[1] We present a level set method for simulating capillary-controlled displacements with nonzero contact angles in porous media. The main feature of the method is a level set evolution velocity which is different in the pore space and solid phase. This augments the standard level set equation with an extra term such that, at steady state, the contact angle is enforced in the solid phase, whereas capillary and interfacial forces are balanced in the pore space. We employ the method to simulate quasistatic drainage and imbibition processes for different contact angles in several pore geometries, and to compute capillary pressure and fluid/fluid specific interfacial area curves in each case. We validate the method by comparing stable fluid configurations computed in idealized two-dimensional geometries and three-dimensional (3-D) straight tubes with known analytical solutions. Simulations performed in a subset of a 3-D sandstone image show that the developed method accounts for well-known pore-scale mechanisms such as piston-like invasion, Haines jump, interface coalescence, and retraction, swelling of wetting films and snap-off. The contact angle is formed by an intersection of the fluid/fluid interface and the void/solid boundary. Therefore, the solid matrix surrounding the pore space is discretized with at least an equal number of grid points as the size of the numerical stencil used to approximate the level set derivatives.Citation: Jettestuen, E., J. O. Helland, and M. Prodanović, A level set method for simulating capillary-controlled displacements at the pore scale with nonzero contact angles, Water Resour. Res., 49,[4645][4646][4647][4648][4649][4650][4651][4652][4653][4654][4655][4656][4657][4658][4659][4660][4661]

[1] Piercement structures such as mud volcanoes, hydrothermal vent complexes, pockmarks and kimberlite pipes, form during the release of pressurized fluids. The goal of this work is to predict under which conditions piercement structures form from the insights gained by sand box experiments injecting compressed air through an inlet of width w at the base of a bed of glass beads of height h. At an imposed critical velocity v f , a fluidized zone consisting of a diverging cone-like structure formed with morphological similarities to those observed in nature. Dimensional analysis showed that v f is correlated to the ratio of h over w. In addition, we derived an analytical model for v f which is compared to the experimental data. The model consists of a force balance between the weight and the seepage forces imparted to the bed by the flowing gas. The analytic model reproduces the observed correlation between v f and h/w, although a slight underestimate was obtained. The results suggest that the gas-particle seepage force is the main triggering factor for fluidization and that the commonly used proxy, which the fluid pressure must equal or exceed the lithostatic weight, needs to be reconsidered. By combining the experiments and the model, we derived critical pressure estimates which were employed to a variety of geological environments. Comparing the estimated and measured pressures prior to the Lusi mud volcano shows that the presented model overestimates the critical pressures. The model paves the way for further investigations of the critical conditions for fluidization in Earth systems.

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