Several reasons could lead to this, water conning, high Sw, if the well is a long time producer and there is an injector near by, it could be water influx from it. However if the volumes are really low, you could consider as a some sort of condensation due to temperature differential. The parameters you need to calculate to start understanding the carbonates formation properties are, Wellbore storage, Skin, radius of investigation, and permeability of course, with this you will determine if there is some sort of damage by the skin, also using the wellbore storage you can count if the water could be from drilling, did you take samples from the DST? what is the salinity? did it has a mixture of drilling mud? An other approach is trying with you geologist to calculate the Hydrodynamic gradient. As a quick approach I would say there is some sort of water conning!