In her project Medium of Exchange, Soleimani charts a fragmented history of the relationship between OPEC nations and western political powers since the 1960s, when the organisation was formed, highlighting the correlation between sovereign oil wealth and civil rights abuse.

Medium of Exchange combines photographic tableaus alongside a scripted film. The freestanding photographs portray theatrical interplays between caricatured OPEC Oil Ministers and the western government officials who together control the oil industry. Solitary or group portraits are staged against backdrops composed of found images of oil fields and refineries, strewn with props relating to the commodities or cultural signifiers that shape each specific narrative.

Soleimani's various characters are engaged in bizarre acts of excess, romance and aggression. In the group portraits, the power plays between the represented countries are illustrated through references to BDSM, proposals of marriage and clandestine liaisons. In one scene, Dick Cheney, wearing only a $100-bill towel and baseball cap, holds hands with Donald Rumsfeld; repeating Halliburton logos signal their shared corporate past and controversial implication in profiting from the war with Iraq. This encounter takes place amidst a gridded environment of repeating pipelines, explosions, and desert landscapes. Elsewhere, a bare-breasted Henry Kissinger, on bended knee, raises an oil-smeared diamond ring to the partially nude José María Botelho de Vasconcelos, Angola's Minister of Petroleum and former President Jimmy Carter consummates a relationship.