Cheap crude oil is encouraging refineries to run at full steam even as demand for their output languishes.

“A lot of the storage space is filling up,” said Andrew Wilson, the analyst in charge of stocks and statistics with the International Energy Agency, the West’s energy watchdog. “I think we are looking at, globally, a headache – a pressure point.”

Data from Europe and the United States reflects the excess. Stocks in the Amsterdam-Rotterdam-Antwerp hub, the main transit point for European oil products, hit three-and-a-half year highs last week. Inventories of naphtha, the main petrochemical feedstock, were double the five-year average.

German household heating oil stocks reached a five-year high of 66 percent of capacity at the beginning of December, and weekly U.S. gasoline and distillate fuel stocks soared by a record amount this week of more than 19 million barrels.

The supply surplus is pushing down prices for nearby delivery, opening the gap against future delivery months, a market structure known as contango. The price of gasoil for delivery at the end of 2015 is roughly $40 a tonne higher than the spot price, a premium that has more than doubled since the end of November and helps to cover the cost of storage.

“Anyone who can try to find a way to play this contango will do it,” a European oil products trader said.

Hans de Willigen, a spokesman for global storage operator Vopak, said the pickup had enabled them to fill tank space in Rotterdam that “had been around for quite some time”, while Port of Antwerp business development manager Rose-Marie Pype said there is “not a huge amount of empty space” remaining there despite aggressive capacity increases.

Terminal operators said that the volume of stored products, while difficult to quantify, remains below 2009 peaks, when traders turned to floating storage as tanks on land ran out of space.

Capacity expansions in Europe of as much as 25 percent from 2008-2013, according to oil market analysts PJK International, mean there is further to go before floating storage is needed.

According to database company TankTerminals.com, there is around 830 million barrels of storage space in Europe across 741 terminals, and 650 million barrels across 1,151 terminals in the United States. This does not include storage at refineries.

Traders though are booking tankers to store crude at sea, further illustrating the glut in that market.

Analysts said that how much oil products flows into storage will depend on whether the gap between oil prices, which have more than halved since June, and the price of products means running refineries remains profitable.

“With crude markets likely in surplus until the third quarter of 2015, this could go on a while,” said Robert Campbell of Energy Aspects.

“It means we’re storing up a large overhang of refined product that will need to be run down by real end-user demand before crude can really rally on its own.”