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

We 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 parameter, R-D, given by the ratio of characteristic times 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, taking into account 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. Our transport model is capable of interpreting both symmetric and highly skewed solute concentration profiles. Effectiveness of the calibration of the two parameters largely depends on the calibration dataset and the selected objective function whose definition can be supported by the implementation of sensitivity analysis. By relying on a sensitivity analysis driven calibration, we are able to provide an accurate and robust interpretation of the concentration profile evolution across different given initial conditions by relying on a unique set of effective parameter values.