Disclosed is a process for converting C2-5 alkanes to higher-value C5-24+ hydrocarbon fuels and fuel blendstocks including reacting the C2-5 alkanes in a thermal olefination reactor operating at a temperature, pressure and space velocity to convent the alkanes to olefins and in the absence of both a dehydrogenation catalyst and steam. At least a portion of the product olefin stream is oligomerized using a zeolite catalyst to crack, oligomerize and cyclize the product olefins to form the fuel products, which are then recovered. The process is useful in removing sulfur and nitrogen-based compounds in a single step process, while reducing total costs of processing and eliminating the need for additives used in the field.