Oil was still flowing Thursday on Enbridge Inc.’s disputed dual-pipe Line 5 across the Straits of Mackinac after an inconclusive round Wednesday in the third court fight since 2018 over Michigan demands to turn off the 540,000 b/d conduit.

No order emerged to enforce a Wednesday shutdown deadline set by Gov. Gretchen Whitmer from the U.S. District Court for Western Michigan. Instead, court-ordered mediation that started in April is to continue.

Whitmer raised prospects of further legal action to try inflicting a financial penalty on Enbridge in a widely circulated letter to Enbridge’s Vern Yu, executive vice president of the Calgary-based pipeline, power and utility conglomerate.

The governor wrote that Line 5 “constitutes an intentional trespass” that began...