Calculation of stain values in the Zagros hydrocarbon reservoirs based on the Perimeter-Number multifractal model and Hypergeometric function, SW Iran

Determination of stress conditions in hydrocarbon reservoirs has important role in well designing, drilling methods and well operation. This investigation proposes a new approach to discuss areal stress distribution in hydrocarbon reservoirs within Zagros folded belt by applying Perimeter-Number multifractal model and solution of Cayley Hypergeometric function. The Zagros hydrocarbon reservoirs with asymmetrical folding are affected by regional deformations, right-lateral strike-slip faults and thrust faults. Applying of non-linear mathematical methods such as multifractal modeling and Cayley Hypergeometric function are an excellent analysis for deformed closed curves. In this work, initially based on satellite image analysis, geological maps and UGS maps, the perimeter of all reservoirs are calculated. Secondly, by applying multifractal P-N model, the variability of\ reservoirs deformations was obtained. Therefore, concerning to Cayley hypergeometric and strain functions, the main axis of reservoirs was expressed. According to the log-log plot, the Zagros hydrocarbon reservoirs divided to 5 population variations with thresholds values 4.42, 4.65, 4.9 and 5.18 that concerning to results of Cayley hypergeometric function are equal to 0.9397, 0.9953, 0.9942, 0.9962, 0.9555. Based on the results, the maximum of elongation and shortening in Zagros 66.41 and 42.29 respectively. Finally, according to calculations the Zagroshydrocarbon reservoirs classified in three categories. 1- average deformations level. 2- tow category of shortening reservoirs variation and 3- five categories of reservoirs elongation. Additionally, the maximum elongation in the Zagros hydrocarbon reservoirs superimposed with thrust faults trending.