GSA Data Repository 2014300 Permeability reduction of fractured rhyolite in volcanic conduits and its control on eruption cyclicity Satoshi Okumura & Osamu Sasaki Typical Displacement During Compression Experiments Figure DR1. Displacements obtained by experiments at temperatures of 800 and 900 C under the loads of 165 and 164 N. Permeability Measurements To determine the permeability of a run product, we measured gas flow rate through the run product and pressure difference between inlet and outlet of the run product according to the method of Okumura et al. (2009). The run products were covered by a high viscosity resin and mounted using low viscosity resin. The prepared samples were placed in a custom made gas permeameter. The gas velocity was calculated from the gas flow rate and the exposed area of the run product. The 1
relationship between the gas velocity and modified pressure gradient is shown in Fig. DR2. The modified pressure gradient was calculated from the relation of (P 2 2 P 2 1 )/2P 0 L, where P 2 and P 1 are the pressures of inlet and outlet, P 0 represents the pressure at which the rate of gas flow is measured, and L is sample thickness (e.g., Takeuchi et al., 2008). Fig. DR2 shows linear relations between the gas velocity and the modified pressure gradient, which means that the inertia effect is small. In the case of vesicular rhyolites, the inertia effect becomes large at the same permeability ranges with those of this study (Okumura et al., 2009). This difference between rhyolite fragments and vesicular rhyolites may be caused by the difference of their pore structures, that is, vesicular rhyolite has rough pathway. Figure DR2. Relationships between the gas velocity and modified pressure gradient for permeability measurements. The solid lines represent the regression of the analytical data that provides Darcian permeability. 2
Vertical Slice Images of Run Products (X-ray CT) Figure DR3. Grey parts in the sample correspond to rhyolite fragments, and black parts represent pores. A: Run product with initial grain size of 75 250 m at 800 C and 8.4 MPa (run# 8-run1). B: Run product with initial grain size of 250 500 m at 800 C and 8.4 MPa (run# 8-run6). C: Run product with initial grain size of 75 250 m at 900 C and 8.3 MPa (run# 9-run2). Each figure is 5.3 mm wide. 3
TABLE DR1. SAMPLE WEIGHT AND LENGTH Sample weight Initial length Initial porosity* Final length Final porosity (vol%) Strain (mg) (mm) (vol%) (mm) Calculated* CT 7-run3 151.1 5.94 45 5.61 42-0.06 8-run1 153.6 6.12 46 4.92 32 28 0.20 8-run4 149.3 6.00 46 5.36 40 35 0.11 8-run6 149.7 5.65 43 3.90 17 15 0.31 8-run8 149.5 6.55 51 6.01 46-0.08 9-run2 152.0 5.93 44 3.59 8 7 0.39 9-run5 151.7 5.92 44 3.96 17 13 0.33 9-run7 151.0 6.32 48 - - 2 0.47 9-run9 151.6 6.44 49 4.94 33 33 0.23 * Porosity calculated from sample weight and length with the assumption of glass density of 2350 kg m -3. Model and Numerical Simulation for Compaction of Brittle Fractured Rhyolite For the calculation of permeability reduction of fractured rhyolite, we assumed the compaction of fractures filled with rhyolite fragments and consider one-dimensional geometry (Fig. 3A). Because the gas permeability of the fracture zone decreases with the compaction of fractured rhyolite in the fracture, that is, the decrease in the porosity, the permeability reduction can be calculated by simulating temporal change of the porosity. The relationship between the gas permeability and porosity was determined experimentally and given by the following equation: 15.8 0.3 2.3 0.3 k 10, (1) where k and represent the permeability and the porosity, respectively. When we assume the compaction in one dimension, the porosity can be expressed as the following relation: initial, (2) 1 where and initial are the strain and initial porosity, respectively. By combining equations (1) and (2), the permeability reduction can be calculated when temporal change of strain is simulated based on the following strain-strain rate and stress-strain rate relations: 4
and t (3) /, (4) where and t represent the strain rate and time, respectively, and and are the stress and the viscosity, respectively. Here, the viscosity for the compression is given by the following relation: 18863 0.78 log 5.71, (5) T 1 where T represents the temperature (Quane et al., 2009). Temporal change of total strain is obtained from the following equation because the viscosity varies with porosity and the porosity is a function of time: dt. (6) The relationship between strain and strain rate is also obtained by substituting equations (2) and (5) into equation (4): A log B, (7) where A and B are constants. By changing equation (6) to a differential form and combining it with equation (7), we finally obtain the following equation: d dt 10 C D, (8) where C and D are given by the following relations: and 0. 78 C 1 initial 18863 T 0.78 1 initial D 5.71. initial 5
Temporal change of the strain was numerically calculated by solving equation (8) using 4 th order Runge-Kutta method; finally, the permeability was obtained based on equations (1) and (2). In this study, the stress ( ) was set to be 1 or 10 MPa and the temperature (T) of 800 to 900 C was used. Initial porosity ( initial ) was assumed to be 60 vol% because shear fracturing zone formed in rhyolite has ~60 vol% porosity, which was obtained from the CT images reported by Okumura et al. (2013). References Okumura, S., Nakamura, M., Takeuchi, S., Tsuchiyama, A., Nakano, T., and Uesugi, K., 2009, Magma deformation may induce non-explosive volcanism via degassing through bubble networks: Earth and Planetary Science Letters, v. 281, p. 267 274. Okumura, S., Nakamura, M., Uesugi, K., Nakano, T., and Fujioka, T., 2013, Coupled effect of magma degassing and rheology on silicic volcanism: Earth and Planetary Science Letters, v. 362, p. 163 170. Quane, A.L., Russell, J.K., and Friedlander, E.A., 2009, Time scales of compaction in volcanic systems: Geology, v. 37, p. 471 474. Takeuchi, S., Nakashima, S., and Tomiya, A., 2008, Permeability measurements of natural and experimental volcanic materials with a simple permeameter: Toward an understanding of magmatic degassing processes: Journal of Volcanology and Geothermal Research, v. 177, p. 329 339. 6