In this work we address the problem of performing uncertainty and sensitivity analysis of complex physical systems where classical Monte-Carlo methods are too expensive to apply due to the high computational complexity. In particular, we consider the Polynomial Chaos Expansion (PCE) as an efficient way of constructing a response surface for a model of gas injection into porous media. We exploit a numerical model representing a two-phase flow of immiscible compressible fluids through an incompressible porous medium aiming at assessing the sensitivity indices and the main distributional features of the maximal spread of the gas cloud. The necessity of an uncertainty study for such a model can arise, for example, in case of CO2 storage risk assessment. Four input parameters have been considered as uncertain: maximal relative gas permeability, reservoir thickness, reservoir total porosity, irreducible water saturation. The sensitivity analysis has been performed by jointly using a numerical scheme to solve the system of partial differential equation (PDE) governing the model and the PCE method to efficiently simulate the physical system response by a meta-model. We thus compare the performance of the PCE method with a standard MC approach through an extended simulation study: here, not only we compare the accuracy in the estimates, but we also show that the computational gain of the PCE approach is remarkable without significant loss in the estimates precision.