A modified surface to volume (SVR) method to calculate nuclear magnetic resonance (NMR) surface relaxivity: Theory and a case study in shale reservoirs

Surface relaxivity (ρ₂) is a critical parameter for converting nuclear magnetic resonance (NMR) T₂ data to pore size distribution (PSD). The surface-to-volume ratio (SVR) method, known for its simplicity and ease of operation, has been widely used for ρ₂ calculation in unconventional reservoirs. However, previous studies often overlooked the equivalence of pore ranges characterized when directly applying the classical SVR model. Moreover, shale reservoirs generally develop layered fractures, whose ρ₂ values are different from matrix pores. The logarithmic mean value of the T₂ distribution (T_2LM) is significantly influenced by layered fractures, therefore, relying solely on the T_2LM value of a whole sample under fluid-saturated state will lead to inaccurate ρ₂ values of matrix pores, particularly in laminated shales where fractures are well developed. However, insufficient attention has been paid to the effect of fractures on the ρ₂ calculation. In this study, a modified SVR method based on the theory of NMR relaxation in partially fluid-saturated pores was proposed to characterize the ρ₂ of shale matrix pores. Twenty-four shale core samples from the Shahejie Formation in the Jiyang Depression, China were selected, and subjected to series of NMR experiments at varying oil-bearing conditions, and low-temperature nitrogen adsorption (LTNA) analysis. The results indicate a strong linear correlation (R² > 0.85) between the inverse T_2LM (1/T_2LM) and the inverse fluid saturation (1/f) when oil molecules across the entire surface layer participate in the exchange process. For a whole core sample, ρ₂ values obtained using the modified SVR model are higher than those obtained using the classical SVR model, especially in samples with numerous fractures. The modified SVR method effectively reduces the impact of fractures on the characterization of ρ₂ of matrix pores. For shale pore ρ₂ characterization, the classical SVR model may be more suitable for pores smaller than 300 nm, with a recommended T₂ range of <33 ms. Additionally, ρ₂ values for different pore ranges (<25 nm, 25–100 nm, and >100 nm) within individual samples were estimated. It is found that the ρ₂ values of smaller pores is greater than those of larger pores, which may be due to differences in mineralogy of the pores across various size ranges. The small pores are more associated with clay minerals while large pores are surrounded by quartz and rigid minerals. In addition, ρ₂ is lower in larger pores and fractures that do not contain organic matter and clays, thus the underestimation of ρ₂ by the classical SVR method can be corrected by modified SVR method. This study represents the first attempt to examine ρ₂ variations across different pore ranges in shale reservoirs. The methodology presented can be applied to other formations, enhancing NMR data application in both laboratory settings and well logging.