The Army Corps of Engineers is carving out a big new niche for itself by paving the future for oil-rich countries.

Saudi Arabia has hired the corps to supervise nearly $2 billion in construction work, including designing and building a whole city for 60,000 people on a spot that is today little more than sandy nothingness.

Nigeria, second only to Saudi Arabia in the aomount of oil it sells to the United States, is in the final stage of negotiation with the corps to supervise the taming of its Mississippi - the Niger River.

And Qatar, another oil-rich state, has been talking with the corps about improving its harbors on the Persian Gulf.

All three countries are memvers of the Organization of Petroleum Exporting Countries, the oil cartel which has become a powerful new force in global politics.

"President Carter said he wanted us out of the dam-building business," said Brig. Gen. Drake Wilson, deputy director of civil works for the Army Corps of Engineers, in an interview yesterday. "He's encouraged us to look for work to do elsewhere."

With such encouragement from the president and the full blessing of the State Department, the corps is providing a new kind of presence in the underdeveloped world - especially in countries that find themselves suddenly rich in "petrodollar."

The Foreign Assistance Act of 1961, and subsequent amendments, authorize the State Department to enter into agreements calling for the corps to manage construction projects for other a corps spokesman said.

What the corps is doing in Saudi Arabia dwarfs any of its previous work abroad and represents a large foothold for the United States in the country with the world's biggest supply of oil.

Starting in 1961, the corps helped Saudi Arabia make the giant leap into the 20th century. A civilian airline terminal, a television and radio network soon came into being in the kingdom under the supervision of the corps.

The corps translated Saudi wishes into contract specifications, negotitiated the contracts for both design and construction, and stayed to make sure the work got done properly. Saudi military leaders, watching civilian projects take shape, asked the corps in 1965 to build facilities for their army, navy and air force.

Today, construction in Saudi Arabia managed by the Army Engineers is running over $1 billion a year, and is likely to reach $2 billion in Saudi Arabia's fiscal 1997 budget, according to corps leaders.

King Khalid Military City, about 270 miles northest of the capital at Riyadh, is an example of how the corps is modernizing the Saudi military literally from the ground up. The mission of hhe corps is to transform what is now a stretch of sand into a city for $60,000 people, at an estimated cost of $6.6 billion.

Water, sewers, houses, stores, schools, streets, restaurants, hotels and playgrounds all are on the blueprint for King Khalid Military City, where about 6,000 Saudi troops and their families are expected to reside by 1984.

From the American standpoint, "this kind of experience" for training people in the corps how to design and build from nothing "is not available anywhere else in the world," said Col. Wiley W. Walker, Saudi Arabia project chief at the corps' Washington headquarters.

U.S. Saudi contracts for corps management services are written so that all the engineers' expenses are paid by the Saudi government. THe corps has estimated that its expenses will run 10 percent of the construction cost.Riyadh saves money if corps expenses run under that 10 percent, but it also must pay for any overruns.

"We're not allowed to make profit." said Col. Walker in a headquarters interview.

"We're not allowed to make a loss either," chimed in Gen. Wilson.

All told, the corps could end up managing $25 billion in construction in Saudi Arabia under current plans. So far, $10 billion worth has been authorized in joint U.S. Saudi agreements, with $1.2 billion of that already finished. The corps has 900 people in Saudi Arabia, and 300 backing them up from an office in Winchester, Va.

At the corps' estimated management fee of 10 percent. KIng Khalid Military City alone would yield about $650 million. Asked if private firms complain about losing this much in project management fees to a government agency, corps leaders replied that the Army is opening markets abroad that private companies could not reach on their own.

Wilson also said governments of many developing countries claim to have been fleeced by private contractors and prefer to deal with a government agency.

"They've been concerned about being taken," Wilson said.