An improvement on the Kumar and Han algorithm for pore-type inversion in carbonate reservoirs: a case study on Majiagou Formation, Ordos Basin, China

The Kuman and Han algorithm has been an effective solution to simultaneously invert for the aspect ratio and volume fraction of different pore types in carbonate characterization. In the algorithm, a key step is the usage of the Wyllie equation to estimate velocities relying on primary porosities of carbonate rocks. However, our research reveals that Wyllie's equation tends to underestimate velocity in the low-porosity range below 25%, and overestimate velocity in the porosity range over 30%. As a result, the Kumar–Han algorithm underestimates the volume of primary porosity and overestimates the volume of stiff pores. Our research further proposes replacing the Wyllie equation in the Kumar–Han algorithm with the Raymer et al. equation, which leads to more accurate estimation of primary porosity trends across the entire porosity range, consequently, makes the algorithm more applicable in practical applications. We applied both the original Kumar–Han algorithm and improved one to synthetic digital models and 68 real carbonate core samples, and the inversion results from both algorithms were compared and verified using available thin-section and scanning electron microscope images. It shows the improved algorithm provided better inversion results in terms of the aspect ratio and the volume fraction of pores. This new algorithm enhances the accuracy of pore-type inversion at well location, leading to improved characterization of carbonate reservoirs.