The present invention is directed to the upgrading of heavy petroleum oils of high viscosity and low API gravity that are typically not suitable for pipelining without the use of diluents. It utilizes a short residence-time pyrolytic reactor operating under conditions that result in a rapid pyrolytic distillation with coke formation. Both physical and chemical changes taking place lead to an overall molecular weight reduction in the liquid product and rejection of certain components with the byproduct coke. The liquid product is upgraded primarily because of its substantially reduced viscosity, increased API gravity, and the content of middle and light distillate fractions. While maximizing the overall liquid yield, the improvements in viscosity and API gravity can render the liquid product suitable for pipelining without the use of diluents. This invention particularly relates to reducing sulfur emissions during the combustion of byproduct coke (or coke and gas), to reducing the total acid number (TAN) of the liquid product, and to reducing the hydrogen sulfide content of one, or more than one component of the product stream. The method comprises introducing a particulate heat carrier into an up-flow reactor, introducing the feedstock at a location above the entry of the particulate heat carrier, allowing the heavy hydrocarbon feedstock to interact with the heat carrier for a short time, separating the vapors of the product stream from the particulate heat carrier and liquid and byproduct solid matter, regenerating the particulate heat carrier in the presence of the calcium compound, and collecting a gaseous and liquid product from the product stream.