Recent developments in model-based optimization and control of subsurface flow in oil reservoirs

The past ten years have seen an increasing application of systems and control theory to porous media flow. This involves in particular the use of optimization, parameter identification, and model reduction techniques in attempts to increase the amount of oil or gas that can be recovered from subsurface hydrocarbon reservoirs. Other applications involve the control of ground water flow for drinking water or pollution control, and the subsurface storage of CO2. The dynamic behavior of subsurface multi-phase porous media flow is typically simulated with large-scale nonlinear numerical models, containing up to millions of state variables and parameters. Moreover, a typical characteristic of these models is a very large uncertainty in the parameter values, reflecting the very large geological uncertainty of the subsurface. Traditionally they are primarily used for ’field development’, i.e. the engineering of well configurations and production strategies, but an emerging use is in the ’real-time’ optimization and control of oil production, known as ’closed-loop reservoir management (CLRM)’. In this paper we describe some recent contributions of our group to the use of systems and control theory for CLRM. This concerns sequential and multi-level production optimization, identifiability of model parameters, and ’control-relevant’ upscaling.