Experimental Support for a Simplified Approach to CTRW Transport Models and Exploration of Parameter Interpretation

• Published in: Water resources research Vol. 58; no. 5
• Main Author: Hansen, Scott K.
• Format: Journal Article
• Language: English
• Published: 01.05.2022
• Subjects: continuous‐time random walk; Laplace transform; mass transfer; model calibration; solute transport; upscaling
• DOI: 10.1029/2021WR031350
• ISSN: 0043-1397

We empirically test our earlier theoretical arguments about simplification of continuous‐time random walk (CTRW) solute transport models, namely that without loss of generality the velocity‐like term, vψ, may be set to mean groundwater velocity, the dispersion‐like term, Dψ, defined by a classical, velocity‐independent dispersivity, and the so‐called time constant, τ, to unity. We also argue that for small‐scale heterogeneous advection (HA) and mobile‐immobile mass transfer (MIMT) CTRW transition time distributions, ψ(t), are unaffected by mean flow velocity. To experimentally test these claims, we re‐analyze two bench‐scale transport experiments—one for HA, one for MIMT—each performed at multiple flow rates in otherwise identical conditions, and show it is possible to simultaneously explain all breakthrough curves in each, subject to the above constraints. We compare our calibrations with earlier efforts for the same data sets. In the HA calibration we identify a ψ(t) of the same functional form as previous authors, and which yielded breakthrough predictions essentially identical to theirs, but with greatly differing parameters. This illustrates how values of individual CTRW parameters may not map one‐to‐one onto underlying physics. We recommend reporting complete model descriptions, discuss how the simplified approach assists in this and other theoretical considerations. Key Points We show how a simplified, physically‐constrained continuous‐time random walk (CTRW) approach and velocity‐independent transition time distributions explain experimental data Breakthrough curves (BTCs) at multiple flow rates are fit with true velocities and shared CTRW parameters (with unit time constant) for two physical setups We show by example how distinct sets of CTRW parameters may fit the same BTC ensemble; parameters cannot be interpreted individually