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Effect of the hydration rate and microstructure of Portland cement slurry on hydrostatic pressure transfer
Powder Technology 352 (2019) 251–261
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Effect of the hydration rate and microstructure of Portland cement slurry on hydrostatic pressure transfer Kaiqiang Liu a,b, Xiaowei Cheng a,b,⁎, Xianshu Gao c, Xingguo Zhang b, Xiaoyang Guo b, Jia Zhuang a,b,⁎ a b c
School of Materials and Engineering, Southwest Petroleum University, 610500, China State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 610500, China State Key Laboratory of Green Building Materials, China Building Materials Academy, 10024, China
a r t i c l e
i n f o
Article history: Received 24 August 2018 Received in revised form 18 March 2019 Accepted 26 April 2019 Available online 30 April 2019 Keywords: Static gel strength Hydration rate Portland cement Hydrostatic pressure Microstructure
a b s t r a c t In cementing operations in oil and natural gas wells, the reduction in hydrostatic pressure of the oil-well cement (OWC) slurry is a serious threat to the quality and safety of the operations. To elucidate the mechanism of hydrostatic pressure transfer in OWC slurries, this study investigates the rules for the hydrostatic pressure transfer of OWC slurries using a hydrostatic pressure testing device. In addition, static gel strength (SGS) analysis, isothermal calorimetry, low-field nuclear magnetic resonance (LF-NMR), environmental scanning electron microscopy (ESEM), and X-ray computed tomography (μ-CT) were used to study the effects of the SGS, hydration rate, pore water, and microstructure on the hydrostatic pressure of OWC slurries. The experimental results show that the trends in the hydrostatic pressure curves of the cement slurries are similar. The hydrostatic pressure and SGS of the cement slurries vary exponentially, while the hydrostatic pressure and free water content vary linearly. Combined with the SGS results, the hydrostatic pressure curves can be divided into two stages. The first stage encompasses the range from the initial hydrostatic pressure to a pressure approximately equal to the hydrostatic pressure of water. From the hydration rate and microstructure results, it can be ascertained that this hydration stage is a dynamic balance stage. The microstructure of the cement slurry will be changed from a dispersed particles state to the gelation state, which increase the SGS of the cement slurry and the bonding ability between the cement particles and the interfaces of the casing and borehole. Part of the gravitational force of the cement particles acts on these interfaces, which reduces the hydrostatic pressure. The hydrostatic pressure in the second stage is less than that of water. This hydration stage is an acceleration stage, and the rapid hydration reactions form a large number of hydration products in the pores, which change the microstructure of the cement slurry from the gelation state to a solid state. The LF-NMR results indicate that the hydration products also reduce the pore size of the cement slurry, which causes the free water in the macropores to become capillary water and gel water. However, in the cement slurry, the hydrostatic pressure is not readily transferred by capillary water and gel water. © 2019 Elsevier B.V. All rights reserved.
1. Introduction In petroleum and natural gas engineering, the operation of running metal casings and pumping oil-well cement (OWC) slurry into the annulus space between the formation and casing is referred to as cementing. Metal casing protection and zonal isolation are the two main objectives of cementing [1,2]. However, achieving zonal isolation is often the greatest challenge, because it is difficult to predict and prevent the migration of formation fluids (including oil, natural gas, and water) into the cement slurry in the annulus space between the ⁎ Corresponding authors at: School of Materials and Engineering, Southwest Petroleum University, 610500, China. E-mail addresses: [email protected] (X. Cheng), [email protected] (J. Zhuang).
https://doi.org/10.1016/j.powtec.2019.04.066 0032-5910/© 2019 Elsevier B.V. All rights reserved.
formation and casing [3–6]. This migration of formation fluids is also called annulus migration. Fig. 1 shows a schematic diagram of annulus migration. In the 1960s, this migration problem was found in the cementing of natural gas storage [7]. Carter et al. [5,8] found that the hydrostatic pressure of the cement slurry decreases with an increase in hydration time, which results in a higher formation pressure than the hydrostatic pressure of the cement slurry. The differential pressure between the cement slurry and formation provides the driving force for the migration of formation fluids into the cement slurry during the gelation state. Therefore, some researchers [7,9,10] have investigated the cause and mechanisms of the reduction in hydrostatic pressure of the cement slurry. Zhang [9] reported that the hydrostatic pressures of various cement slurries with different properties were reduced, largely owing to the volume shrinkage of the cement slurries. Li et al. [1,10] developed a
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Fig. 2. Particle size distribution of the G-class cement determined using laser particle size.
Fig. 1. Schematic of the annulus migration process.
wellbore simulation chamber (WSC) to study the effects of the formation condition, cement type, curing temperature, and accelerator on the hydrostatic pressure of the cement slurry. The results indicated that the change law for the hydrostatic pressure of the cement slurries was nearly identical. However, hydrostatic pressure experiments conducted with an impermeable formation exhibit a faster reduction rate. Cement slurries containing greater content of accelerator or cured at higher temperatures also have a faster hydrostatic pressure reduction rate. In addition, it was suggested that the rate of cement hydration is one of the most important factors affecting the hydrostatic pressure. Some mechanisms have been proposed to describe the hydrostatic pressure reduction of the OWC slurry. By assuming that the space between the formation and casing is enclosed, Zhou et al. [4,9,11] proposed that the volume shrinkage of the cement slurry due to fluid loss and hydration will decrease the force of the cement slurry on the formation, resulting in a reduction in the hydrostatic pressure. This mechanism has also been referred to as the volume shrinkage mechanism. Tinsley et al. [5] proposed the localisation bridging mechanism. This mechanism postulates that in cement suspensions, particles may sink or the liquid of the cement slurry may be lost, which causes the particles to accumulate and form a bridge, decreasing the hydrostatic pressure of the cement slurry. Sabins et al. [12,13] proposed that the shear stress between the cement slurry and formation increases with the hydration time, which causes the hydrostatic pressure to act on the surface of the formation and casing, and decreases the hydrostatic pressure; this mechanism is referred to as the interface support mechanism.
However, in practice, these mechanisms have limitations, and some experimental results cannot be explained effectively [1,9,14]. For example, the localisation bridging mechanism can only describe the hydrostatic pressure reduction of a cement slurry in the liquid state. When cement slurry enters the gelation state, liquid loss and sedimentation in the cement slurry are negligible, but the hydrostatic pressure reduction is obvious in this stage. In the interface support mechanism, the cement slurry is assumed to be a single-phase homogeneous material. The static gel strength (SGS) [15,16] of the cement slurry is used to describe the hydrostatic pressure reduction, and the SGS of the cement slurry is proportional to the hydrostatic pressure. However, the results of practical experiments are not consistent with the interface support mechanism because this relationship is not linear, which has also been reported in Refs. [1, 9]. In the volume shrinkage mechanism, the space between the formation and casing is not enclosed. The space and
Table 1 Chemical composition and density of experimental materials. Sample Name
Density Chemical composition (wt%) (g·cm−3) C2S C3A + MgO SO3 C3S C4AF
Cement 3.25 Accelerator 2.15
60.70 16.87 17.07 0 0 0
1.99 0
K2O + CaCl2 Loss Na2O
0.75 1.23 0 0
0 100
1.39 0
Fig. 3. Fourier transform infrared (FT-IR) spectra of the: (a) dispersant, and (b) filtrate reducer.
K. Liu et al. / Powder Technology 352 (2019) 251–261 Table 2 Formulation of the cement slurries.
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Table 3 Conventional properties of cement slurries.
ID
Cement
Dispersant
Filtrate reducer
Accelerator
Water
A-1 A-2 A-3
/ / /
0.2 wt% 0.2 wt% 0.2 wt%
2 wt% 2 wt% 2 wt%
0.0 wt% 0.5 wt% 1.0 wt%
44 wt% 44 wt% 44 wt%
formation undergo mass exchange and transfer (shown in Fig. 1(b)). Therefore, the mechanism of hydrostatic pressure transfer in OWC slurries needs to be investigated further to establish a theoretical principle to describe the annulus migration in oil and natural gas wells. In actual cementing operations, different hydration rates and thickening times (shown in API specification 10-B [17]) of the OWC slurry are required in oil and natural gas wells with different depths. In this study, a CaCl2 accelerator was used to control the hydration rate of the OWC slurries, as reported in previous literature [18–20], and the cement slurry was considered a solid–fluid two phase material, as reported by Qi et al. [21–23]. The hydrostatic pressure of the cement slurries with hydration time was investigated. A number of methods, such as static gel strength (SGS) analysis, isothermal calorimetry, low-field nuclear magnetic resonance (LF-NMR), environmental scanning electron microscopy (ESEM), and X-ray computed tomography (μ-CT), were applied to investigate the effect of the SGS, hydration rate, pore water, and microstructure of the cement slurry on the hydrostatic pressure during the early hydration stage. Finally, some possible causes and mechanisms for the reduction in hydrostatic pressure of the cement slurry are presented and analysed. These results suggest some theoretical principles for understanding the hydrostatic pressure transfer in OWC slurries, and can provide some guidance for avoiding annulus migration in oil and natural gas wells. 2. Experimental program
ID
Density (g·cm−3)
Rheological index
Initial setting time (min)
Static fluid loss (mL)
Free-fluid (%)
A-1 A-2 A-3
1.90 1.91 1.91
0.79 0.77 0.76
495 441 372
35 36 34
0 0 0
2-acrylamido-2-methyl-1-propane sulfonic acid / acrylamide / acrylic acid (AMPS/AM/AA) terpolymer contains a large number of hydrophilic amides, sulfonates, and carbonyls, which can increase the viscosity of the cement slurry and adsorb on the surface of cement particles; it is used as the filtrate reducer, which has also been called the fluid loss additive in previous studies [29–31]. Fig. 3 shows the spectra of the dispersant and filtrate reducer. In addition, calcium chloride (CaCl2) is used as the accelerator, as reported by Ref. [18–20]. These additives were supplied by the Weihui Chemical Co. Table 2 lists the formulation of the cement slurries used in the experiments. The additives content was calculated based on the weight of the cement. The cement slurries were prepared, and properties including the density, rheological properties, static fluid loss, thickening time, and free-fluid content were tested according to API specification 10B2 [17]. 2.2. Methods 2.2.1. Hydration rate analysis The hydration of cement slurry is an exothermic reaction, and thus the hydration rate can be obtained by measuring the heat flow of the hydration processes [32,33]. In these experiments, a TAM Air 8channel isothermal calorimeter (TA instruments, USA) was used to measure the heat flow of the cement slurries at 30 °C.
2.1. Materials The G-class high sulphate-resistant OWC (G-class cement) used in these experiments was supplied by the Sichuan Jiahua Co. The chemical composition of the cement was tested according to API specification RP10A [24] and is listed in Table 1. Fig. 2 shows the particle size distribution of the G-class cement; its specific surface area is 0.5611 m2/g. In the cement slurries, sulfonated acetone-formaldehyde condensate is used as a dispersant, as reported by George et al. [25–28]. The
2.2.2. Hydrostatic pressure analysis Fig. 4 shows an image and schematic illustration of the hydrostatic pressure testing device used to evaluate the hydrostatic pressure of the cement slurries. The device consists of computer, pressure measurement, temperature control, and simulated borehole systems. To ensure the bonding ability between the cement sample and the simulated borehole and casing, the inner surface of the simulated borehole and the surface of the simulated casing were roughened. The experimental
Fig. 4. Image and schematic illustration of the hydrostatic pressure testing device.
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Fig. 5. Hydrostatic pressure curves for the cement slurries.
procedure is as follows: ① the hydrostatic pressure testing device is assembled and the experimental temperature is set to 30 °C; ② the cement slurry is prepared according to API specification 10B-2 [17], and the prepared slurry is poured into the annulus space between the simulated borehole and the casing; ③ the hydrostatic pressure of the cement slurry is recorded. 2.2.3. Static gel strength (SGS), setting time, and volume change ratio The SGS is an important parameter in the investigation of the hydrostatic pressure and inter-microstructure of cement slurries [16,34]. In previous studies, mechanical methods were used to determine the shear strength between cement particles and evaluate the SGS of the cement slurry [12,35,36]. In these experiments, an SGS analyser (model 5265 U, Chandler engineering, USA) was used to determine the SGS of the cement slurry. This is an in situ non-destructive detection method that determines the SGS (b600 Pa) by monitoring ultrasonic signal changes through the cement slurry. Meanwhile, the setting times of the cement slurries were measured with a Vicat Needle according to ASTM specification C191 [37]. The volume change ratio of the cement
Fig. 7. Static gel strength curves for the cement slurries.
slurries was tested with a cement volume testing analyser (Applied Technology Research Institute of SAU, China). 2.2.4. Pore water distribution analysis In these experiments, an LF-NMR analyser (Suzhou Niumag, China) was used to investigate the water distribution and pore structure of the cement slurry during the stage of hydrostatic pressure reduction. LF-NMR imaging can probe the transverse relaxation time (T2) of the water molecules in pores to analyse the pore characteristics [38,39]; T2 is given by Eq. (1) [40]. Cement slurry is a porous material, and the pores are filled with water. 1 1 1 1 1 S ¼ ρ2 ¼ þ þ ≈ T 2 T 2s T 2b T 2d T 2s V
ð1Þ
where T2s is the value of T2 associated with the surface relaxation, T2b is the value of T2 for the pore water in the bulk state, T2d is the value of T2 associated with diffusion in the magnetic field gradient, ρ2 is the surface relaxivity, S is the surface area of the pores, and V is the pore water vol ume. In general, T2b and T2d are much larger than T2s, and thus 1 T and 2d 1 are negligible. Therefore, in Eq. (1), T2 is dominated by T2s. T 2b
2.2.5. Microstructure analysis In these experiments, X-ray computed tomography (μ-CT; GE Sensing & inspection technologies GmbH, Germany) was used for continuous in situ monitoring of microstructural changes in the cement slurry; the microstructure of the cement slurry was analysed at 1 h intervals at 30 °C. In addition, environmental scanning electron microscopy (ESEM; FEI Company, USA) was used to analyse the microstructure of the cement slurry. After the cement slurry specimen was cured for the
Fig. 6. Hydrostatic pressure and hydration heat of the cement slurries.
Fig. 8. Mathematical relationship between the hydrostatic pressure and SGS.
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Fig. 9. Photos of the interfaces between the simulated borehole, casing, and cement samples after the experiments.
scheduled amount of time at 30 °C, it was frozen in liquid nitrogen and vacuum freeze-dried to prepare the sample for the ESEM analysis. Finally, gold was sprayed on the dried specimen, and the microstructure of the cement slurry was analysed using ESEM. 3. Results and discussion 3.1. Hydrostatic pressure and hydration rate of the cement slurries Table 3 summarises the conventional properties of cement slurries according to API specification 10B-2 [17], which meet the requirements for cementing operations. As CaCl2 can increase the hydration rate of cement slurries, the initial setting time is reduced. Fig. 5 shows the hydrostatic pressure curves for the cement slurries. The hydrostatic pressure of the cement slurries decreases with the increase in hydration time. These hydrostatic pressure curves can be divided into two stages. The first stage occurs before the hydrostatic pressure of cement slurry decays to that of water, and the second stage encompasses the hydrostatic pressure decay from the hydrostatic pressure of water to zero. In the first stage, the cement slurries retain hydrostatic pressure, which decreases slowly; the three curves are similar. In the second stage, the hydrostatic pressure decreases rapidly, and the hydrostatic pressure of the cement slurry with a high CaCl2 content decreases faster than that of the other cement slurries. Fig. 6(a) shows the heat flow curves for the A-1, A-2, and A-3 cement slurry specimens. There is no obvious difference between the peak height and peak width in the heat flow curves for the cement slurries. However, when the hydration time of the A-1 cement slurry is 986 min, the heat flow reaches a maximum; the peak value of the A-2 cement slurry occurs at 930 min, and the peak value of the A-3 cement slurry occurs at 820 min. Moreover, these results and the hydrostatic
pressure curves for the A-1, A-2, and A-3 cement slurries (shown in Fig. 5) indicate that the hydrostatic pressure of the cement slurries decreases with an increase in heat flow, particularly when the hydrostatic pressure is in the second stage (as shown in Fig. 6(b)). When the hydration rate of the cement slurries is accelerated, the rate of reduction of the hydrostatic pressure increases markedly. Thus, with an increase in hydration time, large amount of hydration products are formed, which change the microstructure and pore structure of the cement slurries. 3.2. SGS of the cement slurries Fig. 7 shows the SGS curves for the cement slurries. At a hydration time of approximately 400 min, the SGS of the A-1 cement slurry (without CaCl2) increases rapidly, and the SGS reaches 600 Pa at a hydration time of 476 min. However, the SGS of the A-3 cement slurry (with 1.0 wt% CaCl2) reaches 600 Pa at a hydration time of only 333 min. Therefore, CaCl2 can improve the hydration rate and develop the intermicrostructure and SGS of the cement slurries. Kishar et al. [18,41–43] also reported that CaCl2 could increase the hydration rate and improve the early strength of cement slurries. 3.3. Relationship between the hydrostatic pressure and SGS Fig. 8 shows the relationship between the hydrostatic pressure and SGS of the A-1, A-2, and A-3 cement slurries. These curves can be divided into 3 stages, which is in agreement with the results reported by Li et al. [1,9,44]. When the SGS of the cement slurries is approximately 36–48 Pa, the change in hydrostatic pressure is not obvious. In this stage, the fluidity of the cement slurry is good and its microstructure is in a dispersed state, and thus the hydrostatic pressure of the cement slurry can be transferred effectively. When the SGS increases to
Fig. 10. Illustrations of the (a) cement slurry column, (b) microstructure of the fresh cement slurry, and (c) microstructure of the hardened cement slurry.
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48–76 Pa, the hydrostatic pressure of the cement slurry decreases sharply. In this stage, the SGS of the cement slurry develops rapidly and the microstructure of the cement slurry changes from a dispersed state to the gelation state, which increases the bonding ability between the cement slurry and the interfaces of the borehole and casing, enabling the hydrostatic pressure of the cement slurry to act on the interfaces. Finally, when the SGS is N76 Pa, the hydrostatic pressure of the cement slurry decreases slowly, and the transfer method of the cement slurry hydrostatic pressure may be changed. The experimental results show that for SGS of approximately 48 Pa to 600 Pa, an exponential function can be employed to describe the relationship between the hydrostatic pressure and the SGS of the cement slurries, which is more appropriate than the linear function previously proposed by Sabins et al. [12,13]. However, even when the SGS reaches 600 Pa and the hydration time is longer than the initial setting time, the cement slurries still retain some hydrostatic pressure. In this stage, the hydrostatic pressure of the cement slurries may be transferred by the pore water. The SGS of the cement slurry can reflect the bonding ability between cement particles, which increases with the SGS, as reported in Refs. [1, 34, 36, 45]. Moreover, the bonding ability between the cement slurry and the borehole and casing may also increase, causing the gravitational force of the cement slurry to act on the borehole and casing. Fig. 9 shows photos of the interfaces between the simulated borehole, casing, and cement sample after the experiments. It can be seen that there is a significant amount of residual cement sample on the surface of the simulated borehole and casing. Therefore, in the early stage of hydration, the hydrostatic pressure of the cement slurry rapidly decreases with the increase in SGS. Fig. 10 depicts the cement slurry column, microstructure of the fresh cement slurry, and microstructure of the hardened cement slurry. Based on the results in Fig. 9, the bonding ability between the cement slurry and the borehole and casing is assumed to be similar to the SGS of the cement slurry. Therefore, based on the law of conservation of mass, when the gravitational force of the cement particles acts on the borehole and casing, the SGS can be calculated from Eq. (2). With an increase in hydration time, the solid-phase density, ρsolid, and porosity, pcem, of the cement slurry will change. h i ρsolid g ð1‐pcem Þ ð1 þ vcem Þ πR2 ‐πr 2 dh ¼ 2τcem π ðR þ r Þdh ρsolid g ð1‐pcem ÞðR‐r Þð1 þ vcem Þ ¼ τ cem 2
ð2Þ
ð3Þ
where ρsolid is the solid-phase density (kg·m−3), pcem is the fluid volume content of the cement slurry, g is the gravitational acceleration (N·kg−1),
Fig. 11. Volume change ratio results for the cement slurries obtained using a cement volume testing analyser.
Fig. 12. Transverse relaxation time (T2) for the A-1 cement slurry at different hydration times, determined using LF-NMR.
R is the internal diameter of the borehole (m), r is the external diameter of the casing (m), vcem is the volume change ratio of the cement slurry, and. τcem is the SGS of the cement slurry (Pa). From Eq. (3), it can be found that the volume change ratio of the cement slurry is a key parameter in the calculation of τcem. Fig. 11 shows the volume change ratio of the cement slurries. From the free-fluid results specified by API [17] (listed in Table 3), it can be seen that the stability of the cement slurries is good, and thus the cement particles are assumed to be evenly dispersed in the cement slurry. In the experiments, the water to cement ratio (W/C) of the cement slurry was 0.44. Thus, the fluid volume content (pcem) of the fresh cement slurry is approximately 0.588, and (R-r) is 0.02 m. Based on the SGS (shown in Fig. 7) and volume change ratio (shown in Fig. 11) results, at a hydration time of 480 min, vcem is approximately −0.0004, which can be ignored. Based on these parameters, when the gravitational force of the cement particles acts on the simulated borehole and casing, τcem is 131.36 Pa. These experimental results (shown in Fig. 5 and Fig. 7) and the calculated results indicate that the decrease in hydrostatic pressure is caused not only by the increase in SGS, but also by other synergistic effects arising with the increase in hydration time. Therefore, to understand the mechanism of the hydrostatic pressure reduction during the hydration of cement slurries, the hydration rate, pore water, and microstructure of the cement slurry must be understood. 3.4. Effect of pore water on the hydrostatic pressure In a cement slurry, the evolution of the pore structure will change the pore water distribution. Fig. 12 shows the transverse relaxation time (T2) for the A-1 cement slurry. The T2 curves for the cement slurry have two peaks: the first peak at 0.01–25 ms, and a second peak at T2 N 100 ms. McDonald et al. [46–48] established a relationship between T2 and the pore diameter of a cement slurry, and the pore water of the
Fig. 13. Relationship between the hydrostatic pressure and T2 curve area.
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Fig. 14. Pore water distribution and the effect of free water on the hydrostatic pressure.
cement slurry was classified into three categories: free water in macropores, capillary water in capillary pores, and the gel water of hydration products. The T2 for the gel water was defined as b1.5 ms, the T2 for capillary water was defined as 1.5–7.5 ms, and the T2 of free water was defined as N7.5 ms. As seen in Fig. 12, the primary T2 peak for the fresh cement slurry (hydration time of 0 min) is around 3.0–20.7 ms with an amplitude of 1543.4. At a hydration time of 120 min, the main T2 peak for the cement slurry is around 2.7–22.2 ms with an amplitude of 1442.3. Thus, the pore water in fresh cement slurry is mainly composed of capillary water and free water. The widening of the T 2 range may be caused by the sedimentation of some particles in the pores with an increase in static time, resulting in a wider distribution of pore sizes. In addition, some components of fresh cement slurry, such as calcium oxide (CaO), hemihydrate gypsum (CaSO4·0.5H2O), and tricalcium silicate (3CaO·SiO 2 ), will react with free water to form structural water and reduce the amplitude of T2. At a hydration time of 180 min, the T2 curve for the cement slurry starts to shift to the left. Finally, at hydration times from about 360 min to 420 min, the T2 curve shifts rapidly to the left. From the heat flow curves (shown in Fig. 6), it can be seen that at a hydration time of about 360–420 min, the hydration rate of the cement slurry is accelerated, and many hydration products are formed. These hydration products decrease the pore size of the cement slurry, which changes the pore water distribution in the cement slurry from free water to capillary water and gel water.
3.4.1. Relationship between the T2 curve area and hydrostatic pressure According to Eq. (1), the distribution of T2 in a cement slurry is related to the volume and surface area of the pores. If the pore shape is assumed to be spherical or cylindrical, T2 will be proportional to the pore diameter, as reported by previous studies [46,49,50]. Therefore, the T2 results for the cement slurry can be used to describe the pore size distribution, and the T2 curve area is related to the pore volume and porosity of the cement slurry. Fig. 13 shows the relationship between the T2 curve area and the hydrostatic pressure of the cement slurry; it can be seen that there is a linear relationship. The results in Fig. 13 confirm that the porosity or pore volume of the cement slurry is proportional to the hydrostatic pressure. 3.4.2. Relationship between the pore water distribution and hydrostatic pressure Based on the experimental results reported by McDonald et al. [46–48], the pore water distribution of the cement slurry can be quantitatively determined from the T 2 curve area (shown in Fig. 12). Fig. 14 shows the change in the free water, capillary water, and gel water content with an increase in hydration time. Combining the results in Fig. 5 and Fig. 14(a), the following information can be obtained: (1) In fresh cement slurry, the pore water consists of free water and capillary water. During the hydrostatic pressure reduction of the cement slurry, much of the free water is converted to capillary
Fig. 15. Evolution of the pore structure and microstructure of the cement slurry.
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Fig. 16. Microstructure of the A-1 cement slurry at different hydration times.
water, and some gel water is formed when the hydration time reaches 540 min. (2) The variation trend for the free water is similar to that of the hydrostatic pressure in the cement slurry, and Fig. 14(b) shows that the free water content and hydrostatic pressure are linearly correlated. The experimental results demonstrate that the decrease in free water content of the cement slurry is one of the most important factors contributing to the hydrostatic pressure reduction. In stage II of the hydrostatic pressure reduction, the hydration rate of the cement slurry is accelerated, and a large number of hydration products are formed in the pores, causing the microstructure of the cement slurry to change as macropores are converted to numerous capillary pores and gel pores, which changes the pore water distribution. At the same time, the bonding ability between the cement particles and interfaces of the simulated borehole and casing will be increased. Fig. 15 shows the evolution of the pore structure and microstructure of the cement slurry. In this study, μ-CT and ESEM were used to investigate the evolution of the microstructure and pore structure of the A-1 cement slurry during the cement hydration process.
hydration products was also reported in Refs. [52, 53]. Finally, these hydration products cause the macropores to split into numerous micropores. According to the ESEM results, the binary images of the pores and solid-phase in the ESEM images were analysed using Image-Pro-Plus. In combination with the inflection point methods [54–56], the gray threshold values of pores in the ESEM images were set to 65 (as shown in Fig. 17), and the solid-phase in the grayscale ESEM images was filled with white, the other area was pores. The pore structure and size in the cement slurry were investigated at different hydration times. Fig. 18 shows the results for the pore structure and size in the cement slurry. The pore size of the cement slurry decreases with an increase in hydration time. From the results in Fig. 18(a) and Fig. 18(b), it can be seen that in stage I of the hydrostatic pressure reduction of the cement slurry, the change in pore structure is not obvious, and there are many macropores in the cement slurry. However, in stage II of the hydrostatic pressure reduction of the cement slurry (i.e. hydration times from 360 min to 600 min), the number of macropores decreases noticeably, and a large number of micropores are formed, as reported by Karakosta et al. [49]. Combining the results in Fig. 12 and Fig. 16, it can be determined that when the hydration
3.5. Microstructure 3.5.1. ESEM microstructure Fig. 16 shows the microstructure of the A-1 cement slurry obtained with ESEM. As seen in Fig. 16(a), the surface of unhydrated cement particles is smooth. When the cement particles, dispersant, filtrate reducer, and water are mixed, polymers adsorb on the surface of the cement particles. This serves to connect the dispersed cement particles and suspend the cement particles in the cement slurry, as shown in Fig. 16 (b), which is in agreement with results reported by Xia et al. [31,51]. At a cement slurry hydration time of 240 min, new hydration products can be observed in the pores and on the surface of the polymers, as shown in Fig. 16(c). At a hydration time of 360 min, the hydration products cover the polymers, as shown in Fig. 16 (d), and connect the cement particles. In Fig. 16(e) and Fig. 16(f), a large number of porous hydration products can be observed, and the presence of these porous
Fig. 17. Assessing pore threshold level via the inflection point method.
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Fig. 18. Pore distribution in the cement slurry.
reaction of the cement slurry is in the acceleration period, many hydration products formed in the pores, which changed the pore size from macropores to micropores. This process will change the pore water state and distribution in the cement slurry; the pore water distribution changes from free water in the macropores to capillary water and even gel water. In the cement slurry, the transmission capacity for hydrostatic pressure of the pore water in micropores is less than that of pore water in macropores. 3.5.2. μ-CT microstructure To observe the change in pore structure of the cement slurry in stage II of the hydrostatic pressure reduction, μ-CT was used analyse the in situ microstructure of the cement slurry. Fig. 19 shows the in situ μ-CT microstructure of the cement slurry. It can be seen that the solidphase volume increases with the hydration time; a new solid phase forms around the cement particles and fills the macropores, which are then divided into many micropores. In the early stage of hydration, the polymers can form a reticular structure that has great deformability. Therefore, the gravitational force of the cement particles can be transferred by the pore water,
which can maintain the hydrostatic pressure in the cement slurry (as shown in Figs. 5 and 16). With an increase in hydration time, some hydration products form on the polymer surface and connect the dispersed cement particles in the cement slurry. Because these hydration products have a higher mechanical strength than the polymers, the transfer of the gravitational force of the cement particles by the hydration products is more difficult. The hydration products connect the cement particles, which increases the mechanical strength of the cement slurry. Moreover, they can also play a role in connecting the cement slurry and the borehole and casing, which causes the gravitational force of the cement particles to act on the casing and borehole. This process will cause the hydrostatic pressure of the cement slurry to decrease slowly in stage I; at the end of stage I, the hydrostatic pressure of the cement slurry is maintained only by the pore water. In stage II of the hydrostatic pressure reduction, the pore size and distribution of the cement slurry change from macropores to micropores with an increase in hydration product content. This process changes the pore water state. In the cement slurry, it is difficult for capillary water and gel water to transfer the hydrostatic pressure.
Fig. 19. Sectional drawing of the 3D microstructure of the A-1 cement slurry at different hydration times.
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4. Conclusion From the experimental results of this study, the following conclusions can be obtained: the increase in SGS and change in pore water distribution during the hydration process are the main factors affecting the hydrostatic pressure reduction in cement slurries. The hydrostatic pressure and SGS of the cement slurry vary exponentially, and the hydrostatic pressure and free water content vary linearly. Therefore, the hydrostatic pressure curve of the cement slurry can be divided into two stages: 1) In the first stage, the cement slurry maintains hydrostatic pressure, and the hydrostatic pressure decreases slowly. At this stage, some hydration products are formed in the pores, and these hydration products connect the dispersed cement particles and increase the SGS of the cement slurry. This increase will cause some of the gravitational force of the cement particles to act on the borehole and casing, and thus the hydrostatic pressure of the cement slurry decreases. 2) In the second stage, the hydrostatic pressure of the cement slurry decreases rapidly. In this stage, the main cause of hydration pressure reduction is the increase in SGS of the cement slurry and the acceleration of the hydration reaction, which changes the microstructure and the distribution of pore water. The rapid hydration reactions form a large number of hydration products in the pores, which causes the macropores to transform into many capillary and gel pores. Owing to the change in pore diameter, the pore water in the cement slurry changes from free water to capillary water and gel water. In the cement slurry, the hydrostatic pressure is less readily transferred by capillary water and gel water.
Acknowledgments The authors are grateful for the support provided by the National Key R&D Program of China (2016YFB0303600) and the China Scholarship Council (No. 201808510194). The authors would also like to thank the Advanced Cementing Materials Research Center of SWPU for the kind assistance in laboratory testing. References [1] Z. Li, J. Vandenbossche, A. Iannacchione, J. Brigham, B. Kutchko, Theory-based review of limitations with static gel strength in cement/matrix characterization, SPE Drill. Complet. 31 (2016) 145–158, https://doi.org/10.2118/178923-PA. [2] K. Liu, X. Cheng, X. Zhang, X. Guo, J. Zhuang, Design of low-density cement optimized by cellulose-based fibre for oil and natural gas wells, Powder Technol. 338 (2018) 506–518, https://doi.org/10.1016/j.powtec.2018.07.016. [3] A. Bonett, D. Pafitis, Getting to the root of gas migration, Oilf. Rev. 8 (1996) 36–49. [4] B.R. Crook, J. Heathman, Predicting Potential Gas-Flow Rates to Determine Best Cementing Practices Short-Term Gas Migration, 1998. [5] J.M. Tinsley, E.C. Miller, F.L. Sabins, D.L. Sutton, Study of factors causing annular gas flow following primary cementing, 54th Annu. Fall Tech. Conf. Exhib., 32, SPE AIME, Las Vegas, Nevada, USA 1980, pp. 1427–1437, https://doi.org/10.2118/ 8257-PA. [6] P.R. Cheung, R. Beirute, Gas flow in cements, J. Pet. Technol. 37 (1985) 1041–1048, https://doi.org/10.2118/11207-PA. [7] T.L. Rigby, Gas Migration in Oilwell Cements, Howard University, 2008. [8] G. Carter, K. Slagle, A study of completion practices to minimize gas communication, J. Pet. Technol. 26 (1972) 1170–1174, https://doi.org/10.2118/3164-PA. [9] X. Zhang, Study on Weightlessness Mechanisms of Slurry Suspension during Cement Gelation, Southwest Petroleum University, 2002. [10] Z. Li, Development of Wellbore Simulator for Better Understanding Oil Well Cement Behavior and Gas Migration during Early Gelation, University of Pittsburgh, 2015. [11] D. Zhou, A.K. Wojtanowicz, New model of pressure reduction to annulus during primary cementing, IADC/SPE Drill. Conf. Society of Petroleum Engineers, New Orleans, Louisiana, 2000, https://doi.org/10.2118/59137-MS , p. SPE-59137-MS. [12] F.L. Sabins, J.M. Tinsley, D.L. Sutton, Transition time of cement slurries between the fluid and set states, SPE J. 22 (1982) 875–882, https://doi.org/10.2118/9285-PA. [13] D.L. Sutton, R. Faul, F. Sabins, Annular gas flow theory and prevention methods described, Oil Gas J. (United States) 82 (1984) 50.
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Effect of the hydration rate and microstructure of Portland cement slurry on hydrostatic pressure transfer Kaiqiang Liu a,b, Xiaowei Cheng a,b,⁎, Xianshu Gao c, Xingguo Zhang b, Xiaoyang Guo b, Jia Zhuang a,b,⁎ a b c
School of Materials and Engineering, Southwest Petroleum University, 610500, China State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 610500, China State Key Laboratory of Green Building Materials, China Building Materials Academy, 10024, China
a r t i c l e
i n f o
Article history: Received 24 August 2018 Received in revised form 18 March 2019 Accepted 26 April 2019 Available online 30 April 2019 Keywords: Static gel strength Hydration rate Portland cement Hydrostatic pressure Microstructure
a b s t r a c t In cementing operations in oil and natural gas wells, the reduction in hydrostatic pressure of the oil-well cement (OWC) slurry is a serious threat to the quality and safety of the operations. To elucidate the mechanism of hydrostatic pressure transfer in OWC slurries, this study investigates the rules for the hydrostatic pressure transfer of OWC slurries using a hydrostatic pressure testing device. In addition, static gel strength (SGS) analysis, isothermal calorimetry, low-field nuclear magnetic resonance (LF-NMR), environmental scanning electron microscopy (ESEM), and X-ray computed tomography (μ-CT) were used to study the effects of the SGS, hydration rate, pore water, and microstructure on the hydrostatic pressure of OWC slurries. The experimental results show that the trends in the hydrostatic pressure curves of the cement slurries are similar. The hydrostatic pressure and SGS of the cement slurries vary exponentially, while the hydrostatic pressure and free water content vary linearly. Combined with the SGS results, the hydrostatic pressure curves can be divided into two stages. The first stage encompasses the range from the initial hydrostatic pressure to a pressure approximately equal to the hydrostatic pressure of water. From the hydration rate and microstructure results, it can be ascertained that this hydration stage is a dynamic balance stage. The microstructure of the cement slurry will be changed from a dispersed particles state to the gelation state, which increase the SGS of the cement slurry and the bonding ability between the cement particles and the interfaces of the casing and borehole. Part of the gravitational force of the cement particles acts on these interfaces, which reduces the hydrostatic pressure. The hydrostatic pressure in the second stage is less than that of water. This hydration stage is an acceleration stage, and the rapid hydration reactions form a large number of hydration products in the pores, which change the microstructure of the cement slurry from the gelation state to a solid state. The LF-NMR results indicate that the hydration products also reduce the pore size of the cement slurry, which causes the free water in the macropores to become capillary water and gel water. However, in the cement slurry, the hydrostatic pressure is not readily transferred by capillary water and gel water. © 2019 Elsevier B.V. All rights reserved.
1. Introduction In petroleum and natural gas engineering, the operation of running metal casings and pumping oil-well cement (OWC) slurry into the annulus space between the formation and casing is referred to as cementing. Metal casing protection and zonal isolation are the two main objectives of cementing [1,2]. However, achieving zonal isolation is often the greatest challenge, because it is difficult to predict and prevent the migration of formation fluids (including oil, natural gas, and water) into the cement slurry in the annulus space between the ⁎ Corresponding authors at: School of Materials and Engineering, Southwest Petroleum University, 610500, China. E-mail addresses: [email protected] (X. Cheng), [email protected] (J. Zhuang).
https://doi.org/10.1016/j.powtec.2019.04.066 0032-5910/© 2019 Elsevier B.V. All rights reserved.
formation and casing [3–6]. This migration of formation fluids is also called annulus migration. Fig. 1 shows a schematic diagram of annulus migration. In the 1960s, this migration problem was found in the cementing of natural gas storage [7]. Carter et al. [5,8] found that the hydrostatic pressure of the cement slurry decreases with an increase in hydration time, which results in a higher formation pressure than the hydrostatic pressure of the cement slurry. The differential pressure between the cement slurry and formation provides the driving force for the migration of formation fluids into the cement slurry during the gelation state. Therefore, some researchers [7,9,10] have investigated the cause and mechanisms of the reduction in hydrostatic pressure of the cement slurry. Zhang [9] reported that the hydrostatic pressures of various cement slurries with different properties were reduced, largely owing to the volume shrinkage of the cement slurries. Li et al. [1,10] developed a
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Fig. 2. Particle size distribution of the G-class cement determined using laser particle size.
Fig. 1. Schematic of the annulus migration process.
wellbore simulation chamber (WSC) to study the effects of the formation condition, cement type, curing temperature, and accelerator on the hydrostatic pressure of the cement slurry. The results indicated that the change law for the hydrostatic pressure of the cement slurries was nearly identical. However, hydrostatic pressure experiments conducted with an impermeable formation exhibit a faster reduction rate. Cement slurries containing greater content of accelerator or cured at higher temperatures also have a faster hydrostatic pressure reduction rate. In addition, it was suggested that the rate of cement hydration is one of the most important factors affecting the hydrostatic pressure. Some mechanisms have been proposed to describe the hydrostatic pressure reduction of the OWC slurry. By assuming that the space between the formation and casing is enclosed, Zhou et al. [4,9,11] proposed that the volume shrinkage of the cement slurry due to fluid loss and hydration will decrease the force of the cement slurry on the formation, resulting in a reduction in the hydrostatic pressure. This mechanism has also been referred to as the volume shrinkage mechanism. Tinsley et al. [5] proposed the localisation bridging mechanism. This mechanism postulates that in cement suspensions, particles may sink or the liquid of the cement slurry may be lost, which causes the particles to accumulate and form a bridge, decreasing the hydrostatic pressure of the cement slurry. Sabins et al. [12,13] proposed that the shear stress between the cement slurry and formation increases with the hydration time, which causes the hydrostatic pressure to act on the surface of the formation and casing, and decreases the hydrostatic pressure; this mechanism is referred to as the interface support mechanism.
However, in practice, these mechanisms have limitations, and some experimental results cannot be explained effectively [1,9,14]. For example, the localisation bridging mechanism can only describe the hydrostatic pressure reduction of a cement slurry in the liquid state. When cement slurry enters the gelation state, liquid loss and sedimentation in the cement slurry are negligible, but the hydrostatic pressure reduction is obvious in this stage. In the interface support mechanism, the cement slurry is assumed to be a single-phase homogeneous material. The static gel strength (SGS) [15,16] of the cement slurry is used to describe the hydrostatic pressure reduction, and the SGS of the cement slurry is proportional to the hydrostatic pressure. However, the results of practical experiments are not consistent with the interface support mechanism because this relationship is not linear, which has also been reported in Refs. [1, 9]. In the volume shrinkage mechanism, the space between the formation and casing is not enclosed. The space and
Table 1 Chemical composition and density of experimental materials. Sample Name
Density Chemical composition (wt%) (g·cm−3) C2S C3A + MgO SO3 C3S C4AF
Cement 3.25 Accelerator 2.15
60.70 16.87 17.07 0 0 0
1.99 0
K2O + CaCl2 Loss Na2O
0.75 1.23 0 0
0 100
1.39 0
Fig. 3. Fourier transform infrared (FT-IR) spectra of the: (a) dispersant, and (b) filtrate reducer.
K. Liu et al. / Powder Technology 352 (2019) 251–261 Table 2 Formulation of the cement slurries.
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Table 3 Conventional properties of cement slurries.
ID
Cement
Dispersant
Filtrate reducer
Accelerator
Water
A-1 A-2 A-3
/ / /
0.2 wt% 0.2 wt% 0.2 wt%
2 wt% 2 wt% 2 wt%
0.0 wt% 0.5 wt% 1.0 wt%
44 wt% 44 wt% 44 wt%
formation undergo mass exchange and transfer (shown in Fig. 1(b)). Therefore, the mechanism of hydrostatic pressure transfer in OWC slurries needs to be investigated further to establish a theoretical principle to describe the annulus migration in oil and natural gas wells. In actual cementing operations, different hydration rates and thickening times (shown in API specification 10-B [17]) of the OWC slurry are required in oil and natural gas wells with different depths. In this study, a CaCl2 accelerator was used to control the hydration rate of the OWC slurries, as reported in previous literature [18–20], and the cement slurry was considered a solid–fluid two phase material, as reported by Qi et al. [21–23]. The hydrostatic pressure of the cement slurries with hydration time was investigated. A number of methods, such as static gel strength (SGS) analysis, isothermal calorimetry, low-field nuclear magnetic resonance (LF-NMR), environmental scanning electron microscopy (ESEM), and X-ray computed tomography (μ-CT), were applied to investigate the effect of the SGS, hydration rate, pore water, and microstructure of the cement slurry on the hydrostatic pressure during the early hydration stage. Finally, some possible causes and mechanisms for the reduction in hydrostatic pressure of the cement slurry are presented and analysed. These results suggest some theoretical principles for understanding the hydrostatic pressure transfer in OWC slurries, and can provide some guidance for avoiding annulus migration in oil and natural gas wells. 2. Experimental program
ID
Density (g·cm−3)
Rheological index
Initial setting time (min)
Static fluid loss (mL)
Free-fluid (%)
A-1 A-2 A-3
1.90 1.91 1.91
0.79 0.77 0.76
495 441 372
35 36 34
0 0 0
2-acrylamido-2-methyl-1-propane sulfonic acid / acrylamide / acrylic acid (AMPS/AM/AA) terpolymer contains a large number of hydrophilic amides, sulfonates, and carbonyls, which can increase the viscosity of the cement slurry and adsorb on the surface of cement particles; it is used as the filtrate reducer, which has also been called the fluid loss additive in previous studies [29–31]. Fig. 3 shows the spectra of the dispersant and filtrate reducer. In addition, calcium chloride (CaCl2) is used as the accelerator, as reported by Ref. [18–20]. These additives were supplied by the Weihui Chemical Co. Table 2 lists the formulation of the cement slurries used in the experiments. The additives content was calculated based on the weight of the cement. The cement slurries were prepared, and properties including the density, rheological properties, static fluid loss, thickening time, and free-fluid content were tested according to API specification 10B2 [17]. 2.2. Methods 2.2.1. Hydration rate analysis The hydration of cement slurry is an exothermic reaction, and thus the hydration rate can be obtained by measuring the heat flow of the hydration processes [32,33]. In these experiments, a TAM Air 8channel isothermal calorimeter (TA instruments, USA) was used to measure the heat flow of the cement slurries at 30 °C.
2.1. Materials The G-class high sulphate-resistant OWC (G-class cement) used in these experiments was supplied by the Sichuan Jiahua Co. The chemical composition of the cement was tested according to API specification RP10A [24] and is listed in Table 1. Fig. 2 shows the particle size distribution of the G-class cement; its specific surface area is 0.5611 m2/g. In the cement slurries, sulfonated acetone-formaldehyde condensate is used as a dispersant, as reported by George et al. [25–28]. The
2.2.2. Hydrostatic pressure analysis Fig. 4 shows an image and schematic illustration of the hydrostatic pressure testing device used to evaluate the hydrostatic pressure of the cement slurries. The device consists of computer, pressure measurement, temperature control, and simulated borehole systems. To ensure the bonding ability between the cement sample and the simulated borehole and casing, the inner surface of the simulated borehole and the surface of the simulated casing were roughened. The experimental
Fig. 4. Image and schematic illustration of the hydrostatic pressure testing device.
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Fig. 5. Hydrostatic pressure curves for the cement slurries.
procedure is as follows: ① the hydrostatic pressure testing device is assembled and the experimental temperature is set to 30 °C; ② the cement slurry is prepared according to API specification 10B-2 [17], and the prepared slurry is poured into the annulus space between the simulated borehole and the casing; ③ the hydrostatic pressure of the cement slurry is recorded. 2.2.3. Static gel strength (SGS), setting time, and volume change ratio The SGS is an important parameter in the investigation of the hydrostatic pressure and inter-microstructure of cement slurries [16,34]. In previous studies, mechanical methods were used to determine the shear strength between cement particles and evaluate the SGS of the cement slurry [12,35,36]. In these experiments, an SGS analyser (model 5265 U, Chandler engineering, USA) was used to determine the SGS of the cement slurry. This is an in situ non-destructive detection method that determines the SGS (b600 Pa) by monitoring ultrasonic signal changes through the cement slurry. Meanwhile, the setting times of the cement slurries were measured with a Vicat Needle according to ASTM specification C191 [37]. The volume change ratio of the cement
Fig. 7. Static gel strength curves for the cement slurries.
slurries was tested with a cement volume testing analyser (Applied Technology Research Institute of SAU, China). 2.2.4. Pore water distribution analysis In these experiments, an LF-NMR analyser (Suzhou Niumag, China) was used to investigate the water distribution and pore structure of the cement slurry during the stage of hydrostatic pressure reduction. LF-NMR imaging can probe the transverse relaxation time (T2) of the water molecules in pores to analyse the pore characteristics [38,39]; T2 is given by Eq. (1) [40]. Cement slurry is a porous material, and the pores are filled with water. 1 1 1 1 1 S ¼ ρ2 ¼ þ þ ≈ T 2 T 2s T 2b T 2d T 2s V
ð1Þ
where T2s is the value of T2 associated with the surface relaxation, T2b is the value of T2 for the pore water in the bulk state, T2d is the value of T2 associated with diffusion in the magnetic field gradient, ρ2 is the surface relaxivity, S is the surface area of the pores, and V is the pore water vol ume. In general, T2b and T2d are much larger than T2s, and thus 1 T and 2d 1 are negligible. Therefore, in Eq. (1), T2 is dominated by T2s. T 2b
2.2.5. Microstructure analysis In these experiments, X-ray computed tomography (μ-CT; GE Sensing & inspection technologies GmbH, Germany) was used for continuous in situ monitoring of microstructural changes in the cement slurry; the microstructure of the cement slurry was analysed at 1 h intervals at 30 °C. In addition, environmental scanning electron microscopy (ESEM; FEI Company, USA) was used to analyse the microstructure of the cement slurry. After the cement slurry specimen was cured for the
Fig. 6. Hydrostatic pressure and hydration heat of the cement slurries.
Fig. 8. Mathematical relationship between the hydrostatic pressure and SGS.
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Fig. 9. Photos of the interfaces between the simulated borehole, casing, and cement samples after the experiments.
scheduled amount of time at 30 °C, it was frozen in liquid nitrogen and vacuum freeze-dried to prepare the sample for the ESEM analysis. Finally, gold was sprayed on the dried specimen, and the microstructure of the cement slurry was analysed using ESEM. 3. Results and discussion 3.1. Hydrostatic pressure and hydration rate of the cement slurries Table 3 summarises the conventional properties of cement slurries according to API specification 10B-2 [17], which meet the requirements for cementing operations. As CaCl2 can increase the hydration rate of cement slurries, the initial setting time is reduced. Fig. 5 shows the hydrostatic pressure curves for the cement slurries. The hydrostatic pressure of the cement slurries decreases with the increase in hydration time. These hydrostatic pressure curves can be divided into two stages. The first stage occurs before the hydrostatic pressure of cement slurry decays to that of water, and the second stage encompasses the hydrostatic pressure decay from the hydrostatic pressure of water to zero. In the first stage, the cement slurries retain hydrostatic pressure, which decreases slowly; the three curves are similar. In the second stage, the hydrostatic pressure decreases rapidly, and the hydrostatic pressure of the cement slurry with a high CaCl2 content decreases faster than that of the other cement slurries. Fig. 6(a) shows the heat flow curves for the A-1, A-2, and A-3 cement slurry specimens. There is no obvious difference between the peak height and peak width in the heat flow curves for the cement slurries. However, when the hydration time of the A-1 cement slurry is 986 min, the heat flow reaches a maximum; the peak value of the A-2 cement slurry occurs at 930 min, and the peak value of the A-3 cement slurry occurs at 820 min. Moreover, these results and the hydrostatic
pressure curves for the A-1, A-2, and A-3 cement slurries (shown in Fig. 5) indicate that the hydrostatic pressure of the cement slurries decreases with an increase in heat flow, particularly when the hydrostatic pressure is in the second stage (as shown in Fig. 6(b)). When the hydration rate of the cement slurries is accelerated, the rate of reduction of the hydrostatic pressure increases markedly. Thus, with an increase in hydration time, large amount of hydration products are formed, which change the microstructure and pore structure of the cement slurries. 3.2. SGS of the cement slurries Fig. 7 shows the SGS curves for the cement slurries. At a hydration time of approximately 400 min, the SGS of the A-1 cement slurry (without CaCl2) increases rapidly, and the SGS reaches 600 Pa at a hydration time of 476 min. However, the SGS of the A-3 cement slurry (with 1.0 wt% CaCl2) reaches 600 Pa at a hydration time of only 333 min. Therefore, CaCl2 can improve the hydration rate and develop the intermicrostructure and SGS of the cement slurries. Kishar et al. [18,41–43] also reported that CaCl2 could increase the hydration rate and improve the early strength of cement slurries. 3.3. Relationship between the hydrostatic pressure and SGS Fig. 8 shows the relationship between the hydrostatic pressure and SGS of the A-1, A-2, and A-3 cement slurries. These curves can be divided into 3 stages, which is in agreement with the results reported by Li et al. [1,9,44]. When the SGS of the cement slurries is approximately 36–48 Pa, the change in hydrostatic pressure is not obvious. In this stage, the fluidity of the cement slurry is good and its microstructure is in a dispersed state, and thus the hydrostatic pressure of the cement slurry can be transferred effectively. When the SGS increases to
Fig. 10. Illustrations of the (a) cement slurry column, (b) microstructure of the fresh cement slurry, and (c) microstructure of the hardened cement slurry.
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48–76 Pa, the hydrostatic pressure of the cement slurry decreases sharply. In this stage, the SGS of the cement slurry develops rapidly and the microstructure of the cement slurry changes from a dispersed state to the gelation state, which increases the bonding ability between the cement slurry and the interfaces of the borehole and casing, enabling the hydrostatic pressure of the cement slurry to act on the interfaces. Finally, when the SGS is N76 Pa, the hydrostatic pressure of the cement slurry decreases slowly, and the transfer method of the cement slurry hydrostatic pressure may be changed. The experimental results show that for SGS of approximately 48 Pa to 600 Pa, an exponential function can be employed to describe the relationship between the hydrostatic pressure and the SGS of the cement slurries, which is more appropriate than the linear function previously proposed by Sabins et al. [12,13]. However, even when the SGS reaches 600 Pa and the hydration time is longer than the initial setting time, the cement slurries still retain some hydrostatic pressure. In this stage, the hydrostatic pressure of the cement slurries may be transferred by the pore water. The SGS of the cement slurry can reflect the bonding ability between cement particles, which increases with the SGS, as reported in Refs. [1, 34, 36, 45]. Moreover, the bonding ability between the cement slurry and the borehole and casing may also increase, causing the gravitational force of the cement slurry to act on the borehole and casing. Fig. 9 shows photos of the interfaces between the simulated borehole, casing, and cement sample after the experiments. It can be seen that there is a significant amount of residual cement sample on the surface of the simulated borehole and casing. Therefore, in the early stage of hydration, the hydrostatic pressure of the cement slurry rapidly decreases with the increase in SGS. Fig. 10 depicts the cement slurry column, microstructure of the fresh cement slurry, and microstructure of the hardened cement slurry. Based on the results in Fig. 9, the bonding ability between the cement slurry and the borehole and casing is assumed to be similar to the SGS of the cement slurry. Therefore, based on the law of conservation of mass, when the gravitational force of the cement particles acts on the borehole and casing, the SGS can be calculated from Eq. (2). With an increase in hydration time, the solid-phase density, ρsolid, and porosity, pcem, of the cement slurry will change. h i ρsolid g ð1‐pcem Þ ð1 þ vcem Þ πR2 ‐πr 2 dh ¼ 2τcem π ðR þ r Þdh ρsolid g ð1‐pcem ÞðR‐r Þð1 þ vcem Þ ¼ τ cem 2
ð2Þ
ð3Þ
where ρsolid is the solid-phase density (kg·m−3), pcem is the fluid volume content of the cement slurry, g is the gravitational acceleration (N·kg−1),
Fig. 11. Volume change ratio results for the cement slurries obtained using a cement volume testing analyser.
Fig. 12. Transverse relaxation time (T2) for the A-1 cement slurry at different hydration times, determined using LF-NMR.
R is the internal diameter of the borehole (m), r is the external diameter of the casing (m), vcem is the volume change ratio of the cement slurry, and. τcem is the SGS of the cement slurry (Pa). From Eq. (3), it can be found that the volume change ratio of the cement slurry is a key parameter in the calculation of τcem. Fig. 11 shows the volume change ratio of the cement slurries. From the free-fluid results specified by API [17] (listed in Table 3), it can be seen that the stability of the cement slurries is good, and thus the cement particles are assumed to be evenly dispersed in the cement slurry. In the experiments, the water to cement ratio (W/C) of the cement slurry was 0.44. Thus, the fluid volume content (pcem) of the fresh cement slurry is approximately 0.588, and (R-r) is 0.02 m. Based on the SGS (shown in Fig. 7) and volume change ratio (shown in Fig. 11) results, at a hydration time of 480 min, vcem is approximately −0.0004, which can be ignored. Based on these parameters, when the gravitational force of the cement particles acts on the simulated borehole and casing, τcem is 131.36 Pa. These experimental results (shown in Fig. 5 and Fig. 7) and the calculated results indicate that the decrease in hydrostatic pressure is caused not only by the increase in SGS, but also by other synergistic effects arising with the increase in hydration time. Therefore, to understand the mechanism of the hydrostatic pressure reduction during the hydration of cement slurries, the hydration rate, pore water, and microstructure of the cement slurry must be understood. 3.4. Effect of pore water on the hydrostatic pressure In a cement slurry, the evolution of the pore structure will change the pore water distribution. Fig. 12 shows the transverse relaxation time (T2) for the A-1 cement slurry. The T2 curves for the cement slurry have two peaks: the first peak at 0.01–25 ms, and a second peak at T2 N 100 ms. McDonald et al. [46–48] established a relationship between T2 and the pore diameter of a cement slurry, and the pore water of the
Fig. 13. Relationship between the hydrostatic pressure and T2 curve area.
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Fig. 14. Pore water distribution and the effect of free water on the hydrostatic pressure.
cement slurry was classified into three categories: free water in macropores, capillary water in capillary pores, and the gel water of hydration products. The T2 for the gel water was defined as b1.5 ms, the T2 for capillary water was defined as 1.5–7.5 ms, and the T2 of free water was defined as N7.5 ms. As seen in Fig. 12, the primary T2 peak for the fresh cement slurry (hydration time of 0 min) is around 3.0–20.7 ms with an amplitude of 1543.4. At a hydration time of 120 min, the main T2 peak for the cement slurry is around 2.7–22.2 ms with an amplitude of 1442.3. Thus, the pore water in fresh cement slurry is mainly composed of capillary water and free water. The widening of the T 2 range may be caused by the sedimentation of some particles in the pores with an increase in static time, resulting in a wider distribution of pore sizes. In addition, some components of fresh cement slurry, such as calcium oxide (CaO), hemihydrate gypsum (CaSO4·0.5H2O), and tricalcium silicate (3CaO·SiO 2 ), will react with free water to form structural water and reduce the amplitude of T2. At a hydration time of 180 min, the T2 curve for the cement slurry starts to shift to the left. Finally, at hydration times from about 360 min to 420 min, the T2 curve shifts rapidly to the left. From the heat flow curves (shown in Fig. 6), it can be seen that at a hydration time of about 360–420 min, the hydration rate of the cement slurry is accelerated, and many hydration products are formed. These hydration products decrease the pore size of the cement slurry, which changes the pore water distribution in the cement slurry from free water to capillary water and gel water.
3.4.1. Relationship between the T2 curve area and hydrostatic pressure According to Eq. (1), the distribution of T2 in a cement slurry is related to the volume and surface area of the pores. If the pore shape is assumed to be spherical or cylindrical, T2 will be proportional to the pore diameter, as reported by previous studies [46,49,50]. Therefore, the T2 results for the cement slurry can be used to describe the pore size distribution, and the T2 curve area is related to the pore volume and porosity of the cement slurry. Fig. 13 shows the relationship between the T2 curve area and the hydrostatic pressure of the cement slurry; it can be seen that there is a linear relationship. The results in Fig. 13 confirm that the porosity or pore volume of the cement slurry is proportional to the hydrostatic pressure. 3.4.2. Relationship between the pore water distribution and hydrostatic pressure Based on the experimental results reported by McDonald et al. [46–48], the pore water distribution of the cement slurry can be quantitatively determined from the T 2 curve area (shown in Fig. 12). Fig. 14 shows the change in the free water, capillary water, and gel water content with an increase in hydration time. Combining the results in Fig. 5 and Fig. 14(a), the following information can be obtained: (1) In fresh cement slurry, the pore water consists of free water and capillary water. During the hydrostatic pressure reduction of the cement slurry, much of the free water is converted to capillary
Fig. 15. Evolution of the pore structure and microstructure of the cement slurry.
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Fig. 16. Microstructure of the A-1 cement slurry at different hydration times.
water, and some gel water is formed when the hydration time reaches 540 min. (2) The variation trend for the free water is similar to that of the hydrostatic pressure in the cement slurry, and Fig. 14(b) shows that the free water content and hydrostatic pressure are linearly correlated. The experimental results demonstrate that the decrease in free water content of the cement slurry is one of the most important factors contributing to the hydrostatic pressure reduction. In stage II of the hydrostatic pressure reduction, the hydration rate of the cement slurry is accelerated, and a large number of hydration products are formed in the pores, causing the microstructure of the cement slurry to change as macropores are converted to numerous capillary pores and gel pores, which changes the pore water distribution. At the same time, the bonding ability between the cement particles and interfaces of the simulated borehole and casing will be increased. Fig. 15 shows the evolution of the pore structure and microstructure of the cement slurry. In this study, μ-CT and ESEM were used to investigate the evolution of the microstructure and pore structure of the A-1 cement slurry during the cement hydration process.
hydration products was also reported in Refs. [52, 53]. Finally, these hydration products cause the macropores to split into numerous micropores. According to the ESEM results, the binary images of the pores and solid-phase in the ESEM images were analysed using Image-Pro-Plus. In combination with the inflection point methods [54–56], the gray threshold values of pores in the ESEM images were set to 65 (as shown in Fig. 17), and the solid-phase in the grayscale ESEM images was filled with white, the other area was pores. The pore structure and size in the cement slurry were investigated at different hydration times. Fig. 18 shows the results for the pore structure and size in the cement slurry. The pore size of the cement slurry decreases with an increase in hydration time. From the results in Fig. 18(a) and Fig. 18(b), it can be seen that in stage I of the hydrostatic pressure reduction of the cement slurry, the change in pore structure is not obvious, and there are many macropores in the cement slurry. However, in stage II of the hydrostatic pressure reduction of the cement slurry (i.e. hydration times from 360 min to 600 min), the number of macropores decreases noticeably, and a large number of micropores are formed, as reported by Karakosta et al. [49]. Combining the results in Fig. 12 and Fig. 16, it can be determined that when the hydration
3.5. Microstructure 3.5.1. ESEM microstructure Fig. 16 shows the microstructure of the A-1 cement slurry obtained with ESEM. As seen in Fig. 16(a), the surface of unhydrated cement particles is smooth. When the cement particles, dispersant, filtrate reducer, and water are mixed, polymers adsorb on the surface of the cement particles. This serves to connect the dispersed cement particles and suspend the cement particles in the cement slurry, as shown in Fig. 16 (b), which is in agreement with results reported by Xia et al. [31,51]. At a cement slurry hydration time of 240 min, new hydration products can be observed in the pores and on the surface of the polymers, as shown in Fig. 16(c). At a hydration time of 360 min, the hydration products cover the polymers, as shown in Fig. 16 (d), and connect the cement particles. In Fig. 16(e) and Fig. 16(f), a large number of porous hydration products can be observed, and the presence of these porous
Fig. 17. Assessing pore threshold level via the inflection point method.
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Fig. 18. Pore distribution in the cement slurry.
reaction of the cement slurry is in the acceleration period, many hydration products formed in the pores, which changed the pore size from macropores to micropores. This process will change the pore water state and distribution in the cement slurry; the pore water distribution changes from free water in the macropores to capillary water and even gel water. In the cement slurry, the transmission capacity for hydrostatic pressure of the pore water in micropores is less than that of pore water in macropores. 3.5.2. μ-CT microstructure To observe the change in pore structure of the cement slurry in stage II of the hydrostatic pressure reduction, μ-CT was used analyse the in situ microstructure of the cement slurry. Fig. 19 shows the in situ μ-CT microstructure of the cement slurry. It can be seen that the solidphase volume increases with the hydration time; a new solid phase forms around the cement particles and fills the macropores, which are then divided into many micropores. In the early stage of hydration, the polymers can form a reticular structure that has great deformability. Therefore, the gravitational force of the cement particles can be transferred by the pore water,
which can maintain the hydrostatic pressure in the cement slurry (as shown in Figs. 5 and 16). With an increase in hydration time, some hydration products form on the polymer surface and connect the dispersed cement particles in the cement slurry. Because these hydration products have a higher mechanical strength than the polymers, the transfer of the gravitational force of the cement particles by the hydration products is more difficult. The hydration products connect the cement particles, which increases the mechanical strength of the cement slurry. Moreover, they can also play a role in connecting the cement slurry and the borehole and casing, which causes the gravitational force of the cement particles to act on the casing and borehole. This process will cause the hydrostatic pressure of the cement slurry to decrease slowly in stage I; at the end of stage I, the hydrostatic pressure of the cement slurry is maintained only by the pore water. In stage II of the hydrostatic pressure reduction, the pore size and distribution of the cement slurry change from macropores to micropores with an increase in hydration product content. This process changes the pore water state. In the cement slurry, it is difficult for capillary water and gel water to transfer the hydrostatic pressure.
Fig. 19. Sectional drawing of the 3D microstructure of the A-1 cement slurry at different hydration times.
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4. Conclusion From the experimental results of this study, the following conclusions can be obtained: the increase in SGS and change in pore water distribution during the hydration process are the main factors affecting the hydrostatic pressure reduction in cement slurries. The hydrostatic pressure and SGS of the cement slurry vary exponentially, and the hydrostatic pressure and free water content vary linearly. Therefore, the hydrostatic pressure curve of the cement slurry can be divided into two stages: 1) In the first stage, the cement slurry maintains hydrostatic pressure, and the hydrostatic pressure decreases slowly. At this stage, some hydration products are formed in the pores, and these hydration products connect the dispersed cement particles and increase the SGS of the cement slurry. This increase will cause some of the gravitational force of the cement particles to act on the borehole and casing, and thus the hydrostatic pressure of the cement slurry decreases. 2) In the second stage, the hydrostatic pressure of the cement slurry decreases rapidly. In this stage, the main cause of hydration pressure reduction is the increase in SGS of the cement slurry and the acceleration of the hydration reaction, which changes the microstructure and the distribution of pore water. The rapid hydration reactions form a large number of hydration products in the pores, which causes the macropores to transform into many capillary and gel pores. Owing to the change in pore diameter, the pore water in the cement slurry changes from free water to capillary water and gel water. In the cement slurry, the hydrostatic pressure is less readily transferred by capillary water and gel water.
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