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Onset of Creation of Residual Strain during the hydration of oil-well cement paste
Cement and Concrete Research 116 (2019) 27–37
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Onset of Creation of Residual Strain during the hydration of oil-well cement paste
T
Nicolaine Agofacka,b,1, Siavash Ghabezlooa, , Jean Sulema, André Garnierb, Christophe Urbanczykb ⁎
a b
Laboratoire Navier, Ecole des Ponts ParisTech, Ifsttar, CNRS UMR 8205, Marne la Vallée, France TOTAL, Exploration & Production, CSTJF, Pau, France
ARTICLE INFO
ABSTRACT
Keywords: Cement hydration Temperature Pressure Cement-sheath integrity Irreversible deformation Boundary Nucleation and Growth (BNG) model
In this paper, the Creation of Residual Strain during the hydration of cement paste is studied by performing oedometric experiments on class G cement pastes during the six first days of hydration. Various conditions of temperature (between 7 and 30 °C) and pressure (between 0.3 and 45 MPa) are explored. It is found that after a hydration degree of about 18%, mechanical loadings can induce residual strain. This state is reached at a time called critical time for Creation of Residual Strain (CRS). It corresponds to the maximum axial strain rate in an oedometric test or to the maximum rate of wave-velocity evolution versus time recorded in a Ultrasonic Cement Analyzer (UCA) test. The Boundary Nucleation and Growth (BNG) model is used to estimate the critical time for CRS. Within the range of studied temperatures and pressures, the predictive capacity of the BNG model for estimation of the critical time for CRS is demonstrated.
1. Introduction When drilling oil & gas wells, a mud is used to support the walls of the geological formation, to maintain wellbore stability, to cool the drill bit, to carry out the cuttings, to control formation pressure, and to seal permeable formations. A tubular is then run in the well and cement slurry is pumped between the tubular and the hole. Time is given for the cement slurry to harden to become a cement sheath. The role of this cement sheath is to provide zonal isolation of different fluids along the well, to protect the tubular against corrosion and to provide mechanical support. The loss of cement-sheath integrity can result in the pressurization of annulus, in gas migration up to a shallower formation or to the surface, and, in catastrophic cases, in a blowout and in the total damage of the infrastructure. During the life of a well, from drilling to completion, production and P&A (plug and abandonment), the cement sheath is submitted to various mechanical and thermal loadings that can potentially damage the cement sheath and alter its performance. Some of these loadings may occur at very early age, when the mechanical properties of the cement sheath are not yet sufficiently developed. This is for example the case during a casing test, which is performed to check the integrity of the well. The applied pressure during a casing test can vary from a few tens of MPa in normally
pressurized reservoirs to > 100 MPa in high pressure reservoirs. The drilling operation in oil and gas wells results in application of loading on previously completed sections at shallower depths, which can excess 40 MPa [1,2]. It is often questioned what is the most suitable moment to perform such a test and to apply loads on the cement sheath. Waiting too long after bumping the plug could result in loading a slurry that is no more a liquid and not yet a strong porous solid. It could induce significant residual strains in the cement and this could lead to the formation of a micro-annulus or to cement damage later in the life of the well [3–6]. With the progress of hydration, cement develops its stiffness and strength and can be able to support external stress cycles, in the limits of usual loading magnitudes in an oil-well, without significant residual strain. Hence, the knowledge of the time interval in which the application of a loading cycle can potentially result in creation of significant residual, i.e. plastic, strains is of major importance to avoid a loss of integrity during life well cycle. We should therefore define and characterize a threshold beyond which a loading application can potentially result in the formation of appreciable plastic strains. This threshold is called here the onset of Creation of Residual Strains (CRS) and is noted by tCRS, which is the time needed after mixing of the cement slurry to reach the onset of CRS for given hydration conditions. Besides the above-mentioned application in petroleum
Corresponding author. E-mail address: [email protected] (S. Ghabezloo). 1 Currently at Norwegian University of Science and Technology (NTNU), Trondheim, Norway. ⁎
https://doi.org/10.1016/j.cemconres.2018.10.022 Received 22 March 2018; Received in revised form 19 September 2018; Accepted 22 October 2018 0008-8846/ © 2018 Elsevier Ltd. All rights reserved.
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industry, the knowledge of tCRS can be important for any structure made from cement-based materials, which is submitted to loading at early age before reaching an advanced degree of hydration. The purpose of this work is to determine the tCRS by measuring the deformations of a cement paste sample hydrated in sealed conditions in a specially designed oedometric cell. Application of loading/unloading cycles during hydration at early age (< 6 days) permits the detection of the time after which significant plastic strains can be produced. A temperature of 7 °C is chosen to slow down the rate of cement hydration [7]. Once the critical time for CRS is found, its dependence on the pressure and temperature during hydration is analyzed by performing oedometric tests on cement paste hydrated at temperatures ranging from 7 °C to 30 °C and under an axial stress ranging from 0.3 MPa to 45 MPa. The Boundary Nucleation and Growth model is used to model the pressure and temperature dependency of critical time for CRS. Ultrasonic Cement Analyzer (UCA), one of the most popular equipment in the petroleum industry, was also used to determine the critical time for CRS.
emphasized that the aim of this paper is to evaluate the onset of creation of plastic strains in a cement paste due to the application of a mechanical loading. It is evident that the creation of plastic strains and their magnitude depends on various factors such as the initial state of stress, the magnitude of the applied loading and the material yield surface. However, during the fluid-solid transition there is a time after which the application of a loading cycle, for example in a casing test, can potentially result is creation of plastic strains. To evaluate this time and to overcome the influence of the other factors (e.g., loading magnitude) the loading cycles are applied with a quite significant change in the stress state in the range between 5 MPa and 65 MPa as presented in Table 1. This is certainly beyond the elasticity limit of the studied cement paste as can be seen from the results of triaxial compression experiments performed on a hardened class G cement paste (Ghabezloo [8]; Ghabezloo et al. [9]).
2. Experimental program
All tests were performed on a slurry made of CEMOIL class G cement from CCB. The slurry is the same as the one used in our previous studies for which various mechanical, hydraulic, thermal and time dependent properties have been investigated and presented in [9–17]. The chemical composition of cement, as provided by the supplier, is presented in Table 2 and is in accordance with the American Petroleum Institute (API) 10A requirements for class G cements [18] (section §4.1.2). The cement slurry presented in Table 3 is composed of class G cement powder, distilled and deaerated water with w/c = 0.44, and three additive agents (anti-foaming, dispersing and anti-settling). The mixing procedure starts with pouring distilled and deaerated water into the mixing container. The dry anti-settling agent is added to the water and the motor is turned on and maintained to 4000 ± 200 rotations per minutes during 5 min. Then the liquid anti-foaming and dispersing agents (poured before cement) and the cement powder are put successively into the container in 20 ± 5 s (according to API 10B-2
2.1. Cement slurry preparation
In order to determine the critical time for CRS (tCRS) due to the mechanical loading, oedometric tests with loading-unloading cycles were performed on hydrating cement paste. The effects of temperature and pressure during hydration on this critical time were studied by running experiments under various conditions. The oedometric tests were performed in undrained conditions using an apparatus specially designed by TOTAL. It was looked also for an alternative method to evaluate the onset of CRS that would use a more widely-available equipment. This was done by comparing the results of oedometric tests with those of Ultrasonic Cement Analyzer (UCA) tests performed in the similar conditions of pressure and temperature. Seventeen oedometric tests, four calorimeter tests and two UCA tests were run and are presented in this study. These tests are classified and presented in Table 1 by categories according to their principal purpose. It should be Table 1 Summary of tests performed in this study. Category
Tests
C1
T7P25a T7P25b T7P25a T7P25-15 T7P25-18 T7P25-20 T7P25-60 T7P25-103 T7P45 T7P45–15
C2
C3 C4
C5 C6 C7
C8
Hydration temperature (°C)
T7P45 T7P25a T7P15 T7P10 T7P3 T7P25a T15P25 T22P25 T10P5 T30P30 C-T7Patm C-T7P25 C-T7P45 C-T30P30 T7P25a U-T7P25 T7P0.3 U-T7P0.3
Hydration pressure (MPa)
Time of first mechanical loading (hours)
Mechanical loading path 0
Purpose of the test
7
25
N/A
7
25
7
45
N/A 15 18 20 60 103 N/A 15
7
45 25 15 10 3 25
N/A
5 65 5 5 45 MPa (see Fig. 4(b)) 0
N/A
0
Effect of temperature on onset of CRS
5 30 Patm 25 45 30 25
N/A
0
Validation of model
N/A
0
Estimation of the degree of hydration
N/A
0
Comparison of the rate of axial strain in oedometric tests with the rate of compression-wave velocity in UCA tests
7 15 22 10 30 7 30 7
25 MPa
65
45 MPa
65
5 65 5 5 25 MPa (see Fig. 4(a))
0.3
“N/A” means “no application”. 28
Repeatability on oedometric tests Creation of Residual Strain in cement paste
Effect of pressure on onset of CRS
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external diameter and 125 mm height) made of steel. Within its elastic domain, the hollow cylinder can support a maximum pressure of 123 MPa applied on its inner surface. The hollow cylinder is surrounded by a cooling/heating system whereby cold/hot fluid is circulated through small-diameter tubing. The tubing is connected to a cryostat that contains a fluid at a controlled temperature. A LVDT sensor ( ± 10 mm) with high precision ( ± 0.2%) is used to measure the displacement of the sample. The LVDT is fixed on the lower header and points at the upper one. The hollow cylinder is not fixed on the lower platen in order to reduce the effects of friction between the sample and the hollow cylinder, according to [19], hence ensuring that the displacements measured by the LVDT only correspond to the displacements that exist in the cement sample. The oedometric cell is cooled/ heated to the test temperature before preparing the slurry. For oedometric tests, the slurry is mixed, poured into the cell which is cooled or heated at the test temperature. The cement slurry is put in the oedometric cell, (50.3 mm in diameter and 85 mm in height). The mass of cement slurry put in the oedometric cell is 322 ± 3 g and all tests are performed without additional water during hydration. The cell is placed under the axial frame (block A in Fig. 1a) and axial stress is applied on the slurry. The test starts 5 min after mixing (API recommendation for thickening-time tests [18] (section §10)). The displacement obtained from the LVDT is initialized when the test temperature and axial stress are reached.
Table 2 Chemical composition of class G cement with Blaine = 323 m2/kg. Chemical composition
Measurements
Magnesium oxide (MgO) % Sulfurtrioxide (SO3) % Loss on ignition % Insoluble residue % C3A % C4AF + 2 C3A % C3S % (0.658 × K2O) + Na2O %
Table 3 Composition of 600 ml of sity = 1900 ± 10 kg/m3).
API Spec 10A requirements
1.8 2.5 0.6 0.1 2.1 17.4 58.9 0.55
cement
Max 6.0 Max 3.0 Max 3.0 Max 0.75 Max 3.0 Max 24.0 Min 48.0 - Max 65.0 Max 0.75
slurry
(w/c = 0.44;
Component
Mass (grams)
Cement (class G) Water (distilled and deaerated) Anti foaming (D047)a Dispersing agent (D604AM)a Anti-settling (D153)a a
den-
783.53 339.54 6.27 9.47 1.18
Commercial identification.
[18], cement powder shall be added in 15 s). The speed is immediately increased to about 12,000 ± 500 rotations per minute and mixing ends after 35 ± 1 s.
3. Experimental results and analysis 3.1. Reliability and repeatability of the experiments
2.2. Experimental device
In order to calibrate the system presented in Fig. 1b, distilled water at ambient temperature was put into the oedometric cell and submitted to mechanical loading cycles (Fig. 2a). The slope of the axial stress – axial strain curve presented in Fig. 2b, gives a bulk modulus Kf of water equal to 2.1 GPa. This value is very close to the compression modulus of pure water at ambient temperature and shows the reliability of the experiment. To verify the repeatability of the experiments, two oedometric tests were performed at 7 °C and under a constant axial stress of 25 MPa. The results, presented in Fig. 3, show that the system gives an excellent repeatability. The axial strain presented in Fig. 3a is due to the macroscopic shrinkage of the cement paste during its hydration under pressure. The rate of the axial strain is presented in Fig. 3b showing that both curves present a maximum near 20 h and a very good repeatability between the two experiments. The rate of the axial strain is evaluated by linear regression method, using the method presented in Ghabezloo and Sulem [20].
The experimental device is shown in Fig. 1. The general system (Fig. 1a) is composed of six elements identified by letters A to F. For the oedometric test, only compounds A, D and F are used. The compounds B, C and E are used for triaxial tests. Block A represents the axial frame, able to apply 650kN through an electromechanical ram. Block D includes six movidrives to control the electromechanical rams. F is the data acquisition center. In Fig. 1b, one can see the oedometric cell composed of a hollow cylinder (50.3 mm internal diameter, 90 mm
3.2. Apparition of additional residual strain due to mechanical loading Oedometric tests were performed on cement paste during hydration at 7 °C and under 25 MPa and 45 MPa. This relatively low temperature was chosen to slow down the kinetics of cement hydration, as shown by Vu [7] using UCA experiments. Some experiments include mechanical unloading/loading cycles at predefined times according to the loading paths presented in Fig. 4. The mechanical paths of Fig. 4a and Fig. 4b were applied on cement samples hydrating respectively under 25 MPa and 45 MPa. As mentioned before, the loading cycles are applied with quite a significant change in the stress level to ensure that the onset of creation of residual strains can be detected in the experiment. For the test T7P25a in Fig. 3a, the axial stress-strain response during the loading/unloading cycle at 144 h of hydration is presented in Fig. 5. One can see that the limit of elasticity is about 36 MPa confirming that the magnitude of applied loading (5 to 65 MPa) is sufficiently high to detect the apparition of plastic strains in the performed experiments. Six tests were performed under 25 MPa. For the test T7P25a presented in Fig. 3, considered as the reference test under these conditions, the
Fig. 1. Uniaxial strain (oedometric) cell. 29
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Fig. 3. Repeatability of oedometric test: (a) development of axial strain with time; (b) rate of axial strain versus time.
Fig. 2. Measure of bulk modulus of distilled water at 22 °C: (a) loading path with loading rate of 3 MPa/min; (b) axial strain-stress curve.
maximum strain rate (at 15 h and 18 h) creates only small additional axial strains, while a loading cycle at the peak of strain rate (at 20 h) results in a sudden increase in the measured residual strain. According to these observations, for hydration at 7 °C and under 25 MPa, and the loading path given in Fig. 4a cycling at and after 20 h creates additional residual strain in the cement paste. To verify this result, two oedometric tests were performed under the same temperature 7 °C, but at a higher pressure of 45 MPa (Fig. 7). The test T7P45 is considered as the reference test as no loading cycle was applied (Fig. 7a). The maximum strain rate in this test, is reached after 15 h (Fig. 7b). In order to analyze the creation of additional strain, a loading cycle was applied at 15 h during the test T7P45-15 (Fig. 4b). As can be seen in Fig. 7a, additional residual strain was created due to this cycling. This confirms that, from the time of the maximum rate of axial strain, application of a mechanical loading cycle on cement paste can create additional residual strain. After mixing cement and water, the slurry behaves like a fluid with suspended particles, without any mechanical strength. Before setting, the external axial strain is entirely related to the chemical shrinkage during hydration (Helinski et al. [21]; Lura et al. [22]). With the progress of the hydration, the cement paste develops its stiffness and mechanical strength and therefore the chemical shrinkage is no longer entirely transformed to an external strain. It results in a decrease of the strain rate as can be seen in the presented experimental results.
axial stress was kept constant at 25 MPa during the 144 h of hydration. Applying the loading/unloading cycles of Fig. 4a allows, to evaluate the influence of a mechanical cycle on the behavior of the cement paste and the creation of the residual strain by comparison with the reference test with no loading/unloading cycle,. The times at which the cycle was performed was chosen based on the observed rate of axial strain in the reference test presented in Fig. 3b for which the maximum is reached at around 20 h. Accordingly, the cycle was performed at 15 h, 18 h, 20 h, 60 h and 103 h in different tests in order to explore the influence of a loading cycle before, near and after the time corresponding to the maximum strain rate. The loading cycles were applied with a rate of 3 MPa/min and the evolution of the hydration degree during the cycle is assumed to be negligible. The evolution of the axial strain with time for different tests is presented in Fig. 6a. It shows that cycling induces additional strains as the curves are identical before 15 h and present a shift after this time when compared with the reference test T7P25a. The curves corresponding to a cycle performed at 15 h or 18 h remain quite close to the reference curve, while cycling at later times creates a clear shift of the strain curve as compared to the reference case. The calculated additional strain at 120 h of hydration (Fig. 6a) is presented in Fig. 6b as a function of the time at which the loading cycle was applied. In the same figure, strain rate in the reference test is also presented. One can see that the additional strain increases with the time at which the cycle was performed. The application of a loading cycle before the 30
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Fig. 4. Stress path of the loading/unloading cycles (loading rate: 3 MPa/min).
Fig. 6. Oedometric tests at 7 °C and 25 MPa: (a) axial strain versus time; (b) additional strain due to the mechanical cycling versus the cycling time. The rate of strain in the reference test (no loading cycle) is also presented.
formation of the solid structure in the cement paste. This can be attributed to the acceleration of the hydration kinetics related to the increase of the pressure [7]. For a more detailed investigation of this effect, it is interesting to evaluate the degree of hydration of cement paste at the onset of CRS. This is done by performing three calorimeter tests at 7 °C, under atmospheric pressure, 25 and 45 MPa. Calorimeter data provide the cumulative heat of hydration Q(t) released until a given time t. The degree of hydration can be evaluated through the following equation:
Fig. 5. Axial stress-strain curve for mechanical loading cycle at 144 h of hydration.
(t ) =
Q (t ) Q T_ CP
(1)
where QT_CP is the total cumulative heat released at complete hydration, which can be estimated when the composition of the cement paste is known (detailed calculation can be found in [7,23]). The results calorimeter tests are presented in Fig. 9a in terms of the degree of hydration as a function time. These results permit to plot the variations of the axial strain rate versus hydration degree for the oedometric tests performed under the same pressure and temperature conditions (Fig. 9b). The results show that the maximum strain rate for different pressures is reached at hydration degrees which are very close together, between 0.18 and 0.22. This indicates that the critical degree of hydration for CRS is almost independent of the pressure during hydration and the observed variations of the tCRS is mostly due to the pressure dependency of cement hydration kinetics. To investigate the effect of temperature on the critical time tCRS, three samples were cured in oedometric conditions under a constant pressure (25 MPa) and at different
Accordingly, the time at which the effect of this phenomenon becomes significant corresponds to the peak of the axial strain rate in the performed experiments. 3.3. Effect of pressure and temperature during hydration on tCRS In order to analyze the influence of pressure during hydration on tCRS, five samples were cured in oedometric conditions at 7 °C and under different axial stresses (3, 10, 15, 25 and 45 MPa). No further loading cycle was applied during these experiments. The measured strain rate and the variation of tCRS (defined as the time at the maximum rate of axial strain), with pressure are plotted in Fig. 8. The results show that tCRS decreases with the increase in pressure during hydration. In other words, increasing the pressure during hydration accelerates the 31
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Fig. 8. (a) Axial strain rate for oedometric experiments performed at 7 °C and under different axial stresses; (b) variation of tCRS with temperature.
Fig. 7. Test at 7 °C and under 45 MPa: (a) reference test and additional residual strain due to mechanical loading at 15 h; (b) rate of the axial strain (maximum at 15 h).
the literature [26,27], the solid structure of the cement paste is still quite weak. Any damage or irreversible strain created at this time by mechanical loading is then healed quickly with subsequent hydration. At CRS time, contrariwise, the solid structure is enough developed and the damage or irreversible strain created from this time is no more completely healed with later hydration, and remains permanently.
temperature during hydration (7, 15 and 22 °C). The samples were not submitted to any mechanical loading cycle during the 6 days of hydration. The axial strain rates and the variations of tCRS with temperature are plotted in Fig. 10. As expected, tCRS decreases with the increase in hydration temperature. This is in agreement with the fact that hydration of cement paste is accelerated by an increase of the temperature during hydration [7,24,25]. Similar to the pressure dependency of tCRS mentioned above, its temperature dependency is due to the temperature dependency of cement hydration kinetics. This is verified by the experiment performed at 30 °C and 30 MPa, and presented in Fig. 9b. It shows that the maximum rate of axial strain is reached at the degree of hydration of 0.20 which is compatible with the above mentioned range of degree of hydration at tCRS. The critical time for creation of residual strains is found to happen at degree of hydration around 0.18 and 0.22. This value is higher than what is mentioned in the literature for the initial setting of cement paste. Using Vicat needle method, Zhang et al. [26] found values between 0.028 and 0.043 for the degree of hydration at the setting-time for class H cement with water-to-cement ratio ranging from 0.25 to 0.40. Garboczi and Bentz [27] also mentioned that cement paste sets at a low degree of hydration (0.02 to 0.08). This means that the critical time for CRS is reached after the initial setting of the cement paste. This can be explained by the fact that, at the setting time usually reported in
4. Modeling of critical time for creation of residual strains 4.1. Boundary Nucleation and Growth (BNG) model Several models have been proposed to describe cement hydration, among which one of the most popular is the Boundary Nucleation and Growth (BNG) model. This model was first proposed in 1939 by Johnson and Mehl [28] and developed by Avrami [29–31] as the Nucleation and Growth (NG) model. Its initial purpose was to describe recrystallization of pure metals and freezing liquids under isothermal condition, without any concentration variation. This transformation is described as random nucleation and random growth within the transforming material. The development of the transformed fraction of material X is given by Eq. (2), where B relates to the transformation properties (rate of nucleation and rate of growth) and k characterizes the dimension of transformation (1D, 2D or 3D).
X=1
exp( Bt k )
(2)
In 1956, Cahn [32] postulated that, in some transformations, 32
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Fig. 10. (a) Axial strain rate for oedometric experiments performed under 25 MPa with different temperatures; (b) variation of tCRS with temperature.
Using the values of parameters OvB, IB and G found by Thomas [33] for hydration of alite (C3S), it is possible to compare the results from Eqs. (3) and (4). As presented in Fig. 11, for a volume fraction of hydrate below 0.2, the approximate equation gives results that differ by < 6% from the ones given by the general equation. It is thus reasonable to use Eq. (3) instead of Eq. (4) within this limit which corresponds to the degree of hydration at the onset of CRS as found in the experimental results (Fig. 9b). Scherer et al. [37] showed that parameters G and IB depend on the conditions of hydration in terms of temperature and pressure through activation energy ΔE and activation volume ΔV as presented in the following equations (the subscripts G and I belong respectively to the growth rate and nucleation rate):
Fig. 9. Calorimeter tests at 7 °C and rate of axial strain versus hydration degree.
nucleation and growth preferably take place at the boundary of the grain. The Nucleation and Growth (NG) model was thus transformed into the Boundary Nucleation and Growth (BNG) model. In 3D transformation, the transformed volume fraction X is governed by Eq. (3), where OvB is the total area of grain boundaries (randomly distributed) per unit non-transformed volume, IB is the nucleation rate per unit area of non-transformed boundary, G the linear growth rate and t the actual time of the reaction. Note that Eq. (3) is obtained from Eqs. (10) and (14) of Thomas [33] by setting y = Gtx. X=1
exp( 2OvB Gt ) exp 2OvB Gt
1 0
exp
3
IB G 2t 3 (1
3x 2 + 2x 3) dx
(3) The BNG model has been used by several authors [33–36] to describe the cement hydration process by linking the volume fraction of hydrate in cement paste to the parameter X in Eq. (3). Thomas [33] showed that the rate of hydration of alite (C3S) is well described by the BNG model during the acceleration period within a temperature range from 10 °C to 40 °C. At a small degree of hydration (around the setting time), Zhang et al. [26] showed that Eq. (3) can be reduced to the simple expression (4). Note that this expression is obtained by using, in Eq. (3), the approximate relation 1 − exp (−x) ≈ x when x ≪ 1.
X
3
OvB IB G 3t 4
G (T , p )
G0 exp
IB (T , p)
I0 exp
EG + p VG RT EI + p VI RT
(5)
where T and p are respectively the temperature and the pressure during hydration, R is the ideal gas constant, I0 and G0 are two constants. Using Eqs. (4) and (5) the following expression is found for the change in the volume fraction of hydrates versus time at a low degree of hydration:
X
(4)
3
where 33
OvB I0 G03 exp
4
E+p V 4 t RT
(6)
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Fig. 12. Undrained Poisson's ratio versus degree of hydration computed using self-consistent homogenization scheme (class G cement paste with w/c = 0.44).
Assumption (a) is based on the analysis presented in Fig. 11. Assumption (b) is based on the fact that under oedometric conditions (see experiment description in Section 2.2), the radial stress σ3 is linked to axial stress σ1 through σ3 = σ1ν/(1 − ν) where ν is the Poisson's ratio. When the cement slurry is a liquid, the Poisson's ratio is equal to 0.5 and the mean stress is equal to axial stress. With hydration, the Poisson's ratio and the macroscopic volume of the sample decrease, leading to a decrease of the radial stress. The variations of the undrained Poisson's ratio of cement paste can be evaluated using the self-consistent homogenization method developed by (Ulm et al. [38] and Ghabezloo [10]). The results, presented in Fig. 12, show that for values of hydration degrees < 0.2, the value of the undrained Poisson's ratio remains close to 0.5. Hence, within this range, it can reasonably be assumed that the pressure during hydration is equal to the applied axial stress. Assumption (c) is compatible with the results of Kada-Benameur et al. [39] who found that the activation energy is a function of the hydration degree and temperature during hydration, but is constant for hydration degrees in the range of 0.05–0.5. Assumption (d) is compatible with the experimental results presented Fig. 9b. A similar assumption was made by Zhang et al. [26] who found that, for a given w/ c the quantity of hydrates is constant at setting time. Using the assumptions (a), (b) and (c) in Eq. (6), the volume fraction of hydrate is given by the following expression:
Fig. 11. Comparison between (2) and (3) for computation of the volume fraction X of hydrate for Alite: (a) Volume fraction of hydrate X versus time; (b) Time at X = 0.2.
E=
3 EG + EI 4
;
V=
3 VG + VI 4
(7)
The BNG model, as expressed in Eq. (6), was used by Scherer et al. [37] to determine the time threshold for which cement is no more pump-able in oil & gas wells. In the next section, this expression will be used to characterize the time tCRS of the onset of Creation of Residual Strain (CRS).
XCRS
3
OvB I0 G03 exp
4
E+p V 4 tCRS RT
(8)
Assumption (d) allows finding a relation between the values of onset of CRS corresponding to two different conditions of hydration. Hence, we have:
4.2. BNG model for pressure and temperature dependency of tCRS In the range of temperatures and pressures explored in this study, the following assumptions are made to model the onset of CRS using the BNG model:
(9)
XCRS (tCRS (T , p)) = XCRS (tCRS (T0 , p0 )) Eqs. (8) and (9) give:
(a) The volume fraction of hydrate at the onset of CRS can be computed based on Eq. (6). (b) Before reaching the onset of CRS (t < tCRS) the stress state in the cement paste is isotropic. Consequently, during an oedometric test, the pressure in Eq. (6) is approximated by the applied axial stress σ1(p ≈ σ1) (c) For a fixed cement slurry composition, the activation energy ΔE and the activation volume ΔV are constant during the hydration and do not depend on the conditions during hydration. (d) For a fixed cement slurry composition, the volume fraction of hydrate at onset of CRS (XCRS) is independent of the conditions of temperature and pressure during hydration.
tCRS (T , p) = tCRS0 exp
E 1 R T
1 T0
+
V p R T
p0 T0
(10)
where tCRS is the time at the onset of CRS and tCRS0 = tCRS(T0, p0) is the time at the onset of CRS under the conditions of temperature T0 and pressure p0 during hydration. 4.3. Model calibration and validation The parameters of the BNG model, energy and volume of activation, ΔE and ΔV respectively, are evaluated using the experimental results presented in Fig. 8b and Fig. 10b at different conditions of pressure and temperature. At a fixed hydration temperature (T = T0), the pressure 34
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Fig. 14. Comparison between experimentally evaluated values of tCRS and the predictions of Eq. (11) for different temperatures and pressures during hydration. The experiments T10P5 and T30P30 are not used for fitting the parameters of Eq. (12) and show the prediction capacity of BNG model for temperature and pressure dependency of tCRS.
corresponding to the two experiments that have not been used for calibration of the parameters, show an excellent agreement with the other points. At fixed temperature (resp. fixed pressure) during hydration, the critical time for CRS decreases with an increase in pressure (respectively in temperature). In accordance with these results, it can be concluded that, the BNG model gives an excellent estimation of tCRS for cement paste in the range of temperatures and pressures during hydration explored in this study: for temperature between 7 °C and 30 °C and under pressures in the range from 3 MPa to 45 MPa.
Fig. 13. Critical time for CRS versus hydration pressure and temperature respectively at fixed temperature and fixed pressure.
dependency of tCRS is given by Eq. (11)(a). From oedometric tests hydrated at 7 °C, the change in tCRS versus pressure is plotted in Fig. 13a. These results and Eq. (11)(a) give an activation volume equal to ΔV = − 34cm3/mol. At fixed pressure (p = p0) during hydration, tCRS depends on temperature through Eq. (11)(b). The change in tCRS for samples hydrated under 25 MPa versus temperature is plotted in Fig. 13b. Knowing the activation volume, the activation energy is found using Eq. (11)(b), equal to ΔE = 32700 J/mol. It is interesting to note that these values of activation parameters are quite close to those found by Scherer et al. [37] for a class H cement. Indeed, looking for the time at “limit of pumpability”, these authors found ΔV = − 34.40 cm3/mol and ΔE = 33800 J/mol.
ln ln
tCRS (T0 , p) tCRS0
tCRS (T , p0 ) tCRS0
= =
V (p RT0
p0 )
E + p0 V 1 R T
4.4. Application of the Ultrasonic Cement Analyzer (UCA) to determine the critical time for CRS The Ultrasonic Cement Analyzer (UCA) is one of the most used equipment in the petroleum industry, which permits to investigate the development of compressive strength of cement paste during its hydration by continuous measurement of the compression-wave velocity. An empirical relation is used to relate the compressive strength of the cement paste to the measured compression-wave velocity. It is interesting to see if a continuous measurement of wave velocity during hydration can permit to detect the critical time for CRS. Even if the measured quantities in these experiments are different (axial strain in oedometric test and wave velocity in UCA test), they are both measures of the progress of cement hydration, the formation of the solid matrix and the development of the mechanical properties. Two UCA tests were performed at 7 °C, under 0.3 MPa and 25 MPa and the evolutions of the wave velocity with time are presented in Fig. 15a. The rate of wave velocity evolution during hydration versus time is presented in Fig. 15b. In the same figure, the axial strain rates for two oedometric tests performed under the same conditions are presented. The comparison of oedometric and UCA experiments shows a very interesting result: for similar conditions during hydration, the maximum rates of wave velocity and axial strain occur at the same time. This observation shows that it is possible to evaluate the critical time for CRS in an easy way by using the results of UCA tests.
(a) 1 T0
(b)
(11)
With the values of ΔE and ΔV, Eq. (10) is reevaluated and the critical time for CRS is given by Eq. (12) which depends only on conditions (of pressure in MPa and temperature in K) during hydration and where tCRS0 = 20h.
tCRS (T , p) = tCRS0 exp 3938
1 T
1 280
4.142
p T
25 280
(12)
The fitting of ΔE and ΔV is performed using the results of seven oedometric tests. The results of two remaining tests, performed under different conditions of pressure and temperature, can now be used for verification of the predictive capacity of Eq. (12). Fig. 14 gives a comparison between estimated (from Eq. (12)) and experimental values of the critical time for CRS of cement paste. The validation points,
5. Conclusion The onset of the creation of residual strains (CRS) in a cement paste is defined as a threshold beyond which a loading application on a cement paste can result in creation of appreciable plastic strains. This 35
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model is used to model the pressure and temperature dependency of the critical time for CRS. By comparing the results of oedometric tests and UCA tests performed under similar conditions, it was demonstrated that the critical time for CRS corresponds to the maximum rate of wave velocity during UCA test. This result is of great of importance, because contrary to the oedometric equipment used in this study, UCA apparatus is widely available and regularly used in petroleum industry laboratories. List of symbols
1.0
API BNG CCB CRS LVDT UCA ΔE ΔV T σ1 σ3 p Patm R tCRS ξCRS XCRS w/c
35
T7P25a
0.8
25
T7P0.3 U-T7P0.3
0.6
U-T7P25
15
0.4 5
0.2
0.0
Rate of wave velocity (m/s/h)
Rate of axial strain (mm/m/h)
(b)
Acknowledgements The authors gratefully acknowledged Total for supporting this research. They also wish to thank Joselin DE-LA-IGLESIA and Sandrine ANNET-WABLE from TOTAL for performing calorimeter experiments and Nicolas CRUZ from ACEI for his assistance in the testing program.
-5 0
20
40
60
80
100
120
American Petroleum Institute Boundary Nucleation and Growth Compagnie des Ciments Belges Creation of Residual Strain Linear Variable Differential Transformer Ultrasonic Cement Analyzer activation energy (J/mol) activation volume (cm3/mol) temperature (K) total axial stress (MPa) total radial stress (MPa) pressure (MPa) atmospheric pressure (MPa) ideal gas constant (=8.314 J/K/mol) time at the onset of CRS hydration degree at the onset of CRS volume fraction of hydrate at the onset of CRS water to cement mass ratio
140
Time (hours) Fig. 15. (a) Evolution of compressive-wave velocity with time in UCA experiments; (b) comparison of axial strain rates in oedometric tests and wave velocity rates in UCA test.
References [1] L.A. Behrmann, J.L. Li, A. Venkitaraman, H. Li, Borehole dynamics during underbalanced perforating, Soc. Pet. Eng. SPE 38139 (1997) 17–24. [2] M.J. Thiercelin, B. Dargaud, J.F. Baret, W.J. Rodriguez, Cement design based on cement mechanical response, Soc. Pet. Eng. SPE 38598 (1997) 337–348. [3] A.-P. Bois, A. Garnier, F. Rodot, J. Saint-Marc, N. Aimard, How to prevent loss of zonal isolation through a comprehensive analysis of micro-annulus formation, SPE Drill. Complet. (2011) 13–31. [4] A.-P. Bois, A. Garnier, G. Galdiolo, J.-B. Laudet, Use of a mechanistic model to forecast cement-sheath integrity, SPE Drill. Complet. SPE 139668 (2012) 303–314. [5] A. Garnier, J. Saint-Marc, A.-P. Bois, Y. Kermanac'h, A singular methodology to design cement sheath integrity exposed to steam stimulation, SPE Drill. Complet. SPE 117709 (2010) 58–69. [6] A.-P. Bois, M.-H. Vu, S. Ghabezloo, A. Garnier, J.-B. Laudet, Cement sheath integrity for CO2 storage – an integrated perspective, Energy Procedia 37 (2013) 5628–5641. [7] M.H. Vu, Effet des contraintes et de la température sur l'intégrité des ciments des puits pétroliers, Champs sur Marne: Ecole des Ponts ParisTech, (2012), p. 240. [8] S. Ghabezloo, Comportement thermo-poro-mécanique d'un ciment pétrolier, Paris, France (2008). [9] S. Ghabezloo, J. Sulem, J. Saint-Marc, The effect of undrained heating on a fluidsaturated hardened cement paste, Cem. Concr. Res. 39 (2009) 54–64. [10] S. Ghabezloo, Association of macroscopic laboratory testing and micromechanics modelling for the evaluation of the poroelastic parameters of a hardened cement paste, Cem. Concr. Res. 40 (2010) 1197–1210. [11] M.-H. Vu, J. Sulem, J.-B. Laudet, Effect of the curing temperature on the creep of hardened cement paste, Cem. Concr. Res. 42 (2012) 1233–1241. [12] S. Ghabezloo, Micromechanic analysis of thermal expansion and thermal pressurization of a hardened cement paste, Cem. Concr. Res. 41 (5) (2011) 520–532. [13] S. Ghabezloo, J. Sulem, S. Guedon, F. Martineau, J. Saint-Marc, Poromechanical behaviour of hardened cement paste under isotropic loading, Cem. Concr. Res. 38 (12) (2008) 1424–1437. [14] S. Ghabezloo, Effect of the variations of clinker composition on the poroelastic properties of harderned class G cement paste, Cem. Concr. Res. 41 (2011) 920–922. [15] M.-H. Vu, J. Sulem, S. Ghabezloo, J.-B. Laudet, A. Garnier, S. Guédon, Time-dependent behaviour of hardened cement paste under isotropic loading, Cem. Concr. Res. 42 (6) (2012) 789–797.
threshold is noted here by tCRS, the time needed after mixing of the cement slurry to reach the onset of CRS for given hydration conditions. The evaluation of tCRS in this paper is motivated by a particular application in petroleum industry related to the integrity of the cement sheath in oil-wells. However, besides this particular application, this can be important for any structure made from cement-based materials, which is submitted to loading at early age before reaching an advanced degree of hydration. The onset of the creation of residual strains for oilwell cements has been studied experimentally for a class G cement paste with water-to-cement ratio of 0.44 under different conditions during hydration. Cement paste was tested under oedometric conditions at temperature ranging from 7 °C to 30 °C and axial stress from 0.3 MPa to 45 MPa in sealed condition (without additional water during hydration). The results show that there is a critical time after which, mechanical loading cycle applied on cement paste creates plastic strain. It was demonstrated that this critical time for CRS corresponds to the time at maximum rate of axial strain in the oedometric experiments. It was also shown that, when the temperature is fixed, the critical time for CRS decreases with the increase of the pressure during hydration. When the pressure is fixed, the critical time for CRS decreases with the increase of the temperature during hydration. These variations are attributed to the pressure and temperature dependency of cement hydration kinetics. Indeed, the degree of hydration at the critical time for CRS for the performed experiments is found to be almost the same, between 0.18 and 0.20. The Boundary Nucleation and Growth (BNG) 36
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N. Agofack et al. [16] S. Bahafid, S. Ghabezloo, M. Duc, P. Faure, J. Sulem, Effect of the hydration temperature on the microstructure of Class G cement: C-S-H composition and density, Cem. Concr. Res. 95 (2017) 270–281. [17] S. Bahafid, S. Ghabezloo, P. Faure, M. Duc, J. Sulem, Effect of the hydration temperature on the pore structure of cement paste: experimental investigation and micromechanical modelling, Cem. Concr. Res. 111 (2018) 1–14. [18] API-10B-2, Recommended Practice for Testing Well Cementing, 24th edition, American Petroleum Institute, 2012, pp. 1–52. [19] R. Castellanza, R. Nova, Oedometric tests on artificially weathered carbonatic soft rocks, J. Geotech. Geoenviron. 130 (2004) 728–739. [20] S. Ghabezloo, J. Sulem, Stress dependent thermal pressurization of a fluid saturated rock, Rock Mech. Rock. Eng. 42 (2009) 1–24. [21] M. Helinski, A. Fourie, M. Fahey, M. Ismail, Assessment of self-desiccation process in cemented mine backfills, Can. Geotech. J. 44 (2007) 1148–1156. [22] P. Lura, O.M. Jensen, K. v. Breugel, Autogenous shrinkage in high-performance cement paste: an evaluation of basic mechanisms, Cem. Concr. Res. 33 (2003) 223–232. [23] N. Agofack, Comportement des ciments pétroliers au jeune âge et integrite des puits, University Paris Est, Paris, 2015. [24] H. Taylor, Cement Chemistry, Academic Press, London, 1990. [25] E. Gallucci, X. Zhang, K. Scrivener, Influence de la température sur le développement microstructural des bétons, Septième édition des Journées Scientifiques du Regroupement francophone pour la recherche et la formation sur le béton, 2006 Toulouse, France. [26] J. Zhang, E.A. Weissinger, S. Peethamparan, Early hydration and setting of oil well cement, Cem. Concr. Res. 40 (2010) 1023–1033. [27] E.J. Garboczi, D.P. Bentz, The microstructure of Portland cement-based materials: computer simulation and percolation theory “Computational and mathematical
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models of microstructural evolution”, Mater. Res. Soc. Symp. Proc. 529 (1998) 89–100. W.A. Johnson, R.F. Mehl, Reaction kinetics in processes of nucleation and growth, Metals Technology 1089 (1939). M. Avrami, Kinetics of phase change I. General theory, J. Chem. Phys. 7 (1939) 1103–1112. M. Avrami, Kinetics of phase change II. Transformation-time relations for random distribution of nuclei, J. Chem. Phys. 8 (1940) 212–224. M. Avrami, Granulation, phase change, and microstructure. Kinetics of phase change III, J. Chem. Phys. 9 (1941) 177–184. J.W. Cahn, The kinetics of grain boundary nucleated reactions, Acta Metall. 4 (1956) 449–459. J.J. Thomas, A new approach to modeling the nucleation and growth kinetics of tricalciumsilicate hydration, J. Am. Ceram. Soc. 90 (10) (2007) 3282–3288. G. Scherer, J. Zhang, J. Quintanilla, S. Torquato, Hydration and percolation at the setting point, Cem. Concr. Res. 42 (2012) 665–672. S. Garrault, T. Behr, A. Nonat, Formation of the C-S-H layer during early hydration of tricalcium silicate grains with different sizes, J. Phys. Chem. 110 (2006) 270–275. S. Bishnoi, K.J. Scrivener, Studying nucleation and growth kinetics of alite hydration using μic, Cem. Concr. Res. 39 (2009) 849–860. G.W. Scherer, G.P. Funkhouser, S. Peethamparan, Effect of pressure on early hydration of class H and white cement, Cem. Concr. Res. 40 (2010) 845–850. F.-J. Ulm, G. Constantinides, F.H. Heukamp, Is concrete a poromechanics material? - a multiscale investigation of poroelastic properties, Materials and Structures/ Concrete Science and Engineering 37 (2004) 43–58. H. Kada-Benameur, E. Wirquin, B. Duthoit, Determination of apparent activation energy of concrete by isothermal calorimetry, Cem. Concr. Res. 30 (2000) 301–305.
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Onset of Creation of Residual Strain during the hydration of oil-well cement paste
T
Nicolaine Agofacka,b,1, Siavash Ghabezlooa, , Jean Sulema, André Garnierb, Christophe Urbanczykb ⁎
a b
Laboratoire Navier, Ecole des Ponts ParisTech, Ifsttar, CNRS UMR 8205, Marne la Vallée, France TOTAL, Exploration & Production, CSTJF, Pau, France
ARTICLE INFO
ABSTRACT
Keywords: Cement hydration Temperature Pressure Cement-sheath integrity Irreversible deformation Boundary Nucleation and Growth (BNG) model
In this paper, the Creation of Residual Strain during the hydration of cement paste is studied by performing oedometric experiments on class G cement pastes during the six first days of hydration. Various conditions of temperature (between 7 and 30 °C) and pressure (between 0.3 and 45 MPa) are explored. It is found that after a hydration degree of about 18%, mechanical loadings can induce residual strain. This state is reached at a time called critical time for Creation of Residual Strain (CRS). It corresponds to the maximum axial strain rate in an oedometric test or to the maximum rate of wave-velocity evolution versus time recorded in a Ultrasonic Cement Analyzer (UCA) test. The Boundary Nucleation and Growth (BNG) model is used to estimate the critical time for CRS. Within the range of studied temperatures and pressures, the predictive capacity of the BNG model for estimation of the critical time for CRS is demonstrated.
1. Introduction When drilling oil & gas wells, a mud is used to support the walls of the geological formation, to maintain wellbore stability, to cool the drill bit, to carry out the cuttings, to control formation pressure, and to seal permeable formations. A tubular is then run in the well and cement slurry is pumped between the tubular and the hole. Time is given for the cement slurry to harden to become a cement sheath. The role of this cement sheath is to provide zonal isolation of different fluids along the well, to protect the tubular against corrosion and to provide mechanical support. The loss of cement-sheath integrity can result in the pressurization of annulus, in gas migration up to a shallower formation or to the surface, and, in catastrophic cases, in a blowout and in the total damage of the infrastructure. During the life of a well, from drilling to completion, production and P&A (plug and abandonment), the cement sheath is submitted to various mechanical and thermal loadings that can potentially damage the cement sheath and alter its performance. Some of these loadings may occur at very early age, when the mechanical properties of the cement sheath are not yet sufficiently developed. This is for example the case during a casing test, which is performed to check the integrity of the well. The applied pressure during a casing test can vary from a few tens of MPa in normally
pressurized reservoirs to > 100 MPa in high pressure reservoirs. The drilling operation in oil and gas wells results in application of loading on previously completed sections at shallower depths, which can excess 40 MPa [1,2]. It is often questioned what is the most suitable moment to perform such a test and to apply loads on the cement sheath. Waiting too long after bumping the plug could result in loading a slurry that is no more a liquid and not yet a strong porous solid. It could induce significant residual strains in the cement and this could lead to the formation of a micro-annulus or to cement damage later in the life of the well [3–6]. With the progress of hydration, cement develops its stiffness and strength and can be able to support external stress cycles, in the limits of usual loading magnitudes in an oil-well, without significant residual strain. Hence, the knowledge of the time interval in which the application of a loading cycle can potentially result in creation of significant residual, i.e. plastic, strains is of major importance to avoid a loss of integrity during life well cycle. We should therefore define and characterize a threshold beyond which a loading application can potentially result in the formation of appreciable plastic strains. This threshold is called here the onset of Creation of Residual Strains (CRS) and is noted by tCRS, which is the time needed after mixing of the cement slurry to reach the onset of CRS for given hydration conditions. Besides the above-mentioned application in petroleum
Corresponding author. E-mail address: [email protected] (S. Ghabezloo). 1 Currently at Norwegian University of Science and Technology (NTNU), Trondheim, Norway. ⁎
https://doi.org/10.1016/j.cemconres.2018.10.022 Received 22 March 2018; Received in revised form 19 September 2018; Accepted 22 October 2018 0008-8846/ © 2018 Elsevier Ltd. All rights reserved.
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industry, the knowledge of tCRS can be important for any structure made from cement-based materials, which is submitted to loading at early age before reaching an advanced degree of hydration. The purpose of this work is to determine the tCRS by measuring the deformations of a cement paste sample hydrated in sealed conditions in a specially designed oedometric cell. Application of loading/unloading cycles during hydration at early age (< 6 days) permits the detection of the time after which significant plastic strains can be produced. A temperature of 7 °C is chosen to slow down the rate of cement hydration [7]. Once the critical time for CRS is found, its dependence on the pressure and temperature during hydration is analyzed by performing oedometric tests on cement paste hydrated at temperatures ranging from 7 °C to 30 °C and under an axial stress ranging from 0.3 MPa to 45 MPa. The Boundary Nucleation and Growth model is used to model the pressure and temperature dependency of critical time for CRS. Ultrasonic Cement Analyzer (UCA), one of the most popular equipment in the petroleum industry, was also used to determine the critical time for CRS.
emphasized that the aim of this paper is to evaluate the onset of creation of plastic strains in a cement paste due to the application of a mechanical loading. It is evident that the creation of plastic strains and their magnitude depends on various factors such as the initial state of stress, the magnitude of the applied loading and the material yield surface. However, during the fluid-solid transition there is a time after which the application of a loading cycle, for example in a casing test, can potentially result is creation of plastic strains. To evaluate this time and to overcome the influence of the other factors (e.g., loading magnitude) the loading cycles are applied with a quite significant change in the stress state in the range between 5 MPa and 65 MPa as presented in Table 1. This is certainly beyond the elasticity limit of the studied cement paste as can be seen from the results of triaxial compression experiments performed on a hardened class G cement paste (Ghabezloo [8]; Ghabezloo et al. [9]).
2. Experimental program
All tests were performed on a slurry made of CEMOIL class G cement from CCB. The slurry is the same as the one used in our previous studies for which various mechanical, hydraulic, thermal and time dependent properties have been investigated and presented in [9–17]. The chemical composition of cement, as provided by the supplier, is presented in Table 2 and is in accordance with the American Petroleum Institute (API) 10A requirements for class G cements [18] (section §4.1.2). The cement slurry presented in Table 3 is composed of class G cement powder, distilled and deaerated water with w/c = 0.44, and three additive agents (anti-foaming, dispersing and anti-settling). The mixing procedure starts with pouring distilled and deaerated water into the mixing container. The dry anti-settling agent is added to the water and the motor is turned on and maintained to 4000 ± 200 rotations per minutes during 5 min. Then the liquid anti-foaming and dispersing agents (poured before cement) and the cement powder are put successively into the container in 20 ± 5 s (according to API 10B-2
2.1. Cement slurry preparation
In order to determine the critical time for CRS (tCRS) due to the mechanical loading, oedometric tests with loading-unloading cycles were performed on hydrating cement paste. The effects of temperature and pressure during hydration on this critical time were studied by running experiments under various conditions. The oedometric tests were performed in undrained conditions using an apparatus specially designed by TOTAL. It was looked also for an alternative method to evaluate the onset of CRS that would use a more widely-available equipment. This was done by comparing the results of oedometric tests with those of Ultrasonic Cement Analyzer (UCA) tests performed in the similar conditions of pressure and temperature. Seventeen oedometric tests, four calorimeter tests and two UCA tests were run and are presented in this study. These tests are classified and presented in Table 1 by categories according to their principal purpose. It should be Table 1 Summary of tests performed in this study. Category
Tests
C1
T7P25a T7P25b T7P25a T7P25-15 T7P25-18 T7P25-20 T7P25-60 T7P25-103 T7P45 T7P45–15
C2
C3 C4
C5 C6 C7
C8
Hydration temperature (°C)
T7P45 T7P25a T7P15 T7P10 T7P3 T7P25a T15P25 T22P25 T10P5 T30P30 C-T7Patm C-T7P25 C-T7P45 C-T30P30 T7P25a U-T7P25 T7P0.3 U-T7P0.3
Hydration pressure (MPa)
Time of first mechanical loading (hours)
Mechanical loading path 0
Purpose of the test
7
25
N/A
7
25
7
45
N/A 15 18 20 60 103 N/A 15
7
45 25 15 10 3 25
N/A
5 65 5 5 45 MPa (see Fig. 4(b)) 0
N/A
0
Effect of temperature on onset of CRS
5 30 Patm 25 45 30 25
N/A
0
Validation of model
N/A
0
Estimation of the degree of hydration
N/A
0
Comparison of the rate of axial strain in oedometric tests with the rate of compression-wave velocity in UCA tests
7 15 22 10 30 7 30 7
25 MPa
65
45 MPa
65
5 65 5 5 25 MPa (see Fig. 4(a))
0.3
“N/A” means “no application”. 28
Repeatability on oedometric tests Creation of Residual Strain in cement paste
Effect of pressure on onset of CRS
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external diameter and 125 mm height) made of steel. Within its elastic domain, the hollow cylinder can support a maximum pressure of 123 MPa applied on its inner surface. The hollow cylinder is surrounded by a cooling/heating system whereby cold/hot fluid is circulated through small-diameter tubing. The tubing is connected to a cryostat that contains a fluid at a controlled temperature. A LVDT sensor ( ± 10 mm) with high precision ( ± 0.2%) is used to measure the displacement of the sample. The LVDT is fixed on the lower header and points at the upper one. The hollow cylinder is not fixed on the lower platen in order to reduce the effects of friction between the sample and the hollow cylinder, according to [19], hence ensuring that the displacements measured by the LVDT only correspond to the displacements that exist in the cement sample. The oedometric cell is cooled/ heated to the test temperature before preparing the slurry. For oedometric tests, the slurry is mixed, poured into the cell which is cooled or heated at the test temperature. The cement slurry is put in the oedometric cell, (50.3 mm in diameter and 85 mm in height). The mass of cement slurry put in the oedometric cell is 322 ± 3 g and all tests are performed without additional water during hydration. The cell is placed under the axial frame (block A in Fig. 1a) and axial stress is applied on the slurry. The test starts 5 min after mixing (API recommendation for thickening-time tests [18] (section §10)). The displacement obtained from the LVDT is initialized when the test temperature and axial stress are reached.
Table 2 Chemical composition of class G cement with Blaine = 323 m2/kg. Chemical composition
Measurements
Magnesium oxide (MgO) % Sulfurtrioxide (SO3) % Loss on ignition % Insoluble residue % C3A % C4AF + 2 C3A % C3S % (0.658 × K2O) + Na2O %
Table 3 Composition of 600 ml of sity = 1900 ± 10 kg/m3).
API Spec 10A requirements
1.8 2.5 0.6 0.1 2.1 17.4 58.9 0.55
cement
Max 6.0 Max 3.0 Max 3.0 Max 0.75 Max 3.0 Max 24.0 Min 48.0 - Max 65.0 Max 0.75
slurry
(w/c = 0.44;
Component
Mass (grams)
Cement (class G) Water (distilled and deaerated) Anti foaming (D047)a Dispersing agent (D604AM)a Anti-settling (D153)a a
den-
783.53 339.54 6.27 9.47 1.18
Commercial identification.
[18], cement powder shall be added in 15 s). The speed is immediately increased to about 12,000 ± 500 rotations per minute and mixing ends after 35 ± 1 s.
3. Experimental results and analysis 3.1. Reliability and repeatability of the experiments
2.2. Experimental device
In order to calibrate the system presented in Fig. 1b, distilled water at ambient temperature was put into the oedometric cell and submitted to mechanical loading cycles (Fig. 2a). The slope of the axial stress – axial strain curve presented in Fig. 2b, gives a bulk modulus Kf of water equal to 2.1 GPa. This value is very close to the compression modulus of pure water at ambient temperature and shows the reliability of the experiment. To verify the repeatability of the experiments, two oedometric tests were performed at 7 °C and under a constant axial stress of 25 MPa. The results, presented in Fig. 3, show that the system gives an excellent repeatability. The axial strain presented in Fig. 3a is due to the macroscopic shrinkage of the cement paste during its hydration under pressure. The rate of the axial strain is presented in Fig. 3b showing that both curves present a maximum near 20 h and a very good repeatability between the two experiments. The rate of the axial strain is evaluated by linear regression method, using the method presented in Ghabezloo and Sulem [20].
The experimental device is shown in Fig. 1. The general system (Fig. 1a) is composed of six elements identified by letters A to F. For the oedometric test, only compounds A, D and F are used. The compounds B, C and E are used for triaxial tests. Block A represents the axial frame, able to apply 650kN through an electromechanical ram. Block D includes six movidrives to control the electromechanical rams. F is the data acquisition center. In Fig. 1b, one can see the oedometric cell composed of a hollow cylinder (50.3 mm internal diameter, 90 mm
3.2. Apparition of additional residual strain due to mechanical loading Oedometric tests were performed on cement paste during hydration at 7 °C and under 25 MPa and 45 MPa. This relatively low temperature was chosen to slow down the kinetics of cement hydration, as shown by Vu [7] using UCA experiments. Some experiments include mechanical unloading/loading cycles at predefined times according to the loading paths presented in Fig. 4. The mechanical paths of Fig. 4a and Fig. 4b were applied on cement samples hydrating respectively under 25 MPa and 45 MPa. As mentioned before, the loading cycles are applied with quite a significant change in the stress level to ensure that the onset of creation of residual strains can be detected in the experiment. For the test T7P25a in Fig. 3a, the axial stress-strain response during the loading/unloading cycle at 144 h of hydration is presented in Fig. 5. One can see that the limit of elasticity is about 36 MPa confirming that the magnitude of applied loading (5 to 65 MPa) is sufficiently high to detect the apparition of plastic strains in the performed experiments. Six tests were performed under 25 MPa. For the test T7P25a presented in Fig. 3, considered as the reference test under these conditions, the
Fig. 1. Uniaxial strain (oedometric) cell. 29
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Fig. 3. Repeatability of oedometric test: (a) development of axial strain with time; (b) rate of axial strain versus time.
Fig. 2. Measure of bulk modulus of distilled water at 22 °C: (a) loading path with loading rate of 3 MPa/min; (b) axial strain-stress curve.
maximum strain rate (at 15 h and 18 h) creates only small additional axial strains, while a loading cycle at the peak of strain rate (at 20 h) results in a sudden increase in the measured residual strain. According to these observations, for hydration at 7 °C and under 25 MPa, and the loading path given in Fig. 4a cycling at and after 20 h creates additional residual strain in the cement paste. To verify this result, two oedometric tests were performed under the same temperature 7 °C, but at a higher pressure of 45 MPa (Fig. 7). The test T7P45 is considered as the reference test as no loading cycle was applied (Fig. 7a). The maximum strain rate in this test, is reached after 15 h (Fig. 7b). In order to analyze the creation of additional strain, a loading cycle was applied at 15 h during the test T7P45-15 (Fig. 4b). As can be seen in Fig. 7a, additional residual strain was created due to this cycling. This confirms that, from the time of the maximum rate of axial strain, application of a mechanical loading cycle on cement paste can create additional residual strain. After mixing cement and water, the slurry behaves like a fluid with suspended particles, without any mechanical strength. Before setting, the external axial strain is entirely related to the chemical shrinkage during hydration (Helinski et al. [21]; Lura et al. [22]). With the progress of the hydration, the cement paste develops its stiffness and mechanical strength and therefore the chemical shrinkage is no longer entirely transformed to an external strain. It results in a decrease of the strain rate as can be seen in the presented experimental results.
axial stress was kept constant at 25 MPa during the 144 h of hydration. Applying the loading/unloading cycles of Fig. 4a allows, to evaluate the influence of a mechanical cycle on the behavior of the cement paste and the creation of the residual strain by comparison with the reference test with no loading/unloading cycle,. The times at which the cycle was performed was chosen based on the observed rate of axial strain in the reference test presented in Fig. 3b for which the maximum is reached at around 20 h. Accordingly, the cycle was performed at 15 h, 18 h, 20 h, 60 h and 103 h in different tests in order to explore the influence of a loading cycle before, near and after the time corresponding to the maximum strain rate. The loading cycles were applied with a rate of 3 MPa/min and the evolution of the hydration degree during the cycle is assumed to be negligible. The evolution of the axial strain with time for different tests is presented in Fig. 6a. It shows that cycling induces additional strains as the curves are identical before 15 h and present a shift after this time when compared with the reference test T7P25a. The curves corresponding to a cycle performed at 15 h or 18 h remain quite close to the reference curve, while cycling at later times creates a clear shift of the strain curve as compared to the reference case. The calculated additional strain at 120 h of hydration (Fig. 6a) is presented in Fig. 6b as a function of the time at which the loading cycle was applied. In the same figure, strain rate in the reference test is also presented. One can see that the additional strain increases with the time at which the cycle was performed. The application of a loading cycle before the 30
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Fig. 4. Stress path of the loading/unloading cycles (loading rate: 3 MPa/min).
Fig. 6. Oedometric tests at 7 °C and 25 MPa: (a) axial strain versus time; (b) additional strain due to the mechanical cycling versus the cycling time. The rate of strain in the reference test (no loading cycle) is also presented.
formation of the solid structure in the cement paste. This can be attributed to the acceleration of the hydration kinetics related to the increase of the pressure [7]. For a more detailed investigation of this effect, it is interesting to evaluate the degree of hydration of cement paste at the onset of CRS. This is done by performing three calorimeter tests at 7 °C, under atmospheric pressure, 25 and 45 MPa. Calorimeter data provide the cumulative heat of hydration Q(t) released until a given time t. The degree of hydration can be evaluated through the following equation:
Fig. 5. Axial stress-strain curve for mechanical loading cycle at 144 h of hydration.
(t ) =
Q (t ) Q T_ CP
(1)
where QT_CP is the total cumulative heat released at complete hydration, which can be estimated when the composition of the cement paste is known (detailed calculation can be found in [7,23]). The results calorimeter tests are presented in Fig. 9a in terms of the degree of hydration as a function time. These results permit to plot the variations of the axial strain rate versus hydration degree for the oedometric tests performed under the same pressure and temperature conditions (Fig. 9b). The results show that the maximum strain rate for different pressures is reached at hydration degrees which are very close together, between 0.18 and 0.22. This indicates that the critical degree of hydration for CRS is almost independent of the pressure during hydration and the observed variations of the tCRS is mostly due to the pressure dependency of cement hydration kinetics. To investigate the effect of temperature on the critical time tCRS, three samples were cured in oedometric conditions under a constant pressure (25 MPa) and at different
Accordingly, the time at which the effect of this phenomenon becomes significant corresponds to the peak of the axial strain rate in the performed experiments. 3.3. Effect of pressure and temperature during hydration on tCRS In order to analyze the influence of pressure during hydration on tCRS, five samples were cured in oedometric conditions at 7 °C and under different axial stresses (3, 10, 15, 25 and 45 MPa). No further loading cycle was applied during these experiments. The measured strain rate and the variation of tCRS (defined as the time at the maximum rate of axial strain), with pressure are plotted in Fig. 8. The results show that tCRS decreases with the increase in pressure during hydration. In other words, increasing the pressure during hydration accelerates the 31
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Fig. 8. (a) Axial strain rate for oedometric experiments performed at 7 °C and under different axial stresses; (b) variation of tCRS with temperature.
Fig. 7. Test at 7 °C and under 45 MPa: (a) reference test and additional residual strain due to mechanical loading at 15 h; (b) rate of the axial strain (maximum at 15 h).
the literature [26,27], the solid structure of the cement paste is still quite weak. Any damage or irreversible strain created at this time by mechanical loading is then healed quickly with subsequent hydration. At CRS time, contrariwise, the solid structure is enough developed and the damage or irreversible strain created from this time is no more completely healed with later hydration, and remains permanently.
temperature during hydration (7, 15 and 22 °C). The samples were not submitted to any mechanical loading cycle during the 6 days of hydration. The axial strain rates and the variations of tCRS with temperature are plotted in Fig. 10. As expected, tCRS decreases with the increase in hydration temperature. This is in agreement with the fact that hydration of cement paste is accelerated by an increase of the temperature during hydration [7,24,25]. Similar to the pressure dependency of tCRS mentioned above, its temperature dependency is due to the temperature dependency of cement hydration kinetics. This is verified by the experiment performed at 30 °C and 30 MPa, and presented in Fig. 9b. It shows that the maximum rate of axial strain is reached at the degree of hydration of 0.20 which is compatible with the above mentioned range of degree of hydration at tCRS. The critical time for creation of residual strains is found to happen at degree of hydration around 0.18 and 0.22. This value is higher than what is mentioned in the literature for the initial setting of cement paste. Using Vicat needle method, Zhang et al. [26] found values between 0.028 and 0.043 for the degree of hydration at the setting-time for class H cement with water-to-cement ratio ranging from 0.25 to 0.40. Garboczi and Bentz [27] also mentioned that cement paste sets at a low degree of hydration (0.02 to 0.08). This means that the critical time for CRS is reached after the initial setting of the cement paste. This can be explained by the fact that, at the setting time usually reported in
4. Modeling of critical time for creation of residual strains 4.1. Boundary Nucleation and Growth (BNG) model Several models have been proposed to describe cement hydration, among which one of the most popular is the Boundary Nucleation and Growth (BNG) model. This model was first proposed in 1939 by Johnson and Mehl [28] and developed by Avrami [29–31] as the Nucleation and Growth (NG) model. Its initial purpose was to describe recrystallization of pure metals and freezing liquids under isothermal condition, without any concentration variation. This transformation is described as random nucleation and random growth within the transforming material. The development of the transformed fraction of material X is given by Eq. (2), where B relates to the transformation properties (rate of nucleation and rate of growth) and k characterizes the dimension of transformation (1D, 2D or 3D).
X=1
exp( Bt k )
(2)
In 1956, Cahn [32] postulated that, in some transformations, 32
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Fig. 10. (a) Axial strain rate for oedometric experiments performed under 25 MPa with different temperatures; (b) variation of tCRS with temperature.
Using the values of parameters OvB, IB and G found by Thomas [33] for hydration of alite (C3S), it is possible to compare the results from Eqs. (3) and (4). As presented in Fig. 11, for a volume fraction of hydrate below 0.2, the approximate equation gives results that differ by < 6% from the ones given by the general equation. It is thus reasonable to use Eq. (3) instead of Eq. (4) within this limit which corresponds to the degree of hydration at the onset of CRS as found in the experimental results (Fig. 9b). Scherer et al. [37] showed that parameters G and IB depend on the conditions of hydration in terms of temperature and pressure through activation energy ΔE and activation volume ΔV as presented in the following equations (the subscripts G and I belong respectively to the growth rate and nucleation rate):
Fig. 9. Calorimeter tests at 7 °C and rate of axial strain versus hydration degree.
nucleation and growth preferably take place at the boundary of the grain. The Nucleation and Growth (NG) model was thus transformed into the Boundary Nucleation and Growth (BNG) model. In 3D transformation, the transformed volume fraction X is governed by Eq. (3), where OvB is the total area of grain boundaries (randomly distributed) per unit non-transformed volume, IB is the nucleation rate per unit area of non-transformed boundary, G the linear growth rate and t the actual time of the reaction. Note that Eq. (3) is obtained from Eqs. (10) and (14) of Thomas [33] by setting y = Gtx. X=1
exp( 2OvB Gt ) exp 2OvB Gt
1 0
exp
3
IB G 2t 3 (1
3x 2 + 2x 3) dx
(3) The BNG model has been used by several authors [33–36] to describe the cement hydration process by linking the volume fraction of hydrate in cement paste to the parameter X in Eq. (3). Thomas [33] showed that the rate of hydration of alite (C3S) is well described by the BNG model during the acceleration period within a temperature range from 10 °C to 40 °C. At a small degree of hydration (around the setting time), Zhang et al. [26] showed that Eq. (3) can be reduced to the simple expression (4). Note that this expression is obtained by using, in Eq. (3), the approximate relation 1 − exp (−x) ≈ x when x ≪ 1.
X
3
OvB IB G 3t 4
G (T , p )
G0 exp
IB (T , p)
I0 exp
EG + p VG RT EI + p VI RT
(5)
where T and p are respectively the temperature and the pressure during hydration, R is the ideal gas constant, I0 and G0 are two constants. Using Eqs. (4) and (5) the following expression is found for the change in the volume fraction of hydrates versus time at a low degree of hydration:
X
(4)
3
where 33
OvB I0 G03 exp
4
E+p V 4 t RT
(6)
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Fig. 12. Undrained Poisson's ratio versus degree of hydration computed using self-consistent homogenization scheme (class G cement paste with w/c = 0.44).
Assumption (a) is based on the analysis presented in Fig. 11. Assumption (b) is based on the fact that under oedometric conditions (see experiment description in Section 2.2), the radial stress σ3 is linked to axial stress σ1 through σ3 = σ1ν/(1 − ν) where ν is the Poisson's ratio. When the cement slurry is a liquid, the Poisson's ratio is equal to 0.5 and the mean stress is equal to axial stress. With hydration, the Poisson's ratio and the macroscopic volume of the sample decrease, leading to a decrease of the radial stress. The variations of the undrained Poisson's ratio of cement paste can be evaluated using the self-consistent homogenization method developed by (Ulm et al. [38] and Ghabezloo [10]). The results, presented in Fig. 12, show that for values of hydration degrees < 0.2, the value of the undrained Poisson's ratio remains close to 0.5. Hence, within this range, it can reasonably be assumed that the pressure during hydration is equal to the applied axial stress. Assumption (c) is compatible with the results of Kada-Benameur et al. [39] who found that the activation energy is a function of the hydration degree and temperature during hydration, but is constant for hydration degrees in the range of 0.05–0.5. Assumption (d) is compatible with the experimental results presented Fig. 9b. A similar assumption was made by Zhang et al. [26] who found that, for a given w/ c the quantity of hydrates is constant at setting time. Using the assumptions (a), (b) and (c) in Eq. (6), the volume fraction of hydrate is given by the following expression:
Fig. 11. Comparison between (2) and (3) for computation of the volume fraction X of hydrate for Alite: (a) Volume fraction of hydrate X versus time; (b) Time at X = 0.2.
E=
3 EG + EI 4
;
V=
3 VG + VI 4
(7)
The BNG model, as expressed in Eq. (6), was used by Scherer et al. [37] to determine the time threshold for which cement is no more pump-able in oil & gas wells. In the next section, this expression will be used to characterize the time tCRS of the onset of Creation of Residual Strain (CRS).
XCRS
3
OvB I0 G03 exp
4
E+p V 4 tCRS RT
(8)
Assumption (d) allows finding a relation between the values of onset of CRS corresponding to two different conditions of hydration. Hence, we have:
4.2. BNG model for pressure and temperature dependency of tCRS In the range of temperatures and pressures explored in this study, the following assumptions are made to model the onset of CRS using the BNG model:
(9)
XCRS (tCRS (T , p)) = XCRS (tCRS (T0 , p0 )) Eqs. (8) and (9) give:
(a) The volume fraction of hydrate at the onset of CRS can be computed based on Eq. (6). (b) Before reaching the onset of CRS (t < tCRS) the stress state in the cement paste is isotropic. Consequently, during an oedometric test, the pressure in Eq. (6) is approximated by the applied axial stress σ1(p ≈ σ1) (c) For a fixed cement slurry composition, the activation energy ΔE and the activation volume ΔV are constant during the hydration and do not depend on the conditions during hydration. (d) For a fixed cement slurry composition, the volume fraction of hydrate at onset of CRS (XCRS) is independent of the conditions of temperature and pressure during hydration.
tCRS (T , p) = tCRS0 exp
E 1 R T
1 T0
+
V p R T
p0 T0
(10)
where tCRS is the time at the onset of CRS and tCRS0 = tCRS(T0, p0) is the time at the onset of CRS under the conditions of temperature T0 and pressure p0 during hydration. 4.3. Model calibration and validation The parameters of the BNG model, energy and volume of activation, ΔE and ΔV respectively, are evaluated using the experimental results presented in Fig. 8b and Fig. 10b at different conditions of pressure and temperature. At a fixed hydration temperature (T = T0), the pressure 34
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Fig. 14. Comparison between experimentally evaluated values of tCRS and the predictions of Eq. (11) for different temperatures and pressures during hydration. The experiments T10P5 and T30P30 are not used for fitting the parameters of Eq. (12) and show the prediction capacity of BNG model for temperature and pressure dependency of tCRS.
corresponding to the two experiments that have not been used for calibration of the parameters, show an excellent agreement with the other points. At fixed temperature (resp. fixed pressure) during hydration, the critical time for CRS decreases with an increase in pressure (respectively in temperature). In accordance with these results, it can be concluded that, the BNG model gives an excellent estimation of tCRS for cement paste in the range of temperatures and pressures during hydration explored in this study: for temperature between 7 °C and 30 °C and under pressures in the range from 3 MPa to 45 MPa.
Fig. 13. Critical time for CRS versus hydration pressure and temperature respectively at fixed temperature and fixed pressure.
dependency of tCRS is given by Eq. (11)(a). From oedometric tests hydrated at 7 °C, the change in tCRS versus pressure is plotted in Fig. 13a. These results and Eq. (11)(a) give an activation volume equal to ΔV = − 34cm3/mol. At fixed pressure (p = p0) during hydration, tCRS depends on temperature through Eq. (11)(b). The change in tCRS for samples hydrated under 25 MPa versus temperature is plotted in Fig. 13b. Knowing the activation volume, the activation energy is found using Eq. (11)(b), equal to ΔE = 32700 J/mol. It is interesting to note that these values of activation parameters are quite close to those found by Scherer et al. [37] for a class H cement. Indeed, looking for the time at “limit of pumpability”, these authors found ΔV = − 34.40 cm3/mol and ΔE = 33800 J/mol.
ln ln
tCRS (T0 , p) tCRS0
tCRS (T , p0 ) tCRS0
= =
V (p RT0
p0 )
E + p0 V 1 R T
4.4. Application of the Ultrasonic Cement Analyzer (UCA) to determine the critical time for CRS The Ultrasonic Cement Analyzer (UCA) is one of the most used equipment in the petroleum industry, which permits to investigate the development of compressive strength of cement paste during its hydration by continuous measurement of the compression-wave velocity. An empirical relation is used to relate the compressive strength of the cement paste to the measured compression-wave velocity. It is interesting to see if a continuous measurement of wave velocity during hydration can permit to detect the critical time for CRS. Even if the measured quantities in these experiments are different (axial strain in oedometric test and wave velocity in UCA test), they are both measures of the progress of cement hydration, the formation of the solid matrix and the development of the mechanical properties. Two UCA tests were performed at 7 °C, under 0.3 MPa and 25 MPa and the evolutions of the wave velocity with time are presented in Fig. 15a. The rate of wave velocity evolution during hydration versus time is presented in Fig. 15b. In the same figure, the axial strain rates for two oedometric tests performed under the same conditions are presented. The comparison of oedometric and UCA experiments shows a very interesting result: for similar conditions during hydration, the maximum rates of wave velocity and axial strain occur at the same time. This observation shows that it is possible to evaluate the critical time for CRS in an easy way by using the results of UCA tests.
(a) 1 T0
(b)
(11)
With the values of ΔE and ΔV, Eq. (10) is reevaluated and the critical time for CRS is given by Eq. (12) which depends only on conditions (of pressure in MPa and temperature in K) during hydration and where tCRS0 = 20h.
tCRS (T , p) = tCRS0 exp 3938
1 T
1 280
4.142
p T
25 280
(12)
The fitting of ΔE and ΔV is performed using the results of seven oedometric tests. The results of two remaining tests, performed under different conditions of pressure and temperature, can now be used for verification of the predictive capacity of Eq. (12). Fig. 14 gives a comparison between estimated (from Eq. (12)) and experimental values of the critical time for CRS of cement paste. The validation points,
5. Conclusion The onset of the creation of residual strains (CRS) in a cement paste is defined as a threshold beyond which a loading application on a cement paste can result in creation of appreciable plastic strains. This 35
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model is used to model the pressure and temperature dependency of the critical time for CRS. By comparing the results of oedometric tests and UCA tests performed under similar conditions, it was demonstrated that the critical time for CRS corresponds to the maximum rate of wave velocity during UCA test. This result is of great of importance, because contrary to the oedometric equipment used in this study, UCA apparatus is widely available and regularly used in petroleum industry laboratories. List of symbols
1.0
API BNG CCB CRS LVDT UCA ΔE ΔV T σ1 σ3 p Patm R tCRS ξCRS XCRS w/c
35
T7P25a
0.8
25
T7P0.3 U-T7P0.3
0.6
U-T7P25
15
0.4 5
0.2
0.0
Rate of wave velocity (m/s/h)
Rate of axial strain (mm/m/h)
(b)
Acknowledgements The authors gratefully acknowledged Total for supporting this research. They also wish to thank Joselin DE-LA-IGLESIA and Sandrine ANNET-WABLE from TOTAL for performing calorimeter experiments and Nicolas CRUZ from ACEI for his assistance in the testing program.
-5 0
20
40
60
80
100
120
American Petroleum Institute Boundary Nucleation and Growth Compagnie des Ciments Belges Creation of Residual Strain Linear Variable Differential Transformer Ultrasonic Cement Analyzer activation energy (J/mol) activation volume (cm3/mol) temperature (K) total axial stress (MPa) total radial stress (MPa) pressure (MPa) atmospheric pressure (MPa) ideal gas constant (=8.314 J/K/mol) time at the onset of CRS hydration degree at the onset of CRS volume fraction of hydrate at the onset of CRS water to cement mass ratio
140
Time (hours) Fig. 15. (a) Evolution of compressive-wave velocity with time in UCA experiments; (b) comparison of axial strain rates in oedometric tests and wave velocity rates in UCA test.
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threshold is noted here by tCRS, the time needed after mixing of the cement slurry to reach the onset of CRS for given hydration conditions. The evaluation of tCRS in this paper is motivated by a particular application in petroleum industry related to the integrity of the cement sheath in oil-wells. However, besides this particular application, this can be important for any structure made from cement-based materials, which is submitted to loading at early age before reaching an advanced degree of hydration. The onset of the creation of residual strains for oilwell cements has been studied experimentally for a class G cement paste with water-to-cement ratio of 0.44 under different conditions during hydration. Cement paste was tested under oedometric conditions at temperature ranging from 7 °C to 30 °C and axial stress from 0.3 MPa to 45 MPa in sealed condition (without additional water during hydration). The results show that there is a critical time after which, mechanical loading cycle applied on cement paste creates plastic strain. It was demonstrated that this critical time for CRS corresponds to the time at maximum rate of axial strain in the oedometric experiments. It was also shown that, when the temperature is fixed, the critical time for CRS decreases with the increase of the pressure during hydration. When the pressure is fixed, the critical time for CRS decreases with the increase of the temperature during hydration. These variations are attributed to the pressure and temperature dependency of cement hydration kinetics. Indeed, the degree of hydration at the critical time for CRS for the performed experiments is found to be almost the same, between 0.18 and 0.20. The Boundary Nucleation and Growth (BNG) 36
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