Systematic comparison of advanced models of two- and three-parameter equations to model the imbibition recovery profiles in naturally fractured reservoirs

Abstract

Abstract The imbibition process can be considered one of the most important mechanisms during the production of naturally fractured formations. In this process, the hydrocarbon production in the matrix blocks surrounded by water-filled fractures can be described by a recovery curve. Different equations have been proposed to describe the recovery process during the imbibition. This work presents a detailed analysis of the performance of two- and three-parameter models including Weibull, Probit, Logit-Hill, one-hit-multi-target (1HMT), and all-hit-multi-target (AHMT). These models were tested against different experimental and numerical simulation data in a wide range of rock and fluid properties and matrix dimensions. Particularly, the functionality of these models was examined in early, mid, and late times. It should be highlighted that the three-parameter models (1HMT and AHMT) have not been used previously to describe the imbibition data. The results show that the three-parameter models are more accurate to describe the imbibition recovery trends compared to the two-parameter models. Moreover, the analysis revealed that the AHMT model is better for the early-time data (Error = 0.5), the Logit-Hill model is more accurate for the mid-time data (Error = 0.075), and the Weibull model can best fit the late-time imbibition data (Error = 0.04). Finally, the best model for predicting the recovery factor in fractured reservoirs is model 1HMT because the lowest average RMSE (Root-Mean-Square Error) value of 0.0165 was obtained. The findings of this work can be used to more precisely select the model to curve fit the imbibition data.

Keywords

• Imbibition
• Fractured reservoir
• Matrix block
• Two- and three-parameter models