We have changed this graph to compare low sulfur residual fuel oil prices with industrial sector natural gas prices.  The black line is coal delivered to electric power plants.  Coal represents a floor for natural gas prices.  

The relationship between the two fuels is very weak. The movement of the fuels began to take different paths in January 2009. The correlation is very low as revealed in the R² value of 0.2452.  This demonstrates the disconnect between crude oil and natural gas prices.  Natural gas has returned to its previous diminished value relative to crude oil.

Source: Oil & Gas Journal Statistics

Additional information is available from Oil & Gas Journal's
electronic information source OGJ Online.

The EIA's Annual Energy Outlook contained an interesting analysis "Factors affecting the relationship between crude oil and natural gas prices." 

The report states that: "Such an apparent lack of responsiveness of natural gas prices to changes in crude oil prices in all cases reflects the changes that have occurred in the underlying uses of the two commodities. The divergence of crude oil and natural gas markets also reflects the fact that opportunities for the substitution of natural gas for crude oil products are limited by the large infrastructure investments that would be required to allow substitution on a significant scale and bring the prices of the two commodities closer together in the U.S. market in the Reference and High Oil Price cases. In the absence of such investments, EIA expects the gap between oil and natural gas prices in U.S. energy markets to remain wide."