Uncertainty propagation in sandstone compaction modeling

The diagenesis of sedimentary basins is the result of a set of contributing processes taking place after deposition. Among these geochemical reactions and mechanical compaction play the most relevant role. Geochemical reaction models entail the definition of basin scale reaction parameters and are typically temperature dependent. Geological evolutionary scales of basin diagenesis do not allow a straightforward evaluation of modeling parameter and are plagued by uncertainty. In this communication we analyze the uncertainty in porosity vertical distributions given by the effects of several uncertain parameters, such as large scale reaction rate and the mechanical compaction coefficients, and boundary conditions. We employ a model driven parametric uncertainty quantification methodology. The technique is based on a sparse grid sampling in the uncertain parameters space. The original mathematical model is then recast in terms of a generalized Polynomial Chaos Expansion. This methodology allows to (i) obtain a computationally efficient surrogate model of the system and (ii) to compute the complete set of the variance based Sobol indices. Uncertainty propagation is analyzed considering the probability density distribution of porosity and temperature in selected locations along the vertical direction. Results are illustrated on a one dimensional basin compaction problem, involving quartz precipitation in sandstones.