Produced Water Reinjection (PWRI- the industry loves it's acronyms doesn't it?) is a bit unusual and also a bit hard: unless all of the oil has been removed from the water (down to a few PPM), you get emulsions forming during the injection and gradual loss of injectivity as the formation essentially gums up.
Also, if you are injecting new water as pressure support or water flood (they are similar but separate things), the thermal difference between the injected water and the formation means you get fracturing in the injection well, increasing injectivity, which is good.
Of course, in certain areas, water may not be easily avaialble, so produced water is better than nothing.
The other thing they might be looking to dispose of down the disposal well is cuttings, especailly oil based mud contaminated cuttings: depending upon the local regulations, slurrification & injection of OBM cuttings might be the only cost effective disposal route.