This is my DIY kalk reactor.
On the left is my clear DI housing (from my RO system), running to a standard clear housing on the right. I have switched the 'in' and 'out' on the housing so that now the water travels down a tube in the centre that I have placed inside, usually it travels around the outside of the standard filters and up the middle. The water travels down the tube to the bottom and percolates through about a cup of kalk, then back up around the outside of the tube and out the 'in'. This housing has 1" outlets I think, so I have two adapters on either side running it down to 3/8" so that I can run my standard 1/4" RO tubing into and out of it. This then runs to my float valve in my sump.
One if the things you want to avoid is exposing your 'kalkified' water to air, as it reacts and you lose your Ca. You also want to dose very slowly otherwise you cause a shift in pH in your tank causing Ca to precipitate out, actually decreasing your Ca rather than increasing it. This system both doses slowly and does not expose your Kalk water to air.
Cautions... don't hook up a reservoir upstream of the housing containing the kalk, otherwise the flow will be too much and the kalk will not settle. Also, I have only had this running for a couple of weeks and have a small concern Ca may build up on my float valve shut off causing it to leak. I don't think this will happen, but it might.
You don't need the special blue top on the housing that I have. It just allows me to shut off or bypass the kalk chamber without shutting my RO system off.
Dan