Occidental Petroleum Corp., the nation's 12th-largest refiner, reported a 51.8 percent increase in its second-quarter earnings to a record $161.1 million ($2 a share) from $106.1 million ($1.36) a year earlier.

Revenues were up 36 percent to $3 billion from $2.2 billion a year earlier.

First-half earnings rose 133 percent to a record $439 million ($5.59) from $188.7 million ($2.40) in the first six months last year. Revenues climbed 53.6 percent to $6.3 billion from $4.1 billion.

Occidental said its oil and gas earnings reflected "favorable margins from foreign oil and gas production, although output from Libya and the British North Sea was below 1979 levels.

Occidental was the first major U.S. oil company to announce its second-quarter results. It attributed the gain to improved profits from its foreign oil and gas production and chemical businesses.

Analysts have predicted oil company profit increases of between 25 percent and 50 percent in the second quarter. The oil companies recorded sharper gains in the first quarter, but second-quarter earnings will reflect the full bite of a "windfall profits" tax which did not take effect until March 1.

Occidental reported a 236 percent rise in first-quarter earnings.

In addition, analysts also said reduced U.S. demand for refined petroleum products, particularly gasoline, and the impact of the recession on some non-energy-related divisions of the diversified oil companies could restrain earnings for the remainder of the year.

Aluminum Co. of America, the world's leading integrated producer of aluminum products, said yesterday that second-quarter earnings were about 11 percent higher than a year earlier.

Earnings were $148.8 million ($4.17 a share) on sales of $1.29 billion. For the same period last year, earnings were $134.4 million ($3.81) on sales of $1.18 billion.

Second-quarter 1980 net income includes a gain of $27.3 million (77 cents) from the sale of a shopping center in Los Angeles, while second-quarter 1979 net income incuded a gain of $12.3 million (35 cents) from the sale of Alcoa's shares in Interway Corp.

"We began to feel the impact of the econonmic downturn in the second quarter," said company Chairman W.H. Krome George. "This impact was delayed by the relatively low inventory positon of our customers and by Alcoa's concentration in high-technology markets, which tend to be less cyclical."

First-half net income was $292.3 million ($8.22) on sales of $2.59 billion compared with a net income a year earlier of $262.1 million ($7.43) on sales of $2.38 billion.

Dow Chemical Co. said its second-quarter dollar sales climbed nearly 9 percent over the same period last year, but inflation and a drop in new orders cut profits 20 percent.

Second-quarter sales stood at $2.52 billion, up from $2.31 billion for the same period in 1979. Profits declined to $171.2 million (94 cents a share) from $214.7 million ($1.19) a year earlier.

G.J. Williams, financial vice president, said costs significantly higher than last year's levels cut into company profits.

Williams said Dow established records for the first half. Net income was $401.7 million ($2.21), compared with $391.2 million ($2.16). Sales stood at $5.33 billion, coompared with $4.38 billion during the same period in 1979.

Despite deteriorating market conditions, Bendix Corp. recorded slightly improved third-quarter results over the same period last year.

William M. Agee, chairman and chief executive officer, said Wednesday that revenues for the April-June quarter totaled $1.14 billion, an 11.9 percent improvement over the third quarter of 1979. Net income was $54.8 million, up 17.9. percent from the $46.5 million reported a year ago.

Nine-month revenues totaled $3.2 billion, compared with $2.9 billion in 1979. Net income was $146.3 million, compared with $128.2 million.

Agee said the acquisition in March of Warner and Swasey co., an industrial machine company, was responsible for "a dramatic rise in the revenues and profits of our industrial business over those of a year ago."