Experimental and numerical investigation of the effect of inner and outer boundary dimensions on collapse of the sample in thick-walled cylinder test

Abstract

© 2017 ARMA, American Rock Mechanics Association. It is well-known that the risk of sanding varies for different completion systems, i.e. open hole versus cased and perforation, in a given wellbore and reservoir. Part of this difference comes from the scale effect of the borehole. Pragmatic approaches are usually taken to consider the borehole scale effect in the sand production prediction analysis. A more rigorous approach is needed to take this effect into account. Experiments have been conducted by researchers on thick-walled cylinder (TWC) samples with different inner to outer diameter ratios (ID/OD) for samples of standard dimensions (1.5 in ID, and 3 in length) to investigate the scale effect on the borehole failure. However, the results partially suffer from the outer boundary effect of the tests and may not purely represent the effects of the inner borehole scale. Here in this paper, the outer boundary effects of TWC experiments were distinguished from the inner borehole scale effect using analytical approaches followed by extensive laboratory experiments. The methodology involves computation and comparison of failure from different criteria (i.e. Mohr-Coulomb, Drucker-Prager, Mogi and Modified Lade) from Tehrani's results (2016). Then, the volumetric strain was formulated against confining pressure to explain the elastic, elastic-plastic, and plastic behaviour of the rock. Variation of the TWC strength of samples with different inner borehole sizes may not be fully captured by the analytical approach, which only considers the effect of the ID/OD. Hence, the differences between the analytical and experimental approaches can be considered as the inner borehole scale effect. As expected, the analysis showed that the size of the inner borehole and the outer boundaries significantly change the TWC strength. Surprisingly, the effect of the samples' OD was obvious, regardless of the corresponding ID. After distinguishing the outer boundary effects, the results show a decreasing trend between the inner borehole size and the TWC strength of the sample, which can be considered as the borehole scale effect. A numerical model was generated to simulate the lab experiments. The discrete element method (DEM) was selected to capture the highly discontinuous nature of the rock samples and the failure mechanisms. The model was built using the commercial Particle Flow Code in Three Dimensions (PFC3D) from Itasca. This study has also broadened the understanding of the effect of the borehole and boundaries dimensions in TWC tests, which may be generalized to real scale cases, i.e. wellbores and perforations.