Migration, trapping, and venting of gas in a soft granular material

Gas migration through a soft granular material involves a strong coupling between the motion of the gas and the deformation of the material. This process is relevant to a variety of natural phenomena, such as gas venting from sediments and gas exsolution from magma. Here, we study this process experimentally by injecting air into a quasi-2D packing of soft particles and measuring the morphology of the air as it invades and then rises due to buoyancy. We systematically increase the confining prestress in the packing by compressing it with a fluid-permeable piston, leading to a gradual transition in migration regime from fluidization to pathway opening to pore invasion. We find that mixed migration regimes emerge at intermediate confinement due to the spontaneous formation of a compaction layer at the top of the flow cell. By connecting these migration mechanisms with macroscopic invasion, trapping, and venting, we show that mixed regimes enable a sharp increase in the average amount of gas trapped within the packing, as well as much larger venting events. Our results suggest that the relationship between invasion, trapping, and venting could be controlled by modulating the confining stress.

Figure 1

(a) We inject air into the bottom of a vertical flow cell filled with a liquid-saturated monolayer of soft particles. The flow area is formed by two glass plates clamped to a rigid spacer, with adjustable height $h$ set by a fluid-permeable piston at the top. We control the initial solid fraction ${\varphi }_s^0$ and therefore also the initial confining effective stress $|{\sigma }_0^{\prime }|$ by changing $h$. After fixing ${\varphi }_s^0$, we inject air with a syringe pump and then record the dynamics of air invasion, migration, trapping, and venting, as well as the deformation of the packing, at high resolution using a digital camera. (b) Snapshots at three representative values of ${\varphi }_s^0$ show that under weak confinement (left), discrete gas bubbles rise by fluidizing the packing; under moderate confinement (middle), gas rises by opening transient, slender, fracture-like pathways; and under strong confinement (right), gas rises by invading the pore space between the grains and the walls.

Figure 2

Horizontal ($v_x$) and vertical ($v_z$) components of the instantaneous particle velocity field for the snapshots shown in Fig. 1, as calculated from particle tracking. Gray patches indicate gas. Fluidization (left two) involves yielding the packing, and is characterized by the flow of grains with and around the rising bubbles. Pathway opening (middle two) involves opening a narrow channel in the packing by pushing grains laterally apart, and is characterized by grain displacement primarily around the tip of the advancing pathway. In pore invasion (right two), the grains are essentially immobile.

Figure 3

Air-occupancy images collapse an ensemble of episodic migration events into a single fingerprint. The darkness of each pixel is proportional to its average air saturation over the entire experiment, such that persistent trajectories and trapped blobs are darker, whereas ephemeral features are lighter. As ${\varphi }_s^0$ increases from 0.46 to 0.69 (left to right), fluidization (vertical streaks) transitions to pathway opening (blurred fans with streaks and dots) and then to pore invasion (particle-scale spattering). The orange panel (${\varphi }_s^0=0.52$) corresponds to the high-capture mode, as discussed in Sec. 3c.

Figure 4

(a) We show the injection capillary pressure $p_c^{\mathrm{inj}}$ as a function of time $t$ for ${\varphi }_s^0=0.49$ (red), 0.59 (green), and 0.69 (blue) (dots indicate local peaks). (b) The average peak value $\langle \max \left(p_c^{\mathrm{inj}}\right)\rangle$ is noisy, but increases relatively steadily and monotonically with ${\varphi }_s^0$. (c) The total volume of air in the cell $V_{\mathrm{air}}$ is also oscillatory in all cases, but the mean value and the amplitude and period of the oscillations are distinctly larger in the intermediate mixed regimes than in either of the two end-member regimes. (d) The time-averaged total air volume $\langle V_{\mathrm{air}}\rangle$ (solid line) exhibits a strongly nonmonotonic dependence on ${\varphi }_s^0$, increasing sharply at ${\varphi }_s^0=0.52$ and then falling gradually. $\langle V_{\mathrm{air}}\rangle$ can be divided into two contributions: The amount of air trapped inside the pore space $\langle V_{\mathrm{pore}}\rangle$ (dotted line) and the amount of air in open bubbles and pathways $\langle V_{\mathrm{open}}\rangle$ (dashed line), where $\langle V_{\mathrm{air}}\rangle =\langle V_{\mathrm{pore}}\rangle +\langle V_{\mathrm{open}}\rangle$. In (b) and (d), the black dots and line show the mean and the gray band has a width of two standard deviations. For ${\varphi }_s^0\ge 0.59$, each result is the average of at least two experiments.

Figure 5

Time evolution of the horizontal ($v_x$, top row) and vertical ($v_z$, bottom row) components of the instantaneous particle velocity field for ${\varphi }_s^0=0.52$ (orange panel in Fig. 3), as calculated from particle tracking. The color scale is the same as in Fig. 2.

Figure 6

(a) The characteristic bubble rise velocity $U$ as a function of ${\varphi }_s^0$. The open squares correspond to the experimental data, while the dashed line is the result of our scaling law. (b) The plot of theoretical $\langle V_{\mathrm{air}}\rangle$ (open circles) is overlaid with experimental data, as a function of ${\varphi }_s^0$. For ${\varphi }_s^0<0.5$, the model qualitatively replicates the gradual increase in $\langle V_{\mathrm{air}}\rangle$ with ${\varphi }_s^0$. The plot also shows the minimum volume of air ($V_{\mathrm{air}}^{\mathrm{req}}$) required to rigidify the packing and to stop the rising bubble in blue squares. When the rigidified packing is assumed to have thickness $l_c=4\mathrm{cm}, \langle V_{\mathrm{air}}\rangle {}^{\mathrm{req}}$ and theoretical $\langle V_{\mathrm{air}}\rangle$ match at ${\varphi }_s^0=0.506$, which signifies the transition to enhanced gas trapping.