d3f++ - Distributed density-driven flow

In Germany, the intention is to dispose of high-level radioactive waste in deep geological formations. The aim is to safely isolate the waste in an area within a host rock or in an area covered by a host rock. Host rock types may be rock salt, clay or crystalline rock (e.g. granite). By its containment, the waste is intended to be kept isolated from humans and the environment for a period of one million years.

In order to provide proof of safe disposal, it is also necessary to investigate the scenario of groundwater penetrating into the repository and contaminants thus escaping from the emplacement area. Where, when and in what concentration can radionuclides enter the biosphere in this way?

Historical development

In the early 1990s, these questions revealed the need to calculate the groundwater flow in the vicinity of a repository in salt rock. Experts then looked for a computer code to calculate the density-driven flow in large-scale model areas with a complicated hydrogeological structures over long periods of time.

A working group of researchers therefore initiated the development of the d³f ("distributed density-driven flow") code. Apart from GRS, the following institutions were involved:

This was followed by the development of the r³t ("radionuclide, reaction, retardation, and transport") code. r³t allowed the modelling of the transport of radionuclides on the basis of the flow field calculated with d³f. Later, the field of application was extended to fractured media, so that it is now also possible to consider other host rock typs than rock salt. Eventually, the d³f and r³t codes were combined to form the d³f++ code.

Initially, five universities worked on the development of the codes under the leadership of GRS. Today, GRS and the Goethe Centre for Scientific Computing (G-CSC) at the University of Frankfurt are continuing to further develop the codes.


The d³f++ code was applied on a regional scale to the Gorleben Trough, the US WIPP repository, and the Swedish Äspö research mine. It is currently used in connection with the prospective Czech Čihadlo repository site. In addition, d³f++ has already been used outside repository research to create models for sea water intrusion in coastal aquifers, such as in the NAWAK project of GRS.