By Selina Williams 

LONDON-- BG Group PLC said Friday that production rose to a record level for the company in the second quarter, providing a window into the logic behind Royal Dutch Shell PLC's decision to buy the U.K. energy giant.

BG, the U.K.'s third-largest oil-and-gas company, said production increased 19% to 703,000 barrels of oil equivalent a day, helping its earnings beat expectations. Its profit was up 63% at $2.23 billion over last year's second quarter, primarily because of a post-tax gain from the sale of an Australian natural-gas pipeline.

The increased production was fueled by output more than doubling in Brazil and at the massive Queensland Curtis liquefied natural gas project in Australia, known as QCLNG--two of the main drivers for Shell's $73 billion takeover of the company.

"What you see in this quarter is that the growth that we have talked about for a while is now happening," said BG Chief Executive Helge Lund.

The new production figures come as Shell is making a renewed effort to sell investors on its decision to buy BG--a move that has sent the bigger company's share price down 17% since April. On Thursday, Shell pointed to BG's Brazil and Australia production growth, calling it a "natural fit." The Anglo-Dutch giant also emphasized that the deal would make sense even during the current sustained slump in oil prices.

Shell is buying BG and its surging production levels just as its own oil-and-gas output is on the decline. In its own second-quarter earnings on Thursday, Shell said its production had fallen 11% compared with last year's second quarter, to about 2.7 million barrels of oil equivalent a day. In 2014, it replaced only about a quarter of its reserves with new production, among the lowest ratios of the big oil companies.

Shell's purchase of BG is expected to be completed in early 2016, with regulatory approval still needed in the U.S., China and the European Union.

BG's gusher represents a big turnaround after years of under delivery on its own output targets. It also underscores Shell's bet that output from BG's stakes in highly prized oil fields in offshore Brazil would start ramping up this year and that facilities at QCLNG would come onstream as planned, bringing with it a big wall of cash that the Anglo-Dutch company hopes to tap into.

The developments in Brazil and QCLNG are big complex projects that were hampered by delays in the early stages, but the company said last year they would be ramping up in 2015.

Once an investor darling for its exploration successes and rapid production growth, BG fell out of favor as the company was rocked by a series of profit warnings and production downgrades.

The company grew rapidly in the early 2000s but its output stalled in the middle of the decade. Frank Chapman, BG's chief executive until 2012, had predicted the company would produce 1 million boe/day by 2015.

BG is now above the 700,000 barrels a day mark for the first time--an achievement that comes at an inopportune moment with oil prices hovering around $50 a barrel, down more than 50% from their peak last year.

The company's underlying earnings, or profit after tax and excluding exceptional items such as disposals and impairments, declined 65% in the second quarter to $429 million from $1.21 billion a year earlier. Analysts had expected net income of $315 million.

Related softness in prices for liquefied natural gas also hit BG's income, even as the company delivered eight more cargoes of the fuel versus a year ago. Revenue was down 28% at $3.95 billion compared with $5.51 billion in the same period a year ago due to the fall in oil prices.

"Our upstream business clearly felt the effect of lower oil prices," Mr. Lund said.

BG moved its full-year production guidance to the upper half of its range of 650,000-690,000 barrels of oil equivalent a day.

Earnings per share decreased 65% to 12.6 cents a share.

Write to Selina Williams at selina.williams@wsj.com

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