PSI - Issue 48

Udaya B Sathuvalli et al. / Procedia Structural Integrity 48 (2023) 207–214

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Sathuvalli and Suryanarayana/ Structural Integrity Procedia 00 (2019) 000–000

Nomenclature A i

ID area of the casing (= π a 2 ) OD area of the casing (= π b 2 )

A o A s

Cross sectional area of the casing (= A o - A i )

Inner radius of casing Outer radius of casing

a b

Inner Diameter (ID) (= 2 a = d o - 2 t ) of casing Outer Diameter (OD) (= 2 b ) of casing

d i d o

Young’s modulus

E

Axial force

F z

Axial force at the structural limit

F z,yp

Pipe Body Yield Strength, i.e. axial force to yield the cross section, (= σ yp,T A s )

F yp H’

Slope of true stress versus plastic strain curve External pressure, Internal pressure

P ext , P int

Collapse pressure

p c

Elastic collapse pressure of a thin-walled cylinder External pressure to yield the ID of a thick-walled-cylinder

p c,e p c,y

Mean radius of cylinder

R o

Radial distance from cylinder axis Wall thickness of casing (= b - a )

r

t

u , u o v ( θ ),

Radial displacement, Amplitude of radial displacement

Tangential displacement

w ( θ ), w o

Radial displacement, Amplitude of radial displacement

Strain, Radial strain, Hoop strain Axial strain, Axial strain at structural limit

ε, ε r ,ε θ ε z , ε z,fp

Strain at yield point

ε yp

Ratio of OD to wall thickness (= d o /t )

γ

Curvature of the median surface of a thin-walled cylinder

κ λ ν θ ρ

Plasticity parameter

Poisson’s ratio

Polar (circumferential) angle

Radial distance of the elastic-plastic boundary ( a ≤ ρ ≤ b ) Stress , Radial stress, Hoop stress, Axial stress

σ, σ r ,σ θ ,σ z

von Mises Equivalent (VME) stress Uniaxial yield stress in compression Uniaxial yield stress in tension

σ VME σ yp,C σ yp,T

The resultant tensile geomechanical strain in the overburden is transmitted, almost entirely, to the production casing. If the production casing is in hydraulic communication with the depleting reservoir, the production casing experiences a differential collapse pressure and axial pull simultaneously (Bickley and Curry, 1992; Bruno, 2002). The structural integrity of the production casing is determined by the axial (geomechanical) strain that it can support at a given differential collapse pressure. The collapse load is the difference between the lateral pressure exerted by the earth outside the casing, and the reservoir fluid inside its bore. Cemented casings in the upper section of steam and geothermal wells experience large temperature swings between injection/production and well shut-in cycles. The relatively thin-walled casings ( d o / t ~ 16 - 26) are compressively plasticized (load path 0-1-2, Fig. 1b). When the wellbore cools to the undisturbed geothermal temperature, the compressively plasticized casings unload and develop residual axial tension (load path 2-3, Fig. 1b). Because the internal pressure in the casing reduces during cooldown, the casing is subjected to tension & collapse differential pressures simultaneously. This condition, known as the “cold collapse” has caused several casing failures (Suryanarayana et al., 2020).