Modelling of Sand Production and Wormhole Propagation in an Oil Saturated Sand Pack Using Stabilized Finite Element Methods

Sand production is a prevalent problem in the oil and gas industry. As sand particles are being dislodged from a sand matrix and transported into the produced fluid, they form cavities or so-called “wormholes” in the formation. The paper presents a finite element simulation of an experiment that involves sand production and wormhole propagation in a sand pack as fluid is drawn from it through a small orifice. The computations are based on a recently developed sand erosion model that describes the disaggregation of sand particles as a function of sand matrix strength and fluid flux. The writing of both particle and fluid transport equations then completes the hydrodynamics of the problem. Special numerical techniques, such as stabilized finite element methods, are developed to solve the resulting nonlinear governing equations that include coupled fields such as fluidized sand concentration, fluid pressure, and porosity. Numerical results are in close agreement with experimental data available for the sand pack experiment. In particular, the computed porosity field and its temporal evolution during wormhole propagation match very well with available CT scan images of the sand pack. PAPER: 2002-227