Permeability of vesicular Stromboli basaltic glass: Lattice Boltzmann simulations and laboratory measurements

Abstract

The permeabilities of vesicular Stromboli basaltic glasses were determined using lattice Boltzmann (LB) simulations and laboratory measurements. Lattice Boltzmann simulations were performed to simulate flow through vesicular Stromboli basaltic glasses with porosities, Φ, from 5% to 92%. The simulations and measurements provide a power law Darcian permeability‐porosity relationship k(Φ) = c (Φ)5 with c = 2.35 × 10−20 from LB simulations and 5.33 × 10−21 from measurements, where k is in m2. These permeabilities of vesiculated basalts are about 1 to 2 orders of magnitude higher than in rhyolitic and dacitic volcanic rocks with the same porosity; this difference is attributed to a higher bubble interconnectivity and larger bubble apertures in our basaltic samples. The Darcian flow permeability k1 (m2) and non‐Darcian flow permeability k2 (m) are highly dependent on bubble size, D, and porosity with k1 = 7.66 × 10−17[D2Φ3/(1 − Φ)2] and k2 = 2.78 × 10−9[DΦ3/(1 − Φ)]. Samples with power law bubble size distributions can produce higher permeabilities than samples with exponential bubble size distributions. The Darcian and non‐Darcian flow regimes are delineated, demonstrating that the Darcian flow occurs at the Forchheimer number, Fo, below 0.2–1, and the transitional flow (Forchheimer flow) occurs in the Forchheimer number range 1 to 10. The correlations between friction factor, fk, and Fo are constrained by the permeability measurements, and are in good agreement with simulations: fk = (1.11 ± 0.17) + [(0.66 ± 0.39)/Fo] (measurements) and fk = (0.59 ± 0.49) + [(1.0 ± 0.01)/Fo] (LB simulations). Our results show that fk depends on k2, pore size, and pore geometry at small Fo and tends to be a constant at large Fo. The fk − Fo correlations imply a gradual transition from Darcian to non‐Darcian flow, rather than an abrupt change. Modeling the relationship between permeability created by water exsolution and depth suggests that significant increases of permeability occur at depths of ∼100–2000 m for melts with initial water concentrations of 1–4 wt %. At these depths, for gas flow through vesicular magma with a velocity 0.1–1 m s−1, Fo is in the range ∼0.5–47, corresponding to the transitional flow regime. For a gas flow with a velocity over ∼10 m s−1, Fo can attain values well above the transition flow regime. Our results imply that transitional flow or turbulent flow probably prevails in vesicular magma.