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[1] In uniform soils that are susceptible to unstable preferential flow, the water saturation may exhibit a nonmonotonic profile upon continuous infiltration. As this nonmonotonicity (also known as saturation overshoot) cannot be described by the conventional Richards equation, there have been proposed possible extensions to the unsaturated flow equations, including a nonmonotonic capillary pressure-saturation curve and a secondorder hyperbolic term. Here, we present analytic traveling wave solutions to the extended Richards equation. These new solutions indeed display a nonmonotonic saturation profile, similar to previous simulation results. We show that these extensions need a regularization term to produce a unique solution. We develop complete analytic solutions using a relaxation regularization term, and we discuss the results in terms of recent measurements of saturation overshoot.

21.11.14 KB. OK to add published version to spiral, OA paper under cc b

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A key aspect of CO 2 storage is the injection rate into the subsurface, which is limited by the pressure at which formation starts to fracture. Hence, it is vital to assess all of the relevant processes that may contribute to the pressure increase in the aquifer during CO 2 injection. Building on an existing analytical solution for immiscible and spatially varying non-Darcy flow, this paper presents a mathematical model that accounts for combined effects of non-Darcy flow, phase miscibility, and gas compressibility in radial two-phase displacements. Results show that in low-permeability formations when CO 2 is injected at high rates, non-Darcy simulations forecast better displacement efficiency compared to flow under Darcy conditions. This will have a positive effect on the formation CO 2 storage capacity. This, however, comes at the cost of increased well pressures. More favorable estimations of the pressure buildup are obtained when CO 2 compressibility is taken into account because reservoir pressures are reduced due to the change in the gas phase properties. Also, non-Darcy flow results in a significant reduction in halite precipitation in the nearwell region, with a positive effect on CO 2 injectivity. In the examples shown, non-Darcy flow conditions may lead to significantly different pressure and saturation distributions in the near-well region, with potentially important implications for CO 2 injectivity.