The Royal Dutch Shell Group of oil companies reported a large increase in third-quarter profits despite a decline in the volume of oil it sold in the period.

The group -- which includes the Shell Oil Co., the eighth-largest oil company in the United States -- said net income rose 146 percent from $621.2 million last year to $1.53 billion. Revenue rose to $15.5 billion from $12.5 billion.

Nine-month profits were $4.34 billion, up from $2.19 billion last year. Revenues rose to $44.5 billion from $37.5 billion.

A statement by the firm said the quarter was "marked by considerable oil-supply problems and uncertainties, and the main effort of Shell companies was directed toward meeting customer requirements."

The company said its total oil and oil product sales fell in the third quarter to 4.9 million barrels a day from 5.3 million a year earlier.

The multinational oil company also said the net income gains were exaggerated by its first-in, first-out method of inventory accounting, which inflates earnings in times of rising oil prices.

It said that if it used the last-in, first-out method, as do a majority of international oil companies, its net income would have shown only a 43 percent rise.

However, foreign exchange translations cut profits by $78.8 million, contrasting with a gain of $13.2 million a year earlier.

F. W. Woolworth Co. said its third-quarter net income rose 112.8 percent from the same quarter last year, mainly because of a $13.1 million gain for an income tax adjustment related to its unconsolidated British unit.

However, company Chairman Edward F. Gibbons said the latest quarter's income of consolidated companies fell by 7.7 percent to $18.8 million from $20.4 million in 1978. He attributed the drop to "escalating footwear and leather costs in Kinney Shoe Corp. and by higher interest expense and a softening of specialty store sales."

The variety store operator said its net income in the quarter ended Oct. 31 was $44.9 million ($1.50 a share) compared with $21.1 million (69 cents) a year earlier. Sales incresed to $1.67 billion from $1.50 billion.

In the first nine months of the year, the company earned $74.7 million ($2.46) compared with $46.6 million ($1.51) in the same period last year. Sales rose to $4.64 billion from $4.18 billion.

McCulloch Oil Corp., a diversified energy producer, reported Wednesday that its third-quarter earnings rose to $25.4 million ($1.32 a share) from $1.53 million (9 cents) in the same period last year. Revenues advanced to $29.9 million from $24.1 million a year earlier.

For the nine months, McCulloch earned $27.6 million ($1.48)8 up from $8.52 million (49 cents) in the comparable 1978 period. Revenues climbed to $77.4 million from $67.2 million.