Experimental investigation of water vapor adsorption isotherm on gas-producing Longmaxi shale: Mathematical modeling and implication for water distribution in shale reservoirs

Mathematical characterization of water vapor adsorption (WVA) isotherms on organic-rich shale is important for both modeling processes such as water flow and mass transport, and accurate evaluation of moisture content in shale. Although several theoretical and empirical models have been proposed to describe WVA on porous materials (e.g, coal, food and carbon black), the applicability of these proposed models for over-mature gas shale (e.g., > 2.0%R-o) is not well understood, which requires both experimental data and a theoretical description of downhole shale. In this work, WVA isotherms were measured at 50 degrees C (323.1 K) using a dynamic vapor sorption apparatus for four over-mature Lower Silurian Longmaxi shales, the leading gas-producing shale reservoir in the Sichuan Basin, China. To describe water adsorption behavior mathematically, five models, including the Guggenheim-Anderson-de Boer (GAB), double log polynomial (DLP), Oswin, Freundlich, and Frenkel-Halsey-Hill (FHH), for WVA isotherm are evaluated for their ability to match the experimental WVA isotherm data. In general, all the models are suitable for fitting the experimental data, with R-2 values larger than 0.95. However, the transformations of non-linear isotherm equations to their linear forms could implicitly alter the error structure and may violate the error variance and normality assumptions. To address this deficiency, six more statistical parameters (AAD, MSE, SEE, RSS, ARE and chi(2)) were used to evaluate the goodness-of-fit results for different models. Comparative studies show that the four-parameter DLP model is the optimal to predict the WVA isotherms on Longmaxi shale, with the smallest fitting errors, rather than the most versatile GAB model documented in the literature. Considering the WVA behavior, the distribution of water (free and adsorbed) in hydrophobic and hydrophilic pores in shales was also discussed, which can provide a reference point for theoretical analysis of water flow and retention.