Reproductions of ancient alcohols have since grown in popularity, largely through a partnership between the Dogfish Head Craft Brewery in Delaware and Patrick E. McGovern, an archaeological chemist at the University of Pennsylvania Museum. Together, they have recreated beers from prehistoric China, from ancient Egypt and from evidence found in what is believed to be the tomb of King Midas.

“Of different people who do fermented beverages, microbrewers are the most willing to experiment,” Dr. McGovern said. “They’re ready to try anything.”

Great Lakes has no plan to sell its brew, also based on the Hymn to Ninkasi, to the public. The project, unlike others that recreate old recipes on modern equipment, is an educational exercise more than anything else. It has been shaped by a volley of e-mails with Sumerian experts in Chicago as both sides try to better understand an “off the grid” approach that has proved more difficult than first thought.

In place of stainless steel tanks, the Oriental Institute gave the brewery ceramic vessels modeled after artifacts excavated in Iraq during the 1930s. In keeping with the archaeological evidence, the team successfully malted its own barley on the roof of the brew house. It also asked a Cleveland baker to help make a bricklike “beer bread” for use as a source of active yeast — by far the most difficult step in the process.

The archaeologists, who have committed their careers to studying Sumerian culture, said having professional brewers involved in the effort had helped them ask questions they had not considered.

“We keep going back to the evidence and finding new hints that can help us choose between different interpretations,” said Tate Paulette, a doctoral student and a lead researcher on the project. “We are immersed in studying Mesopotamia, and this is a fundamental thing that we don’t understand well enough.”

While the project continues, Great Lakes’ brewing vessels are already a popular addition to guided tours of the brewery. The company is making plans to showcase its Sumerian beer at events in Cleveland and Chicago by the end of this summer, offering a public tasting of the final brew alongside an identical recipe made with more current brewing techniques.