Entropy production and attractors: Measures to quantify uncertainty and complexity introduced by convection

Abstract

We present two measures which help quantifying the impact of oscillating, convection cells on model convergence, and model certainty:
(i) The measure of an attractor in a phase space of specific enthalpy vs change in specific enthalpy is used in order to evaluate if our model reaches a dynamic steady state after a number of time steps. Attractors are calculated first for an aquifer with homogeneous permeability and then for a case where permeability is affected by compaction. Both model solutions converge towards a point in phase space, a point attractor, thus suggesting that a dynamic steady-state is reached from the same initial conditions. The analysis indicated that the compaction scenario requires more time steps to reach this dynamic steady-state.
(ii) The thermodynamic measure of entropy production, which characterises the convective state of a system. We calculate entropy production for different scenarios of a reservoir model, where free convection occurs. Resulting entropy production values suggest that the modelled convective pattern is not significantly influenced by spatially heterogeneous permeability, but more by the reservoir structure, i.e. the effective thickness of the layer in which convection occurs. A significantly higher average entropy production of a scenario considering compaction compared to a homogeneous permeability distribution supports these findings.