Rigorous framework determining residual gas saturations during spontaneous and forced imbibition using gene expression programming

Aquifer encroachments toward the producing gas zones can substantially decrease the volumetric gas flowrate due to the bypassing of large gas volumes in the porous media. It is well-known that the main parameter monitoring the cumulative gas production is the residual gas saturation; therefore, a complete information about strong aquifer drive gas reservoirs is required relying on both operational and petrophysical parameters. Despite the abundance of studies, attempting to establish comprehensive and adequately precise models for estimating the residual gas saturations is still challenging. In present work, the new method namely, Gene Expression Programming (GEP), was used to propose 9 correlations for force, spontaneous imbibition and the overall waterflood conditions. For this reason, a comprehensive database including 897 residual gas saturation data were adopted from the open source literatures. The variation ranges of the employed dataset include 0.013 to 1 for initial gas saturation, 0.001 to 12950 mD for absolute permeability of rock, 0.008 to 0.494 for porosity (as the input parameters) and 0 to 0.79 for residual gas saturation (as the model output). Numerous types of error analyses such as statistical and visual tools are employed to assess the prediction capability of the new methods developed here as compared with a commonly applied literature model. As a result, it is perceived that the General I, Imbibition I and Force I are the most effective correlations with the root mean square error (RMSE) of 0.09, 0.06 and 0.14, consecutively. The results of the literature model are less efficient than our newly suggested methods. Moreover, the so-called technique of sensitivity analysis revealed that the porosity and permeability have insignificant impacts on predicting the residual gas saturation in the case of spontaneous imbibition. To end with, the results of this study can be the good nominees for fast, accurate and inexpensive estimation of the residual gas saturation especially during reservoir engineering simulation and calculation at the time in which the whole information may not be available to the researches.