1-D modeling of radionuclide transport via heterogeneous geological formations for arbitrary length decay chains using numerical inversion of Laplace transforms

Abstract

a b s t r a c tWe present the Laplace-transformed analytical solution (LTAS) to the one-dimensional radionuclide transport equation for an arbitrary length decay-chain through an arbitrary combination of multiply fractured and porous transport segments subject to an arbitrary time-dependent release mode at the entrance point to the series of transport segments. The LTAS may be numerically inverted to obtain the time-dependent concentration of the radionuclides of interest at an arbitrary down gradient location. For a special case, where the source function is defined as the band release with a single radionuclide without precursors, the Laplace inverse transformation could be performed analytically, yielding a closed-form analytical solution. A computer code, TTBX, has been developed by implementing the LTAS, and benchmarked against the closed-form analytical solution. Numerical examples are presented to demonstrate the utility of these solutions and the importance of increased fidelity in the transport pathway for reliable performance assessment for the geological disposal of spent nuclear fuels.

Effects of depth on transport of 129I in crystalline rock

“…The governing Eqs. (13) and (14) can be solved analytically with appropriate side conditions, as shown in van den Akker and Ahn (2014). The analytical solution is shown below for the reader's convenience: …”

“…Iodine speciation at initial iodine molalities 10-4 g atom/kg as a function of pH at 25°C (a) Palmer et al (1985), (b) with PHREEQC. ment in heterogeneous geological media are given in van den Akker and Ahn (2014).…”

“…Ahn (1998) developed the Transport to Biosphere (TTB) code by combining this Hodgkinson and Maul model with a detailed source-term model. Recently, a model and an extended code (TTBX) for release and transport of radionuclides through a 1-D fractured medium have been developed by van den Akker and Ahn (2014), which accommodates a multi-segmented transport pathway through an arbitrary number of rock types for a multiple-member decay chain. A numerical illustration of the TTBX code was given for disposal of TRISO spent fuel at the Yucca Mountain Repository (van den Akker and Ahn, 2013).…”

“…In this study, the TTBX model developed by van den Akker and Ahn (2014) for the release and transport of radionuclides through multi-segmented geological media has been used for simulating iodine transport. See Fig.…”

“…The first stage has been achieved by utilizing the model and code, TTBX, previously developed by van den Akker and Ahn (2014), for a multi-segmented 1-dimensional pathway for a multiple-member decay chain. The variation of transport parameters along the pathway has been accommodated by segmenting the pathway and assigning average values to each of these segments.…”