Projected double-digit growth in cargo handled at Miami International Airport during the next several years will allow it to continue to outpace competitors, the head of development for the airport's owner said.

This year, for example, Miami International will process a total of 800,000 tons of cargo, up from 627,000 tons in 1987, a 21 percent increase, estimated Peter Reaveley, development director of the Metro Dade Aviation Department, the regional government agency that runs Miami International.The anticipated spurt this year follows a 13 percent gain in 1987, Mr. Reaveley said in an interview here. Based on current forecasts, Mr. Reaveley estimated that cargo traffic at Miami International will exceed 1 million tons by 1990, about double that reported just five years earlier.

This 12 percent-plus annual increase is about double the industry average.

Fueling that growth is an increase in international shipments, which account for about 80 percent of Miami International's total volume.

In fact, because of those international shipments, Miami International is the fourth-busiest airport in the United States in terms of freight; it follows John F. Kennedy International Airport in New York, Los Angeles International Airport and Chicago's O'Hare.

Simply in terms of international cargo Miami ranks second only to Kennedy Airport.

Most of Miami International's freight results from trade with Caribbean and Latin America, for which the airport serves as the primary U.S. gateway.

Recently this trade has been spurred by a weak-value dollar that makes U.S.-made goods more affordable overseas.

During this year's first quarter, for example, Miami International overseas shipments increased 27 percent from the year earlier level to 143,000 tons. Domestic cargo was up 12 percent to 40,000 tons.

Cargo to and from Europe will double in market share from the current 10 percent level, Mr. Reaveley predicted. This will result from more airlines serving Miami International.

In looking still further down the road, Mr. Reaveley saw Far Eastern carriers inaugurating service to Miami International. Over time he expects All Nippon Airways Co. to seek a Miami stopover on its Tokyo-Sao Paulo flight.

Moreover, the airline might seek to expand its Tokyo-Washington service to Miami.

In addition, Japan Air Lines Co. in the past has expressed interest in serving Miami.Company officials, however, concede that winning a Chicago gateway has a much higher priority.

Mr. Reaveley stressed that any such service would be a long time in the future, given that trade relations with both Brazil and Japan are seriously strained.

Under existing rules, the federal government must approve any such new schedule service before it can begin.