Royal Dutch-Shell Group net income in the second quarter soared 80 percent to $1.54 billion ($7.04 a share) from $855 million ($3.71) in the year earlier period.

The rise was achieved despite a drop in oil sales to 5.16 million barrels a day from 5.24 million.

Revenues rose from $13.098 billion to $15.231 billion.

First-half net income totalled $2,882 billion ($12.81) compared with $855 million ($3.71) in the first 1978 half. Revenues were $29.883 billion, up from $25.589 billion.

It said the results for the second quarter of 1979 were very substantially affected by the first-in, first-out method of inventory valuation used by most Shell companies and by currency translations gains.

The Shell Group had virtually no earnings in the 1978 first quarter because of foreign currency translation losses, leaving net income figures the same for the quarter and first half.

F. W. Woolworth Co., one of the nation's largest department store chains, said that its profits and sales rose in the second quarter and first half ended July 31.

The firm said second-quarter earnings were $20.1 million (69 cents a share) compared with $15 million (48 cents) a year ago. Sales in the quarter rose from $1.4 billion to $1.6 billion.

First-half net income was $29.8 million (96 cents), up from $25.9 million (82 cents) in the first half of 1978. Sales rose from $2.964 billion to $2.973 billion.

Quaker Oats Co. earned $4.01 a share in the year ended June 30, up from $3.42 the previous year on a rise in sales to $1.966 billion from $1.685 billion. Net income rose from $68.8 million to $94.4 million.

Fourth-quarter profit was $1.06 a share on sales of $495.7 million compared with 99 cents a share a year earlier on sales of $418.5 million.

The reported earnings for the year don't include a nonrecurring 74 cents a share book profit resulting from an accounting change in regards to the investment tax credit.