Cement sheath stress

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: