1876-6102 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the organizing committee of GHGT-13.doi: 10.1016/j.egypro.2017.03.1680

Energy Procedia 114 ( 2017 ) 5241 – 5248

ScienceDirect

13th International Conference on Greenhouse Gas Control Technologies, GHGT-13, 14-18November 2016, Lausanne, Switzerland

Assessment of thermal stress on well integrity as a function of sizeand material properties

Pratanu Roya,∗, Joseph P. Morrisa, Stuart D. C. Walsha, Jaisree Iyera, Susan Carrolla, JelenaTodorovicb, Kamila Gawelb, Malin Torsæterb

aLawrence Livermore National Laboratory, Livermore, CA, USAbSINTEF Petroleum Research, Trondheim, Norway

AbstractWellbore integrity is critical to long term carbon storage. During CO2 injection, changes in temperature may result in large stress

variations that can damage the well, threatening its integrity. The different materials comprising the wellbore and near-wellbore

environment (namely the casing, cement and surrounding rock) possess different thermal properties. Consequently, there can be con-

siderable variations in both material properties and thermal gradients across these layers, resulting in different amounts of contraction

and expansion of these materials. This may generate sufficient thermal stresses to lead to fracture within the cement and/or host rock,

or delamination of the cement/casing or cement/rock interfaces. Downsized wellbore samples have been used in laboratory studies

to investigate the failure modes and failure criteria during thermal cycling operations. However, it is not clear to what extent such

results can be reliably used to predict well failure at field scale conditions. In this work, we conduct a parameter study involving the

size and material properties of the wellbore samples subjected to different rates of thermal loading, with the objective of predicting

how these parameters can affect the thermal stress in field scale well conditions.

A state-of-the-art parallel multiscale, multiphysics code named GEOS, developed at Lawrence Livermore National Laboratory,

was used to study the thermal response of wellbore materials. A finite element solver considering linear elastic materials was coupled

with a finite volume heat equation solver to simulate the wellbore deformation and fracture during thermal cycling. To understand the

effect of wellbore size on thermal fracturing, simulations were conducted at different height to diameter ratios. The wellbore sample

size was systematically varied from the lab scale to field scale with several intermediate scales. The change in thermal stresses were

compared for different scales. Additionally, the effect of elastic modulus and cooling rates were studied.

c© 2017 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the organizing committee of GHGT-13.

Keywords: Thermal stress; Wellbore integrity; Upscaling wellbore model

1. Introduction

The well barrier materials, namely casing and cement, provide mechanical and hydraulic sealing in the well. Ther-

mal loading, in particular repeated thermal loading, of wells is a potential source of failure in well barrier materials.

∗Corresponding author: Tel: +1-925-423-5917; Fax: +1-925-423-3886. E-mail address: roy23@llnl.gov

Available online at www.sciencedirect.com

Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the organizing committee of GHGT-13.

5242 Pratanu Roy et al. / Energy Procedia 114 ( 2017 ) 5241 – 5248

CO2 injection wells are often subjected to large temperature variations. When the liquid or supercritical CO2 is injected

through the wellbore, the temperature of the CO2 is considerably lower than the surrounding formation temperature.

Conversely, wellbore temperature may rise during shut-downs or well servicing. This thermal loading and unloading

generates thermo-elastic stresses inside the wellbore materials, which in turn reduces the critical pressure needed to

initiate fracture [1]. Thus, thermal cycling operation is one of the possible failure mechanisms for the well barrier

materials.

A number of experimental studies have been conducted investigating the failure of wellbore materials. These studies

simulated the thermal effects by applying mechanical loading, such as metal rings [2], hydraulic press [3] and pressure-

cycling cells [4]. Radial cracking perpendicular to the applied stress and disking failures with increased number of

cycles were reported in these studies. One obvious limitation of these studies is the unpredictability of temperature

range that corresponds to similar mechanical loading in the experiments. Furthermore, the thermal properties of the

materials and the interfaces are completely ignored, which may play important roles in variations of thermal stresses.

Recent experiments by Albawi et al. [5] and De Andrea et al. [6] emphasized the role of a thermal platform to

understand the effect of thermally induced stresses. They applied cyclic thermal loading on a downsized wellbore

sample to study how the annular cement integrity varies as a function of time and temperature profiles. Their results

showed that the pre-existing cracks in the samples can extend upon thermal cycling operations.

A number of studies involving numerical modeling of thermal stresses during CO2 injection have also been reported.

Lou et al. [1] described a simplified model for heat transfer in the wellbore and estimated the safe injection pressure

range to avoid fracture initiation in an injection well. Gor et al. [7] studied the effect of CO2 injection temperature on

caprock stability using a fully coupled thermo-poromechanical model. By simulating 10 years of continuous injection

of CO2 at different temperatures, they showed that the thermal stresses can overcome tensile strength resulting in a

failure of the caprock when the CO2 is injected at a temperature of 40-50◦C. Preisig et al. [8] used a coupled multi-

phase model to study the thermo-poromechanical effects of CO2 injection at In Salah, Algeria. Their study revealed

that the temperature difference between the injected CO2 and the reservoir can reduce the compressive stresses and even

create tensile stresses due to the inability of the rock to contract freely, leading to creation or re-opening of fractures.

In spite of the reported studies, a systematic investigation on thermally induced casing expansion and contraction

with varying temperature range, and thermal and mechanical properties of the well barrier materials is yet to be per-

formed. In an effort to accomplish this, a combination of experiments and numerical simulations on downscaled well

section were recently performed by the SINTEF Petroleum Research, and the Lawrence Livermore National Laboratory.

The numerical study involves a coupled, three-dimensional thermo-mechanical modeling of thermal cycling using the

same sample geometry that was used in the experimental work. The numerical results showed that some radial cracking

is likely to occur because of the thermal expansion of wellbore materials during the heating stage whereas the thermal

contraction of the materials during the cooling stage may result in interfacial debonding [9]. It was also experimentally

observed that extreme cooling can create radial fractures upon freezing the pore water [10].

This report further summarizes the results found in this collaborative effort. More specifically, we present the com-

parison of numerical and experimental results which emphasizes the role of thermal conductivity and contact resistance

between the sealing materials. After calibrating the numerical model using this comparison, we demonstrate how the

stresses in wellbore materials are affected by the variation of material properties, different heating/cooling rates and

scaling.

2. Thermal Cycling Experiment

A series of experiments investigating the effects of thermal fluctuations on wellbore integrity were conducted on

downscaled wellbore analogues. The downscaled samples consisted of an inner steel casing and an intermediate cement

layer with a larger cylindrical sandstone sample of 20 cm in diameter. The inner radius of casing, cement and sandstone

were approximately 0.26 cm, 0.3 cm, and 0.375 cm, respectively. The experimental setup consisted of a thermal

platform with a copper rod, a nitrogen cooling tank, and a data acquisition system, as shown in Fig. 1. The thermal

platform (T600 from Environmental Stress Systems (ESS) ) was used to heat or cool the copper rod at a specific heating

or cooling rate. During the experiment, the temperature of the thermal platform was varied between -50 oC and 80 oC by

temperature controller (Watlow EZ PM9, also from ESS). Thermocycling associated temperature changes at different

places within the specimen were measured using a set of pre-calibrated thermocouples (Type K) and the temperature

Pratanu Roy et al. / Energy Procedia 114 ( 2017 ) 5241 – 5248 5243

values were logged using a thermocouple data logger (TC8, Pico Technology). Thermocouples were placed at four

different interfaces within the specimen, namely: (1) Cu rod/casing; (2) casing/cement; (3) cement/rock; (4) rock/air.

Further details of the experimental setup and procedure are described in [9] and [10].

(a) Schematic of the thermal cycling setup (b) Technical drawing of sample and thermal platform

Fig. 1: Experimental setup

3. Numerical Modeling

The LLNL-GEOS code, a multi-physics, multi-scale simulator, was used to model the problem numerically. A

linear elastic stress model was coupled with conduction heat transfer model to study the mechanical response of the

materials subjected to thermal loading. The initial objectives of the simulations were to predict the temperature profiles

for prescribed thermal boundary conditions and compare them with the experimental results. The virtual wellbores

employed in the numerical models have the same sample dimensions as in the experiments described above. The initial

temperature of the well and host rock was set to 24 ◦C (∼ room temperature) at the beginning of each simulation.

Then, the temperature at the inner radius of the casing was increased or decreased instantaneously or at a specific

heating/cooling rate, depending on the nature of the numerical test. The thermoelastic properties of the materials used

in the simulations are tabulated in Table 1.

Fig. 2: Material layers used to model the experiment

5244 Pratanu Roy et al. / Energy Procedia 114 ( 2017 ) 5241 – 5248

Table 1: Thermo-elastic Properties of Materials [6, 11, 12]

Properties/Material Steel Cement Rock

Thermal Expansion Coeff. (K−1) 12.0 ×10−6 7.9 ×10−6 10.0 ×10−6

Thermal Conductivity (W/m/K) 50 1 2.1

Specific Heat Capacity (J/kg/K) 450 1600 2000

Young’s Modulus (GPa) 200 10-47 10-47

Bulk Modulus (GPa) 140 25 25

Poisson’s Ratio 0.26 0.18 0.18

4. Results and Discussions

4.1. Temperature profiles: comparison with experiments

A two-dimensional model with different material layers was used to predict the temperature profiles (Fig. 2). Early

simulations, which assume perfect thermal contact between the casing and the copper rod, were found to result in

an overestimation of heat transfer in the materials compared to the experimental data. When a contact resistance was

introduced between the two materials (as might arise, for example, due to an air gap or an imperfect contact between the

cooling/heating element and the casing), the numerical results matched well with the thermocouple readings (Fig. 3). A

similar air gap was also used by Lund et al. [13] to match the experimental temperature profiles. Further improvement

was achieved by assuming a variable thermal conductivity at the contact surface, varying it from 0.05 to 0.10 W/m/K

during cooling and heating respectively. The variation of thermal conductivity is representative of the improved contact

during the heating process due to the thermal expansion of the copper and steel.

(a) Copper-casing interface temperature (b) Casing-cement interface temperature

(c) Rock-cement interface temperature (d) Rock outer face temperature

Fig. 3: Comparison of numerical and experimental temperature profiles. Top and bottom thermocouple readings at each interface are

indicated by solid red and blue lines, respectively.

From the experimental data, it was also evident that, in spite of using the insulating material around the sample

Pratanu Roy et al. / Energy Procedia 114 ( 2017 ) 5241 – 5248 5245

during the experiment, there was considerable heat loss along the radial direction. Therefore, a constant temperature

boundary condition was applied at the outer boundary in the numerical modeling, which produced a better match with

the experimental results than a zero heat flux or insulating boundary condition. The heat transfer process was also found

to be very sensitive to the thermal properties of the materials, especially the thermal conductivity.

4.2. Effect of elastic modulus

As the thermal stress is directly proportional to the elastic modulus of the material, the stresses are affected by the

change in elastic modulus. Fig. 4 shows the radial and circumferential stress profiles after 1 hour of cooling starting

from the room temperature at a rate of 1 ◦C/min. Both cement and rock elastic moduli were varied from 47 GPa to

10 GPa, which reduced the radial stress in cement by approximately three times. The corresponding circumferential

stresses became close to 0 MPa in cement and rock. We also varied only the cement elastic modulus while keeping the

elastic moduli of other materials constant, and observed that depending on the value of the cement elastic modulus, the

maximum radial stress can appear at the cement-casing interface or cement-rock interface (not shown here) .

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10Radial distance (m)

0

2

4

6

8

10

12

Rad

ialS

tress

,σr(

MP

a)

Steel Cement Rock

Ecem/rock = 47 GPaEcem/rock = 10 GPa

(a) Radial stress profile during cooling

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10Radial distance (m)

0

20

40

60

80

Circ

umfe

rent

ialS

tress

,σΘ(M

Pa)

Steel Cement Rock

Ecem/rock = 47 GPaEcem/rock = 10 GPa

(b) Circumferential stress profile during cooling

Fig. 4: Effect of elastic modulus on stress profiles

4.3. Effect of cooling/heating rates

To study the effects of heating and cooling rates, the inner casing temperature was varied at a specific rate. Four

cases were considered for this study: 1) instantaneous heating or cooling to a constant temperature; 2) heating or

cooling at 0.5◦C/min; 3) heating or cooling at 1.0◦C/min; and 4) heating or cooling at 1.25◦C/min. Figure 5 shows the

variations of temperature and stresses along the radial direction for all cases. The casing temperature reaches the target

temperature -50 ◦C for case 1 due to its instantaneous nature of cooling, and case 4 within 1 hour due to the high cooling

rate of 1.25◦C/min. For lower cooling rates (0.5◦C/min and 1.0◦C/min), the casing temperature reaches about -5 ◦C and

-35◦C within an hour.

The temperature profiles show that both cement and rock are at higher temperature for instantaneous cooling case

than other cases because the casing has been exposed to the target temperature for a longer period of time. However,

the stress profiles show that 1.25 ◦C/min case has higher radial and circumferential stresses inside cement and part

of the rock (near the rock-cement interface) than the radial and circumferential stress achieved in the instantaneous

cooling case. Although thermal stress depends only on the temperature difference from the initial undeformed states

of the materials, the overall stress depends also on the temperature gradient along the materials. In this case, higher

temperature gradients inside cement and rock can be noticed for 1.25 ◦C/min cooling case, which created higher stresses

inside these materials than in the instantaneous cooling case. The difference in stress profiles diminishes near the outer

periphery of the rock as the temperature gradient decreases to match the zero heat flux or insulated boundary condition.

Further observation reveals that the thermal gradient obtained in the 1.0 ◦C/min cooling case is in fact higher than the

instantaneous cooling case, but it produces lower radial stress inside the cement due to its lower absolute temperature.

5246 Pratanu Roy et al. / Energy Procedia 114 ( 2017 ) 5241 – 5248

This emphasizes the fact that the overall stress inside wellbore materials subjected to thermal loading or unloading is

not exclusively dependent on the temperature difference or the spatial gradient of temperature, rather it is a combined

effect of both. Similar phenomena has been observed for varying heating rates.

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10Radial distance (m)

−50

−40

−30

−20

−10

0

10

20

30

Tem

pera

ture

(o C)

Steel Cement Rock

0.5 oC/min.1.0 oC/min.1.25 oC/min.Constant

(a) Temperature profiles for different cooling rates

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10Radial distance (m)

0

2

4

6

8

10

12

14

16

Rad

ialS

tress

,σr(

MP

a)

Steel Cement Rock 0.5 oC/min.1.0 oC/min.1.25 oC/min.Constant

(b) Radial stress profiles for different cooling rates

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10Radial distance (m)

−20

0

20

40

60

80

100

120

Circ

umfe

rent

ialS

tress

,σΘ(M

Pa)

Steel Cement Rock

0.5 oC/min.1.0 oC/min.1.25 oC/min.Constant

(c) Circumferential stress profiles for different cooling rates

Fig. 5: Effect of cooling rates on the temperature distribution and stress profiles

4.4. Effect of wellbore size

The effect of wellbore size was studied by systematically varying the length of the wellbore from 0.8 m to 80 m.

The casing and cement radius were maintained at field scale i.e. four times the dimensions of the experimental sample.

The inner casing temperature was varied from room temperature (25 ◦C) to 70 ◦C in a duration of 24 hours. Fig. 6

shows how the shear stress (σrz) varies as a function of longitudinal distance (z) after 16 hours of heating. For small

sized domain (L = 0.8 m), large variations of shear stress can be seen throughout the whole length with the maximum

magnitude occurring near the bottom and top. As the domain length is increased (L = 8 m and 80 m), only the top and

bottom ends are affected showing virtually zero shear stress in the rest of the domain. This emphasizes the fact that, for

very long cylindrical wellbore (L/r1 ≥ 20 in this case), the stresses inside the materials do not depend on the variation

of the length, provided that zero or uniform confinement pressure is applied at the outer radius of rock. Under such

circumstances, a plane strain condition is sufficient to characterize the stress behavior.

1r = Radial distance measured from center of the wellbore

Pratanu Roy et al. / Energy Procedia 114 ( 2017 ) 5241 – 5248 5247

0.0 0.2 0.4 0.6 0.8 1.0Nondimensional longitduinal distance, z/L

−4

−2

0

2

4

She

arS

tress

,σrz(M

Pa)

L = 0.8 mL = 8 mL = 80 m

Fig. 6: Scaling effect on shear stress

Another important parameter for upscaling the model is the outer radius (rout) of the rock or formation. Sufficient

separation between the wellbore and the outer radius of the rock should be maintained to make sure that the outer

boundary condition is not influencing the wellbore stresses and temperature. To investigate this, two cases were tested:

rout/rin = 4, and rout/rin = 20. It was observed that the stress profiles in the near wellbore region (inside cement and rock)

are affected in the first case, whereas in the second case, the stress profiles reach the outer radius pressure around rout/rin

= 10.

5. Conclusions

A combination of numerical and experimental studies were performed to understand and mitigate the risk associated

with the thermal cycling operations of CO2 injection wells. The comparison of numerical and experimental temperature

profiles revealed that estimating the contact resistance between the casing and cement is crucial to accurately predict

the heat transfer process for thermal cycling operations. Upon achieving good agreement between the experimental

data and the numerical results, the calibrated model was used to investigate the effect of thermal stresses produced

by predetermined heating and cooling rates. By studying the variation of cooling rates, we showed that the stresses

generated by thermal loading or unloading are dependent on both temperature difference of the material from its initial

undeformed state and the spatial gradient of temperature. The upscaling of the domain length demonstrated that plane

strain condition can be used when L/r ≥ 20 for uniform or zero confinement pressure. Future studies will involve the

variation of formation properties along the length representing different rock layers and its effect on the stress profiles.

6. Acknowledgement

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National

Laboratory under the Contract DE-AC52-07NA27344. This work has been produced in collaboration with the BIGCCS

Centre, performed under the Norwegian research program Centres for Environment-friendly Energy Research (FME)

and the KPN project “Ensuring well integrity during CO2 injection”. The authors from SINTEF Petroleum Research

laboratory acknowledge the following partners for their contributions: Gassco, Shell, Statoil, TOTAL, Engie and the

Research Council of Norway (193816/S60 and 23389).

References

[1] Z. Luo, S. Bryant, Influence of thermo-elastic stress on fracture initiation during CO2 injection and storage, Energy Procedia 4 (2011) 3714–

3721.

[2] L. Boukhelifa, N. Moroni, S. James, L. Roy-Delage, M. J. Thiercelin, G. Lemaire, et al., Evaluation of cement systems for oil and gas well

zonal isolation in a full-scale annular geometry, in: IADC/SPE Drilling Conference, Society of Petroleum Engineers, 2004.

5248 Pratanu Roy et al. / Energy Procedia 114 ( 2017 ) 5241 – 5248

[3] C. Teodoriu, C. Kosinowski, M. Amani, J. Schubert, A. Shadravan, Wellbore integrity and cement failure at hpht conditions, International

Journal of Engineering 2 (2) (2013) 2305–8269.

[4] A. Shadravan, J. Schubert, M. Amani, C. Teodoriu, et al., Using fatigue-failure envelope for cement-sheath-integrity evaluation, SPE Drilling

& Completion 30 (01) (2015) 68–75.

[5] A. Albawi, J. De Andrade, M. Torsæter, N. Opedal, A. Stroisz, T. Vrlstad, et al., Experimental set-up for testing cement sheath integrity in arctic

wells, in: OTC Arctic Technology Conference, Offshore Technology Conference, 2014.

[6] J. De Andrade, M. Torsæter, J. Todorovic, N. Opedal, A. Stroisz, T. Vralstad, et al., Influence of casing centralization on cement sheath integrity

during thermal cycling, in: IADC/SPE Drilling Conference and Exhibition, Society of Petroleum Engineers, 2014.

[7] G. Y. Gor, J. H. Prevost, Effect of co 2 injection temperature on caprock stability, Energy Procedia 37 (2013) 3727–3732.

[8] M. Preisig, J. H. Prevost, Coupled multi-phase thermo-poromechanical effects. case study: Co 2 injection at in salah, algeria, International

Journal of Greenhouse Gas Control 5 (4) (2011) 1055–1064.

[9] P. Roy, S. D. Walsh, J. P. Morris, J. Iyer, Y. Hao, S. Carroll, K. Gawel, J. Todorovic, M. Torsæter, Studying the impact of thermal cycling on

wellbore integrity during CO2 injection, in: 50th US Rock Mechanics/Geomechanics Symposium, 2016.

[10] J. Todorovic, K. Gawel, A. Lavrov, M. Torsæter, Integrity of downscaled well models subject to cooling, in: SPE Bergen One Day Seminar,

Society of Petroleum Engineers, 2016.

[11] Engineering Toolbox, Properties of Portland cement concrete, http://www.engineeringtoolbox.com/concrete-properties-d_1223.html (2015).

[12] ThyssenKrupp Materials International., Products & Services Brochures, http://www.tkmna.com/tkmna/Resources/ProductBrochures/index.html (2015).

[13] H. Lund, M. Torsæter, S. T. Munkejord, et al., Study of thermal variations in wells during carbon dioxide injection, SPE Drilling & Completion.