Analytical and numerical modeling of salt caverns

Stability is the principal aspect that characterizes underground storage, especially if it is a salt cavity. For this reason, it is important to examine factors that effected the most stability. Cavern geometry, depth and geothermal temperature are among them. At first, sensitivity analysis was made using the analytical method in order to compare the steady state volume loss rate experienced by spherical and cylindrical cavern in two reference cases, which are Etrez (France) and Salina (USA). As expected, volume loss rate increases as internal pressure drops. The comparison showed that Etrez case has higher volume loss rate for shallower cavern, for both cylindrical and spherical; for deeper cavern, the situation is reversed and Salina case shows a faster closure rate. In addition, spherical cavern is characterized by slower convergence rate as internal pressure decreases, for both reference cases and depths. The next step was to study cavern closure using numerical method based on the finite difference model (DFM) which is Flac 8.0 (Itasca): both cylindrical and spherical cavern are taken into account. It is assumed that caverns are leaked in a homogenous salt formation and that the initial state of stress is isotropic. The result of modeling was then compared with the analytical solution. There is an agreement between results when minimum depth (1000 m) is considered; however, differences increase with depth. In fact, numerical solution underestimates the closure rate when internal pressure is minimum and overestimates it when the internal pressure is maximum. However, spherical cavern closure rate does not exceed the cylindrical one for all the simulations in accordance with what evidenced by the previous sensitivity analysis. Finally, influence of geothermal temperature was assessed in the case of Waste Isolation Pilot Plant (WIPP) of Carlsbad, New Mexico (USA). First, temperature in the model was assumed equal to 300 K, then increased to 310 K and, finally, was imposed equal to 320 K. Halite layer, that hosts the room, was assumed behaving as visco-plastic and strain softening material. A shear band development, that cased roof failure, was observed during creep time simulation. It appears clear that delay in shear band formation reduces significantly with the increase in temperature.