Production rate limits for perforated casing completions in weak rock formations are estimated for a material obeying a quadratic yield condition. Plastic stresses around a spherical cavity are calculated to determine the well pressure value which precipitates solids production. Elastic solutions for a cylindrical cavity are utilized to place upper and lower bounds on the well pressure value which initiates yielding around a perforated casing. The separate analyses define consistent critical well pressure values for initial yield and solids production as a function of rock properties and in-situ conditions.
Incipient Yielding and Solids Production for Perforated Casing Completions
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Fahrenthold, E. P., and Cheatham, J. B., Jr. (December 1, 1986). "Incipient Yielding and Solids Production for Perforated Casing Completions." ASME. J. Energy Resour. Technol. December 1986; 108(4): 321–325. https://doi.org/10.1115/1.3231284
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