Outside Cattlesburg, Ky., where mountains of coal loom over a forest of oil refineries, construction workers are forging a stainless steel link between America's most abundant energy resource and the nation's most critical energy need.

In a few months, coal from the Appalachian mountains will be dumped into one end of that link - a $200 million chemistry set - and oil will flow out the other end into a nearby refinery.

Making oil from coal is the heart of President Carter's synthetic fuels program, and the Cattletsburg complex will be the biggest coal liquification plant in America. It is designed to turn 250 tons of coal a day into 625 barrels of "syncrude" that can be refined into gasoline and heating oil.

Cattletsburg's 625 barrels of synthetic oil will make barely enough gasoline to supply a single service station, let alone contribute significantly to the President's goal of producing 1 million to 1.5 million barrels of coal-derived synfuels a day by 1990.

The Cattletsburg coal liquification plant is symbolic of how far the nation has to go to meet the president's target of energy independence. It also is symbolic of the obstacles that are faced - it is at least a year behind schedule and is costing nearly four times as much as expected.

"If you look at the growing pains of the whole national energy situation, you'll see what happened in this development," says Bronek Dutkiewicz, who is in charge of commercializing the coal-to-oil conversion process patented by Hydrocarbon Research Inc., a subidiary of Dynalectron Inc. of McLean.

Known as "H-coal" Dynalectron's process was developed by Hydrocarbon ReResearch scientists and tested in three laboratory-size pilot plants at Trenton, N.J., for more than 10 years before the Department of Energy agreed to finance the "scale up" project in Kentucky with Ashland Oil and half a dozen other companies as partners.

Since the project was started, the DOE has changed its objectives several times, has switched project managers twice and haspicked up the tab for more than $135 million of cost overruns.

Though the Cattletsburg plant has yet to squeeze its first drop of oil from a lump of coal, Dynalectron and some of its partners already are asking the federal government to provide $7 million in planning money for a full-scale commercial plant, a 50,000-barrel-a-day facility that will cost upwards of $2 billion.

Thirty or 40 similar-sized synfuel factories will have to be built in the next decade to achieve the president's energy independence goal.

Dynalectron's H-coal process is one of five coal liquification techniques that are struggling toward commercialization, and the coal liquids industry is but one of the alternative energy businesses that will need to be created under Carter's plan.

To eliminate the need for 2.5 million barrels of imported oil a day by 1990, the president proposes producing the equivalent of 1 million to 1.5 million barrels of oil from coal liquids and coal gasification - making a natural gas substitute from coal.

Another 400,000 million barrels a day would come from the infant oil shale industry under the White House plan, and about 100,000 barrels a day from a virtually-non-existent "biomass" business under which crops would be cooked into alcohol and other fuels.

Carter also is counting on replacing half a million to a million barrels of oil a day with natural gas from sources that cannot be tapped with today's production methods and with using solar collectors, windmills, co-generation plants and a host of other nascent technologies to "back out oil."

Achieving energy independence will require creation of a whole new alternative energy industry, a business as big as nuclear power or aerospace.

To a great extent the new energy industry will be the same old energy industry. In the emerging coal liquifications field, Dynalectron's competitors include Exxon, Mobil, Gulf and the Government of South Africa. Virtually every major oil and energy company already owns a piece of the rock that one day may replace conventional oil as America's chief fuel.

At least four other methods of converting coal to liquid fuels are roughly the same distance from commercial feasibility as H-coal; they work on paper, they produce oil a barrel or two at a time in the laboratory; they appear to be economically eligible for full-scale testing.

The five processes are rivals, but not competitors, DOE officials insist. It is possible - likely if the president's accelerated energy independence program is adopted - that full-scale commercial plants will be built using all five technologies. Development of all five processes is proceeding simultaneously.

Exxon - the world's largest corporation - has invested heavily in a process called Exxon Donar Solvent and later this year will open a federally financed synthetic fuel plant about the same size as Cattletsburg's at Baytown, Tex.

Exxon's EDS process is chemically similar to Gulf's Solvent Refined Coal, which is known as the SRC II process because Gulf is already into the second generation of its development. Gulf runs what is currently the biggest coal liquification plant in the nation, converting 30 tons a day into oil at a research facility outside Tacoma, Wash.

By the end of July, Gulf will complete a DOE contract for Phase Zero - the planing - of the nation's first full-scale cole liquification plant which Gulf hopes to build at Morgantown, W Va. DOE approval of that project could come this fall.

The South Africans are the world leaders in synfuel production, regularly producing 20,000 barrels a day. But their SASOL process - being pushed in this country by Fluor Corp. - has political, technical and economic problems. (See separate story on Page F1)

Mobil has yet to get its M-gasoline process out of the laboratory stage, but may be able to scale up faster than the others because 85 percent to 90 percent of the M-gasoline system uses off-the-shelf equipment already proved in commercial use.

Scale-up is the name of the game in synfuels. The trick is to take a process that works in the laboratory or small pilot plant and do it in a big enough way to make it economically feasible. That can require building a plant 50,000 times bigger than a laboratory demonstration unit - the equivalent of going from building lifeboats to building an ocean liner.

But along with efficiencies come risks. Tiny amounts of coal ash that cause no problems in a laboratory coal-to-oil process can clog filters and shut down a 50,000-barrel-a-day plant. Micropollutants unnoticed when they leak from a one-ton-a-day coal cooker can be an ecological disaster in a full-scale plant. Under hundreds of pounds of pressure and intense heat, valves break, 8-inch-thick stainless steel tanks corrode and computer models prove useless.

Environmental and health questions also are being answered by the pilot plant operations, where workers are monitored closely for long-term and short-term medical problems. Virtually all coal liquid products are toxic, most of them more toxic than ordinary petroleum products, and many coal liquid products - including fuel oils produced from coal - are known cancer-causing agents. The danger to production workers is not yet known.

"The only way you learn these things is to build a full-scale plant and run it," said Dynalectron's Dutkiewicz. But, he added, "The risks are too great for even the largest corporations to do that with their money." money."

Carter's plan calls for the government to take the risk of building the first two or three plants and for private enterprise to put up the rest with some sort of government financing. A number of federal subsidies are under consideration in Congress, ranging from loan guarantees to government contracts to purchase synfuels at a premium above petroleum prices to accelerated depreciation and tax credits for synfuel investments.

The money would come from the president's windfall profits tax on the oil companies, which would finance the president's "moral equivalent of war" to launch the synfuels industry by 1990.

Ironically the government program to protect against the risks of launching a new synfuels industry may also exaggerate those risks, warns a Rand Corp. study. Jumping directly from the laboratory to full-scale plants in a crash program requires plant construction to start before designs are completed, before environmental rules are written, before all the contingencies have been accounted for, the Rand study said.

Those factors are part of why first-generation energy facilities have proved to cost an average of 2.5 times as much as estimated and why several multi-million-dollar projects have been built and abandoned because they did not work, Rand warned.

"For government officials, cost growth has made (research and development) decisions difficult, has increased the uncertainty in supply planning and has hampered commercialization," Rand said. If cost estimates of coal liquification plants prove to be as far off as the Rand study suggested, plants expected to cost $2 billion could cost upwards of $5 billino, and the contention that synthetic fuels can compete with imported oil would prove false.

Until Carter launched his crash program to develop alternatives to oil earlier this month, the DOE was scaling up its coal conversion projects in steps, providing funds for a sequence of increasingly larger plants - with daily outputs of one, 20,250 and 10,000 tons - gradually approaching commercial scale.

DOE analysts say It isn't necessary to build that sequence of plants for each of the five promising coal liquification processes because many technical problems are common to all the processes, permitting much leapfrogging.

Intermediate-size plants like the Cattletsburg H-coal facility and Exxon's Baytown EDS facility, both utilizing some commercial-scale components, can answer many of the engineering problems, but they can provide only clues about the most difficult question, and the greatest risk - the cost of producing synthetic fuels.

The price of the product that will flow from Exxon's plant "isn't a relevant question," a corporate spokesman said. "That's not what we expect to learn there."

The most recent estimate of how much synthetic fuels will cost to make was issued this month by the Engineering Societies Commission on Energy (ESCOE), which has made a series of studies of alternative energy technologies.

Because the various processes turn out different products - gasoline, natural gas, boiler fuel and others - the engineering study estimated how much it would cost to produce 1 million BTUs of energy by each processes: $3.58 from H-coal, $3.62 with Gulf's SRC-88, $3.96 via Exxon's EDS, $4.84 via Mobil's M-gasoline and $4.99 by the Fischer-Tropsch process used in South Africa.

Those prices are competitive with an equivalent amount of energy from a barrel of imported oil, which yields 5 .8 million BTUs and costs $20 to $24 delivered in the U.S.

But spokesmen for the companies involved in building coal liquification plants are skeptical of those estimates, calling them lower than their own estimates of synfuel costs, which range from $25 to $35 a barrel.

DOE analysts point out that the price of an equivalent amount of energy may not be the right question to ask when comparing synfuels processes because the products of some processes are in greater demand than the output of others.

The competing coal liquids processes yield varying quantities and qualities of products.

Technically the Exxon, Gulf and Dynalectron processes are known as direct coal liquification; Mobil and South Africa use indirect liquification, first turning the solid coal into a gas, then converting the gas into a liquid.

Exxon and Gulf dissolve finely powdered coal in a liquid solvent, then process it to added more hydrogen to the coal, converting it to a liquid. The big difference between the two processes is the solvent used; each has its own patented product.

Mobil contends M-gasoline can be commercialized more quickly than the others because only the final step involves new technology. A DOE study of where to locate synfuel plants assumes that indirect liquification plants will be built first, but only a couple of years ahead of direct liquification.

Conoco (Continental Oil Co.) advocates short-cutting the M-gasoline process and simply converting coal into methanol on a large-scale basis. Methanol, or methyl alcohol, can be burned directly as a fuel in power plants or internal combustion engines, although both require modification.

Conoco officials say methanol is a highly desirable substitute for imported oil in urban power plants because it is clean-burning, and the company is promoting the fuel for use in California where pollution regulations rule out burning coal.

The ESCOE synfuels evaluation concludes that, on cost factors alone, the South African process "has a severe disadvantage." Among the others, the engineering analysis said, "The choice of fuel process depends strongly on the desired products.

"The M-gasoline process appears both competitive and relatively free of process risk. If industrial boiler fuel (to replace oil for power plants) is the needed fuel, the H-coal, EDS or SRC are all serious contenders."