A conservative flux postprocessing algorithm is presented for both steady-state and dynamic flow models. The postprocessed flux is shown to have the same convergence order as the original flux. An arbitrary flux approximation is projected into a conservative subspace by adding a piecewise constant correction that is minimized in a weighted $L^2$ norm. The application of a weighted norm appears to yield better results for heterogeneous media than the standard $L^2$ norm which has been considered in earlier works. We also study the effect of different flux calculations on the domain boundary. In particular we consider the continuous Galerkin finite element method for solving Darcy flow and couple it with a discontinuous Galerkin finite element method for an advective transport problem.Comment: 34 pages, 17 figures, 11 table

Steady-state upscaling of relative permeability is studied for a range of reservoir models. Both rate-dependent upscaling and upscaling in the capillary and viscous limits are considered. In particular, we study fluvial depositional systems, which represent a large and important class of reservoirs. Numerical examples show that steady-state upscaling is rate dependent, in accordance with previous work. In this respect we introduce a scale-dependent capillary number to estimate the balance between viscous and capillary forces. The difference between the limit solutions can be large, and we show that the intermediate flow rates can span several orders of magnitude. This substantiate the need for rate-dependent steady-state upscaling in a range of flow scenarios. We demonstrate that steady-state upscaling converges from the capillary to the viscous limit solution as the flow rate increases, and we identify a simple synthetic model where the convergence fails to be monotone. Two different sets of boundary conditions were tested, but had only minor effects on the presented reservoir models. Finally, we demonstrate the applicability of steady-state upscaling by performing dynamic flow simulation at the reservoir scale, both on fine-scaled and on upscaled models. The considered model is viscous dominated for realistic flow rates, and the simulation results indicate that viscous limit upscaling is appropriate.

Liquid hydrogen (LH₂) spills share many of the characteristics of liquefied natural gas (LNG) spills. LNG spills on water sometimes result in localized vapor explosions known as rapid phase transitions (RPTs), and are a concern in the LNG industry. LH₂ RPT is not well understood, and its relevance to hydrogen safety is to be determined. Based on established theory from LNG research, we present a theoretical assessment of an accidental spill of a cryogen on water, including models for pool spreading, RPT triggering, and consequence quantification. The triggering model is built upon film-boiling theory, and predicts that the mechanism for RPT is a collapse of the gas film separating the two liquids (cryogen and water). The consequence model is based on thermodynamical analysis of the physical processes following a film-boiling collapse, and is able to predict peak pressure and energy yield. The models are applied both to LNG and LH₂, and the results reveal that (i) an LNG pool will be larger than an LH₂ pool given similar sized constant rate spills, (ii) triggering of an LH₂ RPT event as a consequence of a spill on water is very unlikely or even impossible, and (iii) the consequences of a hypothetical LH₂ RPT are small compared to LNG RPT. Hence, we conclude that LH₂ RPT seems to be an issue of only minor concern.

We present a model framework for dynamic simulation of the flow of ${\text{CO}}_{\mathrm{2}}$ and other components in an injection well coupled with a near‐well reservoir. With a partitioned approach, we employ numerical methods adapted to the governing equations in each domain. In both well and reservoir, accurate thermodynamics are used. This model can be used for various design and operational considerations for ${\text{CO}}_{\mathrm{2}}$‐injection wells, that is, the quantification of pressure and temperature transients, and phase composition, including the appearance of a water‐rich phase. We study cases where the flow in the well and the near‐well reservoir is dynamically coupled. The rock properties are seen to strongly affect the well dynamics, both regarding magnitude and transient evolution of the bottom‐hole pressure. We consider a variation of this case where water is co‐injected with ${\text{CO}}_{\mathrm{2}}$, showing that this is a potential method to mitigate salt precipitation. We also consider intermittent injection, representing the case of direct injection from ships transporting ${\text{CO}}_{\mathrm{2}}$. Finally, we observe that in the present cases, a coupled model (as opposed to a well‐only model) is necessary in order to capture the dynamics in the well during injection. © 2020 Society of Chemical Industry and John Wiley & Sons, Ltd.