Despite the wide publicity surrounding Exxon Corp.'s withdrawal from the Colony Oil Shale project, 37 new applications have been filed asking government support for synthetic fuels projects, the U.S. Synthetic Fuels Corp. announced yesterday.

Yesterday's group of applicants in the second round of bid solicitations was smaller than the first group to bid for government aid and included 23 applicants making a second bid, but Synfuels officials said they were pleased with the results. They noted, however, that new proposals appear to be for somewhat smaller projects.

"These projects will be the pioneers of a new industry," said Synfuels Corp. Chairman Edward E. Noble. "They will provide the foundation on which a commercial synthetic fuels industry can develop."

Synfuels Corp. officials said the number of applicants was limited by more detailed standards that require greater initial effort and investment. In addition, officials said they were not surprised by repeat contenders. "Any sort of serious synfuels project can't spring out of nowhere," said Ralph Bayrer, deputy vice president for projects. Some of the projects may not have been ripe when first proposed, he indicated.

The projects include 16 that involve conversion of coal, eight that would produce oil from shale, and nine that would extract fuel from tar sands. The proposed projects are located in 15 states.

The Synfuels Corp. will have some part of $8.6 billion that it already had on hand and an additional $6.2 billion that it expects June 30 to give the projects it selects. The corporation can provide assistance in a number of ways, including price supports and loan guarantees.

First the projects must survive several tests of their worthiness, a process expected to take six to nine months. The Synfuels Corp. is still in the process of selecting which projects it will support from the first round of applications.