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.

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