The Effect of Inner Borehole and Outer Boundary Dimensions in Thick-Walled Cylinder Test

Abstract

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 with standard dimensions (1.5in ID, and 3in length) to investigate the borehole scale effect on the failure of the inner borehole. However, the results partially suffer from the outer boundary effect of the tests and may not purely represent the inner borehole scale effect. 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. For this purpose results from comparing different failure criteria (i.e. Mohr-Coulomb, Drucker-Prager, Mogi and modified Lade) from Tehrani's results (2016) were used. Then, the volumetric strain was formulated against confining pressure to explain the elastic, elastic-plastic, and plastic behaviour of the rock. Variation of 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 of the rock. After distinguishing the outer boundary effects, the results shows a decreasing trend between the inner borehole size and the TWC strength of the sample, which can be considered as the borehole scale effect. This study has also broadened the understanding of the effect of borehole and boundaries dimensions in TWC test, which may be generalized to real scale cases, i.e. wellbores and perforations.