Cement Sheath Thick-Walled Cylinder Stress Calculator
Model radial, tangential (hoop), and shear stresses across the annular cement barrier under casing pressure and thermal expansion to evaluate debonding risk.
Annular Well Geometry
Radius = Casing OD / 2 (7" casing = 3.5")
Radius = Hole size / 2 (8.75" hole = 4.375")
Sheath Boundary Stresses
Max Inner Hoop Stress (σ_θi):
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Radial Interface Stress (σ_ri):
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Tensile Cracking Risk:
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Shear Failure / Debonding:
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Maximum von Mises Stress:
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Sheath Thickness (r_o - r_i):
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Lamé Theory for Annular Cement Sheath Integrity
During hydraulic fracturing, steam injection, or pressure testing, expanding casing imposes intense mechanical strains on the set cement sheath. If the hoop stress σ_θ exceeds the tensile strength of the set cement (T_0 ≈ 250 - 450 psi), radial cracks propagate, creating gas migration micro-annuli.
Lamé Cylindrical Stress Equations
σ_r(r) = (P_i·r_i² - P_o·r_o²)/(r_o² - r_i²) - (P_i - P_o)·r_i²·r_o² / [r²·(r_o² - r_i²)] σ_θ(r) = (P_i·r_i² - P_o·r_o²)/(r_o² - r_i²) + (P_i - P_o)·r_i²·r_o² / [r²·(r_o² - r_i²)]