Big oil companies on Thursday reported sharply higher second-quarter profits, crediting a stronger market for chemicals and a $2 per barrel surge in the price of crude oil.

Exxon, the country's biggest oil company, reported an 84 percent profit increase.

The stronger economy has increased demand for petrochemicals and higher prices have meant healthier profits for a business that had been a drain on oil company profits during the recession.

Profits from Exxon's chemical business tripled in the quarter.

Exxon Corp.

The Irving, Texas-based company earned $1.63 billion, or $1.30 per share, on revenues of $31.7 billion. A year earlier, the company had a profit of $885 million, or 70 cents per share, on revenues of $27.32 billion.

``Crude oil prices were volatile during the quarter, strengthening early in the period but then weakening by the end of the quarter,'' Raymond said. ``However, relative to the second quarter of last year, average crude prices were stronger.''

Oil exploration and production earnings rose 36 percent to $281 million. Exxon's chemicals business earned $571 million, up from $190 million a year ago.

In the first six months of the year, Exxon said it earned $3.3 billion, or $2.63 per share, on revenues of $61.45 billion. In last year's first half the company earned $2 billion, or $1.62 per share, on revenues of $53.28 billion.

Exxon's stock rose 75 cents to $73.12 1/2 per share Thursday on the New York Stock Exchange.

Sun Co.

The Philadelphia-based company reported an 89 percent increase in second-quarter profits, rising to $109 million, or $1.02 a share, from $12 million, or 11 cents, a year earlier.

Revenues rose to $5.5 billion, a 21.5 percent increase over the same period a year ago, when revenues were $4.3 billion, the company said.

Sun credited the rise to its chemicals business and international oil production. Chemicals profits rose to $24 million from $2 million and international oil profits rose more than 60 percent to $13 million.

The company also cut losses from its fuels and lubricants operations and realized income from the sale of its remaining interest in Suncor, a Canadian petroleum company.

In the first half of the year, Sun earned $102 million, or 95 cents per share, on revenues of $5.5 billion. A year earlier the profit was $39 million, or 36 cents per share, on revenues of $4.3 billion.

Sun's stock was up 62 1/2 cents per share Thursday on the NYSE at $26.62 1/2.

Occidental Petroleum Corp.

The Los Angeles-based company had a profit of $187 million, or 51 cents per share, for the second quarter of 1995, compared with a net loss of $19 million, or 12 cents per share, for the second quarter of 1994. Sales were $2.7 billion, up from $2.2 billion a year earlier.

In the first six months of the year, the company earned $365 million, or $1 per share, on revenues of $5.4 billion. A year earlier the company lost $59 million, or 31 cents per share, on sales of $4.3 billion.

Occidental's stock was 25 cents per share lower at $23.50 Thursday afternoon on the NYSE.