Fig. 3
Representative results of variations of porosity (a, d), velocities of the liquid and the gas (b, e), and the parameters ε and θ (c, f) as a function of P during magma ascent from the magma chamber to the vent. The parameters used for the calculation are rc = 10 m, T = 1123 K, n0= 0.04, L = 4000 m and P0 = 100 MPa where L is conduit length and P0 is pressure at the magma chamber. (a, b, c) Results for βph = 0.4 and q = 13.35 kg m-2 s-1 ; (d, e, f) results for βph = 0.55 and q = 0.11 kg m-2 s-1. In (a), (b), (d) and (e), red and green curves show the results based on DE-2BV and Eq. (10), respectively. The results of u1 and u g as a function of P based on Eq. (10) in (b) and (e) are obtained by substituting Φ(P) into Eqs. (1) and (2). The result for the flow without gas escape is also shown in (a) and (d) (dashed and dotted curve).