LAWRENCE — Oil production in Kansas increased in 2013, mainly in south-central and southwestern counties, while natural gas production continued to decline, although at a slower pace than in recent years, according to estimates from the Kansas Geological Survey at the University of Kansas.Oil production in Kansas rose 7 percent, from about 43.7 million barrels in 2012 to 46.8 million barrels in 2013. Natural gas production declined 1.5 percent, from 299 billion cubic feet (bcf) in 2012 to just under 295 bcf in 2013.The cumulative value of the state’s oil production increased from an estimated $3.7 billion in 2012 to $4.1 billion in 2013 as prices remained relatively. The cumulative value of natural gas rose from about $790 million in 2012 to $1.1 billion in 2013.