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ADE	reducing the complexity of the problem. According to the results of the foregoing analyses, the parameters of the uniaxial compressive strength (𝑈𝐶𝑆), Young’s modulus (𝐸) and horizontal pressure coefficient (𝐾) were identified as the most influential parameters for modelling of 𝜎 ; while, the parameters of Young’...
ADE	• The specimens which experienced more cycles in the pre-peak regime failed at stress levels higher than the determined average 𝑈𝐶𝑆 for Tuffeau limestone specimens, i.e. the strength hardening occurred. [see Chapter 6] • The following four main stages were distinguished for the evolution of damage parameters of Tuff...
ADE	• Below the fatigue threshold stress, the rock behaviour under cyclic loading in the pre-peak and the post-peak regimes was approximately similar to those in monotonic loading conditions. For the specimens subjected to the cyclic loading below the fatigue threshold stress, no considerable damage was incurred within the...
ADE	• According to the calculated energy-based brittleness index for the rock specimens which did not fail in cycles, a transition point at 𝜎 /𝑈𝐶𝑆 = 65% was identified, where the rock 3 𝑎𝑣𝑔 specimens switch from the brittle failure behaviour to ductile one. It was found that the cyclic loading at confinement levels ...
ADE	variation of Gosford sandstone as a function of the applied stress level (𝑞 /𝑞 ) and 𝑢𝑛 𝑚−𝑎𝑣𝑔 confinement level (𝜎 /𝑈𝐶𝑆 ). The coefficient of determination (𝑅2) for this practical 3 𝑎𝑣𝑔 model was 90% which proved the high prediction performance of this model. [see Chapter 8] 9.2. Recommendations Accordi...
ADE	are significant precursors of rockburst occurrence. However, the genuine rock microseismic signals usually interfere with the signals/noises induced by other sources, such as mechanical excavations, haulage systems, drilling and blasting operations, etc. The correct distinguishing of the genuine signals from the noise ...
ADE	Abstract The exploration and exploitation of hydrocarbon wells should not cause any environmental hazards including contamination of groundwater (aquifers) and atmosphere. The cement placed in the annular gaps between the casing strings and the formation acts as a key barrier to provide zonal isolation and maintain the...
ADE	Therefore, the experimental aspect of this study intends to expand the cement class G inventory. The experimental data and analyses added to inventory are as followed. The investigations of curing temperature and pressure confinements effects on the strength and post-peak response of the cement class G under compressio...
ADE	Statement of originality I certify that this work contains no material which has been accepted for the award of any other degree or diploma in my name, in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, exc...
ADE	1. Introduction There are more than four million onshore hydrocarbon wells drilled worldwide [9] with nearly 10000 in Australia alone [9] (from data retrieved from Geoscience Australia). A wellbore provides access to natural sources such as oil and gas. The wellbores are encased in different layers of steel casings and...
ADE	casing is isolating the freshwater-bearing formations [1]. The intermediate casing or protective casing is placed between the surface casing and production casing to protect any unusual high- pressure rock from initiating wellbore instability. An additional layer of intermediate casing might be required corresponding t...
ADE	faults can threaten the integrity of the wellbores even before the commencement of production procedures [20, 27]. The casing centralization should be executed properly. Otherwise, the cement would not be able to move the mud from the annulus completely during cementing procedures and leads to the formation of eccentri...
ADE	system during the lifetime of a wellbore [10]. Leakage paths are divided into two categories, primary and secondary. Primary category is more related to the time of primary cementing and secondary are associated with the events and conditions after cementing is complete [6]. Figure 1.2 illustrates the possible location...
ADE	The cement sheath is subjected to variations of mechanical and thermal cycles due to different wellbore operational processes, i.e. drilling, hydraulic fracturing, production operations, etc. during the lifetime of a wellbore. Hence, the integrity of the cement sheath and the cement sheath bonding integrity [37] affect...
ADE	c) Disking Cracks a) Radial Cracking b) Shear d) Interface debonding Figure 1.3: Different Types of Cracks within the Cement Sheath after [6, 8] displacement of the surrounding wellbore components which leads to the creation of micro- annulus within the wellbores (Figure 1.3d) [8]. Consequently, understanding of cement...
ADE	To this point, the linear elastic was employed in a few cement integrity analyses, i.e. [28, 37, 49]. However, the obtained stress-strain curves from the isotropic drained compression tests on the cementitious specimens by [36] are non-linear. Therefore, the employment of linear elastic theory in cement integrity simul...
ADE	plasticity models [55]. The modified version of CDP by [55] benefits from considering the difference in tensile and compressive responses of geo-materials since geo-materials experience different states of damage while subjected to different loading conditions. This model also considers the materials pressure-dependenc...
ADE	2. Thesis Overview This thesis is organised into nine chapters where the main contributions are presented in Chapter 5 to Chapter 7. Each of these chapters is presented in the form of a technical paper. The first of these has been published in the Journal of Petroleum Science and Engineering, the second has been publis...
ADE	3. Literature Review The importance of applying a comprehensive model to simulate the cement sheath behaviour under downhole conditions has been highlighted throughout the introduction chapter. In the following sections, the cement sheath numerical modelling and the cement experimental studies are reviewed. 3.1. Cement...
ADE	the interfaces. Their results showed the mechanical response of the set cement is dependent on the mechanical properties of the cement and the rock, and wellbore geometry. Honglin, Zhang, Shi and Xiong [64] have proposed a 2-Dimensional (2-D) analytical model using Mohr-Coulomb failure criterion to investigate the effe...
ADE	To this point, the elastic linear principle was utilised in a few cement integrity studies reviewed as follows. Nabipour, Joodi and Sarmadivaleh [28] simulated downhole stresses using Finite Element Method (FEM) along with sensitivity analyses on casing internal pressure, anisotropic horizontal in-situ stresses, and ca...
ADE	and bonding failure is higher in cooling scenarios compared to the heating scenarios. The effect of casing centralisation and controlled heating/cooling rates seemed to be trivial. The employment of linear elastic theory to simulate the cement sheath behaviour can affect the accuracy and reliability of the results due ...
ADE	The modified Cam-Clay model has been suggested as a method to incorporate cement micro cracking mechanisms by Bois, Garnier, Rodot, Sain-Marc and Aimard [36] owing to the nonlinearity of stress-strain curve achieved from the isotropic drained compression tests [72] and heterogeneous nature of cement at the microscale. ...
ADE	The combination of Mohr-Coulomb with smeared cracking is one of a few suitable approaches for modelling the real conditions in the cement integrity numerical simulations. However, despite the broad application of Mohr-Coulomb criteria, it has its own limitations. The model assumes a linear relationship between √J and I...
ADE	Therefore, in this study, Concrete Damage Plasticity (CDP) model developed by [54] and then modified by [55] has been employed. The Concrete Damage Plasticity model combines plasticity and damage mechanics and uses the concept of fracture-based damage. In the modified revision, two damage variables one for compressive ...
ADE	and Scott [85], Evans and Carter [86] to determine the corresponding parameters of the cohesive criterion. Evans and Carter [86] designed a push-out test setup to measure the cement shear bond and hydraulic bond to the casing and the formation. Carter and Evans [84] continued their experimental work and identified more...
ADE	modelling approaches. Considering that, the mechanical properties of the cement are significantly dependent on the curing conditions, which vary along its depth and its exposure to formation fluids [20, 88, 89]. Subsequently, many laboratory tests have been carried out on well cement to determine the key parameters for...
ADE	Nasvi, Ranjith and Sanjayan [92] used cylindrical samples with the size of 50 ×100 mm to measure the uniaxial compression strength of cement class G. The samples were oven cured at different temperatures between 300C to 800C for 24 hours excluding the samples required to be cured at room temperature. Afterwards, all of...
ADE	performed at different curing times on cement class G, cement class G with bentonite, and cement class G with other additives. They demonstrated that the outcomes of ultrasonic methods should be calibrated using the mechanical (destructive) measuring methods. The importance of achieving an extensive database on wellbor...
ADE	Labibzadeh, Zahabizadeh and 38 2.8 2 14.24 Khajehdezfuly [104] Labibzadeh, Zahabizadeh and 68 17.2 2 12.72 Khajehdezfuly [104] Labibzadeh, Zahabizadeh and 82 41.4 2 18.82 Khajehdezfuly [104] Labibzadeh, Zahabizadeh and 121 51.7 2 16.4 Khajehdezfuly [104] Labibzadeh, Zahabizadeh and 149 51.7 2 4.59 Khajehdezfuly [104] 3...
ADE	regards to high pressure and high temperature in harsh conditions, i.e. downhole conditions [97, 98]. Table 3.2 demonstrates that the measurement of tensile strength and particularly the fracture energy of cement class G, in particular over long-term periods, were simply overlooked in many experimental studies. Subsequ...
ADE	4. Research Objectives The overall objective of this study is to improve the modelling capabilities to assess cement sheath integrity by employing a more suitable constitutive model for the cement sheath. The experimental outcomes on the behaviour of the cement-based specimens under compression tests showed a strong no...
ADE	calibrated constitutive parameters obtained from the experimental data. The connections between the research aims and the associated publications are discussed as follows. 4.1. Objective 1: Evaluation of Cement Sheath Integrity Subject to Enhanced Pressure (Paper-1) The cement sheath should be designed and placed in a ...
ADE	simulate the tensile behaviour mechanism. However, in the absence of API guidelines for measuring the cement tensile properties, the methods for measuring cement tensile and / flexural strength were not consistent, and the measurement of cement fracture energy was mostly ignored. The effect of curing temperature on the...
ADE	Evaluation of Cement Sheath Integrity Subject to Enhanced Pressure (PAPER-1) ABSTRACT Well-cementing (cementation) is an influential stage of a wellbore completion, as the cement sheath is responsible for providing complete zonal isolation. Therefore, it is of utmost importance to understand the cement mechanical failu...
ADE	cement failure mechanisms under different operating conditions is of the utmost importance for better assessment of wellbore integrity. Failure of the cement sheath within a wellbore is affected and governed by material mechanical properties (cement compressive strength [31, 44, 45], Young’s modulus [31, 44, 45], tensi...
ADE	determined by running inverse analyses on the bonding studies carried out by Evans and Carter [86]. Despite, the massive progress regarding interface modelling, the use of elastic behaviour for cement sheath is an over-simplification that can affect the accuracy and reliability of the results. Fleckenstein, Eustes and ...
ADE	heterogeneous nature of cement at the microscale. Although important aspects of materials behaviour (material strength, compression or dilatancy, and critical state of elements under high distortion) are considered in this model, the tensile post-peak material is not incorporated into this framework. Numerical modellin...
ADE	Experimental Procedures The concrete damage plasticity model (CDP) has been calibrated and verified according to the experiments have been performed by Arjomand, Bennett and Nguyen [116]. The specimens were made of cement class G cured at 300C for 28 days in a pre-heated water tank with a manageable thermostat. The slu...
ADE	Figure 5.1: Cement Class G Compressive and Tensile Response Respectively To determine the tensile stress of the cement according to ASTM standard C348-02 “Standard Test Method for Flexural Strength of Hydraulic-Cement Mortars” [120] three-point bending tests were run on beams with dimensions of 160×40×40 mm. The sugges...
ADE	the concrete damage plasticity (CDP) model initially developed by Lubliner et al. (1989) and expanded by Lee and Fenves (1998). This model includes two damage variables for tensile and compressive failure, taking into account unilateral effects. The elastoplastic behaviour is decoupled from degradation damage response ...
ADE	𝜎 ( 𝑏𝑜)−1 𝜎 𝛼 = 𝑐 (5.6) 𝜎 2( 𝑏𝑜)−1 𝜎 𝑐 𝜎 where 𝑏𝑜 is the ratio of biaxial compressive yield stress to uniaxial compressive yield stress. 𝜎𝑐 𝜎 Experimental values used for concretes for 𝑏𝑜 vary between 1.10 and 1.16 which result in 𝜎𝑐 parameter 𝛼 in the range of 0.08 ≤ 𝛼 ≤ 0.1212 [54, 122]. The sh...
ADE	Some data pertaining to the confinement dependent strength of well cements is available in the open literature, for example [129, 130]. However, the biaxial to uniaxial strength ratio required for the characterisation Lubliner, Oliver, Oller and Onate [54] plasticity model is difficult to extract from triaxial data. In...
ADE	Table 5.1: Cement Class G Mechanical Properties Obtained from the Experiments and Calibration Process Young’s modulus Dilation angle Fracture energy 𝑬 (GPa) 𝝍 (degrees) 𝑮 (N/mm) 𝟎 𝒇 6.8 42 35 Inelastic Eccentricity 𝑲 Initial compressive 𝒄 strain 𝜺 stress 𝝈 (MPa) 𝒄 𝜺̃𝒄 𝒊𝒏 0.1 0.8 50 0.007353 Ultimate Tensi...
ADE	Figure 5.6: Linear Softening Traction-Separation Law The cohesive constraint is enforced at each slave node for cohesive surfaces. Contact separation is expressed as the relative displacements between the slave surface nodes and their matching opposite nodes on the master surfaces along the contact normal and shear dir...
ADE	Determination of Cohesive Model Parameters Carter and Evans [84] designed experimental setups to measure cement shear bond and the hydraulic bond between casing and cement and demonstrated that the bond properties were both pressure and temperature dependent. Shear bond is essential to support the pipe mechanically, wh...
ADE	/ Standard software package [57]. Pressure tests are performed after the casing cementation, such as casing integrity tests or formation integrity tests (leak-off test) by applying pressure upon recently set cement [26]. In order to have more realistic simulations, stress-related factors which induce wellbore failure i...
ADE	Geometry and Discretisation The model consists of a casing, cement sheath with eccentricity, formation rock and the interfaces of cement sheath with casing and formation shown in Figure 5.7. To reduce the computational cost of the model, half symmetry has been exploited and a 5 in. horizontal slice considered. The casi...
ADE	Initial State of Stress and Boundary Conditions Initial geo-stress components were defined as 𝜎 and, 𝜎 in the initial step of the analyses. 𝐻 ℎ Maximum and minimum horizontal stresses were applied parallel to X-axis and Y-axis in an exchangeable way. The anisotropy of geo-stresses would cause shear stresses to the w...
ADE	confinement effects on cement mechanical failure was analysed by varying four different rock formations' stiffness given in Table 5.3 (sections 5.5.1 and 5.5.2). Table 5.4: In-situ Stress Arrangements 𝝈 𝝈 𝝈 = 𝝈 (MPa) 𝝈 = 𝝈 (MPa) In-situ stress arrangements 𝑿𝑿 𝒀𝒀 𝑿𝑿 𝑯 𝒀𝒀 𝒉 Basis Case (Isotropic) 𝜎 𝜎 12...
ADE	Figure 5.11 shows compression damage along the cross-sectional paths for rocks’ stiffness simulations at which 𝐸 <1 (Soft rock 𝐸 =0.12, Shale 𝐸 =0.47) considering three cases of 𝑁 𝑁 𝑁 applying in-situ stresses. As can be seen in all the scenarios considering two different rocks’ mechanical properties, the highest...
ADE	(a) (b) (c) (d) (e) (f) Figure 5.11: Compression Damage along the Three Paths for Simulations with 𝐸 <1 (vertical red lines indicate the corners) 𝑁 Figure 5.12 shows compression damage along the cross-sectional paths for rock’s stiffness simulations at which E >1 (Hard Rock-1(E =2.51), Hard Rock-2 (E =3.96) consideri...
ADE	Figure 5.13: Global Compression Damage Indicator vs. 𝐸 𝑁 Considering the contour plots, and the global compression damage indicator in Figure 5.13 confirms that compression damage was more distributed within the cement sheath in Case-1 and Case-2 in comparison with the Basis-Case for scenarios involving the softer ro...
ADE	Figure 5.14: Tensile Damage Contours within the Cement Sheath The maximum tensile damage for the Basis-Case reached 0.48 for the softest rock (E =0.12). N In contrast, the maximum tensile damage magnitude reached 0.67 and 0.58 for the softest rock in Case-1 and Case-2 respectively and covered a relatively large zone on...
ADE	and propagation of tensile cracks through the whole thickness of the narrow side of the cement sheath. To compare all the zones within the cement sheath experiencing tensile cracking, a global tensile damage indicator (D ) was computed as follows. t 𝐷 =∑𝑁(𝑑𝑡) (5.14) 𝑡 0 𝑁 where d is the local tensile damage magni...
ADE	Propensity of Forming Micro Annuli The soundness of the cement sheath bonds with the casing and the rock formation is examined through a contact stiffness degradation index. Figure 5.16 demonstrates the starting location of the selected paths along the cement sheath interfaces with the casing and rock formations. Figur...
ADE	(a) (b) (c) Figure 5.18: Contact Stiffness Degradation at Cement Sheath Interface with the Rock Formation The interfaces are the most vulnerable part of a wellbore due to the high difference in the stiffness of surrounding materials, and high contact shear stresses in tangential and normal directions of the interface l...
ADE	Effect of Curing Conditions on the Mechanical Properties of Cement Class G with the Application to Wellbore Integrity ABSTRACT Wellbore integrity is highly dependent on the cement sheath integrity. Cement sheaths play an essential role in preventing any communication between the formation fluids and the surrounding env...
ADE	designed and placed so that it withstands the external conditions imposed upon it, including, in- situ stresses, high internal pressures and high temperature. Portland Cement Class G is mostly utilised as the base of oil wells in the oil and gas industry. Additives may also be incorporated to achieve certain properties...
ADE	the interaction between flexible cement and expanding agents and concluded that the cement with both flexible and expanding additives shows more durability in long-term periods. Cyclic pressure tests were run on hollow cylinders (50×100 mm) of cement class G by Yuan, Teodoriu and Schubert [103]. The samples were cured ...
ADE	Rogers [99] continued their study by curing samples at two different temperatures of 54.40C or 82.20C for 48 hours in an atmospheric water bath. The authors compared the results of splitting tensile strength (STS) tests with direct tensile tests on the dog-bone sample. The splitting tensile strength test results overes...
ADE	values (the uniaxial strength measured using sufficiently slender specimens is usually around 70%-90% of the cube strength [106]. In cubic samples, the restraining effect of the platens spreads over the total height of a specimen, but in cylindrical samples, some parts of specimens stay unaffected [107]. Another proble...
ADE	samples cured at two different curing temperatures (30oC and 70oC). Section 3 also describes the execution of the three-point bending test on the prismatic samples cured at 30oC and the challenges involved with measuring fracture energy. Modifications are incorporated to the three- point bending test set-up, explained ...
ADE	investigated by testing two slower rates: 0.1 mm/min and 0.04 mm/min, shown in Figure 6.1. The axial displacement of the loading platen was measured with the help of two external, linear, variable differential transformers (LVDT) that were installed 180oapart at the top platen. As can be seen in Figure 6.1, the samples...
ADE	Unconfined Compression Test at a Curing Temperature of 70°C To investigate the effects of curing temperatures on the mechanical properties of the cement, the samples were prepared as described in section 6.2.1 except for a change in curing temperature. For these tests, the temperature was set to 70oC. The rest of the t...
ADE	and the graph obtained from the three-point bending test on one of the un-notched beams, are shown in Figure 6.5. The tensile strength σ for prisms was calculated from the bending tests, as follows. t0 3𝐹𝑆 𝜎 = (6.1) 𝑡0 2𝑑 𝑑2 1 2 where F is the maximum load, S is the span of the beam, d is the width and d is the d...
ADE	where U is the area under the load-deflection is graph; A is the ligament area and defines as A = o B(W−a ); B is the width of the beam; W is the depth of the beam; a is the initial depth of the o o notch; mg is the weight of the beam; and d is the final deflection at the load point. o As can be seen in Figure 6.6, the...
ADE	For a beam in a three-point bending test, the load-deflection graph consists of three stages. In the first stage, the deflection rises linearly, as the load increases. A fracture process zone develops during the second stage, at which micro-cracks are created. In the third stage, which is a strain- softening zone, crac...
ADE	before and during loading process [142-144]. The DIC system (3D) used in the experiments consisted of two monochrome 2.8-megapixel, conventional charge-coupled device (CCD) cameras. It had a sensor size of 1/1.8" and a maximum resolution of 1928×1448 pixels. The camera lens was a 75-mm Fujifilm prime lens with an apert...
ADE	p (x ,y ) from the reference image is selected and used for tracking the associated displacement o o in the deformed image [143]. The relationship between these two functions is defined as follows [144] . 𝑝′(𝑥′,𝑦′)−𝑝(𝑥+𝑢(𝑥,𝑦),𝑦+𝑣(𝑥,𝑦))= 0 (6.3) where u(x,y) and v(x,y) are the displacement field for a patter...
ADE	along with a 20 mm pitch grid for calibration purposes. To examine the degrees of similarity between the reference and deformed image, a correlation criterion should be employed [143]. The default criterion is Normalised Sum of Square Difference (NSSD) [143] defines as follows. 𝑀 𝑀 𝑝(𝑥 ,𝑦 ) 𝑝′(𝑥 ′,𝑦 ′) 2 𝑖 𝑗 ...
ADE	0.8 0.2 Load Clip Gauge DIC 0.6 0.15 ) ) m N m k ( d a0.4 0.1 ( D O o M L C 0.2 0.05 0 0 5 10 15 20 250 Image Number Figure 6.12: Load and CMOD versus DIC during the Three-point Bending Test 6.5. Interpretation of Results in the Concrete Damage Plasticity Model Framework The non-linear behaviour of cement under compres...
ADE	The parameters on the yield surface can be obtained using the experimental results. To approximate the shape of the loading/yield surface in I and √3J plane, the results of compression 1 2 tests shown in Figure 6.15 (on samples cured at 30𝑜C) at different confinements were used. Figure 6.15: Compression Tests on Cylin...
ADE	deform during the simulations. The defined boundary condition for the bottom surface constrains all the degrees of freedom, and the top surface displacement rate was applied in the direction of the cylinder axis. The results and corresponding failure patterns in the laboratory and ABAQUS are shown in Figures 6.17 and 6...
ADE	Evaluation of Cement Sheath Integrity Reflecting Thermo-Plastic Behaviour of the Cement in Downhole Conditions (PAPER-3) ABSTRACT The cement sheaths play an important role to provide complete zonal isolation during the wellbores lifetime. The cement sheaths are subjected to pressure and temperature variations which may...
ADE	mechanical and thermal operational procedures applied by the production and recovery phases during a well lifetime. Well-cementing (cementation) is an important stage in the wellbore completion procedure as the cement sheath is responsible for maintaining the integrity of the wellbores [40]. The permeability of cement ...
ADE	tensile stresses develop and lead to the creation of fractures in the inner surface of the cement sheath. Guo, Bu and Yan [49] presented a numerical study to investigate the effect of the heating period, cement thermal expansion, and overburden pressure on the cement integrity under steam stimulation conditions. All ma...
ADE	confirms the incompatibility of linear elastic theory in cement integrity evaluations again as the elastic theory does not incorporate the time-dependency and materials hysteresis law [50]. The non-linear approaches including those using Von-Mises [51], Ottosen model [5, 53], Drucker-Prager [52], modified Cam-Clay [36]...
ADE	The modified Cam-Clay model has been suggested as a method to incorporate cement micro cracking mechanisms by Bois, Garnier, Rodot, Sain-Marc and Aimard [36] owing to the nonlinearity of stress-strain curve achieved from the isotropic drained compression tests [72] and heterogeneous nature of cement at the microscale. ...
ADE	hexagon, whereby the sharp corners can hinder convergence in numerical simulations [70, 78]. Moreover, quasi-brittle materials experience a huge volume change due to a large amount of inelastic strains (dilatancy) which has been overlooked so far by using associated flow rules in the aforementioned modelling approaches...
ADE	geo-materials including rocks, and cement-based materials [55] compared to the rest of model used . The corresponding CDP model parameters were obtained from the previous experimental- numerical study on cement class G by [116, 147]. In this paper, the susceptibility and magnitude of compression damage, tensile damage,...
ADE	The heating and cooling scenarios represent the different operational procedures leading to pressure and temperature variations applied to wellbore-2. For instances, during the commencement of production procedures, the pressure and temperature are increased within the wellbores to enforce the hydrocarbon flow from the...
ADE	1 𝜀 = (𝑢 +𝑢 ) (7.2) 𝑖,𝑗 2 𝑖,𝑗 𝑗,𝑖 Motion equation: 𝜎 +𝜌𝐹 = 𝜌𝑢̈ , 𝜎 = 𝜎 (7.3) 𝑖𝑗,𝑗 𝑖 𝑖 𝑖,𝑗 𝑗,𝑖 where 𝜌 is the mas density, and 𝐹 is external force per unit mass, . 𝑖 Energy-scale equation: 𝑞 +𝜌(𝑇 𝑠̇ −𝑅)= 0 (7.4) 𝑖,𝑖 𝑜 where 𝑞 is the heat flux per unit area, 𝑇 is the initial temperat...
ADE	overburden stress (σH) and the ratio of ansitropic in-situ stresses (σH) is assumed to be 0.8 and σV σV 0.7 respectively. The variation of overburden (vertical) initial stress in depth is negligible since the ratio of model height to the width is comparatively small. The corresponding overburden effective stress at the...
ADE	where the superscript 0 denotes the maximum traction or initiation traction value, n,s,t are representing the normal and shear directions respectively, and K represents the contact stiffness. The dashed-line demonstrates the stiffness degradation after the peak. Equation (7.9) describes a linear relationship traction-s...
ADE	cement and formation. Afterwards, Wang and Taleghani [37] performed inverse analyses on the experimental results of [84-86] to determine the cohesive parameters. Table 7.1 summarised the obtained cohesive parameters by Wang and Taleghani [37] adopted in this study to model the mechanical behaviour of the interfaces. Ta...
ADE	The gap conductance coefficient decreases linearly as the clearance increases due to the creation of gaps and flaws between the contact surfaces as shown in Figure 7.3. The effect of surrounding temperature on the gap conductance coefficient is not seen in this study also the Figure 7.3: Gap Conductance vs. Separation ...
ADE	7.2.3.1. Cement Constitutive Modelling The observed non-linearity in obtained stress-strain curve studying cement mechanical behaviour under compression tests [10, 55] results from two different microstructural changes which happen in the materials while subjected to different loading conditions. One is plastic flow ca...
ADE	In this study, the compression damage d was computed using Equation (7.15) [4] as shown in c Figure 7.4: d = 1− σ c, (7.15) c σcu where 𝜎 ′ is the axial stress of the cement on the descending branch, and 𝜎 is the peak point of 𝑐 𝑐𝑢 the stress-strain curve. Tensile damage d was defined using a linear relationship [...
ADE	𝜎 ( 𝑏𝑜)−1 𝜎 𝛼 = 𝑐 (7.18) 𝜎 2( 𝑏𝑜)−1 𝜎 𝑐 𝜎 where 𝑏𝑜 is the ratio of biaxial compressive yield stress to uniaxial compressive yield stress. The 𝜎𝑐 shape of loading surface in the deviatoric plane is controlled by parameter 𝛾 in Equation (7.11) [123] and define as 3(1−𝐾 ) 𝑐 𝛾 = (7.19) 2𝐾 +3 𝑐 where �...
ADE	until failure occurred. Three-point bending tests on notched and un-notched beam samples were performed to obtain the cement class G tensile strength and fracture energy accompanied by applying modifications on three-point bending set-up. The approximate shape of the yield surface for concrete damage plasticity models ...
ADE	wellbore failure in some fields were incorporated within the frameworks including employing anisotropic in-situ stresses as stated in section 7.2.1, and 50% eccentricity applied to the layers of the cement sheath. Figure 7.6 shows different geometries considered for wellbore-1. The effect of model size including the su...
ADE	compression and tensile damage. The obtained results are in good agreement with the other studies carried out on this case-study, for instance, Asamoto, Le Guen, Poupard and Capra [5]. However, wellbore-1 was placed in a critical location due to its vicinity to the underground water. Therefore, the injection of higher ...
ADE	1.2oC 0.5oC heating, and controlled heating rates of and . All the damage contours were scaled from min min zero to one for comparison purposes. Figure 7.9: Local Compression Damage Contours within the Cement Sheaths Subjected to Pressure during Heating Scenarios The additional shear stress caused by the anisotropy of ...
ADE	eccentricity (the maximum local compression damage occurred within the wellbores subjected to instant heating). The considerable difference in maximum compression damage magnitude is indicative of the destructive impact of instant heating on causing crushing damage within the cement sheaths. Figure 7.10 shows the tempe...
ADE	Figure 7.11: Heat Flux Magnitude at the Interface of the Cement Sheaths with the Casing and the Formation Subjected Instant Heating Scenarios The narrower sides of the cement sheath with 70% and 50% eccentricity are also experiencing some disking cracks as a result of steel casing expansion and highly unbalanced stress...
ADE	Figure 7.12: Global Compression Damage Indicator vs. Eccentricity for Different Heating Scenarios under High Temperature Changes The critical effect of eccentricity and application of controlled heating rates on the integrity of cement sheaths again can be confirmed by considering the compression damage contour in Figu...
ADE	Figure 7.14 demonstrates the magnitude of global tensile damage indicators within the cement sheath subjected to heating scenarios. Figure 7.14: Global Tensile Damage Indicator vs. Eccentricity during Heating Scenarios As can be seen in Figure 7.14 the magnitude of global tensile damage reaches the highest value in the...
ADE	In addition, the compression/shear damage was observed at the wider side of the cement sheath with 70% eccentricity while in heating scenarios the heating scenarios compression damage was mainly concentrated at the narrower side of the cement sheath. The maximum local compression damage (d ≈0.3) occurred at the narrowe...
ADE	Figure 7.19 shows the corresponding thermal strains for the three different cooling rates. As can be seen in Figure 7.19 the gradient of thermal strain corresponding to the slowest rate is the steepest which resulted in higher global tensile damage among the three rates. As applying thermal loads in this scenario with ...

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