SPE Reservoir Evaluation & Engineering
Volume 13, Number 4, August 2010, pp. 688-698

SPE-136701-PA

On the Wellbore Stress Change Caused by Drawdown and Depletion: An Analytical Model for a Vertical Well in a Thin Reservoir

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DOI  More information 10.2118/136701-PA http://dx.doi.org/10.2118/136701-PA

Citation

  • Schutjens, P. and Kuvshinov, B.N. 2010. On the Wellbore Stress Change Because of Drawdown and Depletion: An Analytical Model for a Vertical Well in a Thin Reservoir. SPE Res Eval & Eng  13 (4): 688-698. SPE-136701-PA. doi: 10.2118/136701-PA.

Discipline Categories

  • 5.3.5 Scale, Sand, Corrosion, and Clay Migration Control
  • 5.8 Fundamental Research in Production and Operations
  • 6.6.5 Well Performance Monitoring, Inflow Performance

Keywords

  • Formation Evaluation

Summary

An analytical model is presented to describe the stress change at the wall of a vertical wellbore because of drawdown and reservoir depletion. The model predicts a lower effective tangential stress and higher effective axial stress (at a given drawdown) than the popular model of Risnes, Bratli, and Horsrud (RBH) model (Risnes et al. 1982; Bratli et al. 1983; Fjær et al. 2008). The reason for this difference is that our model is valid for a finite reservoir thickness ("thin reservoir"), whereas the RBH model is constrained by the condition of an infinite reservoir thickness.

We modeled the production-induced stress change in two reservoirs with different rock properties: Reservoir A has a porosity of approximately 20% and a permeability of up to 30 md; Reservoir B has a porosity of approximately 30% and a permeability of a few darcies. Calculated wellbore stress paths were combined with mechanical properties from core deformation experiments to evaluate the risk of drawdown-induced/depletion-induced shear failure. If we consider only the experimental shear-failure data collected on samples from Reservoir A for the shear-failure limit, then, according to the present model, the planned drawdown of 34 MPa will not lead to wellbore shear failure. Even after 34 MPa of depletion, a drawdown of 34 MPa can be applied safely in Reservoir A. For high-permeability Reservoir B, the model predicts that shear failure of the borehole wall will not occur in the first phase of production, when there is only a drawdown of up to 2 MPa and no depletion. Depending on the shear-failure criterion chosen, the model predicts shear failure after 25 to 42 MPa of depletion. Massive sand production was observed only after some 40 MPa of depletion, confirming that elastic-brittle models are conservative in predicting drawdown-induced or depletion-induced shear failure in a borehole, notably in high-porosity rocks. Our examples show their value in qualitative comparative analysis of shear failure and sand-production risk.

© 2010. Society of Petroleum Engineers

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History

  • Original manuscript received: 8 August 2007
  • Meeting paper published: 5 December 2007
  • Revised manuscript received: 9 July 2009
  • Manuscript approved: 3 March 2010
  • Published online: 12 August 2010
  • Version of record: 24 August 2010