Reliable predictions of reservoir flow response require a realistic geological model of heterogeneity and an understanding of its relationship with the flow properties. This paper presents a novel approach for the integration of dynamic data into reservoir models that combines stochastic techniques for the simultaneous calibration of geological models and multiphase flow functions associated with pore-level spatial representations of porous media. In this probabilistic approach, a stochastic simulator is used to model the spatial distribution of rock types identified by rock/connectivity indexes (CIs). Each CI corresponds to a particular pore network structure with a characteristic connectivity. Displacements are modeled on the pore networks to generate multiphase flow functions linked to the CIs. During assisted history matching, the stochastic simulator perturbs the spatial distribution of the CIs to match the simulated pressures and flow rates to historic data. Perturbation of the CIs in turn result in the update of all the flow functions. Comparison is made with the history-matched model obtained only by perturbing permeability and it is argued that reliable predictions of future production can only be made when the entire suite of flow functions is consistent with the real reservoir.