We simulate future global oil production using a model that accounts for oil-deposit heterogeneity, in order to estimate future emissions and global warming associated with oil development. Oil-deposit heterogeneity causes development costs to increase as the stock of oil deposits is depleted. We calibrate our simulations to best estimates of heterogeneous global development costs. The underlying theory implies, and our simulations confirm, that when oil-deposit heterogeneity is large enough, some crude oil may optimally be left in the ground. Our results indicate that increasing degrees of deposit heterogeneity and higher carbon taxes lead to fewer cumulative emissions from oil by 2100, but that the Paris Agreement climate goals will be difficult to meet.