On the fertile dark soil of the savanna here along the White Nile, the world's second largest sugar mill and refinery has finally begun production--a reminder of this nation's past dreams of prosperity as the imagined "breadbasket" of the Arab world.

The 83,400-acre sugar cane plantation, with an ultramodern plant capable of producing 330,000 tons a year, cost between $700 million and $800 million to put up and is without doubt a towering monument to western technology and ingenuity.

It was built 200 miles south of Khartoum and its constructors faced every conceivable obstacle, from the absence of roads to the site to repeated shortages of capital to cover huge overruns on the initially projected $100-$125 million cost.

Now that it is operating, the mammoth plant has given new hope to the government and outside investors that ailing Sudan is, as one western analyst put it, "beginning to get back on the right path" after years of wallowing in economic mismanagement and stagnation despite its enormous land and water resources.

Yet controversy still swirls around Kenana, which stands as a test case of a theory of economic development, fashionable in the mid-1970s, called "trilateralism." The idea was to combine western technology and Arab "petrodollars" to tap Africa's vast agricultural resources.

The question remains, however, whether the supposed beneficiaries, like Sudan, one of the world's poorest nations, can afford the theory--now or ever.

The strategy for Sudan was worked out by the Kuwait-based Arab Fund for Economic and Social Development, which drew up an initial $5.7 billion investment program as part of an overall 20-year plan to make this country, Africa's largest, the granary of the Arab world.

The strategy was partly a response to Arab fears that the United States, after the Arab oil boycott of 1973, might be tempted to retaliate with its own food boycott, a notion former secretary of state Henry Kissinger reportedly implanted in the Arab mind.

Today, few talk about Sudan any longer as anything but a "basket case" of economic development--so huge are its outstanding debts ($7.8 billion), so far behind is it in payment of arrears ($3 billion rescheduled for this year) and so bankrupt is its treasury, facing a current $1.6 billion gap in its balance of payments.

The Persian Gulf states that were supposed to bankroll the "breadbasket" strategy look on Sudan today as a major economic and political liability, and its main financial backers, Saudi Arabia and Kuwait, have turned inward to spur a boom in farming by their own nationals on far more difficult desert terrain.

What went wrong is an intriguing question to which there appear to be as many answers as there are pundits, economists and theorists of Sudan's disastrous performance. But one common reply is "changed circumstances" in the world economy beyond anyone's wildest imagination in the early 1970s.

"The breadbasket idea was based on projecting the short-term circumstances over 20 years. But these were overtaken by events," one western economist remarked. "Inflation outstripped commodity prices and the Arab strategy changed toward Sudan as the breadbasket. That idea is now more or less consignable to the dustbin of history." But even this pessimist did not rule out the possibility that "maybe in 20 years" it would come alive again.

Meanwhile, Sudan is trying to cope with a landscape strewn with new but closed factories, faulty schemes and half-completed projects that have turned this country into a junkyard of development programs and a nightmare for the government.

The sugar industry is one case in point. The government once planned to boost production to 750,000 tons by 1980, enough to cover all local consumption and allow exports of 300,000 tons to the Arab gulf states. Since Sudan was once spending $1 million a day on sugar imports and was still spending half a million dollars daily last year, the plan seemed sound economic sense.

But just about everything that could go wrong did so, and the country still will not even cover its own needs in sugar for another two years, let alone export any.

One major disaster occurred 20 miles northwest of here at Assalaya, where a 110,000-ton sugar refinery was built in 1978 but closed almost immediately because of a variety of problems, including insufficient steam generation, faulty lubrication devices and a poorly managed irrigation system.

To top off its troubles, the plant is now listing, with one side two feet higher than the other, because it was built on soil that swells and cracks with the weather. Outside consultants are now discussing how to repair the mill and whether it will have to be moved to a new location.

Kenana has been the lone success in Sudan's plan to build a viable sugar industry. But even the economics of Kenana are full of "ifs" because of the nature of the world sugar market and it is far from clear when, if ever, it will turn a profit.

Two years after inauguration, its production has already surpassed 200,000 tons. If all goes well, it should reach its peak capacity of 330,000 in another two years. This should be enough, together with four ailing state-run sugar plants now being overhauled, to meet Sudan's needs.

Kenana's Sudanese managing director, Osman Abdullah Nazir, and its American plant manager, Francis C. Schaffer of the Baton Rouge-based Arkel International Co., are proud of the huge plant's performance so far. Schaffer, who was responsible for putting it up, said the plant's "efficiency" is in the top 1 percent worldwide, with the rate of extraction of sugar from the 2.3 million tons of cane it now processes averaging 96.6 percent.

Kenana has some unique features. It produces 42 megawatts of electricity daily, making it the second largest source of power in Sudan and enabling it to inject 32 surplus megawatts into the national grid during the six months of production.

Moreover, the plant is self-sufficient in fuel during those months, since it makes use of the fibrous byproduct of cane known as bagasse to produce all the needed energy.

Still, the plant is extremely costly to maintain and operate even with major government concessions on taxes and land, and free water. It has to be disassembled every year and it takes a computer to keep track of orders for the 32,000 spare parts needed from abroad to keep it and its farm machinery going.

Neither Nazir nor Schaffer would say what the present cost of production was. But they did estimate that once the plant was producing 300,000 tons, it would average $370 a ton, putting it at about the middle of the worldwide range varying from $320 to $470 a ton.

Nazir also spoke of a "financing gap" during the next five years that the shareholders, primarily the Sudanese, Kuwaiti and Saudi governments, presumably will have to meet in addition to the $430 million they have already sunk into the plant.

The immediate problem facing Kenana is the price it will get for its sugar, both from the Sudanese government and abroad. World prices, nearly $1,000 per metric ton in 1980, have fallen to $180, far below production costs.

But Nazir and Schaffer argued that the world price is nearly meaningless because it reflects only the 10 to 15 percent of total world sugar production on the "spot" market, where prices fluctuate wildly. Most sugar is sold through a quota system at a prearranged price. This is the way the Soviet Union, for example, buys sugar from Cuba, and France and Britain buy from their former colonies.

Thus, Kenana's fate would seem to hang on how good a price it can squeeze out of the Sudanese government or other countries. Company officials would not say what price had been offered but noted that the government was now selling sugar to the public at 26 piasters (20 cents) a pound, or $446 a metric ton at the official exchange rate.

They said Kenana had a deal with the government to sell it the first 150,000 tons in local currency but any additional amounts in dollars, which are badly needed by the company to pay off its debts and keep the plant going. Other sources, however, said the government was supposed to pay in dollars for all sugar until debts are paid off.

But the government can ill afford to pay out dollars for sugar. In effect, it could end up paying in precious hard currency to the Kenana company a good portion of the $170 million it paid last year for sugar imports.

Kenana may shortly make Sudan self-sufficient in sugar. But it appears that either the government or the company will have to pay the price for reaching this goal.