Tracer tests with finite element modeling (FeFlow)

I have been working on creating a synthetic case scenario for a tracer test recently and I thought I would share some of what I have learned. First of all, it is important to realize that two types of tracer tests exist, whether you want to study the contamination under ambient flow conditions or under perturbed flow conditions. The former type of tracer tests would represent, what some call a pulse, or in other words, when a bucket of water containing the tracer at a given concentration is dumped into a well, whereas the latter type implies a tracer injection at a given rate.

Modeling a tracer test under natural flow can be done by setting initial concentrations at nodes coinciding with the well location. This implies knowledge of how the volume affected by the initial concentrations is defined in the finite-element model, to ensure the adequacy of the simulated mass injection. In Feflow, the volume associated to a certain node, e.g. the node at which the concentration is initially set, can be calculated as the sum of a fraction of the elemental volumes adjacent to the node. For example, if you have a rectangular grid, the volume will be equivalent to the sum of the quarter of the volume of each rectangle adjacent to the node, since each element has four nodes. Note, that in 2D modeling, the volume is calculated by multiplying the area by 1 length unit. Once the volume is known, it is then possible to obtain the mass, by multiplying the concentration at each node by the affected fluid volume. The latter is equivalent to the product of corresponding element volume, porosity and saturation. Therefore, if one desires to model the dissemination of a tracer mass with a given initial concentration, the well will have to be discretized to allow simulation of true mass injection.

Modeling of a tracer test under perturbed flow conditions is straightforward. Indeed, Feflow allows you to model a well as a sink/source boundary condition (BC) for the flow model. When using the convective (default) form of the transport equation, it is mass nodal sink or source should be avoided at nodes where a flow BC is defined (as suggested by the Feflow help). Therefore, a mass concentration BC can be assigned to these nodes, where the well is defined. Time-series can be assigned to the source term and the mass concentration BC, allowing one to set these terms only for a given period of time. By setting these two conditions in parallel, it is then possible to determine the total mass of the tracer injected.