An efficient fractional-in-time transient storage model for simulating the multi-peaked breakthrough curves

Abstract

The multi-peaking phenomenon in a breakthrough curve (BTC) is a typical character of solute transport in complex flow fields such as a karst aquifer. Previous understanding and modeling techniques for the single-peaked BTCs would no longer be adequate for the multi-peaked one. In a traditional non-Fickian model, the overall non-Fickian effect is simply the summation of contributions from each immobile zone or heterogeneous flow path. Therefore, a resultant BTC is not sensitive to the exact location of the immobile zones on the pathway of solute, and the local peaks cannot be reproduced effectively. In this study, we introduce a fractional-in-time transient storage (TS) model (FTTS), in which, the TS zones are arranged in series (e.g., triggered at specific times) to simulate different locations of each TS zone or immobile zone along the river channel. The simulation power of the FTTS was tested by simulating observations from a tracer experiment conducted in a subterranean river and data generated from two synthetic cases. Meanwhile, the simulation results of the FTTS were compared with those from the fractional mobile/immobile model (FMIM) and the multi-rate transient storage model (MRTS). Results show that both FTTS and MRTS models could well simulate the multi-peaking phenomenon in BTC and perform better than FMIM. Further to that, compared to MRTS, the FTTS is a more efficient model because (1) when containing the same number of TS zones, the FTTS performs significantly better, and (2) when achieving similar accuracy, the FTTS uses fewer TS terms (corresponding to a smaller number of parameters) than MRTS. Moreover, all TS terms in the FTTS can form a one-to-one correspondence with the local peaks of BTC, which may be helpful for better characterizing the internal morphology of a flow field.