Geostatistical techniques are widely used for modeling reservoir heterogeneity and uncertainty assessment. Although multiple geostatistical reservoir models are typically generated, only a small fraction can be considered for comprehensive flow simulation due to the computational cost. In this study, we propose an efficient data-driven framework to identify the reservoir connectivity, which can be used as a measure for screening and ranking the geostatistical reservoir models. While purely data-driven models are extensively used because of efficiency and simplicity, it lacks physical interpretability and predictive power. To address these challenges, a physics-informed machine learning framework is utilized. Our machine learning framework takes routine well measurements, including injection rate and pressure data as input and multiphase production rates as output. To enhance the predictive power while maintaining the efficiency, a reduced physics model is incorporated into a physics informed neural network (PINN) architecture. The physics-based regularization terms are embedded to the loss function and incorporate the governing partial differential equation (PDE) of the reduced physics system. The trained PINN model satisfies the governing PDE, making it physically interpretable, and provides preferential fluid flow paths in terms of flux allocation. The estimated flux allocation help screen and rank geostatistical reservoir models, which significantly saves computational burden compared to full flow simulations. Furthermore, the physics-based regularization helps the PINN model avoid overfitting and provides improved predictive performance. The power and efficacy of our proposed framework are demonstrated using a benchmark reservoir simulation case. The proposed PINN method provided comparable forecasting performance of the multiphase production rates. The flux allocations estimated by the trained PINN model provided good agreement with the streamline-based flux allocation. Moreover, the proposed screening workflow is shown to successfully rank and select the plausible geostatistical reservoir models in a computationally efficient manner.