Oil prices traded in a steady manner Thursday, close to seven-week highs ahead of key official U.S. inventory data.By 08:55 ET (12.55 GMT), the U.S. crude futures traded 0.4% higher at $81.04 a barrel and the Brent contract climbed 0.6% to $85.58 a barrel. There was no WTI settlement on Wednesday because of a U.S. public holiday.Official US crude inventories dueInvestors are awaiting release of U.S. inventory data from the Energy Information Administration later on Thursday, a day later than usual because of the Juneteenth holiday on Wednesday.The American Petroleum Institute, an industry body, released a report which showed that U.S. crude stocks rose by 2.26 million barrels in the week ended June 14.If the official data replicates the industry report it would be a disappointment  as the summer driving season is expected to see a depletion of crude inventories.Middle East conflict adds geopolitical riskOil prices have been supported because of a growing geopolitical risk premium driven by conflict in the Middle East.A Greek-owned ship attacked by Yemen's Houthi militants in the Red Sea last week has sunk, salvagers confirmed on Wednesday, after it was hit by missiles and an explosive-laden remote-controlled boat.Iran-aligned Houthi militants first launched drone and missile strikes on the important trade route in November in what they say is solidarity with Palestinians in Gaza. Israeli Foreign Minister Israel Katz warned earlier this week of a possible "all out war" with Lebanon's Hezbollah, as the country continues its conflict with Hamas in Gaza.Strength in physical marketWhile a broader risk-on move has proved supportive for oil, there are also some signs of strength in the physical market. “The prompt ICE Brent time spread has strengthened, while the Dated to Frontline (NYSE:FRO) Brent (DFL) swap has moved deeper into positive territory and to its highest level since early May,” said analysts at ING, in a note.“Our balance shows the market tightening in the third quarter of this year after the rollover of OPEC+ cuts, so we should be seeing signs of a tightening in the physical market. However, how tight it becomes depends on how demand performs.“