Numerical simulations are a highly valuable tool to evaluate the impact of the uncertainties of various modelparameters, and to optimize e.g. injection-production scenarios in the context of underground storage (of CO2typically). Finite volume approximations of Darcy’s parabolic model for flows in porous media are typically run many times, for many values of parameters like permeability and porosity, at costly computational efforts. We study the relevance of reduced basis methods as a way to lower the overall simulation cost of finite volume approximations to Darcy’s parabolic model for flows in porous media for different values of the parameters such as permeability. In the context of underground gas storage (of CO2 typically) in saline aquifers, our aim is to evaluate quickly, for many parameter values, the flux along some interior boundaries near the well injection area—regarded as a quantity of interest—. To this end, we construct reduced bases by a standard POD-Greedy algorithm. Our POD-Greedy algorithm uses a new goal-oriented error estimator designed from a discrete space- time energy norm independent of the parameter. We provide some numerical experiments that validate the efficiency of the proposed estimator.