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. (c) 2005 Elsevier Ltd. All rights reserved.