Investigating the risk of sand production is a common practice for developing unconsolidated and weakly consolidated reservoirs, particularly with designing the completion system of development wells. The risk of sanding may be different for open hole and cased and perforated completion systems. Part of this difference is a result of the different size of the boreholes—that is, open hole versus perforation tunnels— which is known as borehole scale effect. The amount of research dedicated to investigate the borehole scale effect on sand production is very limited. Research has been carried out by conducting thick-walled cylinder (TWC) tests on samples with different inner to outer diameter ratios. The impacts of sample size and boundaries on the induced stresses around the borehole and failure were, however, not differentiated from the borehole scale effect. In this paper, a comprehensive analytical approach is performed to investigate the effect of the size of the sample and boundaries on TWC tests and borehole failure. To do this, four different failure criteria—Mohr-Coulomb, Drucker-Prager, Mogi and modified Lade—are compared with previously published experimental results. The analysis shows that the size of the sample and the boundaries may significantly change the TWC strength of the rock. The TWC changes by different inner to outer diameter ratios, however, may not be fully justified by the analytical approach. Hence, a scale effect factor must be introduced to replicate the experimental results.

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.