Cement sheath stress
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Cement sheath stress model
Strain in radial direction for thick cylinder:
r - radius withing cylinder where:
mu - Poisson's ratio
EM - Young's modulus
r - cylinder inner radius
R - cylinder outer radius
p - inner pressure
P - outer pressure
Let's use cylinder properties with next indexes: 1 - casing, 2 - cement, 3 - formation
Strain of outer casing edge is equal to strain of inner casing edge:
Strain of outer cement edge is equal to strain of inner formation edge:
Solving two equations above relative to P1 and P2 allows now calculation of stresses in cementing sheath using Lame's equations
for radial stress:
and for tangential stress:
