predictable using the Fractional-Flow-Mobility control method. Both Fractional-Flow and Fractional-flow-Mobility control methods can be calculated in advance without running a fine scale model where the analysis is based on analytical solution even though produced a non-monotonic pseudo relative permeability curve. It simplified the polymer model so that it is much easier and faster to simulate. It offers the opportunity to quickly predict oil and water phase behaviour.

Stress level effect on mobility of dry granular flows of angular rock fragments

Granular flows of angular rock fragments such as rock avalanches and dense pyroclastic flows are simulated numerically by means of the discrete element method. Since large-scale flows generate stresses that are larger than those generated by small-scale flows, the purpose of these simulations is to understand the effect that the stress level has on flow mobility. The results show that granular flows that slide en mass have a flow mobility that is not influenced by the stress level. On the contrary, the stress level governs flow mobility when granular flow dynamics is affected by clast agitation and collisions. This second case occurs on a relatively rougher subsurface where an increase of the stress level causes an increase of flow mobility. The results show also that as the stress level increases, the effect that an increase of flow volume has on flow mobility switches sign from causing a decrease of mobility at low stress level to causing an increase of mobility at high stress level. This latter volume effect corresponds to the famous Heim’s mobility increase with the increase of the volume of large rock avalanches detected so far only in the field and for this reason considered inexplicable without resorting to extraordinary mechanisms. Granular flow dynamics is described in terms of dimensionless scaling parameters in three different granular flow regimes. This paper illustrates for each regime the functional relationship of flow mobility with stress level, flow volume, grain size, channel width, and basal friction.