Two groups have filed separate legal challenges to the federal environment minister’s approval of Woodside’s North West Shelf extension, one of the world’s biggest liquified natural gas projects.

The Australian Conservation Foundation and Friends of Australian Rock Art have commenced federal court proceedings in a bid to have the decision overturned.

The environment minister, Murray Watt, gave final approval last month to Woodside’s proposal to extend the life of its North West Shelf gas processing plant – on the Burrup peninsula in northern Western Australia – from 2030 to 2070.

“We’re challenging the lawfulness of Minister Watt’s approval of this gas hub extension, which is the centrepiece of the most polluting gas project in the southern hemisphere,” ACF’s general counsel, Adam Beeson, said.

Beeson said many Australians were “shocked” by Watt’s decision, with the group’s research estimating the project’s total emissions would be more than 13 times Australia’s annual emissions.

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The ACF will argue the minister wrongly considered the economic benefits of the unapproved Browse gas project – a separate Woodside proposal to develop an untapped conventional gas field off the Kimberley coast – in his statement of reasons for approving the extension.

The group will also argue the minister left critical details out of his decision, including approving the project without knowing the details of the gas it would process and the pollution it would cause, and that he failed to consider the physical effects of climate breakdown as an “impact”.

“A child born today will be 45 in 2070. We will argue the minister was wrong to cite the claimed economic benefits of the proposed Browse gas project – which Woodside hopes will feed the gas hub, but which has not been approved – when he approved the North West Shelf extension,” Beeson said.

Friends of Australian Rock Art’s case will assert the approval was invalid because the minister failed to properly take into consideration the economic and social harms that would result from ongoing damage to Murujuga heritage.

The group also has a separate challenge running in the WA supreme court to the state government approval of the project.

The government’s published statement of reasons for approving the project shows it agreed to weaken conditions it had proposed to protect world heritage-listed Indigenous rock art after Woodside argued it could be forced to shut the plant.

The statement shows Watt accepted environment department advice that “multiple lines of scientific and other evidence” suggested industrial emissions were having a “significant adverse impact” on rocks in Murujuga, a cultural landscape in northern WA that is home to more than 1m pieces of rock art, known as petroglyphs.

The minister also accepted advice that future pollution from the North West Shelf liquefied natural gas (LNG) processing facility could cause “degradation, damage, notable alteration, modification, obscuring or diminishing” of the area’s natural heritage.

But the minister said in the statement of reasons that the final conditions for the project were “stringent” and he did not believe there would be an unacceptable impact on the area’s heritage values.

Susan Swain, a co-convenor of Friends of Australian Rock Art, said the Murujuga petroglyphs and cultural heritage were unique in the world and priceless.

“The Unesco world heritage site contains the oldest and most extensive rock art on the planet, with the earliest recorded depiction of the human face among its treasures,” she said.

“The environment minister had to look at this heritage site and how to protect it, and we say that he failed to do that in accordance with the law.”

Swain said the social and economic harms that would be caused by the government’s decision included “impacts on tourism, extreme heat and human health”.

Watt declined to comment on the legal proceedings.

Guardian Australia has sought comment from Woodside.