Control-Relevant Upscaling

Abstract

An ‘upscaling/order-reduction’ solution transfers the relevant features of a geological model to a flow simulation model such that cost-efficient simulation, prediction and control of the fluid flow in an oil reservoir become feasible. In addition to the computational issues, in most reservoir applications and for a given configuration of wells, there is only a limited amount of information (output) that can be observed from production data, while there is also a limited amount of control (input) that can be exercised by adjusting the well parameters. From a system-theoretical point of view, this means that a large number of combinations of the state variables (pressure and saturation values) are not actually controllable and observable from the wells, and accordingly, they are not affecting the input-output behavior of the system. In this research, therefore, we aim at adjusting (reducing) the level of model complexity (order) to the level of relevant dynamics in terms of input-output behaviour. In particular, we present a multi-level selective (i.e. non-uniform) grid coarsening method, in which the criterion for grid size adaptation is based on the spatial quantification of the controllability and observability properties of the reservoir system. Based on the numerical examples, this method can accurately reproduce the flow response of the fine scale models.