Hydro-mechanical erosion models for sand production E. Gravanis 1 , E. Sarris 1,2, * ,† and P. Papanastasiou 1,2 1 International Water Research Center (IWRC) NIREAS, University of Cyprus, 1678 Nicosia, Cyprus 2 Department of Civil and Environmental Engineering, University of Cyprus, 1678 Nicosia, Cyprus SUMMARY Sand production is a complex physical process that depends on the external stress and flow rate conditions as well as on the state of the material. Models developed for the prediction of sand production are usually solved numerically because of the complexity of the governing equations. Testing of new sand production models can very well be performed through calibration with laboratory experiments, which by construction possess geometric symmetry facilitating explicit mathematical analysis. We introduce an erosion model that is built upon the physics (poro-mechanical coupling of the fluid-solid system) usually incorporated in ero- sion models for the prediction of sand production. Around this model, we set up a mathematical framework in which sand production models because of erosion can be tested and calibrated without having to resort to complex numerical work or specialised software. The model is validated by data of volumetric sand produc- tion from a hollow cylinder test on synthetic sandstone. Generalisations of the model, which are naturally incorporated in the same framework and have useful phenomenological features, are discussed. Copyright © 2015 John Wiley & Sons, Ltd. Received 18 August 2014; Revised 20 February 2015; Accepted 9 March 2015 KEY WORDS: sand production; volumetric sand prediction; erosion hydromechanics; hollow cylinder; poro-plasticity 1. INTRODUCTION Sand erosion, in the sense that interests us in this work, is the phenomenon where a fluid saturated rock loses its mechanical integrity because of the applied stress field and is transported away in the presence of pore pressure gradients. The unintended by-product of solid particles of oil and gas production is generally referred to as sand production. In practice, the aggressive pumping of oil from the well causes grain dislocation from the solid matrix of the rock, thereby leading to mechanical problems such as accumulation of sand in the wellbore and the creation of unstable cavities in the geological formation. Particle influx into the wellbore may lead to various problems such as erosion of valves and pipelines, plugging of production liners and sand deposits in the separators. Additionally, during production, sudden erosion in high-pressure gas wells represents a major safety risk [1, 2]. The design issue that arises from this problem, and it is of considerable interest to the oil and gas operating companies, is the prediction or control of these particles. In the view of modelling, the different processes that are involved in the sand production problem are associated with (1) fluid and solids transport; (2) fluid/rock interaction; and (3) rock deformation. Modelling of the sand production physical problem is not a trivial process as it involves the following coupled mechanisms: (a) the mechanical instabilities and localised compressional or tensile failure (damage) of the rock in the vicinity of the wellbore because of stress concentration *Correspondence to: E. Sarris, Department of Civil and Environmental Engineering, University of Cyprus, 75 Kallipoleos street, P.O.Box 20537, 1678 Nicosia, Cyprus. † E-mail: esarris@ucy.ac.cy Copyright © 2015 John Wiley & Sons, Ltd. INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. 2015; 39:2017–2036 Published online 4 May 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nag.2383