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 (rho(2)) is a critical parameter for converting nuclear magnetic resonance (NMR) T-2 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 rho(2) 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 rho(2) values are different from matrix pores. The logarithmic mean value of the T-2 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 rho(2) 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 rho(2) 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 rho(2) 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 (R-2 > 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, rho(2) 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 rho(2) of matrix pores. For shale pore rho(2) characterization, the classical SVR model may be more suitable for pores smaller than 300 nm, with a recommended T-2 range of <33 ms. Additionally, rho(2) values for different pore ranges (<25 nm, 25-100 nm, and >100 nm) within individual samples were estimated. It is found that the rho(2) 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, rho(2) is lower in larger pores and fractures that do not contain organic matter and clays, thus the underestimation of rho(2) by the classical SVR method can be corrected by modified SVR method. This study represents the first attempt to examine rho(2) 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.