Effects of large-scale heterogeneity and temporally varying hydrologic processes on estimating immobile pore space: A mesoscale-laboratory experimental and numerical modeling investigation.

The advection-dispersion equation (ADE) often fails to predict solute transport, in part due to incomplete mixing in the subsurface, which the development of non-local models has attempted to deal with. One such model is dual-domain mass transfer (DDMT); one parameter that exists within this model type is called immobile porosity. Here, we explore the complexity of estimating immobile porosity under varying flow rates and density dependencies in a large-scale heterogeneous system. Immobile porosity is estimated experimentally and using numerical models in 3-D flow systems, and is defined by domains of comparatively low advective velocity instead of truly immobile regions at the pore scale. Tracer experiments were conducted in a mesoscale 3-D tank system with embedded large impermeable zones and the generated data were analyzed using a numerical model. The impermeable zones were used to explore how large-scale structure and heterogeneity affect parameter estimation of immobile porosity, assuming a dual-porosity model, and resultant characterization of the aquifer system. Spatially and temporally co-located fluid electrical conductivity (σ) and bulk apparent electrical conductivity (σ)-using geophysical methods-were measured to estimate immobile porosity, and numerical modeling (i.e., SEAWAT and R3t) was conducted to explore controls of the immobile zones on the experimentally observed flow and transport. Results showed that density-dependent flow increased the hysteresis between measured fluid and bulk electrical conductivity, resulting in larger interpreted immobile pore-space estimates. Increasing the dispersivity in the model simulations decreased the estimated immobile porosity; flow rate had no impact. Overall, the results of this study highlight the difficulty faced in determining immobile porosity values in field settings, where hydrogeologic processes may vary temporally. Our results also highlight that immobile porosity is an effective parameter in an upscaled model whose physical meaning is not necessarily clear and that may not align with intuitive interpretations of a porosity.