Ireland's first bond auction since it began to exit its bailout by international creditors in December went with a bang on Tuesday.

There was believed to be between 11-13 billion euros ($15-17.7 billion) worth of orders for the auction, two sources in Dublin told CNBC. While the Irish government had planned to sell 3-3.5 billion euros of 10-year debt, this may be raised to close to 5 billion euros after greater-than-expected demand at the bond sale.