Cement-Formation Debonding Due to Temperature Variation in Geothermal Wells: An Intensive Numerical Simulation Assessment ^†

Abstract

Geothermal wells are subjected to higher loads compared to conventional oil and gas wells due to the thermal cycles that occur during both production and non-production phases. These temperature variations can affect the cohesion of the cement within the formation and casing, creating micro-annuli channels that can ultimately compromise the integrity of the well. Therefore, this study employs an intensive finite element methodology to analyze the debonding criteria of casing–cement systems in geothermal wells by examining over 36 independent models. The wellbore cooling and heating processes were simulated using three cohesive zone models (CZM): Type I (tensile), Type II (shear), and mixed (Type I and II simultaneously). The analysis revealed that Type I debonding occurs first during cooling at a temperature of around 10 °C, while Type II is the primary failure mode during heating. Evaluations of interfacial bonding shear strength (IBSS) values indicated that the debonding of the cement would even occur at high IBSS values (3 and 4 MPa) at a differential temperature of 300 °C, while the other IBSS of 1 MPa withstands only 60 °C. However, achieving an IBSS of 4 MPa with current technology is highly unlikely. Therefore, geothermal well operation and construction must be modified to keep the differential temperature below the critical temperature at which the debonding of the cement initiates. The study also found that debonding during cooling happens at lower differential temperatures due to generally lower values for interfacial bonding tensile strength (IBTS), typically less than 1 MPa. The novelty of the study is that it provides new insights into how specific temperatures trigger different types of debonding, highlights that high IBSS values may not prevent debonding at high differential temperatures, and recommends operational adjustments to maintain temperatures below critical levels to enhance cement integrity. Additionally, this study reveals that debonding during cooling occurs at a lower differential temperature change due to the reduced value of the interfacial bonding tensile strength (IBTS).

1. Introduction

As energy demand is on the rise because of the sharp rise in population, the importance of geothermal energy has become more than ever. Ref. [1] reports that by 2035, the world’s population will be around 8.8 billion, and the energy demand will rise by 30%. According to the Energy Information Administration (EIA), the rise in the global population will be as high as 40% by 2040. Therefore, both fossil and renewable energies must play their role in meeting the future energy demand. Nonetheless, the extensive use of fossil fuels for power generation and its widespread exploitation have created a critical issue around the globe, which is global warming. It is reported that from 1901 to 2022, the temperature of the Earth increased by 1.1 °C (1.98 °F), which comes with the increase in sea levels, flooding, drought, and much more [2]. Climate change affects the things on which the human race depends, such as water, ecosystems, health, agriculture, and wildlife. Therefore, global warming is a complex and multi-faceted challenge that encompasses a wide range of environmental, social, and economic issues. In this respect, the Paris Agreement under the UN Climate Change Conference (COP21) was signed by different countries in which the emission of CO₂ (one of the main greenhouse gases) has to be reduced by 45% by 2030, and the net zero goal has to be achieved by 2050. It is also reported that the top five countries and regions that emitted 60% of the greenhouse gases into the atmosphere in 2021 consisted of India, USA, the European Union, China, and Russia [3]. The contribution of the developing countries was only 3.8% [3].

Hence, the developed countries have tilted their focus to the use of renewable energy for power generation. Though different non-conventional energy sources can be used for energy generation, such as solar, hydro, biomass, wind, etc., geothermal is the only source of energy that is not affected by the weather conditions and remains in the operational mode most of the time [4]. Moreover, its reserves are widely distributed around the globe. In geothermal energy, the heat is collected from the subsurface and is transported to the wellhead with the help of the working fluid. Therefore, the only connection that is from the earth’s interior to the surface is the well. If, in any case, the well integrity is compromised, the success of the whole project can be jeopardized and can have severe financial and human injury consequences. Hence, it is of utmost importance that the integrity of the well is maintained throughout the project’s life. In that respect, casing and cement play a crucial role, and failure of any one of the components can compromise the integrity of the well. Debonding and micro-annuli creation are parameters that significantly affect the integrity of the well. Debonding occurs when the cement sheath behind the casing separates from the casing or the formation. On the other hand, a micro-annulus is defined as a minute annular or degraded space that can form between the cement and casing, potentially creating a pathway for leakage within the wellbore [5].

At present, the construction of the geothermal well follows the configuration and standard of oil and gas wells with two major differences. The first is that in the geothermal well, high flow rates are required because the size of the production casing is large, or, in some cases, a tubing-less completion method is used where the production is taken from the casing [6]. The second is that the bottom hole temperature of the geothermal wells is usually greater than the temperature present in the conventional oil and gas wells [7]. As for the annular isolation between the casing and the formation, geothermal wells use the API standard cement that is also used in oil and gas wells. Though there are solutions presented for cementless zonal isolation by using metallic sealing units, they are in the initial phase of research and are not currently feasible [8,9]. Annular isolation and well integrity play an important role in well completion and performance, whether for oil, gas, or geothermal wells. The function of the cement in the well is that it provides zonal isolation, supports the casing and protects it from corrosion, prevents crossflow, and protects the groundwater aquifer and surface sustained pressure [10,11]. However, when subjected to thermal variation in the geothermal wells, the cement sheath is exposed to different stresses that can lead to the formation of micro-annuli and even micro-cracks that can compromise the cement integrity. Therefore, the mechanical properties of the cement should be sufficient to resist thermal loading. Ref. [12] presented different cement mechanical properties that are important for the interfacial casing–cement interaction, which are as follows:

• Interfacial bonding tensile strength (IBTS) or tensile bonding stress: This represents the axial force required to remove the cement axially from the interface.
• Interfacial bonding shear strength (IBSS) or shear bonding stress: This is the interface property that represents the force required to shear the cement from the casing interface.
• Ultimate unconfined compressive strength (UCS): This is the mechanical property that represents the resistance of cement in compression
• Shear strength (pure shear strength—PSS): Like UCS and tensile strength, shear strength is a mechanical property. The PSS represents the difference between the coupling and outer casing diameter.

Ref. [13] states that one of the main objectives of the cement in a geothermal well is to constrain the elongation of the casing and assist in thermal fatigue when subject to temperature variation. As the casing is exposed to the temperature loading, the casing tends to expand longitudinally, which is prevented by the cement. Due to this, compressive stresses are generated in the casing, while tensile stresses are developed in the cement. If the differential temperature (ΔT) rises above 230 °C, plastic deformation in the cement sheath is developed, which causes the development of the micro-annuli. A similar observation was presented by [14], who suggested that the debonding of the cement from the casing and formation is dominant when the temperature difference is large. Moreover, the cold and hot thermal cycle during the shut-in and production phases results in the contraction and expansion of the cement sheath that leads to the development of the micro-annuli [15].

Possible failure modes in the cement sheath include radial cracking caused by the tangential stresses, debonding, or shear failure at the casing–cement–formation interface [16,17]. Some of the numerical models on the cement sheath that considered thermal and mechanical (shear, tensile, and compression) loading conditions suggested that cement annular failure mainly happens when the cement has high brittleness and low tensile strength [18,19]. On the other hand, in the view of some authors, a high Poisson’s ratio and low Young’s modulus can lower the tangential and radial stresses in the cement sheath which is developed by the internal wellbore pressure [14,17]. Hence, it is recommended that the cement used in the geothermal well should be properly designed so that it has the capability to withstand harsh conditions and maintain its integrity.

A thermal stress model was developed by [20] for the casing–cement–formation, which was integrated with thermodynamics and elastic mechanic model for the geothermal wells. The approach used in the model was based on the Gaussian main elimination method. They found that the axial and radial thermal stresses were bigger than the tangential tensile thermal stress. Whereas, at the casing cement interface maximum axial and radial stresses are always present while the location of the maximum tangential stress varies. Generally, thermal stresses are more likely to cause axial and radial micro-cracks in the cement, leading to a higher likelihood of failure at the casing interface during the fracturing of geothermal wells.

A numerical model was developed by [21] that was based on the geothermal wells of Utah FORGE. They examined the effect of the temperature difference and casing pressure on the casing–cement–formation system by using a 2D finite element numerical model. The result from the sensitivity analysis revealed that the temperature variation has a more pronounced effect on the cement sheath than the casing pressure. For the same temperature difference ΔT between the formation and the wellbore, the transfer of heat from formation to pipe in which the temperature of the pipe is lower than that of the formation is more detrimental to the cement sheath as compared to the heat transfer from pipe to a formation where the pipe is at a higher temperature than formation. They also concluded that the hoop stresses developed in the cement are dependent upon ΔT and the thermal expansion coefficient of the cement.

A CZM (cohesion zone material) numerical model was developed by [22] in which the micro-annuli created between the cement and casing interface in the geothermal well were discussed. They showed that due to the expansion of casing in the geothermal wells, shear and tensile debonding coexist, resulting in the creation of micro-annuli. They concluded that the long sheath of cement behind the casing cannot be fully debonded because of the initial bottom pressure. Moreover, they estimated the size of the gap in the micro-annuli and suggested that it would be in the range of 0 to 0.3 mm and would be dependent on the pressure present inside the gap.

Ref. [18] conducted a 2D field scale numerical study that was developed with the help of COMSOL Multiphysics. Their objective was to examine the effect that temperature variation during the steam injection will have on the casing–cement–formation section. For the modeling, two formation scenarios that consisted of compliant (sandstone) and stiff (carbonate) materials were considered. It was found that the wellbore material was more prone to stresses in the carbonate formation as compared to sandstone. This was because the retention time for the temperature was higher in sandstone. Moreover, they concluded that irrespective of the cement sheath thickness, the highest strains were present in the cement–casing interface in carbonates. However, when the temperature and pressure in the sandstone were increased, tensile radial cracks developed along the thinnest layer of the cement sheath.

As seen from the above discussion, in the geothermal well, the cement is faced with temperature variation that can lead to the failure of the cement sheath. Within the framework of this task, we plan to determine the effect of thermal variation on the IBTS and IBSS of the cement sheath, which can lead to the creation of micro-annuli, using a finite element analysis approach.

2. FEA Modelling of Cement Bonding or Debonding

For the finite element analysis, the 2021 R2 ANSYS version was used in this study. The symmetric model used in this numerical approach, along with the assumptions and limitations, was the same as that presented in our previous studies [7,23,24]. The mesh and its model are illustrated in Figure 1. The cement and casing were fixed to a length “l” where l is equal to L/100, in which L is the length of the casing and cement. The value of L varied to 2000 mm, 10,000 mm, and 100,000 mm. Elastic support was utilized for the analysis of cement exterior interaction with the formation, while for other analyses, the cement exterior was considered free. For this study, two major models were taken into consideration: the free boundary, which means that the cement is free to move in the radial direction, and the elastic boundary, which shows that the formation and the casing are bonded through the elastic component. In the axial direction, both the systems are free to move; however, the movement of the casing–cement was totally restricted in all the directions at the top of the model. It should be noted that the development of any stress or strain in that zone is not presented as it was not the focus of this study. The free boundary model considers the cement–formation bonding scenario to be negligible or non-existent.

Table 1. Effect of the model length on axial and radial (gap) displacement.

CZM Models	Gap [mm]		Axial Displacement [mm]		Adjusted Values [mm]
	Elastic Boundary	Free Boundary	Elastic Boundary	Free Boundary	Elastic Boundary	Free Boundary
2 m Model	0.34398	0.11707	5.2918	4.7114	5.2918	4.7114
10 m Model	0.34398	0.12276	26.445	23.254	5.289	4.6508
100 m Model	0.34398	0.12304	267.11	253.91	5.3422	4.6782

shows the axial displacement and the radial gap for models of 2, 10, and 100 m lengths, considering elastic support for the exterior cement diameter, free exterior diameter, and a mixed debonding mechanism. The gap remains nearly identical across all three cases (2, 10, and 100 m), while the axial displacement is directly proportional to the length of the cement/casing. The table also includes scaled values (recorded values divided by the ratio between the casing length) of the axial displacement. The differences are minimal, with an error margin of less than 1%. Figure 2 and Figure 3 show plots of the radial gaps and the axial displacements for the cases of 2, 10, and 100 m, respectively.

The above table and graphs show that the 2 m casing/cement length can also represent a longer section of casing/cement. Because of this finding, the problem dimension was reduced significantly, resulting in a decrease in computation time.

2.1. Contact Zone and Model Formation

To achieve better results, quadratic axisymmetric elements with three or four edges were utilized for the entire cell. The interface between the cement and the casing’s external face was modelled as bonded, with a cohesive zone material (CZM) being applied subsequently. For the CZM, the bilinear model and debonding mechanisms for Type I, Type II, and mixed modes were selected.

The parameters set in the engineering data section in the Ansys Manual are as fp;;pws:

• T_tmax—the maximum equivalent tangential contact debonding and its values, as obtained from experimental work.
• δt*—the tangential slip at the completion of debonding, also determined from experimental data.
• Artificial damping coefficient–as per the Ansys Manual [25], this parameter is employed solely for convergence purposes and is typically associated with the incremental time step used in the simulation.

2.2. Boundary Definition and Load Condition

The only load applied was a thermal condition, which simulated the cell’s cooling from 20 °C to 320 °C or from 320 °C down to 20 °C, which implies a delta T of 300 °C. These temperature variations were chosen because the simulations involving 100 and 200 °C temperature differentials have concluded that a differential temperature of 300 °C will also cover the other two cases, since the output parameters, like gap, strain, and stress, are linearly proportional with the temperature difference. This will be shown later. While specific geothermal wells may have different conditions, this choice covers a wide range. Due to the different coefficients of thermal expansion of the cement and the casing, debonding is expected to occur at their interface. The mechanical properties of the cement and steel used in the model are presented in

Table 2. Steel and cement material properties used in this study.

Material	Young’s Modulus (MPa)	Poisson Ratio (-)
Cement	9000	0.3
Steel	210,000	0.3

[7,26]. It must be noted that the reason for selecting 300 °C is because high enthalpy geothermal resources have temperatures between 180 °C and 390 °C, offering significant potential for electricity generation and district heating [27]. The typical output power from such a source ranges from 10–100 MWe. One such field that has a temperature range of 150–350 °C is Cerro Prieto, Mexico [28].

2.3. Failure Mode Definition

As the cell cools, the difference in the contraction between cement and casing can create a gap that can be taken as Type 1 debonding. However, it can also be taken as a Type II debonding, as the casing and cement have different axial contractions. As no structural load was applied (pushing force or pressure), the failure mode cannot be presented in the traditional way. However, in this study, the methodology suggested by [24] was adopted to estimate when the contact breaks; hence, an unconventional failure mode was utilized in this paper. This unconventional approach consists of the use of selected nodes on the casing–cement and cement–rock interface and analyzing their axial and radial displacement.

3. Cement Models and Results

For the mixed mode failure, the CZM model was utilized, whereas the single CZM mode was also run simultaneously for Type I (tensile) and Type II (shear) modes. Three different temperatures were considered, which are represented as delta T (ΔT) and correspond to the difference between the casing cement system and the initial and final temperature. The results of all the cases are illustrated in

Table 3. Scenarios used in this study.

CZM Models	Mixed (Type I and II)	Type I	Type II
Elastic Boundary	Delta T (100, 200, 300 °C)	Delta T (100, 200, 300 °C)	Delta T (100, 200, 300 °C)
Free Boundary	Delta T (100, 200, 300 °C)	Delta T (100, 200, 300 °C)	Delta T (100, 200, 300 °C)
Mixed CZM cement–formation	Delta T (100, 200, 300 °C)	Delta T (100, 200, 300 °C)	Delta T (100, 200, 300 °C)

.

For the cooling scenario, 18 runs were performed, with temperature drops of about 100, 200, and 300 °C, while the same procedure was adopted for the heating situation. It should be noted that 2 m casing/cement length was used for this modeling, as it has already been proved in the previous section that the same results were obtained whether a 2 m, 10 m, or 100 m casing/cement assembly was used. A total of 36 simulations have been carried out.

For the correct identification between the cement and casing, a total of six simulations were performed. This was accomplished by altering the boundary conditions from a free-to-move outer cement layer (indicating poor cement bonding with the formation) to an elastic (deformable) cement–formation system. It was observed from the simulation that the gap created with the elastic boundary scenario had a larger gap as compared to the free-to-move outer boundary. However, the difference between the mix and the Type I CZM model was not significant (Figure 4).

Figure 5 shows the axial displacement obtained for the same outer boundary conditions. Similar to the gap scenario, the simulation results for the mixed and the Type I cases are similar, while the Type II case leads to slightly different results. This will be discussed further in the next part of the paper.

Figure 6 compares the gap between three different temperatures (100, 200, and 300 °C). The 100 °C represents the temperature difference that exists between the casing and cement when the well temperature is reduced for different operational purposes, such as workover, logging, and stimulation. As expected, the magnitude of the gap increased with the increase in ΔT. However, the scenario of the Type II CZM model remained unsolved, as no convergence was reached. This is because, once shear debonding occurs (Type II), the casing behaves independently from the cement, causing the system to lose convergence. Figure 6 also demonstrates that the gap size is linearly proportional to the differential temperature.

Figure 7 presents the model deformation at 200 °C differential cooling. It illustrates both the radial (gap) and the axial displacement for the two main scenarios discussed in this paper: free and elastic boundary. As indicated in Figure 6, the overall system deformation demonstrates that the elastic boundary results in a significantly larger radial gap (debonding) because the cement–formation bond restricts the cement’s movement when the casing’s contraction occurs. Figure 8 represents the system deformation under a heating scenario. Radial debonding does not occur during heating because the casing expands and pushes itself against the cement.

It was observed that the free boundary case results in less axial cement shrinkage compared to the elastic boundary case. This is because, in the case of an elastic boundary, limited shrinkage is observed because of the partial bonding with the formation, while in the case of a free boundary, the cement is allowed to change its dimensions in all directions. The different elongation of the cement and casing also suggests that shear between the two will occur at the same time. Therefore, in the next section of the paper, a full CZM cement–formation contact model is presented, especially for the mixed case failure.

To better illustrate when debonding occurs and to identify the primary failure mode, the equivalent differential temperature at which a failure gap forms was determined.

Table 4. ΔT at which failure occurs.

CZM Models	Elastic Boundary
Mixed (Type I and II)	Delta T 60 °C
Type I	Delta T 60 °C
Type II	Delta T 174 °C

presents the values calculated for the onset of debonding based on the methodology described by [23,24]. The data shows that it only takes 60 °C of cooling to induce Type I (tensile) debonding and 174 °C of cooling for Type II (shear) debonding.

To better understand the effect of different bonding strengths (interfacial bonding shear strength (IBSS)), several cases were examined in which the following parameters were varied: bonding type (Type I, Type II, mixed—Type I and II), fully bonded, frictionless and friction-based models. For all these cases, IBSS values of 1, 2, 3, and 4 MPa were used for the CZM models at the casing–cement and cement–formation interfaces. A total of 40 individual simulations were conducted, with various parameters varied. Four cases were selected for in-depth analysis: these cases were examined with IBSS values of 1, 2, 3, and 4 MPa, respectively, for the casing–cement contact in the CZM mixed case. This simulates a normal IBSS of 1 MPa, as reported by multiple authors [12], while the other three cases represent improved bonding. In the new set of simulations, a constant IBSS of 2 MPa was applied to the cement–formation interface, while the IBSS between the casing and cement was varied, as shown above. Both cooling and heating situations were considered. Figure 9 illustrates an interesting behavior regarding the sliding distance between the casing and cement, a parameter that defines the CZM bonding. For IBSS values of 1 and 2 MPa, the sliding distances are similar, with only minor variations observed at the start of the simulation (heating up to 300 s). In contrast, for IBSS values of 3 and 4 MPa, the system demonstrates different behavior, highlighting the significance of good bonding. Focusing on the IBSS of 1 MPa in Figure 9, it is evident that around 290 s, the sliding distance begins to decrease. This observation supports the earlier finding that the elastic boundary experiences larger deformation compared to the free-to-move system [23]. For higher IBSS values (3 and 4 MPa), the sliding distance exhibits a more abrupt change, lacking a maximum point and, therefore, not showing a reduction in the value. The data also indicate that stronger bonding results in a delayed onset of sliding. The peak values observed for IBSS of 1 and 2 MPa correspond to debonding between the casing and cement, while the inflection points for IBSS of 3 and 4 MPa reflect the same debonding phenomenon.

To further illustrate this behavior, the axial displacement of two selected nodes was analyzed: node 591, located on the casing–cement interface (casing side node), and node 6084, located on the cement–formation interface (cement side node). Both nodes were situated at the same vertical position (Figure 10).

Figure 11 displays the axial displacement of node 6084 across the four IBSS cases. It is evident that at higher IBSS values (3 and 4 MPa), the axial displacement of node 6084 increases (with negative values indicating compression and heating) until the bonding between the casing and cement fails. At this moment (224.10 for IBSS 3 MPa and 263.13 s for IBSS 4 MPa), the elasticity of the cement causes it to pull back, reversing the axial displacement. This effect is not observed at lower IBSS values, as debonding occurs only at the casing–cement interface, resulting in no “elastic pull” on the cement. It is also interesting that at 300 s (the end of heating) node 6084’s axial displacement is the same for all cases. This was also observed in the sliding distance graph shown in Figure 11. At 500 s of simulation time, when the system cooled back to its original temperature (20 °C), the axial displacement was the same across all cases. However, the final displacement no longer matches the initial position, with a change from −1 mm to 0 mm.

Figure 12 presents the axial displacement graph for node 591, located on the casing side. Initially, the axial displacement of node 591 appears identical across all cases, which is anticipated since the node is part of the casing, and casing expansion should be linear with minimal deformation. To gain a clearer understanding of the axial displacement behavior of node 591, a zoomed section is provided in Figure 13. It was noticed that debonding between the casing and cement also occurs at high IBSS values. The debonding times at node 6084 were 224.10 s for IBSS of 3 MPa and 263.13 s for IBSS of 4 MPa. These debonding times are also reflected in the axial displacement chart of node 591 and indicate the point at which the cement begins to contract during the heating phase. The temperature at which debonding takes place at node 591 for an IBSS value of 3 MPa was 224.87 °C, and for 4 MPa it was 265.53 °C, as shown in Figure 13. These temperatures are closely correlated with the simulation times observed at node 6094. This study demonstrates that even with improved casing–cement bonding (IBSS of 4 MPa), debonding will still inevitably occur. It is important to note that achieving an IBSS of 4 MPa with current cement formulations is unlikely.

Figure 14 shows the axial displacement for node 591 for the cooling process using Type I debonding; hence, the IBTS has been used for the simulation. The chart is symmetrical to the heating shape, with a small anomaly at the beginning of the simulation. After carefully analyzing the results, we noticed that the debonding in CZM Type I will be produced very early, hence the rest of the process acting as if no bonding exists. We have modeled various IBTS values ranging from 0.1 to 2 MPa and the results were identical, showing that the value of IBTS will be exceeded in the early stages of cooling.

4. Discussion

To date, no detailed study has explored the CZM model for casing–cement and cement–formation contact in such depth. Our extensive simulations have precisely identified the timing and temperature at which debonding occurs and its location. The study clearly shows that casing–cement debonding will occur even with IBSS values of 3 or 4 MPa at differential temperatures of 300 °C. This underscores the need for alternative well operation strategies for high-temperature geothermal wells, such as avoiding significant temperature fluctuations by not injecting cold fluids into the casing after the well is put into production. Additionally, the upper part of the well will inevitably face high differential temperature variations. Therefore, different well construction methods, such as cementless designs or cement recipes with linear expansion coefficients compatible with casing materials, should be considered.

Table 5. Temperature difference at which failure occurs as a function of IBSS value.

IBSS (MPa)	Delta Temperature (°C)
2	60
3	224
4	263

presents the estimated debonding temperatures between casing and cement as a function of IBSS values for the Mixed CZM model. These findings are consistent with the results shown in Table 4, where various CZM types were investigated using an IBSS of 2 MPa for the casing–cement bonding conditions. Please note that the data in Table 4 were generated using an IBSS of 2 MPa for the casing–cement bonding conditions. The results further emphasize that even an exceptionally strong bond between casing and cement may not prevent debonding under high differential temperature conditions.

For comparison reasons, the debonding temperature for the cooling process was analyzed. Cooling induces Type I debonding [23], whereas heating results in shear debonding (Type II). Since Type I debonding occurs before Type II, there is minimal axial movement observed in nodes 6084 and 591. However, we examined the radial stress evolution at node 591, located at the casing–cement interface. Figure 15 shows that the radial stress reaches a maximum level of around 90 MPa. The radial stress of 2 MPa, which is considered extremely high for the interfacial bonding tensile strength (IBTS), is reached at a temperature of 30 °C, corresponding to a differential cooling of 10 °C. Laboratory measurements reported by [26] have recorded IBTS values up to 1.3 MPa.

To better highlight when the debonding takes place during cooling and, respectively, heating, we constructed Figure 16, which shows a zoomed-in representation of the beginning of the simulation time for the axial displacement of node 591. It can be seen that while CZM Type II shows a debonding at 45 s (60 °C), the CZM Type I will fail after around 5 to 10 s of the simulation time, which corresponds to about 10 °C. In order to validate the CZM simulations, we also constructed two extra cases that include frictionless contact and with added pressure inside the casing. While there is a clear difference between frictionless and CZM cases for the heating process, there is no difference for the cooling, leading to the conclusion that the debonding takes place very early, after which the casing cement contact will behave in a frictionless manner.

5. Conclusions

An intensive finite element methodology and analysis have been performed to understand the main debonding criteria of casing cement systems in geothermal wells. This study considered more than 40 independent models.

Wellbore cooling and heating processes have been simulated using three CZM modes: Type I (tensile), Type II (shear), and mixed (Type I and II simultaneously). The Type I failure mode will cancel the Type II mode when it first occurs, since the bonding will not exist. It was observed that Type I debonding occurs first during cooling situations only, while Type II debonding is the primary failure mode during wellbore heating.

The required IBSS values to withstand specific differential temperatures were evaluated, and it was found that for an IBSS of 4 MPa, the maximum allowable differential temperature is 265 °C, whereas for an IBSS of 1 MPa, it is only 60 °C. It should be noted that achieving an IBSS of 4 MPa is highly unlikely with current technology.

In a cooling situation, the debonding will take place at a much lower differential temperature, especially due to the lower values for the IBTS, which are typically lower than 1 MPa. The main solution to avoid casing cement debonding is to reduce the temperature change at the casing or to keep this temperature below a specific threshold.

The main limitation of this study was neglecting the in situ stresses acting around the wellbore, which may impact the results positively; however, not using the in situ stresses allows the comparison of the interface in different modes.