Abstract
AbstractIn this work, we study the behavior of saturation fronts for two‐phase flow through a long homogeneous porous column . In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the permeabilities. The analysis uses traveling wave approximation. Entropy solutions are derived for Riemann problems that are arising in this context. These solutions belong to a much broader class compared to the standard Oleinik solutions, where hysteresis and dynamic effects are neglected. The relevant cases are examined and the corresponding solutions are categorized. They include nonmonotone profiles, multiple shocks, and self‐developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we discuss the implication of our findings in the context of available experimental results.
Highlights
Modeling of two-phase flow through the subsurface is important for many practical applications, from groundwater modeling and oil and gas recovery to CO2 sequestration
The one-dimensional case is relevant when one spatial direction is dominant; it approximates flow through viscous fingers12,55,56 and it can explain results from the standard experimental setting shown in Figure 2.33-35 In this study, the behavior of the fronts is investigated by traveling wave (TW) solutions
Having derived the nondimensional hysteretic two-phase flow System ( ̃ ), we investigate under which conditions TW solutions exist
Summary
Modeling of two-phase flow through the subsurface is important for many practical applications, from groundwater modeling and oil and gas recovery to CO2 sequestration. The one-dimensional case is relevant when one spatial direction is dominant; it approximates flow through viscous fingers and it can explain results from the standard experimental setting shown in Figure 2.33-35 In this study, the behavior of the fronts is investigated by traveling wave (TW) solutions. The TW solutions can approximate the saturation and pressure profiles in infiltration experiments through a long column, and the existence conditions of the TWs act as the entropy conditions for the corresponding hyperbolic model when the viscous terms are disregarded. Hysteresis and nonlinearities were not included in the viscous term This is taken into consideration in Ref. 64 where the authors add a dynamic term to model permeability hysteresis, while disregarding hysteresis and dynamic effects in capillary pressure.
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