The gas displacement in porous media is a crucial process with extensive industrial and environmental applications. A notable example is underground hydrogen storage, where it is important to understand hydrogen mixing with cushion gas. The current paper explores anomalies in dispersion behaviour of gas mixtures under opposing flow directions (injection and production) from a modelling perspective. Due to the gaseous nature of the system, it presents significant complexities due to non-ideal mixing, compressibility, and higher diffusivity compared to Newtonian fluid transport. The findings reveal distinct dispersion behaviour during injection and production, where augmenting the mixture non-ideality enhanced the non-unique behaviour. In contrast to the dispersivity seen in Newtonian fluid flow in porous media, our research identifies that dispersivity in gas displacement depends not only on the porous medium but also on the gaseous components’ properties.

Hypothesis: Underground hydrogen storage in depleted hydrocarbon reservoirs and aquifers has been proposed as a potential long-term solution to storing intermittently produced renewable electricity, as the subsurface formations provide secure and large storage space. Various phenomena can lead to hydrogen loss in subsurface systems with the key cause being the trapping especially during the withdrawal cycle. Capillary trapping, in particular, is strongly related to the hysteresis phenomena observed in the capillary pressure/saturation and relative-permeability/saturation curves. This paper address two key points: (1) the sole impact of hysteresis in capillary pressure on hydrogen trapping during withdrawal cycles and (2) the dependency of optimal operational parameters (injection/withdrawal flow rate) and the reservoir characteristics, such as permeability, thickness and wettability of the porous medium, on the remaining hydrogen saturation. Model: To study the capillary hysteresis during underground hydrogen storage, Killough [1] model was implemented in the MRST toolbox [2]. A comparative study was performed to quantify the impact of changes in capillary pressure behaviour by including and excluding the hysteresis and scanning curves. Additionally, this study investigates the impact of injection/withdrawal rates and the aquifer permeability for various capillary and Bond numbers in a homogeneous system. Findings: It was found that although the hydrogen storage efficiency is not considerably impacted by the inclusion of the capillary-pressure scanning curves, the impact of capillary pressure on the well properties (withdrawal rate and pressure) can become significant. Higher injection and withdrawal rates does not necessarily lead to a better performance in terms of productivity. The productivity enhancement depends on the competition between gravitational, capillary and viscous forces. The observed water upconing at relatively high capillary numbers resulted in low hydrogen productivity. highlighting the importance of well design and placement.

Pore-network models have been used to derive relative-permeability and capillary-pressure relations, which are important for oil-recovery predictions and processes. Here, we show that relative-permeability and capillary-pressure relations on large scales can be obtained much faster with the effective-medium approximation. Our approach differs from previous work in that we use various shapes of non-circular pores and combinations of different shapes. We use a finite-element approach to compute the hydraulic conductivity of arbitrarily shaped prisms, which are partly filled with oil and water. Our present interest is confined to water-wet media. Striking features of the obtained constitutive relations are that the water relative permeabilities show a marked reduction below a critical water saturation—at which there is no infinite cluster of completely filled water pores—but the water relative permeabilities continue to be finite even at very low water saturations because of corner flow. The capillary pressure remains finite even at low water saturations. Primary-drainage oil relative permeabilities are non-zero at low oil saturations, which is in line with early gas breakthrough for the solution-gas drive oil-recovery mechanism. We compare the results obtained with the effective-medium approximation to the results obtained with a pore-network model consisting of a simple-cubic lattice of prisms. The comparison shows that the pore-network generated relative-permeability curves are completely dissimilar to the effective-medium approximation derived relative-permeability curves. Furthermore, below and near the percolation threshold, the pore-network results differ significantly from one realization to another and/or from one network size to another network size. The network-model results show discontinuous behavior at the percolation threshold. This implies that pore-network results are scale dependent and the pore-network sizes up to 301 × 301 × 301 (the limitation determined by the available computer power) studied here are still far from a representative elementary volume (REV).