Modeling Two-Phase Flow with Hysteresis: Comparative Study of Hysteresis Models and Application

International audienceDrainage (drying) and imbibition (wetting) cycles are expected in many applications involving subsurface flows, such as underground CO2 storage, hydrocarbon extraction and production, and deep geological disposal of radioactive waste (particularly in the potential production of hydrogen due to corrosion and radiolysis). In the presence of imbibition/drainage cycles, the two-phase constitutive relations between water saturation, capillary pressure and relative permeability to liquid and gas, cannot be represented by simple one-to-one functions: they depend on the history of wetting/drying processes. Recent numerical and experimental studies highlight the importance of hysteresis and its effect on two-phase flows in porous media. In this study, an extensive critical review of conceptual hysteretic models is first presented. The performance of these models is evaluated and tested from a theoretical point of view based on their assumptions, and by confronting them with measured data for various porous materials extracted from the literature (cement, sands, Bentonite MX80). The advantages and disadvantages of the different hysteretic constitutive models are discussed. Finally, we implement the five hysteresis models in the iTOUGH2 code, and we develop a numerical simulation of a two-phase flow experiment with immiscible Modeling two-phase flow with hysteresis fluids at the laboratory scale (meters), in order to compare the flow results obtained with or without hysteresis, and also, with or without capillary entrapment. The results highlight the need to take into account hysteresis in the modeling of multiphase porous media flows, especially when they are subjected to drying-wetting cycles. It is suggested that the model of Beriozkin and Mualem 2018 should be preferred both from a theoretical standpoint and for its computational advantages. Highlights • Quantitative assessment of several significant and representative conceptual models for hysteretic two-phase flow in porous media. • Identification of best hysteresis model in terms of physical parametrization, accuracy, and ease of implementation. • Gas entrapment in hysteresis models is found to be essential for accurate simulations of gas-liquid flow in porous media