tracer injection and boundary condition?

We try to simulate injection of certain amount of the tracer into the flow fileld. Injection (in laboratory) is done by water flux 0.029 m3/day with concentration 10 g/liter.
In Feflow we use boundary condition of the injection well (4th  type for flow) and constant concentration at the same node (1st type for transport). But with this approach (logically) the tracer amount released into water depends on the surroundig flow field magnitude. Which boundary condition should we use to obtain fixed mass flux of the tracer? Thank you for your answer very much.

Jan,

I would always try to use a fixed concentration (1st kind BC) as you have done. Refine the mesh around the injection point until you no longer see a change in the injected mass (using the budget analyzer on a nodal basis). The probable reason for a too high mass injection in your case is a too coarse discretization, leading to a lateral freshwater flow also at the injection node. Mesh refinement makes sure that flow velocity vectors point away from the injection nodes to all surrounding node, only having injected water at the injection node.

The alternative would be the use of a 4th king (well) mass transport BC for the injection node. However, this would require the usage of the so-called "divergence form" of the transport equation for the mass transport equation, leading possibly to instabilities at "free-outflow" boundaries, such as pumping wells etc.

Best regards,
Peter

Dear Peter,
Thank you for your answer but refinement does not solve our problem. We probably described our problem in a bad way.
We try to simulate injection of tracer into the fracture. There is steady state, relatively rapid, flow field in the fracture (that we simulate with discrete elements). Into this flow field we injected (under pressure) tracer through borehole filed with porous material. We know exact concentration of tracer (e.g. 100 mg/l), exact injection flux (e.g. 1 m3/day), but we are not able to force our simulation to get balanced mass flux as product of these two values (100 g/day) in the injection node (when we use 4th type boundary flow condition and 1st type boundary transport condition). When we use 4th type flow and transport boundary condition we are not able to achieve appropriate concentration 100 mg/l in this node (it means bad breakthrough curve). Tracer mass flux (for both described variant of boundary condition) depends on flow velocity of fresh water in the fracture. Disproportion grows with increase of  flow rate of the fresh water through model domain. Is it possible simulate such a tracer test in FEFLOW?
It is not easy to describe our problem clearly. If somebody have enough time it is possible to download simple example of our problem at “http://www.1progeo.cz/download.php”.   

I've had a look at your model now. The reason for the higher boundary balance for solute transport is the following: The total inflow of mass is the sum of the advective inflow with the injected water and the dispersive/diffusive inflow caused by the concentration gradient between the injection node and the neighboring nodes. The advective part is always 100 g/d, which is OK. In addition, you get dispersive/diffusive mass inflow because the concentration at the neighboring nodes is not 100 mg/l. Especially the vertical gradient between the injection node and the fracture node below with a significant component of horizontal freshwater is important. Vertical mesh refinement between the injection node and the fracture should help to reduce this effect.

Dear Peter, thank you for your patient help.  I'm afraid vertical refinement didn't solve our problem.  When we compare the 3 slice and the 25 slice model (between injection node and fracture is 17 slices) the results are very similar. The total tracer flux goes to 140 g/day (advective 100 + dispersive 40 g/day).
We also try to reduce dispersivity at the barrier nodes. It allows us to have concentration at the barrier nodes approximately 100 mg/l and also tracer mass flux close to 100 g/day. And that is great. But now we are not able balance injected tracer flux at the free outflow b.c. Outflow from the model is simulated via 1st kind flow b.c. only.  Product of modeled concentration and outflow rate gives us tracer output flux only about 5g/day instead of 100 g/day. What should we do?