It will be interesting to see how much ash gets ejected. I remember when the Icelandic volcano erupted in spring 2010 and it shut down Europe's sky for about a month. Imagine that happening again now? It would be an absolute nightmare with all the Christmas travel going on.
Grindavik is only 25km from Keflavik, Iceland's International Airport, so I expect the authorities are watching closely.
Nevertheless, I don't think ash is expected unless/until the lava comes into contact with water, either as sea water or ice, which would generate the explosive activity seen at Eyjafjallajokull.