Numerical Modeling of the Slit Mode of Cavity Evolution Associated With Sand Production

Abstract

Summary This paper documents progress in the development of a numerical model to predict the amount and rate of sand production at the scale of a wellbore or perforation. The model uses a continuum hydro-mechanical description of the rock mass, coupled with a superficial erosion scheme with evolving geometry. Different modes of cavity evolution have been observed in laboratory experiments to study sand production (uniform, dog-ear, and slit), and the various modes have been associated with different rock failure types (tension, shear, and compaction). In this work, the sand-production model (which can accommodate tension and shear failure) is also expanded to account for the combination of volumetric collapse (compaction band formation) and transport of failed material by hydrodynamic forces. It is shown, using numerical experiments, that those two basic ingredients can lead to the development of the slit mechanism. In this paper, we review the basic conditions for the compaction mode of failure to occur by considering a simple cap constitutive law and give examples of numerical simulations that illustrate band formation in a (dry) hollow cylinder test. Also, using numerical experiments, we show that the sand-production model, enhanced with a constitutive law featuring a volumetric cap, is able to reproduce qualitatively the slit mode of cavity evolution that has been observed in laboratory settings. One key feature of the computational model is a sand-production curve giving sand-mass production versus simulation time. With the documented enhancement, the model can generate sand-production curves associated with tension, shear, and compaction failure. The sand-production model needs to be developed and validated further, and calibrated using laboratory experiments. However, at this stage, it shows good potential as an engineering tool to help characterize the impact of rock strength on sand production associated with oil production.