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Key Points The 15 January 2022 Hunga Tonga‐Hunga Ha'apai eruption had four episodic seismic subevents with similar waveforms within ∼300 s An unusual upward force jump‐started each subevent A magma hammer explains the force and estimates the subsurface magma mass flux which fits the vent discharge rate based on satellite data 

We present simulations of two-phase flow using the Rothman and Keller colour gradient Lattice Boltzmann method to study viscous fingering when a “red fluid” invades a porous model initially filled with a “blue” fluid with different viscosity. We conducted eleven suites of 81 numerical experiments totalling 891 simulations, where each suite had a different random realization of the porous model and spanned viscosity ratios in the range$$M\in [0.01,100]$$$M\in [0.01,100]$and wetting angles in the range$$\theta _w\in [180^\circ ,0^\circ ]$$${\theta }_w\in [{180}^{\circ },0^{\circ }]$to allow us to study the effect of these parameters on the fluid-displacement morphology and saturation at breakthrough (sweep). Although sweep often increased with wettability, this was not always so and the sweep phase space landscape, defined as the difference in saturation at a given wetting angle relative to saturation for the non-wetting case, had hills, ridges and valleys. At low viscosity ratios, flow at breakthrough is localized through narrow fingers that span the model. After breakthrough, the flow field continues to evolve and the saturation continues to increase albeit at a reduced rate, and eventually exceeds 90% for both non-wetting and wetting cases. The existence of a complicated sweep phase space at breakthrough, and continued post-breakthrough evolution suggests the hydrodynamics and sweep is a complicated function of wetting angle, viscosity ratio and time, which has major potential implications to Enhanced Oil Recovery by water flooding, and hence, on estimates of global oil reserves. Validation of these results via experiments is required to ensure they translate to field studies.

 

Abstract We conduct pore-scale simulations of two-phase flow using the 2D Rothman–Keller colour gradient lattice Boltzmann method to study the effect of wettability on saturation at breakthrough (sweep) when the injected fluid first passes through the right boundary of the model. We performed a suite of 189 simulations in which a “red” fluid is injected at the left side of a 2D porous model that is initially saturated with a “blue” fluid spanning viscosity ratios $$M = \nu _\mathrm{r}/\nu _\mathrm{b} \in [0.001,100]$$ M = ν r / ν b ∈ [ 0.001 , 100 ] and wetting angles $$\theta _\mathrm{w} \in [ 0^\circ ,180^\circ ]$$ θ w ∈ [ 0 ∘ , 180 ∘ ] . As expected, at low-viscosity ratios $$M=\nu _\mathrm{r}/\nu _\mathrm{b} \ll 1$$ M = ν r / ν b ≪ 1 we observe viscous fingering in which narrow tendrils of the red fluid span the model, and for high-viscosity ratios $$M \gg 1$$ M ≫ 1 , we observe stable displacement. The viscous finger morphology is affected by the wetting angle with a tendency for more rounded fingers when the injected fluid is wetting. However, rather than the expected result of increased saturation with increasing wettability, we observe a complex saturation landscape at breakthrough as a function of viscosity ratio and wetting angle that contains hills and valleys with specific wetting angles at given viscosity ratios that maximize sweep. This unexpected result that sweep does not necessarily increase with wettability has major implications to enhanced oil recovery and suggests that the dynamics of multiphase flow in porous media has a complex relationship with the geometry of the medium and the hydrodynamical parameters.