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

Abstract 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 non-linear 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. Introduction Cold production is an economical mainstream process for heavy oil recovery in which oil and sand particles are produced together from unconsolidated formation with an abnormal higher rate up to 20 times than that predicted by Darcy's law based on typical reservoir parameters. However, the majority of operators report very high sand cuts from 10% to 40%. As massive sand is being produced, a variety of problems arise, i.e., erosion and plugging of facilities, ground settlement, and sand disposal. Since this prevalent phenomenon is not well understood, sand production and control (management) has been a research topic for more than five decades. Extensive studies have shown that the cause of the abnormality is a combination of many factors - notably, stresses, fluid flow, thermal, solution gas drive and reservoir heterogeneity in porosity. Even though it is well known that large amounts of sand accumulate into the well bore, their origin is still unclear. Based on tracer and injectivity tests, a common belief is that high-permeability channels - so-called cavities or wormholes in the petroleum geomechanics jargon - are formed after a period of time. In order to visualize the production process at the laboratory scale, Tremblay et al (1996, 1997, 1999) preformed sand pack experiments to model the production of oil, gas and sand into a perforation in a vertical well. A high-porosity channel was observed with the aid of X-ray computed tomography techniques. It was found that, besides hydromechanical effects, the solution gas drive enhanced the propagation of the wormhole as gas bubbles expand under a pressure decline. This in turn unlocks the sand grain structure so that the porosity of the skeleton increases, which in turn leads to a drop in its mechanical strength. Hence, the wormhole propagates further in regions where strength weakening takes place.

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