Personal tragedies which have befallen five Mpumalanga men prompted them to take a 319km journey to .
South Sudan became Africa's newest nation in July under a 2005 peace deal that ended decades of civil war, but many issues remain unresolved, including oil, debt and violence.
Tension escalated last month after Khartoum began taking oil from its landlocked southern neighbour, which exports its crude through Sudan's pipelines to a port on the Red Sea. South Sudan shut down its entire oil production of 350,000 barrels a day in protest.
Sudan Foreign Minister Ali Ahmed Karti denied "confiscating" the oil, saying the South had used Sudan's facilities, equipment and ports without "paying a penny".
Karti said the African Union held the key to solving the oil impasse and invited China National Petroleum, Malaysia's Petronas and India to help mediate.
The African Union sponsored talks between Khartoum and Juba last month.
The two sides were meant to conclude an oil agreement that would have both sides sharing revenues, with the South paying fees to export its oil through Sudan.
Having failed to reach an agreement on transit fees, Khartoum started seizing South Sudan's oil and has sold at least some of it, industry sources said.
Talks are expected to resume early next month but diplomats say it is hard to envision a mutually acceptable compromise.
Diplomats say China, the biggest investor of oil facilities in both countries, has the best chance of brokering a deal.
Beijing sent an envoy to both nations in December to help bridge differences.
Karti said he had assured China that Sudan would safeguard Chinese workers and investments, weeks after the kidnapping of 29 Chinese workers in the main oil-producing state of South Kordofan where Khartoum has been fighting insurgents.
Most Western firms have shunned Sudan since it was indicted by the International Criminal Court in the Hague for war crimes and genocide. China, having maintained close ties throughout a US trade embargo and acted as Khartoum's top arms supplier, opposes the indictment.
Sudan was also the sixth-largest source of Chinese oil imports in 2011 and the tricky transit and pipeline arrangement gives Beijing an incentive to promote good relations between the two Sudans. In December, it sent an envoy to both nations to help bridge differences.
Chinese Vice-President Xi Jinping told Karti China was "worried" about the escalating tensions between Sudan and South Sudan, adding he hoped both countries would "properly handle the dispute at an early date," said Foreign Ministry spokesman Hong Lei.