Semi-analytical model to predict the performance of cyclic steam stimulation oil wells

Prediction of the performance of oil wells under Cyclic Steam Stimulation (CSS) is challenging in complex and heterogeneous reservoirs, especially with limited data. Analytical and numerical simulation models do not usually give accurate predictions in such conditions. In this work, a semi-analytical model was developed to determine consistent mathematical relationships between the injected steam and some of the effective oil production parameters for more accurate prediction of oil production rates. Field investigation indicates that the change of the Cumulative Oil to Steam Ratio (COSR) to production days is related to a group of effective oil production parameters. This group of parameters includes the cumulative injected steam relative to the drainage volume, the oil net pay thickness relative to the gross pay thickness, and the vertical permeability relative to the thermal diffusivity. These parameters were arranged in two dimensionless groups. It was found that plotting these two dimensionless groups on Log-Log scale for any reservoir yields a straight line (correlation). For any reservoir under CSS, measurements of two steam cycles are sufficient to identify the constants of the proposed correlation. This method has been applied and validated on six reservoirs with different reservoir characterizations. Six different wells with a total of 43 steam cycles from these reservoirs were analyzed with the same approach. The mathematical relationships of the dimensionless groups were calculated, and the Log-Log plot was constructed for each well using the data of the first two cycles. Then, the proposed correlation was developed for each well and used to predict the well performance starting from the third steam cycle. At the end, the predicted performance of each well was compared with the corresponding actual measurements. The results showed that the average absolute percentage deviation between the actual and the predicted cumulative oil production through the well lifetime is less than 5% for the six wells. In addition, the absolute instantaneous deviation between the actual and the predicted cumulative oil production for each individual cycle in all cases is (1) less than 15% for about 42% of the tested CSS cycles, (2) between 15 to 25% for about 39% of the tested CSS cycles, and (3) higher than 25% for about 19% of the tested CSS cycles. This work is considered an original contribution to develop dimensionless relationships that can be used to predict the oil production of the CSS operations for reservoirs with limited data. The required data are the historical production rate, steam injection rate, and basic petrophysical parameters.