Dynamic optimization for the core-flooding problem in reservoir engineering

Relative permeability and capillary pressure correlations are required for reservoir simulation and hence for proper exploitation of petroleum resources. These flow functions are typically estimated from laboratory scale two-phase flow displacement experiments. This work aims at estimating these flow functions from multi-fractional-flow experiments. The system is governed by partial differential equations (PDEs). The PDEs are discretized spatially giving rise to a differential-algebraic equation (DAE) system. The DAE optimization problem is then solved using a simultaneous approach wherein the differential and the algebraic variables are fully discretized leading to a large-scale nonlinear programming (NLP) problem. This core-flooding problem is also governed by the “outlet-end effect”, which is an on-off condition relating capillary pressure, flow rates and pressures of individual phases at the outlet. This effect is modeled using a complementarity formulation. The multi-fractional-flow experiment is modeled by appending several blocks of models, each corresponding to a given fractional flow. The resulting optimization problem is solved using an interior point algorithm capable of handling large-scale NLPs. Our methodology is reliable and robust and is demonstrated on several cases with good parameter estimates.