Finite element calculations applied to salt dome analysis

Abstract The two-dimensional low-Reynolds-number dynamics of a viscous layer of fluid (salt) moving bouyantly through a viscous fluid of another viscosity and density (sedimentary strata) is modeled by means of a special finite element model. The numerical calculation follows the movement of the interface between the two fluids through a finite element mesh, which remains stationary in space. This approach facilitates the study of the large deformations of the interface caused by a small initial disturbance. The finite element model takes care of different physical parameters such as the ratios of viscosities and heights of the two layers, the density contrast between the two fluids and the boundary conditions. The first stage (salt pillow) of the growing “salt dome” can be described by a linearized Rayleigh-Taylor instability. Close agreement exists between the results of the finite element model and known analytical solutions. In the second stage (diapir stage) distortion of the interface between the two different fluids is large enough to invalidate the linearized analysis. Now the results of model experiments with oils and glycerine can be directly compared with the finite element calculations. Distinct similarity has been found between photographs from model experiments published by Whitehead and Luther (1975) and computer plots derived from the finite element model. If an isolated initial disturbance in the interface between the two fluids is used instead of a sinusoidal deflection, even the development of salt dome families can be analysed by means of this finite element model. The model shows the growing pattern of each salt dome as well as the distance in space and time between the different members of the salt dome family. The analytical description of this phenomena is possible for the linear stage by means of a Fourier analysis of the initial disturbance.