The phrase 'immense demand' is correct and can be used in written English.
You can use it to refer to a large amount of demand, for example, "The company has seen an immense demand for their new product."
In order to meet its immense demand for raw materials, China began to buy unprecedented quantities of wood from abroad; it is now the largest importer of logs and also the largest exporter of finished wood products.
Despite the immense demand for the bonds, Secretary of State Judah Benjamin accepted the deal only because, he figured, it would make European financiers financially invested in Confederate success.
Despite immense demand, it is still taking beta sign-ups here. . . .
There is an immense demand for development of novel agents that can overcome the MDR in cancer.
But by 1989 the company, just a blip on the telecom horizon, was ready to exploit the immense demand for bandwidth cell phones would bring.
During the late 1880s, European and American industries producing gaskets, electrical insulators, bicycle tires, and other goods created an immense demand for rubber.
War exacts immense demands on the human capacity to cope, but a forthright recognition of our capacity for resilience does no disservice to the afflicted.
"It is a job of immense demands and I would hope that my successor has the constitution of an ox and the skin of a rhinoceros, really.
Dr Williams has described the post of Archbishop of Canterbury as one of "immense demands" and has said his successor will need the "constitution of an ox and the skin of a rhinoceros".
It seemed that the political will to continue transforming the economy had been sapped by the immense demands of preparing the country for membership of the European Union, which Poland joined in 2004.
"River of Smoke," the second volume of his ambitious Ibis trilogy, is the work of a writer with a historical awareness and an appetite for polyphony that are equal to the immense demands of the material he seeks to illuminate.
