SimTech-Projekt: Large-scale arrival time statistics and risk assessment for transport in complex multi-scale formations

Department of Hydromechanics and Modelling of Hydrosystems

Funded by the Cluster of Exzellenc "Simtech" from 1st October 2014 until 30th September 2016


Heterogeneity and scale issues make fine-scale simulations of flow and transport in natural large-scale systems necessary, but at the same time unfeasible. Due to heterogeneity at all scales in realistic conditions, ergodic macroscopic descriptions do not apply. The goal of the project is to analyse the statistics of particle arrival times and dilution in anomalous and pre-ergodic transport at large scales. This forms the basis for probabilistic risk assessment tools in large-scale containment problems such as the far-field transport of radio-nuclides from nuclear waste disposal sites, which is the common driving question of the surrounding Project Network "Multi-phase and Multi-physics Modelling" within SimTech.

This project will play a decisive role in translating the common benchmark case of the Project Network to decision-relevant quantities on the large scale, driven by the SimTech vision "Towards Interactive Environmental Engineering".

We will use stochastic descriptions of large-scale, non-Fickian transport processes in heterogeneous fractured-porous media with heterogeneity at the scale of interest and at many scales below. The targeted formulation is based on a newly developed temporal moment formulation of non-Fickian contaminant arrival time distributions in individual small-scale stream tubes. This formulation will be hierarchically extruded over several scales to obtain large-scale system responses.

The core idea is a novel scale aggregation scheme, a set of statistical rules that exploits the additivity of appropriately chosen time statistics: arrival time distributions of stream tubes in parallel are combined analytically by mixing their statistical distributions, and hence by averaging their temporal moments. For stream tube sections in series, aggregation requires conceptually to add the arrival time random variables from both segments. This is a convolution of their distributions, and leads to adding their temporal cumulants. For linear transport, this aggregation concept allows an analytic and fast analysis of large-scale arrival time statistics in arbitrarily complex heterogeneous systems, and analysis of their corresponding scaling laws.

Project manager

Nowak, Wolfgang

Research assistant

Most, Sebastian




10/2014 - 09/2016


Cluster of Excellence "SimTech" / German Research Foundation (DFG)

Cooperation partners

Dr. Branko Bijeljic, Department of Earth Science & Engineering, Imperial College London


This image shows Lehrstuhl für Hydromechanik und Hydrosystem-modellierung

Lehrstuhl für Hydromechanik und Hydrosystem-modellierung



Pfaffenwaldring 61, 70569 Stuttgart

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