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Hydration kinetics modeling of the effect of curing temperature and pressure on the heat evolution of oil well cement
Cement and Concrete Research 54 (2013) 69–76
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Hydration kinetics modeling of the effect of curing temperature and pressure on the heat evolution of oil well cement Xueyu Pang ⁎, Walmy Cuello Jimenez, Benjamin J. Iverson Halliburton, 3000 N Sam Houston Pkwy E, Houston, TX 77032, USA
a r t i c l e
i n f o
Article history: Received 1 April 2013 Accepted 26 August 2013 Keywords: Hydration (A) Kinetics (A) Temperature (A) Modeling (E) Oil well cement (E)
a b s t r a c t The heat evolution of Class G and Class H oil well cements cured under different temperatures (25 °C to 60 °C) and pressures (2 MPa to 45 MPa) was examined by isothermal calorimetry. Curing pressure was found to have a similar effect on cement hydration kinetics as curing temperature. Under isothermal and isobaric conditions, the dependency of cement hydration kinetics on curing temperature and pressure can be modeled by a scale factor which is related to the activation energy and the activation volume of the cement. The estimated apparent activation energy of the different cements at 2 MPa varies from 38.7 kJ/mol to 41.4 kJ/mol for the temperature range of 25 °C to 40 °C, which decreases slightly with increasing curing temperature and pressure. The estimated apparent activation volume of the cements at 25 °C varies from −23.1 cm3/mol to −25.9 cm3/mol for the pressure range studied here, which also decreases slightly in magnitude with increasing curing temperature. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Cementing is one of the most important procedures during oil or gas well construction, the purpose of which is to create a cement sheath in the annulus between the steel casing and the wellbore. Its primary function is to isolate different zones of formations and prevent the migration of hydrocarbons or water from one layer to another as well as to bond and protect the casing from corrosion and mechanical loading [1]. As both temperature and pressure increase with the depth of the wellbore, oil well cements are subjected to wide ranges of temperature and pressure. It is important to study the effects of these different curing conditions on the various properties of oil well cements. At atmospheric pressure, the effect of curing temperature (below 100 °C) on the properties of cement-based materials is relatively well understood as extensive studies have been conducted for construction cement, which is not fundamentally different from oil well cement. Viscosity and acoustic properties of oil well cements are routinely tested under different temperatures and pressures in cementing labs to estimate their rheological profile, setting time, and compressive strength development. However, systematic studies regarding the effect of curing pressure on cement hydration kinetics are very rare in the open literature. The overall degree of hydration, defined as the total weight fraction of cement reacted, is directly related to many different physical and mechanical properties of cement-based materials, such as viscosity [2], setting time [3–5], autogenous shrinkage [6], compressive strength ⁎ Corresponding author. E-mail address: [email protected] (X. Pang). 0008-8846/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cemconres.2013.08.014
[7,8], tensile strength [9], and modulus of elasticity [6,9]. It is arguably the most important parameter that can be used to model the timedependent characteristics of cement-based materials [10]. The extent of the cement hydration process can be determined by in-situ X-ray diffraction (XRD), non-evaporable water (or chemically bound water) content, chemical shrinkage and isothermal calorimetry analyses. Isothermal calorimetry is the most commonly used and arguably the most effective test method to monitor cement hydration kinetics [11] as it directly measures the heat flow during the hydration process, which is approximately proportional to the rate of hydration. In the past few decades, significant efforts have been devoted to studying the hydration mechanism of cement and model its hydration kinetics. Although several different models proposed recently can accurately simulate the hydration of cement during early ages, many details of the hydration mechanism are still uncertain today. In earlier studies, an increase in the degree of hydration with increasing curing pressure has been observed by different experimental methods [12–15]. However, mathematical modeling of the effect of curing pressure on cement hydration kinetics was nonexistent until Lin and Meyer proposed an empirical function [16]. A few years later, Scherer et al. [2] made a breakthrough study by incorporating the concept of the activation volume into the boundary nucleation and growth (BNG) model for cement hydration to explain the dependency of cement slurry viscosity on curing pressure. Similar concepts were then further employed to explain the effect of curing pressure on in-situ XRD test results [17,18]. A much more straightforward scale factor model was developed by Pang et al. [19], which allows the effect of curing temperature and pressure on cement hydration kinetics to be modeled without knowing the detailed cement hydration mechanism.
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Table 1 Estimated main compound compositions (by mass percentage) of the different cements. Cement
Method
C3S
C2S
C3A
C4AF
C2F
CaSO4
Free lime
Lehigh-H
Bogue Rietveld Bogue Rietveld Bogue Rietveld
47.11 48.2 59.32 55.8 48.02 58.1
27.18 29.4 18.53 18.5 26.03 19.8
0 0 0.33 0 2.29 0
17.67 17.2 14.05 13.4 17.56 18.2
0.67 0a 0 0a 0 0a
4.63 5.1b 4.94 12.7c 3.98 3.9b
0.18 – 0.18 – 0.28 –
Lafarge-H Dyckerhoff-G a b c
Refinement for C4AF only. Conversion to C2F accounted for in lattice parameter shift. Gypsum content. Sulfate content comprised both gypsum (2.2%) and anhydrite (10.5%).
This was achieved by representing hydration kinetics with functions whose exact expressions are not known. The model can be applied to predict hydration kinetic curves at different curing conditions based on hydration kinetic curves at a reference curing condition. The scale factor model was first validated with chemical shrinkage test data of oil well cements obtained at different curing temperatures and pressures [19]. Due to difficulties associated with accurate temperature control of the tests and the fact that the temperature and pressure dependency of the molar volume of cement hydration products are still uncertain, the chemical shrinkage test is a relatively less accurate method of evaluating cement hydration kinetics. In particular, it is difficult to derive accurate derivative curves from chemical shrinkage test results. Hence, the model was further validated with isothermal calorimetry test data conducted with oil well cements at different temperatures and atmospheric pressure [20]. In this study, we present the first systematic isothermal calorimetry test results of different oil well cements cured at both different temperatures and pressures, employing one of the few types of commercial calorimeters that allow cement heat of hydration to be measured at elevated pressures. The scale factor model will be further applied to model the test results. 2. Theoretical background It has been shown in previous studies [19–21] that the effect of curing temperature and pressure on cement hydration can be modeled by incorporating a scale factor C into the hydration kinetics functions (defined here as the evolution of degree of hydration or rate of hydration as a function of time). The model states that if hydration kinetics functions at the reference temperature Tr and pressure Pr is represented by the following functions, ′
Fig. 1. Particle size distributions of different classes of cements.
activation volume (m3/mol); R is the gas constant (8.314 J/(mol K)); T and P are the temperature (K) and pressure (Pa) of an arbitrary curing condition, while Tr and Pr are the temperature (K) and pressure (Pa) of the reference curing condition; C is the scale factor associated with the temperature change from Tr to T and the pressure change from Pr to P. Detailed derivation of the model can be found in Ref. [19]. It should be pointed out that the scale factor model was developed for a single reaction process assuming that the curing condition only changes the rate of the reaction, but not its nature. In reality, Portland cement hydration is a much more complex process with all the different clinker phases having different reaction rates as well as different sensitivities to curing condition changes. Therefore, the scale factor model is only approximate when applied to Portland cement hydration. The activation energy and activation volume of Portland cement obtained as such are usually called “apparent” activation energy and “apparent” activation volume, respectively. The early hydration of cement is believed to be primarily dominated by C3S and C3A, which are known to have significantly different sensitivities to temperature changes (i.e. activation energies). Therefore, it also appears that the model is more accurate for cement that contains little or no C3A or for relatively small changes in curing condition (e.g. with C ≤ 2) [20]. 3. Experimental method
Integral curve : α ¼ α T r ;Pr ðt Þ; Derivative curve : dα=dt ¼ α T r ;Pr ðt Þ ð1Þ
3.1. Materials
then the hydration kinetics functions at temperature T and pressure P are
API Class H (by Texas Lehigh Cement Co. and Joppa Plant of Lafarge Co., respectively) and Class G (by Dyckerhoff Co.) cements as provided by the manufacturers were used in this study. The main compound compositions of the cements derived from oxide analysis test results using the Bogue calculation method [22] as well as powder X-ray diffraction (XRD) with accompanying Rietveld refinement [23], are presented in Table 1. Although both methods are known to have inaccuracies, the estimated main phase compositions agree reasonably well with each other. The C3A contents in the cements studied here are probably too low to be accurately measured by XRD. Relatively large
Integral curve : α ¼ α T;P ðt Þ ¼ α T r ;Pr ðC ðt−t 0 ÞÞ; ′
′
Derivative curve : dα=dt ¼ α T;P ðt Þ ¼ C α T r ;Pr ðC ðt−t 0 ÞÞ
ð2Þ
where t0 is the offset time introduced to account for the potentially different hydration mechanism during the very early period (before the end of the induction period), which may have a different temperature and pressure dependence than the main hydration. The degree of hydration α in the above equations is interchangeable with any other parameter that has an approximately one-to-one relation with it, such as heat of hydration for this particular study. The dependence of the scale factor on curing temperature and pressure can be modeled by the following equation [19], ! Ea 1 1 ΔV ‡ P r P C ðT r −T; P r −P Þ ¼ exp þ − − T R Tr T R T
ð3Þ
where Ea is the apparent activation energy (J/mol); ΔV‡ is the apparent
Table 2 Isothermal calorimetry test program. Lehigh H
Lafarge H
Dyckerhoff G
Curing condition
2 MPa 15 MPa 30 MPa 45 MPa 2 MPa 45 MPa 2 MPa 45 MPa
25 °C 40 °C 60 °C
✓ ✓ ✓
✓
✓
✓
✓
✓ ✓ ✓
✓ ✓ ✓
✓ ✓ ✓
✓ ✓
✓ ✓
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Fig. 2. Results of replicate tests.
differences were also observed for the sulfate content in the Lafarge Class H cement and the silicate phases in the Dyckerhoff Class G cement. The particle size distributions of the cements were measured by the laser scattering technique with dry dispersion methods. The average test results are presented in Fig. 1. The median particle sizes for Lehigh Class H, Lafarge Class H, and Class G cements were 28.6 μm, 20.1 μm, and 17.6 μm, respectively, while their calculated specific surface areas (assuming spherical particles and a density of 3150 kg/m3 for cement) were 254 m2/kg, 314 m2/kg, and 329 m2/kg, respectively. All slurries were prepared in a Waring blender at room temperature with deionized water and cement according to the procedures outlined in API RP 10B [24]. To reduce variability of test results, the mixing water is allowed to reach an equilibrium temperature with the lab (around 21 °C) before mixing. A water-to-cement (w/c) mass ratio of 0.44 was used for Class G cement while a w/c ratio of 0.38 was used for both Class H cements. These ratios are standard values defined in API Specification 10A [25]. 3.2. Isothermal calorimetry Isothermal calorimetry measurements were carried out in a Setaram™ C80 microcalorimeter with the controlled static high pressure cells according to standard test procedures [11]. The pressure cells were connected to a Quizix® Q5000 precision pump (Chandler Engineering®) for pressure control with deionized water as the pressurizing medium. To facilitate quicker clean-up after each test, the cement slurry sample was transferred into an open-end glass vial with a volume capacity of 1.4 mL before being placed in the pressure cell. The cement sample mass was approximately 2.7 g for Class G cement and 2.8 g for Class H cement. The heat capacity of the cement slurry sample was balanced with an inert specimen (i.e. a mixture of sand and water) of the same volume in the reference cell. Baselines were collected at different curing temperatures with inert
specimens in both the test cell and the reference cell. The baseline is very stable with a long-term drift of less than 0.02 mW and a random noise level of less than 0.003 mW. The absolute value of the baseline changes with curing temperature, from 0 mW at 25 °C to about 0.65 mW at 60 °C, which were subtracted from the test results. Timing of each test starts at the point when cement first comes in contact with water. Typically, approximately 6 minutes are needed to get the sample into the calorimeter after mixing. To reduce the test set-up time, the reference cell was kept in the calorimeter at all times and the calorimeter was pre-set at the target curing temperature. After introducing the test cell (which is at room temperature), it takes about 1 to 1.5 hours for the calorimeter to reach an equilibrium state to obtain accurate heat flow readings. The pressure cells have a maximum pressure rating of 50 MPa and tests were performed in the range of 2 MPa to 45 MPa at three different temperatures (Table 2). Reproducibility of test results is illustrated in Fig. 2. Slight differences in the induction period as well as in the peak hydration rate were observed between replicate tests. Maximum differences in the induction period and the peak hydration rate are 7 minutes (0.12 hours) and 0.11 mW/g cement, respectively. 4. Test results and discussion 4.1. Texas Lehigh Class H cement Fig. 3 shows the effect of curing pressure on the evolution of the heat flow for the Lehigh Class H cement (w/c = 0.38) at 25 °C and 60 °C. The effect of curing pressure on hydration kinetics is similar at both temperatures. With increasing curing pressure, the rate of heat flow during the acceleration period increases while the duration of the acceleration period decreases. Due to the fact that the heat flow rate decreases earlier and faster at higher curing pressures, a relatively lower rate is observed
Fig. 3. Effect of curing pressure on the heat flow rate at 25 °C and 60 °C (Lehigh Class H cement, w/c = 0.38).
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X. Pang et al. / Cement and Concrete Research 54 (2013) 69–76 Table 3 Peak hydration rates and model parameters obtained at different curing conditions. Curing condition Temp. (°C)
Press. (MPa)
25
2 2 15 15 30 45 2 45 2 2 15 15 30 45
40 60
Fig. 4. Cumulative heat evolution test results of the Lehigh Class H cement cured at different temperatures and pressures.
Peak rate (mW/g cement)
Scale factora C
Offset time t0 (h)
ΔV‡b (cm3/mol)
ΔV‡c (cm3/mol)
2.82 2.84 3.15 3.12 3.69 4.20 5.96 8.76 12.75 12.86 14.45 14.45 15.52 17.68
1.00 1.01 1.12 1.11 1.31 1.49 2.11 3.11 4.52 4.56 5.12 5.12 5.50 6.27
0 0 0 0 0 0 0.72 0.28 1.3 1.2 0.9 0.98 0.75 0.62
N/A N/A −21.3 −19.1 −23.8 −23.0 N/A −23.3 N/A N/A −26.7 −26.7 −19.5 −21.1
−23.1
N/A −20.1
a
Obtained by the peak hydration rate (heat flow rate) method. Calculated based on comparisons with tests cured at 2 MPa and the same temperature. c Calculated by linear regression analysis with all test data at the same temperature. b
during the later stage of the deceleration period. Such behavior is very similar to the relatively well-known effect of curing temperature on the hydration kinetics of cement [26–28]. The hydration kinetics shown here are also in good agreement with our previous observations with chemical shrinkage tests [19,29]. It appears that curing pressure has a much smaller effect on cement hydration kinetics than curing temperature, with the peak rate increasing less than 50% (i.e. C b 1.5) for a pressure increase of 43 MPa. For comparison, the peak rate typically increases more than 100% (i.e. C N 2) for a temperature increase of 15 °C. Similarly, Scherer et al. also estimated that a pressure change of 3.7 MPa is approximately equivalent to a temperature change of 1 °C [2], in terms of its effects on the rate of reaction of certain cements. The cumulative heat evolution data of all tests performed for the Lehigh Class H cement are presented in Fig. 4. The total amount of heat released at any given time generally increases with both curing temperature and pressure during the entire test period (2 days for 60 °C and 7 days for 25 °C). Some tests presented in this study were unintentionally stopped early, but this has no effect on further validation of the scale factor model and derivation of the model parameters as long as the main hydration peak was measured. Test results were obtained by integrating the heat flow data with the zero point set at 1 hour for tests conducted at 25 °C, and 1.1 hours for tests conducted at 40 °C and 60 °C. Slight errors in test data are expected before 1.5 hours as the calorimeter has not reached a true equilibrium state. Truncating test data at 1.5 hours are not desirable as the heat flow
rates had already become very significant for tests conducted at high temperatures and pressures. Therefore, it appears that 60 °C is close to the maximum temperature that can be studied for neat cement slurries mixed outside the calorimeter. To conduct hydration kinetics studies at higher temperatures, one needs to either use retarder in the mix design or mix the slurry inside the calorimeter. One of the most important assumptions of the scale factor model is that the normalized rate of hydration vs. degree of hydration curve of a given cement paste is more or less invariant with curing condition (for isothermal and isobaric tests) [19]. The assumption has been shown to be valid for Class G and Class H cements cured at the ambient temperature and elevated pressures [19] as well as those cured at low pressures and elevated temperatures [19,20]. Test results conducted here at both elevated temperatures and pressures are presented in Fig. 5. Similar to previous findings, it can be seen that the assumption is particularly accurate during the acceleration period, where hydration is primarily dominated by C3S. Slight deviations were observed shortly after the peak, primarily due to the reaction of other phases that potentially have different sensitivities to temperature and pressure changes. To obtain the scale factor C, one first needs to choose a reference condition. In this case, the condition at 25 °C and 2 MPa is selected as the reference, i.e. Tr = 25 °C, Pr = 2 MPa. According to Eq. (2), the scale factor at other curing conditions (T, P) can be estimated by applying basic coordinate transformation rules to transform the hydration kinetics curve at
Fig. 5. Heat flow vs. cumulative heat of hydration before (left) and after (right) normalization (Lehigh Class H cement).
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Table 4 Peak hydration rates and model parameters obtained at different curing conditions. Curing condition Temp. (°C)
Press. (MPa)
25
2 45 2 45 2 45
40 60 a
Fig. 6. Linear fits as used to obtain the activation volumes for Lehigh Class H cement.
(Tr, Pr) to achieve the best agreement with the experimental curve obtained at (T, P). Hence, this method may be referred to as the best fit method. However, determination of the scale factor based on the best fit method is somewhat subjective and the results may vary slightly with the time duration of the test data. Alternatively, the scale factor may also be estimated by simply calculating the ratio of the peak hydration rates at condition (T, P) and condition (Tr, Pr), as they correlate approximately with the same degree of hydration. The latter method should not be used when C3A content is significant, as superposition of the C3S and C3A peaks tends to significantly overestimate the scale factor [20]. The scale factor obtained by the best fit method should reflect the average temperature and pressure sensitivities of all phases reacted during the studied period, while that obtained by the peak hydration rate method should primarily reflect the temperature and pressure sensitivities of the dominating C3S phase. Test results for the Lehigh Class H cement and the obtained model parameters are listed in Table 3. It should be pointed out that the offset time obtained here may be partially attributed to variations of the time required to heat up the samples, which were prepared at the ambient condition. The activation volume of the cement can be estimated based on any two tests conducted at the same temperature and different pressures by recalculating the scale factor using one of the two tests as the reference condition, i.e. ! C ðT r −T; P r −P 2 Þ ΔV P 1 P 2 C ðT; P 1 −P 2 Þ ¼ ¼ exp − C ðT r −T; P r −P 1 Þ R T T ‡
Peak rate (mW/g cement)
Scale factora C
Offset time t0 (h)
ΔV‡ (cm3/mol)
3.08 4.83 6.70 10.0 16.0 22.9
1.00 1.57 2.17 3.25 5.20 7.43
0 −0.2 0.7 0.4 1.3 0.75
−25.9 −24.4 −22.9
Obtained by the peak hydration rate (heat flow rate) method.
where T is the common curing temperature, while P1 and P2 are the different curing pressures. However, the estimation based on such a method may carry a significant error if the pressure difference between the two tests is small. For example, a 1% error in the scale factor is translated to around 10% error in the estimated activation volumes if test results obtained at 2 MPa and 15 MPa were used. The error is dramatically reduced with increasing pressure differences. A 1% error in the scale factor will only result in around 3% error in the activation volume, if the pressure difference is 43 MPa. A more accurate method of determining the activation volume is by linear regression analysis using all test data obtained at the same curing temperature (Fig. 6). Table 3 lists the activation volumes obtained from both methods. As shown in the results, the activation volumes obtained using the largest pressure difference of 43 MPa is within 5% of the value determined by the linear regression analysis. The apparent activation volume of the Lehigh Class H cement obtained from linear regression is −23.1 cm3/mol at 25 °C, and −20.1 cm3/mol at 60 °C, respectively. The decreases in the magnitude of the activation volume with increasing curing temperature may be because certain phases (perhaps C4AF) that become more reactive at higher temperatures (i.e. with higher activation energies) are less sensitive to pressure changes. Validation of the model can be achieved by comparing predicted hydration kinetics curves (by transforming the hydration kinetics curve at the reference condition) with the actual experimental curves obtained for different curing conditions. Previous validations of the model were limited to either the same curing pressure or the same curing temperature due to experimental limitations [19–21]. As shown in Fig. 7, test results of this study suggest that the model is equally valid when both temperature and pressure are different. The errors in the cumulative heat evolution at the end of the test are within 3%.
4.2. Lafarge Class H cement ð4Þ
As it appears that smaller pressure differences do not give accurate estimations of the activation volumes, tests for the Lafarge Class H
Fig. 7. Prediction of hydration kinetics at elevated temperatures and pressures by transforming experimental results at a reference condition (25 °C, 2 MPa), Lehigh Class H cement.
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Fig. 8. Normalized heat flow vs. Cumulative heat of hydration (Class G cement).
cement were only conducted at the minimum and maximum pressures (i.e. 2 MPa and 45 MPa). The peak hydration rates and model parameters obtained at different curing conditions are shown in Table 4. Consistent with the test results obtained for the Lehigh Class H cement, the apparent activation volume of the Lafarge Class H cement also decreased in magnitude with increasing curing temperature. Interestingly, the magnitude of decrease from 25 °C to 60 °C was also similar (i.e. 3 cm3/mol, or 12–13%). Comparisons between the model-predicted hydration kinetics and the experimental results also showed excellent agreements. The absolute values of the activation volumes of the Lafarge Class H cement were slightly higher than those of the Lehigh Class H cement at all temperatures tested. Since the Lafarge Class H cement has a higher C3S content, the results may suggest that C3S has a higher activation volume (absolute value) than C2S and/or C4AF. 4.3. Dyckerhoff Class G cement As mentioned previously, the further reaction of the C3A phase (after the initial reaction) in Portland cement is known to cause a second peak (also known as the sulfate depletion peak) in the heat flow curve [30,31]. The sulfate depletion peak is typically (but not necessarily) observed during the deceleration period of hydration. As both Class H cements used in this study have negligible or no C3A content, the sulfate depletion peak is hardly observable. The Dyckerhoff Class G cement has a slightly more appreciable amount of C3A and can be used to study its effect on the overall cement hydration. As shown in Fig. 8 (left), the sulfate depletion peak becomes more pronounced with increasing curing temperature, with the C3A peak higher than the C3S peak at 40 °C and 2 MPa because C3A hydration has a higher sensitivity to curing temperature changes (i.e. activation energy) than C3S hydration. Such observation is consistent with previous test results [20]. On the other hand, Fig. 8 (right) shows that the sulfate depletion peak becomes less
pronounced with increasing curing pressure, suggesting that C3A hydration probably has a lower sensitivity to curing pressure changes (i.e. activation volume) than C3S hydration. The peak hydration rates and model parameters obtained at different curing conditions for the Dyckerhoff Class G cement are shown in Table 5. Note that the main C3S peak (i.e. the first peak) is used for calculation when two peaks are present at the same time. Possibly due to the contribution of C3A, the activation volume (absolute value) of the Class G cement appears to decrease faster with increasing curing temperature. Comparisons of predicted hydration kinetics with the experimental results also showed excellent agreements, suggesting that the presence of C3A in a small quantity (2.29%) did not severely affect the accuracy of the model. This is consistent with previous studies [19,20]. At 25 °C, the activation volume of the Class G cement falls between those of the two Class H cement tested. Explanation of the results is difficult because the composition of the Class G cement is uncertain (see Table 1). In general, the activation volumes of different cements obtained in this study agree reasonably well with those obtained from chemical shrinkage test results of similar cements [19]. However, they appear to be lower in magnitude than those determined for the C3S phase in similar cements by the in-situ XRD method [18], further suggesting that most other phases in Portland cement probably have lower activation volumes (absolute value). It should be noted that the analysis method employed in Ref. [18] does not take into account the potentially different hydration mechanisms during the induction period (i.e. t0 in Eq. (2) is ignored).
Table 6 Activation energies of different cements calculated for different curing conditions. Cement
P (MPa) T1 − T2 (°C) Ea (kJ/mol) Ea (kJ/mol) by linear regression
Lehigh H
2
Table 5 Peak hydration rates and model parameters obtained at different curing conditions. Curing condition Temp. (°C)
Press. (MPa)
25
2 45 2 45
40 a
a
Peak rate (mW/g cement)
Scale factor C
3.01 4.64 6.71 9.69
1.00 1.54 2.23 3.22
Offset time t0 (h)
ΔV (cm3/mol)
0 0 0.9 0.4
−24.9
Obtained by the peak hydration rate (heat flow rate) method.
45
‡
Lafarge H
2
45
−22.3 Dyckerhoff G 2 45
25–40 25–60 40–60 25–40 25–60 40–60 25–40 25–60 40–60 25–40 25–60 40–60 25–40 25–40
38.7 35.6 33.0 38.0 33.9 30.5 40.2 38.9 37.8 37.8 36.7 35.8 41.4 38.1
35.6
33.8
38.9
36.7
N/A N/A
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Fig. 9. Linear fits as used to obtain the activation energies of two Class H cements.
4.4. Variations of the apparent activation energies with temperature and pressure As shown in previous sections, the apparent activation volume of the different cements used in this study decreases slightly in magnitude with increasing curing temperature (evaluation of its dependence on curing pressure would require testing in a higher pressure range). In this section, we will investigate the variations of the apparent activation energy with temperature and pressure. The apparent activation energy of the cement can be derived by using test results of any two tests performed at the same pressure and different temperatures based on the following equation, C ðT 1 −T 2 ; P Þ ¼
C ðT r −T 2 ; P Þ E 1 1 ¼ exp a − C ðT r −T 1 ; P Þ R T1 T2
ð5Þ
Table 6 lists the apparent activation energies of different cements estimated in different temperature ranges as well as those estimated by linear regression analysis (Fig. 9). The values estimated by linear regression are almost identical to those estimated using the two tests performed at the minimum and maximum curing temperature (i.e. 25 °C and 60 °C), respectively. Similar to our previous study [20], the apparent activation energy of both Class H cements is found to decrease with increasing curing temperature. In addition, test results obtained here suggest that the activation energy of all cement tested also decreases slightly with increasing curing pressure, consistent with our speculation that the phases with higher activation energies are also less sensitive to pressure changes. The magnitude of reduction is only around 5%, with curing pressure increasing from 2 MPa to 45 MPa. 5. Conclusion This study shows that the effect of curing pressure on the overall hydration kinetics of oil well cement can be evaluated by the isothermal calorimetry method employing pressurized cells. Test results confirm previous findings that curing temperature and pressure have similar effects on cement hydration kinetics which may be represented by a more or less constant change in hydration rate when it is expressed as a function of degree of hydration. The hydration kinetics at an arbitrary curing condition (within the range studied) can be accurately predicted by transforming the experimental test results at a reference curing condition with a scaling factor and a small offset time (b1.3 hours). The offset time cannot be modeled based on the current data as the tests were not performed at true isothermal and isobaric conditions (i.e. not mixed insitu). The scale factor can be estimated based on the apparent activation energy (Ea) and the apparent activation volume (ΔV‡) of the cement. Although both Ea and ΔV‡ appear to vary slightly with temperature and pressure, they can be reasonably assumed to be constant in the relatively small range investigated in this study. Qualitative analyses
of hydration kinetics of Class G cement at different curing conditions suggest that in Portland cement C3A hydration probably has a higher activation energy and a lower activation volume than C3S hydration. The presence of C3A in small quantities does not seem to substantially influence the accuracy of the scale factor model.
References [1] D.K. Smith, Cementing, SPE Monograph Series, vol. 4, 1990. [2] 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. [3] R.C.A. Pinto, K.C. Hover, Application of maturity approach to setting times, ACI Mater. J. 96 (1999) 686–691. [4] Á. García, D. Castro-Fresno, J.A. Polanco, Maturity approach applied to concrete by means of Vicat tests, ACI Mater. J. 105 (5) (2008) 445–450. [5] J. Zhang, E.A. Weissinger, S. Peethamparan, G.W. Scherer, Early hydration and setting of oil well cement, Cem. Concr. Res. 40 (2010) 1023–1033. [6] F. Lin, Modeling of hydration kinetics and shrinkage of Portland cement paste, (Ph.D. Thesis) Columbia University, 2006. [7] K.O. Kjellsen, R.J. Detwiler, O.E. Gjørv, Development of microstructures in plain cement pastes hydrated at different temperatures, Cem. Concr. Res. 21 (1991) 179–189. [8] ASTM C1074, Standard Practice for Estimating Concrete Strength by the Maturity Method, ASTM International, West Conshohocken, PA, 2010. (10 pp.). [9] M. Krauss, H. Karim, Determination of initial degree of hydration for improvement of early-age properties of concrete using ultrasonic wave propagation, Cem. Concr. Compos. 28 (2006) 299–306. [10] I. Pane, W. Hansen, Concrete hydration and mechanical properties under nonisothermal conditions, ACI Mater. J. 99 (6) (2002) 534–542. [11] ASTM C1679, Standard Practice for Measuring Hydration Kinetics of Hydraulic Cementitious Mixtures Using Isothermal Calorimetry, ASTM International, West Conshohocken, PA, 2009. (14 pp.). [12] A.A. Rahman, D.D. Double, Dilation of Portland cement grains during early hydration and the effect of applied hydrostatic pressure on hydration, Cem. Concr. Res. 12 (1) (1982) 33–38. [13] B. Bresson, F. Meducin, H. Zanni, C. Noik, Hydration of tricalcium silicate (C3S) at high temperature and high pressure, J. Mater. Sci. 37 (2002) 5355–5365. [14] Q. Zhou, J.J. Beaudoin, Effect of applied hydrostatic stress on the hydration of Portland cement and C3S, Adv. Cem. Res. 15 (1) (2003) 9–16. [15] F. Meducin, H. Zanni, C. Noik, G. Hamel, B. Bresson, Tricalcium silicate hydration under high pressure at ambient and high temperature (200 °C), Cem. Concr. Res. 38 (2007) 320–324. [16] F. Lin, C. Meyer, Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure, Cem. Concr. Res. 39 (2009) 255–265. [17] A.C. Jupe, A.P. Wilkinson, G.P. Funkhouser, Oil-well cement and C3S hydration under high pressure as seen by in situ X-ray diffraction, temperatures ≤80 °C with no additives, J. Am. Ceram. Soc. 94 (5) (2011) 1591–1597. [18] A.C. Jupe, A.P. Wilkinson, G.P. Funkhouser, The effect of pressure on tricalcium silicate hydration at different temperatures and in the presence of retarding additives, Cem. Concr. Res. 42 (2012) 1083–1087. [19] X. Pang, C. Meyer, R. Darbe, G.P. Funkhouser, Modeling the effect of curing temperature and pressure on cement hydration kinetics, ACI Mater. J. 110 (2) (2013) 137–148. [20] X. Pang, D.P. Bentz, C. Meyer, G.P. Funkhouser, R. Darbe, A comparison study of Portland cement hydration kinetics as measured by chemical shrinkage and isothermal calorimetry, Cem. Concr. Compos. 39 (2013) 23–32. [21] X. Pang, D.P. Bentz, C. Meyer, Modeling cement hydration kinetics using the equivalent age concept, 3rd International Symposium on UHPC and Nanotechnology for High Performance Construction Materials, Kassel, March 7–9, 2012, 2012, pp. 291–299. [22] R.H. Bogue, Calculation of the compounds in Portland cement, Ind. Eng. Chem. Anal. Ed. 1 (4) (1929) 192–197.
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[23] B. Iverson, R. Loghry, C. Edwards, Rietveld refinement of an oil field cement blend, Materials Science & Technology 2011 Conference & Exhibition, Columbus, OH, October 16–20, 2011, 2011, pp. 356–366. [24] API Recommended Practice 10B, Recommended Practice for Testing Well Cements, 22nd edition American Petroleum Institute, 1997. (146 pp.). [25] API Specification 10A, Specification for Cements and Materials for Well Cementing, American Petroleum Institute, 2010. (38 pp.). [26] J.L. Poole, K.A. Riding, K.J. Folliard, M.C.G. Juenger, A.K. Schindler, Methods for calculating activation energy for Portland cement, ACI Mater. J. 104 (1) (2007) 303–311. [27] H.W. Reinhardt, J. Blauwendraad, J. Jongendijk, Temperature development in concrete structures taking account of state dependent properties, International Conference on Concrete at Early Ages, RILEM, Paris, France, 1982, pp. 211–218.
[28] G. DeSchutter, L. Taerwe, General hydration model for Portland cement and blast furnace slag cement, Cem. Concr. Res. 25 (3) (1995) 593–604. [29] X. Pang, C. Meyer, Cement chemical shrinkage as measure of hydration kinetics and its relationship with non-evaporable water, ACI Mater. J. 109 (3) (2011) 341–352. [30] C. Hesse, F. Goetz-Neunhoeffer, J. Neubauer, A new approach in quantitative in-situ XRD of cement pastes: correlation of heat flow curves with early hydration reactions, Cem. Concr. Res. 41 (2011) 123–128. [31] D. Jansen, F. Goetz-Neunhoeffer, B. Lothenbach, J. Neubauer, The early hydration of Ordinary Portland Cement (OPC): an approach comparing measured heat flow with calculated heat flow from QXRD, Cem. Concr. Res. 42 (2012) 134–138.
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Cement and Concrete Research journal homepage: http://ees.elsevier.com/CEMCON/default.asp
Hydration kinetics modeling of the effect of curing temperature and pressure on the heat evolution of oil well cement Xueyu Pang ⁎, Walmy Cuello Jimenez, Benjamin J. Iverson Halliburton, 3000 N Sam Houston Pkwy E, Houston, TX 77032, USA
a r t i c l e
i n f o
Article history: Received 1 April 2013 Accepted 26 August 2013 Keywords: Hydration (A) Kinetics (A) Temperature (A) Modeling (E) Oil well cement (E)
a b s t r a c t The heat evolution of Class G and Class H oil well cements cured under different temperatures (25 °C to 60 °C) and pressures (2 MPa to 45 MPa) was examined by isothermal calorimetry. Curing pressure was found to have a similar effect on cement hydration kinetics as curing temperature. Under isothermal and isobaric conditions, the dependency of cement hydration kinetics on curing temperature and pressure can be modeled by a scale factor which is related to the activation energy and the activation volume of the cement. The estimated apparent activation energy of the different cements at 2 MPa varies from 38.7 kJ/mol to 41.4 kJ/mol for the temperature range of 25 °C to 40 °C, which decreases slightly with increasing curing temperature and pressure. The estimated apparent activation volume of the cements at 25 °C varies from −23.1 cm3/mol to −25.9 cm3/mol for the pressure range studied here, which also decreases slightly in magnitude with increasing curing temperature. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Cementing is one of the most important procedures during oil or gas well construction, the purpose of which is to create a cement sheath in the annulus between the steel casing and the wellbore. Its primary function is to isolate different zones of formations and prevent the migration of hydrocarbons or water from one layer to another as well as to bond and protect the casing from corrosion and mechanical loading [1]. As both temperature and pressure increase with the depth of the wellbore, oil well cements are subjected to wide ranges of temperature and pressure. It is important to study the effects of these different curing conditions on the various properties of oil well cements. At atmospheric pressure, the effect of curing temperature (below 100 °C) on the properties of cement-based materials is relatively well understood as extensive studies have been conducted for construction cement, which is not fundamentally different from oil well cement. Viscosity and acoustic properties of oil well cements are routinely tested under different temperatures and pressures in cementing labs to estimate their rheological profile, setting time, and compressive strength development. However, systematic studies regarding the effect of curing pressure on cement hydration kinetics are very rare in the open literature. The overall degree of hydration, defined as the total weight fraction of cement reacted, is directly related to many different physical and mechanical properties of cement-based materials, such as viscosity [2], setting time [3–5], autogenous shrinkage [6], compressive strength ⁎ Corresponding author. E-mail address: [email protected] (X. Pang). 0008-8846/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cemconres.2013.08.014
[7,8], tensile strength [9], and modulus of elasticity [6,9]. It is arguably the most important parameter that can be used to model the timedependent characteristics of cement-based materials [10]. The extent of the cement hydration process can be determined by in-situ X-ray diffraction (XRD), non-evaporable water (or chemically bound water) content, chemical shrinkage and isothermal calorimetry analyses. Isothermal calorimetry is the most commonly used and arguably the most effective test method to monitor cement hydration kinetics [11] as it directly measures the heat flow during the hydration process, which is approximately proportional to the rate of hydration. In the past few decades, significant efforts have been devoted to studying the hydration mechanism of cement and model its hydration kinetics. Although several different models proposed recently can accurately simulate the hydration of cement during early ages, many details of the hydration mechanism are still uncertain today. In earlier studies, an increase in the degree of hydration with increasing curing pressure has been observed by different experimental methods [12–15]. However, mathematical modeling of the effect of curing pressure on cement hydration kinetics was nonexistent until Lin and Meyer proposed an empirical function [16]. A few years later, Scherer et al. [2] made a breakthrough study by incorporating the concept of the activation volume into the boundary nucleation and growth (BNG) model for cement hydration to explain the dependency of cement slurry viscosity on curing pressure. Similar concepts were then further employed to explain the effect of curing pressure on in-situ XRD test results [17,18]. A much more straightforward scale factor model was developed by Pang et al. [19], which allows the effect of curing temperature and pressure on cement hydration kinetics to be modeled without knowing the detailed cement hydration mechanism.
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Table 1 Estimated main compound compositions (by mass percentage) of the different cements. Cement
Method
C3S
C2S
C3A
C4AF
C2F
CaSO4
Free lime
Lehigh-H
Bogue Rietveld Bogue Rietveld Bogue Rietveld
47.11 48.2 59.32 55.8 48.02 58.1
27.18 29.4 18.53 18.5 26.03 19.8
0 0 0.33 0 2.29 0
17.67 17.2 14.05 13.4 17.56 18.2
0.67 0a 0 0a 0 0a
4.63 5.1b 4.94 12.7c 3.98 3.9b
0.18 – 0.18 – 0.28 –
Lafarge-H Dyckerhoff-G a b c
Refinement for C4AF only. Conversion to C2F accounted for in lattice parameter shift. Gypsum content. Sulfate content comprised both gypsum (2.2%) and anhydrite (10.5%).
This was achieved by representing hydration kinetics with functions whose exact expressions are not known. The model can be applied to predict hydration kinetic curves at different curing conditions based on hydration kinetic curves at a reference curing condition. The scale factor model was first validated with chemical shrinkage test data of oil well cements obtained at different curing temperatures and pressures [19]. Due to difficulties associated with accurate temperature control of the tests and the fact that the temperature and pressure dependency of the molar volume of cement hydration products are still uncertain, the chemical shrinkage test is a relatively less accurate method of evaluating cement hydration kinetics. In particular, it is difficult to derive accurate derivative curves from chemical shrinkage test results. Hence, the model was further validated with isothermal calorimetry test data conducted with oil well cements at different temperatures and atmospheric pressure [20]. In this study, we present the first systematic isothermal calorimetry test results of different oil well cements cured at both different temperatures and pressures, employing one of the few types of commercial calorimeters that allow cement heat of hydration to be measured at elevated pressures. The scale factor model will be further applied to model the test results. 2. Theoretical background It has been shown in previous studies [19–21] that the effect of curing temperature and pressure on cement hydration can be modeled by incorporating a scale factor C into the hydration kinetics functions (defined here as the evolution of degree of hydration or rate of hydration as a function of time). The model states that if hydration kinetics functions at the reference temperature Tr and pressure Pr is represented by the following functions, ′
Fig. 1. Particle size distributions of different classes of cements.
activation volume (m3/mol); R is the gas constant (8.314 J/(mol K)); T and P are the temperature (K) and pressure (Pa) of an arbitrary curing condition, while Tr and Pr are the temperature (K) and pressure (Pa) of the reference curing condition; C is the scale factor associated with the temperature change from Tr to T and the pressure change from Pr to P. Detailed derivation of the model can be found in Ref. [19]. It should be pointed out that the scale factor model was developed for a single reaction process assuming that the curing condition only changes the rate of the reaction, but not its nature. In reality, Portland cement hydration is a much more complex process with all the different clinker phases having different reaction rates as well as different sensitivities to curing condition changes. Therefore, the scale factor model is only approximate when applied to Portland cement hydration. The activation energy and activation volume of Portland cement obtained as such are usually called “apparent” activation energy and “apparent” activation volume, respectively. The early hydration of cement is believed to be primarily dominated by C3S and C3A, which are known to have significantly different sensitivities to temperature changes (i.e. activation energies). Therefore, it also appears that the model is more accurate for cement that contains little or no C3A or for relatively small changes in curing condition (e.g. with C ≤ 2) [20]. 3. Experimental method
Integral curve : α ¼ α T r ;Pr ðt Þ; Derivative curve : dα=dt ¼ α T r ;Pr ðt Þ ð1Þ
3.1. Materials
then the hydration kinetics functions at temperature T and pressure P are
API Class H (by Texas Lehigh Cement Co. and Joppa Plant of Lafarge Co., respectively) and Class G (by Dyckerhoff Co.) cements as provided by the manufacturers were used in this study. The main compound compositions of the cements derived from oxide analysis test results using the Bogue calculation method [22] as well as powder X-ray diffraction (XRD) with accompanying Rietveld refinement [23], are presented in Table 1. Although both methods are known to have inaccuracies, the estimated main phase compositions agree reasonably well with each other. The C3A contents in the cements studied here are probably too low to be accurately measured by XRD. Relatively large
Integral curve : α ¼ α T;P ðt Þ ¼ α T r ;Pr ðC ðt−t 0 ÞÞ; ′
′
Derivative curve : dα=dt ¼ α T;P ðt Þ ¼ C α T r ;Pr ðC ðt−t 0 ÞÞ
ð2Þ
where t0 is the offset time introduced to account for the potentially different hydration mechanism during the very early period (before the end of the induction period), which may have a different temperature and pressure dependence than the main hydration. The degree of hydration α in the above equations is interchangeable with any other parameter that has an approximately one-to-one relation with it, such as heat of hydration for this particular study. The dependence of the scale factor on curing temperature and pressure can be modeled by the following equation [19], ! Ea 1 1 ΔV ‡ P r P C ðT r −T; P r −P Þ ¼ exp þ − − T R Tr T R T
ð3Þ
where Ea is the apparent activation energy (J/mol); ΔV‡ is the apparent
Table 2 Isothermal calorimetry test program. Lehigh H
Lafarge H
Dyckerhoff G
Curing condition
2 MPa 15 MPa 30 MPa 45 MPa 2 MPa 45 MPa 2 MPa 45 MPa
25 °C 40 °C 60 °C
✓ ✓ ✓
✓
✓
✓
✓
✓ ✓ ✓
✓ ✓ ✓
✓ ✓ ✓
✓ ✓
✓ ✓
X. Pang et al. / Cement and Concrete Research 54 (2013) 69–76
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Fig. 2. Results of replicate tests.
differences were also observed for the sulfate content in the Lafarge Class H cement and the silicate phases in the Dyckerhoff Class G cement. The particle size distributions of the cements were measured by the laser scattering technique with dry dispersion methods. The average test results are presented in Fig. 1. The median particle sizes for Lehigh Class H, Lafarge Class H, and Class G cements were 28.6 μm, 20.1 μm, and 17.6 μm, respectively, while their calculated specific surface areas (assuming spherical particles and a density of 3150 kg/m3 for cement) were 254 m2/kg, 314 m2/kg, and 329 m2/kg, respectively. All slurries were prepared in a Waring blender at room temperature with deionized water and cement according to the procedures outlined in API RP 10B [24]. To reduce variability of test results, the mixing water is allowed to reach an equilibrium temperature with the lab (around 21 °C) before mixing. A water-to-cement (w/c) mass ratio of 0.44 was used for Class G cement while a w/c ratio of 0.38 was used for both Class H cements. These ratios are standard values defined in API Specification 10A [25]. 3.2. Isothermal calorimetry Isothermal calorimetry measurements were carried out in a Setaram™ C80 microcalorimeter with the controlled static high pressure cells according to standard test procedures [11]. The pressure cells were connected to a Quizix® Q5000 precision pump (Chandler Engineering®) for pressure control with deionized water as the pressurizing medium. To facilitate quicker clean-up after each test, the cement slurry sample was transferred into an open-end glass vial with a volume capacity of 1.4 mL before being placed in the pressure cell. The cement sample mass was approximately 2.7 g for Class G cement and 2.8 g for Class H cement. The heat capacity of the cement slurry sample was balanced with an inert specimen (i.e. a mixture of sand and water) of the same volume in the reference cell. Baselines were collected at different curing temperatures with inert
specimens in both the test cell and the reference cell. The baseline is very stable with a long-term drift of less than 0.02 mW and a random noise level of less than 0.003 mW. The absolute value of the baseline changes with curing temperature, from 0 mW at 25 °C to about 0.65 mW at 60 °C, which were subtracted from the test results. Timing of each test starts at the point when cement first comes in contact with water. Typically, approximately 6 minutes are needed to get the sample into the calorimeter after mixing. To reduce the test set-up time, the reference cell was kept in the calorimeter at all times and the calorimeter was pre-set at the target curing temperature. After introducing the test cell (which is at room temperature), it takes about 1 to 1.5 hours for the calorimeter to reach an equilibrium state to obtain accurate heat flow readings. The pressure cells have a maximum pressure rating of 50 MPa and tests were performed in the range of 2 MPa to 45 MPa at three different temperatures (Table 2). Reproducibility of test results is illustrated in Fig. 2. Slight differences in the induction period as well as in the peak hydration rate were observed between replicate tests. Maximum differences in the induction period and the peak hydration rate are 7 minutes (0.12 hours) and 0.11 mW/g cement, respectively. 4. Test results and discussion 4.1. Texas Lehigh Class H cement Fig. 3 shows the effect of curing pressure on the evolution of the heat flow for the Lehigh Class H cement (w/c = 0.38) at 25 °C and 60 °C. The effect of curing pressure on hydration kinetics is similar at both temperatures. With increasing curing pressure, the rate of heat flow during the acceleration period increases while the duration of the acceleration period decreases. Due to the fact that the heat flow rate decreases earlier and faster at higher curing pressures, a relatively lower rate is observed
Fig. 3. Effect of curing pressure on the heat flow rate at 25 °C and 60 °C (Lehigh Class H cement, w/c = 0.38).
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X. Pang et al. / Cement and Concrete Research 54 (2013) 69–76 Table 3 Peak hydration rates and model parameters obtained at different curing conditions. Curing condition Temp. (°C)
Press. (MPa)
25
2 2 15 15 30 45 2 45 2 2 15 15 30 45
40 60
Fig. 4. Cumulative heat evolution test results of the Lehigh Class H cement cured at different temperatures and pressures.
Peak rate (mW/g cement)
Scale factora C
Offset time t0 (h)
ΔV‡b (cm3/mol)
ΔV‡c (cm3/mol)
2.82 2.84 3.15 3.12 3.69 4.20 5.96 8.76 12.75 12.86 14.45 14.45 15.52 17.68
1.00 1.01 1.12 1.11 1.31 1.49 2.11 3.11 4.52 4.56 5.12 5.12 5.50 6.27
0 0 0 0 0 0 0.72 0.28 1.3 1.2 0.9 0.98 0.75 0.62
N/A N/A −21.3 −19.1 −23.8 −23.0 N/A −23.3 N/A N/A −26.7 −26.7 −19.5 −21.1
−23.1
N/A −20.1
a
Obtained by the peak hydration rate (heat flow rate) method. Calculated based on comparisons with tests cured at 2 MPa and the same temperature. c Calculated by linear regression analysis with all test data at the same temperature. b
during the later stage of the deceleration period. Such behavior is very similar to the relatively well-known effect of curing temperature on the hydration kinetics of cement [26–28]. The hydration kinetics shown here are also in good agreement with our previous observations with chemical shrinkage tests [19,29]. It appears that curing pressure has a much smaller effect on cement hydration kinetics than curing temperature, with the peak rate increasing less than 50% (i.e. C b 1.5) for a pressure increase of 43 MPa. For comparison, the peak rate typically increases more than 100% (i.e. C N 2) for a temperature increase of 15 °C. Similarly, Scherer et al. also estimated that a pressure change of 3.7 MPa is approximately equivalent to a temperature change of 1 °C [2], in terms of its effects on the rate of reaction of certain cements. The cumulative heat evolution data of all tests performed for the Lehigh Class H cement are presented in Fig. 4. The total amount of heat released at any given time generally increases with both curing temperature and pressure during the entire test period (2 days for 60 °C and 7 days for 25 °C). Some tests presented in this study were unintentionally stopped early, but this has no effect on further validation of the scale factor model and derivation of the model parameters as long as the main hydration peak was measured. Test results were obtained by integrating the heat flow data with the zero point set at 1 hour for tests conducted at 25 °C, and 1.1 hours for tests conducted at 40 °C and 60 °C. Slight errors in test data are expected before 1.5 hours as the calorimeter has not reached a true equilibrium state. Truncating test data at 1.5 hours are not desirable as the heat flow
rates had already become very significant for tests conducted at high temperatures and pressures. Therefore, it appears that 60 °C is close to the maximum temperature that can be studied for neat cement slurries mixed outside the calorimeter. To conduct hydration kinetics studies at higher temperatures, one needs to either use retarder in the mix design or mix the slurry inside the calorimeter. One of the most important assumptions of the scale factor model is that the normalized rate of hydration vs. degree of hydration curve of a given cement paste is more or less invariant with curing condition (for isothermal and isobaric tests) [19]. The assumption has been shown to be valid for Class G and Class H cements cured at the ambient temperature and elevated pressures [19] as well as those cured at low pressures and elevated temperatures [19,20]. Test results conducted here at both elevated temperatures and pressures are presented in Fig. 5. Similar to previous findings, it can be seen that the assumption is particularly accurate during the acceleration period, where hydration is primarily dominated by C3S. Slight deviations were observed shortly after the peak, primarily due to the reaction of other phases that potentially have different sensitivities to temperature and pressure changes. To obtain the scale factor C, one first needs to choose a reference condition. In this case, the condition at 25 °C and 2 MPa is selected as the reference, i.e. Tr = 25 °C, Pr = 2 MPa. According to Eq. (2), the scale factor at other curing conditions (T, P) can be estimated by applying basic coordinate transformation rules to transform the hydration kinetics curve at
Fig. 5. Heat flow vs. cumulative heat of hydration before (left) and after (right) normalization (Lehigh Class H cement).
X. Pang et al. / Cement and Concrete Research 54 (2013) 69–76
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Table 4 Peak hydration rates and model parameters obtained at different curing conditions. Curing condition Temp. (°C)
Press. (MPa)
25
2 45 2 45 2 45
40 60 a
Fig. 6. Linear fits as used to obtain the activation volumes for Lehigh Class H cement.
(Tr, Pr) to achieve the best agreement with the experimental curve obtained at (T, P). Hence, this method may be referred to as the best fit method. However, determination of the scale factor based on the best fit method is somewhat subjective and the results may vary slightly with the time duration of the test data. Alternatively, the scale factor may also be estimated by simply calculating the ratio of the peak hydration rates at condition (T, P) and condition (Tr, Pr), as they correlate approximately with the same degree of hydration. The latter method should not be used when C3A content is significant, as superposition of the C3S and C3A peaks tends to significantly overestimate the scale factor [20]. The scale factor obtained by the best fit method should reflect the average temperature and pressure sensitivities of all phases reacted during the studied period, while that obtained by the peak hydration rate method should primarily reflect the temperature and pressure sensitivities of the dominating C3S phase. Test results for the Lehigh Class H cement and the obtained model parameters are listed in Table 3. It should be pointed out that the offset time obtained here may be partially attributed to variations of the time required to heat up the samples, which were prepared at the ambient condition. The activation volume of the cement can be estimated based on any two tests conducted at the same temperature and different pressures by recalculating the scale factor using one of the two tests as the reference condition, i.e. ! C ðT r −T; P r −P 2 Þ ΔV P 1 P 2 C ðT; P 1 −P 2 Þ ¼ ¼ exp − C ðT r −T; P r −P 1 Þ R T T ‡
Peak rate (mW/g cement)
Scale factora C
Offset time t0 (h)
ΔV‡ (cm3/mol)
3.08 4.83 6.70 10.0 16.0 22.9
1.00 1.57 2.17 3.25 5.20 7.43
0 −0.2 0.7 0.4 1.3 0.75
−25.9 −24.4 −22.9
Obtained by the peak hydration rate (heat flow rate) method.
where T is the common curing temperature, while P1 and P2 are the different curing pressures. However, the estimation based on such a method may carry a significant error if the pressure difference between the two tests is small. For example, a 1% error in the scale factor is translated to around 10% error in the estimated activation volumes if test results obtained at 2 MPa and 15 MPa were used. The error is dramatically reduced with increasing pressure differences. A 1% error in the scale factor will only result in around 3% error in the activation volume, if the pressure difference is 43 MPa. A more accurate method of determining the activation volume is by linear regression analysis using all test data obtained at the same curing temperature (Fig. 6). Table 3 lists the activation volumes obtained from both methods. As shown in the results, the activation volumes obtained using the largest pressure difference of 43 MPa is within 5% of the value determined by the linear regression analysis. The apparent activation volume of the Lehigh Class H cement obtained from linear regression is −23.1 cm3/mol at 25 °C, and −20.1 cm3/mol at 60 °C, respectively. The decreases in the magnitude of the activation volume with increasing curing temperature may be because certain phases (perhaps C4AF) that become more reactive at higher temperatures (i.e. with higher activation energies) are less sensitive to pressure changes. Validation of the model can be achieved by comparing predicted hydration kinetics curves (by transforming the hydration kinetics curve at the reference condition) with the actual experimental curves obtained for different curing conditions. Previous validations of the model were limited to either the same curing pressure or the same curing temperature due to experimental limitations [19–21]. As shown in Fig. 7, test results of this study suggest that the model is equally valid when both temperature and pressure are different. The errors in the cumulative heat evolution at the end of the test are within 3%.
4.2. Lafarge Class H cement ð4Þ
As it appears that smaller pressure differences do not give accurate estimations of the activation volumes, tests for the Lafarge Class H
Fig. 7. Prediction of hydration kinetics at elevated temperatures and pressures by transforming experimental results at a reference condition (25 °C, 2 MPa), Lehigh Class H cement.
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Fig. 8. Normalized heat flow vs. Cumulative heat of hydration (Class G cement).
cement were only conducted at the minimum and maximum pressures (i.e. 2 MPa and 45 MPa). The peak hydration rates and model parameters obtained at different curing conditions are shown in Table 4. Consistent with the test results obtained for the Lehigh Class H cement, the apparent activation volume of the Lafarge Class H cement also decreased in magnitude with increasing curing temperature. Interestingly, the magnitude of decrease from 25 °C to 60 °C was also similar (i.e. 3 cm3/mol, or 12–13%). Comparisons between the model-predicted hydration kinetics and the experimental results also showed excellent agreements. The absolute values of the activation volumes of the Lafarge Class H cement were slightly higher than those of the Lehigh Class H cement at all temperatures tested. Since the Lafarge Class H cement has a higher C3S content, the results may suggest that C3S has a higher activation volume (absolute value) than C2S and/or C4AF. 4.3. Dyckerhoff Class G cement As mentioned previously, the further reaction of the C3A phase (after the initial reaction) in Portland cement is known to cause a second peak (also known as the sulfate depletion peak) in the heat flow curve [30,31]. The sulfate depletion peak is typically (but not necessarily) observed during the deceleration period of hydration. As both Class H cements used in this study have negligible or no C3A content, the sulfate depletion peak is hardly observable. The Dyckerhoff Class G cement has a slightly more appreciable amount of C3A and can be used to study its effect on the overall cement hydration. As shown in Fig. 8 (left), the sulfate depletion peak becomes more pronounced with increasing curing temperature, with the C3A peak higher than the C3S peak at 40 °C and 2 MPa because C3A hydration has a higher sensitivity to curing temperature changes (i.e. activation energy) than C3S hydration. Such observation is consistent with previous test results [20]. On the other hand, Fig. 8 (right) shows that the sulfate depletion peak becomes less
pronounced with increasing curing pressure, suggesting that C3A hydration probably has a lower sensitivity to curing pressure changes (i.e. activation volume) than C3S hydration. The peak hydration rates and model parameters obtained at different curing conditions for the Dyckerhoff Class G cement are shown in Table 5. Note that the main C3S peak (i.e. the first peak) is used for calculation when two peaks are present at the same time. Possibly due to the contribution of C3A, the activation volume (absolute value) of the Class G cement appears to decrease faster with increasing curing temperature. Comparisons of predicted hydration kinetics with the experimental results also showed excellent agreements, suggesting that the presence of C3A in a small quantity (2.29%) did not severely affect the accuracy of the model. This is consistent with previous studies [19,20]. At 25 °C, the activation volume of the Class G cement falls between those of the two Class H cement tested. Explanation of the results is difficult because the composition of the Class G cement is uncertain (see Table 1). In general, the activation volumes of different cements obtained in this study agree reasonably well with those obtained from chemical shrinkage test results of similar cements [19]. However, they appear to be lower in magnitude than those determined for the C3S phase in similar cements by the in-situ XRD method [18], further suggesting that most other phases in Portland cement probably have lower activation volumes (absolute value). It should be noted that the analysis method employed in Ref. [18] does not take into account the potentially different hydration mechanisms during the induction period (i.e. t0 in Eq. (2) is ignored).
Table 6 Activation energies of different cements calculated for different curing conditions. Cement
P (MPa) T1 − T2 (°C) Ea (kJ/mol) Ea (kJ/mol) by linear regression
Lehigh H
2
Table 5 Peak hydration rates and model parameters obtained at different curing conditions. Curing condition Temp. (°C)
Press. (MPa)
25
2 45 2 45
40 a
a
Peak rate (mW/g cement)
Scale factor C
3.01 4.64 6.71 9.69
1.00 1.54 2.23 3.22
Offset time t0 (h)
ΔV (cm3/mol)
0 0 0.9 0.4
−24.9
Obtained by the peak hydration rate (heat flow rate) method.
45
‡
Lafarge H
2
45
−22.3 Dyckerhoff G 2 45
25–40 25–60 40–60 25–40 25–60 40–60 25–40 25–60 40–60 25–40 25–60 40–60 25–40 25–40
38.7 35.6 33.0 38.0 33.9 30.5 40.2 38.9 37.8 37.8 36.7 35.8 41.4 38.1
35.6
33.8
38.9
36.7
N/A N/A
X. Pang et al. / Cement and Concrete Research 54 (2013) 69–76
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Fig. 9. Linear fits as used to obtain the activation energies of two Class H cements.
4.4. Variations of the apparent activation energies with temperature and pressure As shown in previous sections, the apparent activation volume of the different cements used in this study decreases slightly in magnitude with increasing curing temperature (evaluation of its dependence on curing pressure would require testing in a higher pressure range). In this section, we will investigate the variations of the apparent activation energy with temperature and pressure. The apparent activation energy of the cement can be derived by using test results of any two tests performed at the same pressure and different temperatures based on the following equation, C ðT 1 −T 2 ; P Þ ¼
C ðT r −T 2 ; P Þ E 1 1 ¼ exp a − C ðT r −T 1 ; P Þ R T1 T2
ð5Þ
Table 6 lists the apparent activation energies of different cements estimated in different temperature ranges as well as those estimated by linear regression analysis (Fig. 9). The values estimated by linear regression are almost identical to those estimated using the two tests performed at the minimum and maximum curing temperature (i.e. 25 °C and 60 °C), respectively. Similar to our previous study [20], the apparent activation energy of both Class H cements is found to decrease with increasing curing temperature. In addition, test results obtained here suggest that the activation energy of all cement tested also decreases slightly with increasing curing pressure, consistent with our speculation that the phases with higher activation energies are also less sensitive to pressure changes. The magnitude of reduction is only around 5%, with curing pressure increasing from 2 MPa to 45 MPa. 5. Conclusion This study shows that the effect of curing pressure on the overall hydration kinetics of oil well cement can be evaluated by the isothermal calorimetry method employing pressurized cells. Test results confirm previous findings that curing temperature and pressure have similar effects on cement hydration kinetics which may be represented by a more or less constant change in hydration rate when it is expressed as a function of degree of hydration. The hydration kinetics at an arbitrary curing condition (within the range studied) can be accurately predicted by transforming the experimental test results at a reference curing condition with a scaling factor and a small offset time (b1.3 hours). The offset time cannot be modeled based on the current data as the tests were not performed at true isothermal and isobaric conditions (i.e. not mixed insitu). The scale factor can be estimated based on the apparent activation energy (Ea) and the apparent activation volume (ΔV‡) of the cement. Although both Ea and ΔV‡ appear to vary slightly with temperature and pressure, they can be reasonably assumed to be constant in the relatively small range investigated in this study. Qualitative analyses
of hydration kinetics of Class G cement at different curing conditions suggest that in Portland cement C3A hydration probably has a higher activation energy and a lower activation volume than C3S hydration. The presence of C3A in small quantities does not seem to substantially influence the accuracy of the scale factor model.
References [1] D.K. Smith, Cementing, SPE Monograph Series, vol. 4, 1990. [2] 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. [3] R.C.A. Pinto, K.C. Hover, Application of maturity approach to setting times, ACI Mater. J. 96 (1999) 686–691. [4] Á. García, D. Castro-Fresno, J.A. Polanco, Maturity approach applied to concrete by means of Vicat tests, ACI Mater. J. 105 (5) (2008) 445–450. [5] J. Zhang, E.A. Weissinger, S. Peethamparan, G.W. Scherer, Early hydration and setting of oil well cement, Cem. Concr. Res. 40 (2010) 1023–1033. [6] F. Lin, Modeling of hydration kinetics and shrinkage of Portland cement paste, (Ph.D. Thesis) Columbia University, 2006. [7] K.O. Kjellsen, R.J. Detwiler, O.E. Gjørv, Development of microstructures in plain cement pastes hydrated at different temperatures, Cem. Concr. Res. 21 (1991) 179–189. [8] ASTM C1074, Standard Practice for Estimating Concrete Strength by the Maturity Method, ASTM International, West Conshohocken, PA, 2010. (10 pp.). [9] M. Krauss, H. Karim, Determination of initial degree of hydration for improvement of early-age properties of concrete using ultrasonic wave propagation, Cem. Concr. Compos. 28 (2006) 299–306. [10] I. Pane, W. Hansen, Concrete hydration and mechanical properties under nonisothermal conditions, ACI Mater. J. 99 (6) (2002) 534–542. [11] ASTM C1679, Standard Practice for Measuring Hydration Kinetics of Hydraulic Cementitious Mixtures Using Isothermal Calorimetry, ASTM International, West Conshohocken, PA, 2009. (14 pp.). [12] A.A. Rahman, D.D. Double, Dilation of Portland cement grains during early hydration and the effect of applied hydrostatic pressure on hydration, Cem. Concr. Res. 12 (1) (1982) 33–38. [13] B. Bresson, F. Meducin, H. Zanni, C. Noik, Hydration of tricalcium silicate (C3S) at high temperature and high pressure, J. Mater. Sci. 37 (2002) 5355–5365. [14] Q. Zhou, J.J. Beaudoin, Effect of applied hydrostatic stress on the hydration of Portland cement and C3S, Adv. Cem. Res. 15 (1) (2003) 9–16. [15] F. Meducin, H. Zanni, C. Noik, G. Hamel, B. Bresson, Tricalcium silicate hydration under high pressure at ambient and high temperature (200 °C), Cem. Concr. Res. 38 (2007) 320–324. [16] F. Lin, C. Meyer, Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure, Cem. Concr. Res. 39 (2009) 255–265. [17] A.C. Jupe, A.P. Wilkinson, G.P. Funkhouser, Oil-well cement and C3S hydration under high pressure as seen by in situ X-ray diffraction, temperatures ≤80 °C with no additives, J. Am. Ceram. Soc. 94 (5) (2011) 1591–1597. [18] A.C. Jupe, A.P. Wilkinson, G.P. Funkhouser, The effect of pressure on tricalcium silicate hydration at different temperatures and in the presence of retarding additives, Cem. Concr. Res. 42 (2012) 1083–1087. [19] X. Pang, C. Meyer, R. Darbe, G.P. Funkhouser, Modeling the effect of curing temperature and pressure on cement hydration kinetics, ACI Mater. J. 110 (2) (2013) 137–148. [20] X. Pang, D.P. Bentz, C. Meyer, G.P. Funkhouser, R. Darbe, A comparison study of Portland cement hydration kinetics as measured by chemical shrinkage and isothermal calorimetry, Cem. Concr. Compos. 39 (2013) 23–32. [21] X. Pang, D.P. Bentz, C. Meyer, Modeling cement hydration kinetics using the equivalent age concept, 3rd International Symposium on UHPC and Nanotechnology for High Performance Construction Materials, Kassel, March 7–9, 2012, 2012, pp. 291–299. [22] R.H. Bogue, Calculation of the compounds in Portland cement, Ind. Eng. Chem. Anal. Ed. 1 (4) (1929) 192–197.
76
X. Pang et al. / Cement and Concrete Research 54 (2013) 69–76
[23] B. Iverson, R. Loghry, C. Edwards, Rietveld refinement of an oil field cement blend, Materials Science & Technology 2011 Conference & Exhibition, Columbus, OH, October 16–20, 2011, 2011, pp. 356–366. [24] API Recommended Practice 10B, Recommended Practice for Testing Well Cements, 22nd edition American Petroleum Institute, 1997. (146 pp.). [25] API Specification 10A, Specification for Cements and Materials for Well Cementing, American Petroleum Institute, 2010. (38 pp.). [26] J.L. Poole, K.A. Riding, K.J. Folliard, M.C.G. Juenger, A.K. Schindler, Methods for calculating activation energy for Portland cement, ACI Mater. J. 104 (1) (2007) 303–311. [27] H.W. Reinhardt, J. Blauwendraad, J. Jongendijk, Temperature development in concrete structures taking account of state dependent properties, International Conference on Concrete at Early Ages, RILEM, Paris, France, 1982, pp. 211–218.
[28] G. DeSchutter, L. Taerwe, General hydration model for Portland cement and blast furnace slag cement, Cem. Concr. Res. 25 (3) (1995) 593–604. [29] X. Pang, C. Meyer, Cement chemical shrinkage as measure of hydration kinetics and its relationship with non-evaporable water, ACI Mater. J. 109 (3) (2011) 341–352. [30] C. Hesse, F. Goetz-Neunhoeffer, J. Neubauer, A new approach in quantitative in-situ XRD of cement pastes: correlation of heat flow curves with early hydration reactions, Cem. Concr. Res. 41 (2011) 123–128. [31] D. Jansen, F. Goetz-Neunhoeffer, B. Lothenbach, J. Neubauer, The early hydration of Ordinary Portland Cement (OPC): an approach comparing measured heat flow with calculated heat flow from QXRD, Cem. Concr. Res. 42 (2012) 134–138.