So the total demand for US dollars to pay for crude is not in fact $1.8 trillion or so, but much less. I would estimate that based on $10 per barrel margins that the net demand is closer to $310 billion net of costs that need to be reconverted back into local currency. It is still a handsome sum to be sure, but your numbers are simply misleading.
No, I stand by my basic statement, and their is plenty of documented evidence to support my analysis, including Dr. Sprio's book. Today, and everyday, the volume of global oil trade is just over $5 billion dollars/petrodollars per day. (I can't find the links for that at the moment, but its not necessary given that oil production and prices are known)
You are trying to confuse the issue by using net margins of oil. That is comparing apples and oranges, and its irrelevant to the discussion about the annual incremental demand for dollars, IMO.
(excerpt from my December 2006 essay)
The propping up of the dollar’s international demand by its monopoly petrocurrency status is illustrated by the huge increase in the price of oil from 2002 to 2005 and the commensurate huge increase in dollar holdings by foreign banks (most often Treasury bills) despite the Federal Reserve’s abnormally low interest rates during most of that period. In 2006, international investment analyst Jephraim P. Gundzik noted this important macroeconomic phenomenon in the Asia Times:
As of mid-2005, foreign investors, including foreign central banks, held an estimated $6.6 trillion worth of US bonds and equities, up from less than $4 trillion in mid-2002. About 60% of this money is parked in long-term US Treasury, agency and corporate bonds. The rapid and sustained increase of international oil prices is the main factor behind the growth in foreign holdings of US securities and the external supply of dollars used to purchase these securities. 
Thus it was the huge demand for petrodollars due to high oil prices — and certainly not high yield spreads — that allowed the Federal Reserve to dramatically expand the credit supply by over $2 trillion during recent years. (Note: the Federal Reserve did not begin to increase the abnormally low overnight interest rates until June 2004). Again, I stand by my statement that the annual global demand for petrodollars is well over $1 trillion dollars - gross.
Unfortuantely this correlation between high oil-prices and international demand for the dollar-denominated instruments such as Treasury bills is rarely mentioned in the mainstream US economic commentary, but a March 2006 issue of Business Week confirmed the decades-long connection. Most importantly however, is the crucial fact that petrodollar flows currently plug almost half of the US’s $805 billion current account deficit (this inflow exceeds your "net" estimate of $310 billion):
[Unlike during the 1970s oil boom] Arab states are now major buyers of goods from Japan, China, and the rest of Asia, where they sell the bulk of their oil. So these petrodollars get recycled as Japanese yen or Chinese yuan – which the Japanese and Chinese governments convert into US Treasuries. Indirectly, then, oil money is bankrolling US deficit spending. Paul Donovan, a global economist for UBS Investment Bank in London, estimates that petrodollars, mostly channeled through Asia and Europe, are funding up to 45% of the US current account deficit. 
Assuming Donovan's calculations are correct, as of 2006 petrodollar flows were supporting about $1 billion per day of the US current account deficit ($805 billion x .45 = $362 billion per year, or approximately $1 billion per day). If a basket of currencies begins to be used for international oil transactions involving bourses in Iran, Russia, and China, it is highly doubtful that Japan and the other East Asian nations will be able to step into the fray and keep propping up the dollar.
As we all know, some of these countries are in the process of diversifying their currency reserves in order to "maximize performance,” a diplomatic term for moving away from the weak dollar. Kuwait is just the latest member to make monetary decisions to reduce their exposure to USD.
The key enabler of the system is of course Saudi Arabia, and just as in the past, the Saudis are reportedly “holding the line” by thwarting proposals within OPEC regarding euro-based oil trades and propping up the dollar as the monopoly pricing and transaction currency.  A major policy change such as a formal transition to euro-based transactions for all OPEC members would likely require a unanimous vote within the cartel — an unlikely event under the present circumstances due to the "special relationship" b/t the Washington and the House of Saud.
However, unfolding developments in Iran, Russia, and China, indicate that a currency basket for international oil trade will begin to unfold in earnest during 2007-2008, thus decreasing the dollar’s liquidity and adversing impacting the ability of the US to service its $2 billion per day debt financing via the "kindness of strangers"...nevermind fight a war that costs $5.8 billion per month (or $11 million dollars per hour).
1. Jephraim P. Gundzik, “Upswings and Downfalls,” Asia Times, January 6, 2006, http://www.atimes.com/atimes/Global_Eco ... 6Dj01.html
2. Stanley Reed, “The New Middle East Oil Bonanza,” Business Week, March 13, 2006, p. 36, online: http://www.businessweek.com/magazine/co ... 975001.htm
3. Faisal Islam, “When Will We Buy Oil in Euros?” Observer, February 23, 2003, http://observer.guardian.co.uk/business ... 67,00.html