By Noah Browning LONDON (Reuters) -Oil rose on Monday as supply concerns driven by lower OPEC output, unrest in Libya and sanctions against Russia outweighed fears of a demand-sapping global recession. Euro zone inflation hit yet another record high in June, strengthening the case for rapid European Central Bank rate increases, while U.S. consumer sentiment hit a record low. Brent crude rose $2.26, or 2%, to $113.89 a barrel by 12:47 p.m. ET (1648 GMT) after falling more than $1 in early trade. U.S. West Texas Intermediate (WTI) crude rose $2.20, or 2%, to $110.63, in thin volume during the U….