Abstract This paper presents a new mathematic model to calculate heated reservoir area based on the heat balance principle in order to determine the well spacing for thermal recovery. The calculation result of the new model was compared with the classical models of J.W Marx and R. H. Langenheim (Petroleum Transactions, AIME Vol. 216, pp. 312–315, 1959), B. T Willman (JPT, July 1961, pp. 681–696), and Farouq. Ali (1970), using data from Liaohe heavy crude oilfield, China. The results showed that the new model is more accordable with oilfield actual condition than the three classical models. Also, this research reveals a new theory on huff ‘n’ puff, which is that the heated radius of the heated region is expanded from the first cycle to the fourth cycle of huff ‘n’ puff; in this case, the heated front was expanded with the increase of cycle. However, subsequent cycles (from fifth cycle to tenth cycle of huff ‘n’ puff) repeat the heating of the previous heated areas, and the expanding heated area of the next cycle is smaller than the last cycle, and the new heating region should hardly be expanded after the 10th cycle. The authors point out the development results of heavy oil, extra heavy oil and super heavy oil deteriorate due to this reason. In addition, the authors emphasize that the traditional huff ‘n’ puff for producing heavy oil, especially for extra-heavy oil and super-heavy oil has to be changed using new technique methods after the fourth cycle. Finally, a suitable well spacing for thermal recovery with huff ‘n’ puff was obtained. The new theory was proved by heavy crude/extra heavy oilfield development.
Introduction Huff ‘n’ puff has been used in heavy oil reservoir development since the 1960's. Heavy oil production techniques have been advanced greatly in Canada and Venezuela. In the early 1980s, many thermal recovery techniques were developed, such as insulation tubing, high temperature packer and measurement instrument of thermal parameters. In Liaohe oilfield, China; the reservoirs are at depth from 800 to 2000 m. Heavy oil development was a great success, with production rate reached 700×104 tons per year. During the 25-year production period (1980 to 2005), 20 % of the oil in place was produced. The mechanism of production was a combination of solution gas expansion and huff ‘n’ puff, as the cycle of huff ‘n’ puff is more and more, the development result become worse and worse. Currently, huff 'n ‘puff has exceeded 15 cycles in some wells. The adjustment of oil development strategy faces great challenges, especially in planning well spacing for different types of reservoirs in the oilfield to reach the maximum thermal recovery. The heating front of steam injection, swept region of hot water and the determination of the heated radius are the main parameters to be taken account for designing the well spacing of the heavy oil reservoirs during huff ‘n’ puff. Well spacing for thermal recovery will not be determined if the heated radius should not be calculated accurately. Therefore, after the three classical models of J. W. Marx-R. H. Langenheim (1959), B. T Willman (1961) and Farouq. Ali (1970) was analyzed [1–3], and the paper presents three generalization calculation equations and a new model for calculating the heated radius of the thermal recovery.
Analysis of Classical Model Many researches have developed the theory for the estimation of the heated radius of the heated region and design of well pattern by some scholars [4–8], and the three classical models of Marx-Langenheim (1959), Willman (1961) and Farouq Ali (1970) were used and introduced widely. However, the three models were not analyzed systematically, and the conclusions and recognizing of the heated radius of actual oilfield were not presented in past published papers. Also, the heated radius calculation of multi-cycle had not been revolved. Three generalization mathematics models of the heated radius with multi-cycle were given on the basis of the three classical models. Different performance characteristics of heavy oil, extra heavy oil and super heavy oil are analyzed by means of the three generalized mathematical models and actual oil field data.