This paper presents the extension of hyperbolic and conservative two-phase flow model to a mixture of porous media containing nanofluids which is known as an aerogel. We focus mainly on the application of non-equilibrium mixture behaviour between phases in one space dimension. The governing equations are solved by finite volume techniques using Godunov methods of centred-type. Special emphasis is given to important and unsteady non-linear phenomena such as shock propagation in low densities aerogels. Simulation results are compared with other methods providing a remarkable agreement. Results show the good capabilities of this mixture formulation in the resolution of discontinuities in aerogel problems. This provides some insights into the fundamental properties of aerogels and helps to better understand some of the inherent difficulties in quantifying them using two-phase flow processes.