Let's assume that both barrels contain 100 litres of wine (wi) and water (wa), respectively, and that you can decant 10 litres with the glass Yann mentioned; I know, it's a big glass ;). So let's start by taking a full glass of water and pouring it into the wine:

100 wa				100 wi

		10 wa
	  ---------------------->

So we have something like this:

90 wa				100 wi + 10 wa

Now we're filling the glass again with 10 litres of liquid from the barrel standing on the right site, which contains 100 litres of wine and 10 litres of water, therefore we have a relation of 100 wi : 10 wa (alternatively 10 : 1). As a consequence, the liquid in the glass consists of 100/11 wi + 10/11 wa (added up this makes 110/11 litres, which is equal to 10 litres.). According to that the situation looks now like this:

90 wa							100 wi + 10 wa

			     100/11 wi + 10/11 wa
     		<---------------------------------------------

90 wa + (100/11 wi  +  10/11 wa ) 			100 wi + 10 wa - (100/11 wi + 10/11 wa)


In total this makes:
1000/11 wa + 100/11 wi              	1000/11 wi + 100/11 wa

As you can see, both barrels contain the same amount of the respective liquids. Repeating the process doesn't change this, although the relation approaches more and more 50 wa + 50 wi (on both sides).