Discrete Element Erosion Modelling -- A Grain-Scale Approach
- Maynard Marrion (U. of Cambridge)
- Document ID
- Society of Petroleum Engineers
- SPE/EAGE Reservoir Characterization and Simulation Conference, 19-21 October, Abu Dhabi, UAE
- Publication Date
- Document Type
- Conference Paper
- 2009. Society of Petroleum Engineers
- 1.8 Formation Damage, 4.3.4 Scale, 4.6 Natural Gas, 2.4.3 Sand/Solids Control, 3.2.5 Produced Sand / Solids Management and Control, 5.6.9 Production Forecasting, 5.5 Reservoir Simulation
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We report a conceptually simple and robust particle-scale model of hydrodynamic erosion. The model treats each particle of the granular matrix as a discrete element, and computes the erosive and cohesive forces acting upon it due to the oil flow and the surrounding particles. A stochastic erosion criterion is then used to determine if the particle is eroded, depending on the nett force acting upon it and the geometrical constraints imposed on it by the neighbouring particles. The erosion is allowed to progress particle-by-particle, and the pressure field is successively recalculated to take account of the modified particle matrix. The model predicts the formation of wormhole-like voids, which grow upstream into the particle matrix, and develop into a dendritic network. Wormhole growth does not begin until the ratio of erosive to cohesive force exceeds a critical value; as this ratio increases, the amount of erosion increases. The model also shows that non-uniform distributions of permeability, such as those due to localized geological features like intrusions, can significantly modify the characteristics of the erosion and reduce the total amount erosion. These findings are in agreement with previous experimental observations.
Erosion of permeable granular media by fluid flow is a widespread phenomenon, occurring in both natural and man-made settings.
In oil wells in poorly consolidated strata, erosion can cause networks of wormhole-like structures to develop upstream from the borehole (Yuan et al., 1999). As a result, the rate of oil production can increase by more than one order of magnitude (Tremblay et al., 1996; Tremblay et al., 1999). However, the erosion can also lead to collapse of the oil well, loss of production time, increased damage and wear to equipment (Vardoulakis et al., 1996); and environmental problems (Bianco & Halleck, 2001).
A considerable body of experimental research and modelling has been performed to elucidate the mechanisms by which erosion occurs in these cases.
It has been proposed that erosion occurs when the drag force imposed by the flow is sufficient to overcome the cohesive strength of the material and carry particles of it away. This erosion preferentially takes place at locations where the solid matrix is weakest or at locations at which flow is focussed due to high permeability - it is likely that both conditions occur simultaneously, in regions of high porosity. This preferential erosion then has the effect of further reducing the strength and/or increasing the permeability of the rock at these sites. Thus, a positive feedback mechanism is set up which causes the formation of channels (Dunne, 1980; Smith & Bretherton, 1972). Similar channel growth has been observed due to flow through beds of cohesionless glass beads (Schorghofer et al., 2004; Cerasi & Mills, 1998).
For oil wells in well consolidated strata, the drag exerted by the flow is negligible in comparison to the cohesive strength of the rock. Therefore, if erosion does occur, it is overwhelmingly due to the in situ stress distribution imposed by the overburden and surrounding rock, with a negligible contribution from the flow (Bratli & Risnes, 1981). In this case, the primary role of the oil flow is to carry the yielded material into the well (van den Hoek et al., 1996). This type of failure can occur in the absence of flow (Morita et al., 1989). In poorly consolidated strata the cohesive strength is much lower, and can be comparable to the flow-induced drag. Therefore, erosion in this case is due to the combination of flow-induced forces and the in situ contact stresses, which are coupled to each other (Tronvoll et al., 1997). The development of wormhole-like structures has been observed in water-wet beds of sand, in which capillary forces are the only significant source of cohesion (Tremblay et al., 1996; Tremblay et al., 1997 and Tremblay et al., 1999).
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