A double-continuum transport model for segregated porous media: derivation and sensitivity analysis-driven calibration

We present and derive a novel double-continuum transport model based on pore-scale characteristics. Our approach relies on building a simplified unit cell made up of immobile and mobile continua. We employ a numerically resolved pore-scale velocity distribution to characterize the volume of each continuum and to define the velocity profile in the mobile continuum. Using the simplified unit cell, we derive a closed form model, which includes two effective parameters that need to be estimated: a characteristic length scale and a ratio of waiting times RD that lumps the effect of stagnant regions and escape process. To calibrate and validate our model, we rely on a set of pore-scale numerical simulation performed on a 2D disordered segregated periodic porous medium considering different initial solute distributions. Using a Global Sensitivity Analysis, we explore the impact of the two effective parameters on solute concentration profiles and thereby define a sensitivity analysis driven criterion for model calibration. The latter is compared to a classical calibration approach. Our results show that, depending on the initial condition, the mass exchange process between mobile and immobile continua impact on solute profile shape significantly. By introducing parameter RD we obtain a flexible transport model capable of interpreting both symmetric and highly skewed solute concentration profiles. We show that the effectiveness of the calibration of the two parameters closely depends on the content of information of calibration dataset and the selected objective function whose definition can be supported by of the implementation of model sensitivity analysis. By relying on a sensitivity analysis driven calibration, we are able to provide a good interpretation of the concentration profile evolution independent of the given initial condition relying on a unique set of effective parameter values.
Comment: 38 pages of manuscript plus 4 pages of Supplementary Material