We present a model-driven uncertainty quantification methodology based on sparse grid sampling techniques in the context of a generalized polynomial chaos expansion (GPCE) approximation of a basin-scale geochemical evolution scenario. The approach is illustrated through a one-dimensional example involving the process of quartz cementation in sandstones and the resulting effects on the dynamics of the vertical distribution of porosity, pressure, and temperature. The proposed theoretical framework and computational tools allow performing an efficient and accurate global sensitivity analysis (GSA) of the system states (i.e., porosity, temperature, pressure, and fluxes) in the presence of uncertain key mechanical and geochemical model parameters as well as boundary conditions. GSA is grounded on the use of the variance-based Sobol indices. These allow discriminating the relative weights of uncertain quantities on the global model variance and can be computed through the GPCE of the model response. Evaluation of the GPCE of the model response is performed through the implementation of a sparse grid approximation technique in the space of the selected uncertain quantities. GPCE is then be employed as a surrogate model of the system states to quantify uncertainty propagation through the model in terms of the probability distribution (and its statistical moments) of target system states.