Since the PC came into the scientific study domain and engineering application for almost two centuries, many researchers conducted quite an amount of theoretical, numerical, and experimental studies on this topic. Some consensus of PC components has been accepted broadly by the present scientific and engineering circles. The main constitutions in PC regardless of its type, e.g. 10 types as per ASTM (American Society for Testing and Materials) (ASTM International, 2019a) or 8 types as per API (American Petroleum Institue) (American Petroleum Institute, 2002) standards actually, are alite (tri-calcium silicate or 3CaO⋅SiO₂ or C₃S), belite (di-calcium silicate or β − 2CaO⋅SiO₂ or C₂S), celite (tri-calcium aluminate or 3CaO⋅Al₂O₃ or C₃A), felite or ferrite (Frederick and Thomas, 2020; Gutteridg and Pomeroy, 1983) (tetra-calcium alumino-ferrite or 4CaO⋅Al₂O₃⋅Fe₂O₃ or C₄AF), and gypsum (calcium sulfate dihydrate or CaO⋅SO₃⋅2H₂O or C S ̄ H₂). The first four phase-notations were invented by Le Chatelier (Chatelier and Mack, 1905) and Törnebohm (Blezard, 1998; Poole and Sims, 2016). Some other minor components possibly exist which come from the different clinker precursors such as the dead burnt magnesia, the sulfates residual, the alkalis (commonly sodium oxide and potassium oxide), etc. These constituents of PC can be elaborated in oxides concentration or cementitious phases concentration that is listed in Table 2. As (Michaux et al., 1989) said, PC hydration speed relies on the relative concentrations of the cementitious components and their particle size or fineness. API (American Petroleum Institute, 2002), ASTM (ASTM International, 2019a), and some researchers (Ramachandran and Feldman, 1996) use some qualitative and quantitative compositions of these cementitious phases to categorize the PC. The summary of these categorizations can be found from one table including five sub-tables (Supplementary Tables S1–S5) in the Supplementary Material.

Because PC is the dominant binder material in construction engineering, there are detailed restrictions on the oxides and mineralogical compositions, e.g. the lime content must meet some specific requirements. The too high content of lime ( > 67%) will probably leave free lime after setting which will cause unsoundness issues (Soroka, 1979). On the contrary, a too low content of lime will slow down the hydration and setting process of the Portland cement apparently (Soroka, 1979) which makes it difficult to meet the civil and geotechnical well construction needs.

Apart from the lime content, another two main oxides in PC, alumina (Al₂O₃) and ferrous oxide (Fe₂O₃), also play a vital role in its physicochemical properties. Firstly, alumina (usually in the form of C₃A) and ferrous oxide (usually in the form of C₄AF) govern the setting time of PC. Gypsum (C S ̄ ⋅ 2H) addition, the function of which is to control the setting time of PC, only works under a certain threshold of SiO₂/R₂O₃ ratio as 1.5 (Soroka, 1979). The notation of R₂O₃ refers to the total amount of alumina and ferrous oxide. Secondly, less composition of C₃A means less susceptibility to sulfate attack. So, the sulfate-resistant grade of different PC is generally classified based on C₃A content.

Commonly, higher content of C₃S compared with C₂S and finer particle size indicates quicker hydration rate and development of initial mechanical strength. By tuning the concentration of C₃S, C₂S, C₃A, and the particle size, different fit-for-purpose PC will be made to qualify diverse engineering requirements.

The debonding phenomenon refers to the physical separation at the cementing interfaces (casing and cement sheath, cement sheath and formation). This is also called “micro-annulus” in the geotechnical well construction field. Avoidance and addressing the debonding issue is the first order of maintaining well integrity. In the petroleum engineering industry, investigation of debonding existence, extent, and location has become the core of cementing quality assessment. CBL and VDL are the commercialized technologies capable of accomplishing this job. Based on the logging mechanism of CBL, some researchers invented a lab-scale acoustic measurement unit (see Figure 5) which had been used to evaluate the closing micro-annulus capability of magnesia blended PC (Thomas J. et al., 2014).

As Figure 6 shown below, the impedance maps for the expansive cement specimens (W/C = 41%, 6% BWOC of dead burnt magnesia, 6% BWOC of dead burnt lime) were conducted at 115 h (just before the heat treatment—cured at 30°C) and at 139 h (just after the heat treatment - curing temperature increased from 30°C to 66°C). Before the heat treatment, the acoustic impedance map on the left, shows zero impedance everywhere with red color, indicating a dry micro-annulus at the first cementing interface. Nonetheless, after the heat treatment, the acoustic impedance map on the right shows good cementing bonding all around the casing demonstrating that the heat-activated expansion from magnesia was able to close a pre-existing micro-annulus and restore the acoustic coupling between the cement and inner casing.

Particle size has an important role in the cement hydration process. For instance, even for the same materials, they will hydrate at different rates which affect the thermal equilibrium of hydration, the acidic/alkaline environment, and produces diverse hydration products. The measurement methods of particle size or particle size analysis have been also developed for over one century corresponding with the development of material science. For cement and cement-based material research, several methods can be used such as the sieve method (Aphane, 2007; Liska et al., 2008; Liska and Al-Tabbaa, 2009, 2012; Mo et al., 2010; Panesar and Mo, 2013; Dung and Unluer, 2016; Ruan and Unluer, 2017; Mo and Al-Tabbaa, 2020), dynamic light scattering (Jafariesfad et al., 2017b), laser scattering (Shand and Jin, 2020), SEM (Qafoku et al., 2015), Blaine specific surface area method (Al-Tabbaa, 2013).

As described in Section 4.3.3, the calorimetry is a useful measure to monitor the exothermal heat accumulation during cementitious material hydration. Hence, this technique is the usual way to analyze the hydration kinetics projecting the cement slurry formulations variations and their potential interacting impacts. For example, in (Thomas J. et al., 2014) research, the authors found out that the retardation effect probably behaved mono-directionally from PC to magnesia.

Scanning electron microscopy (SEM) is one of the principal characterization methods for imaging the micromorphology and microstructure of materials. By projecting a beam of low energy electrons onto the material sample, some detector will be used to monitor the photons and electrons emitted from the interaction between the source beam electrons and the sample atom electrons. If equipped with other energy-dispersive X-ray microanalysis functions (such as EDX, EDS), this technique can determine the composition and orientation of individual crystals or features (Omidi et al., 2017; Raval et al., 2019). Similar to XRD and XRF, almost all the research work cited in this work used this method to investigate the micromorphology and microstructure characteristics of target materials and to provide the scientific evidence corresponding to certain analysis.

As mentioned in Section 2, the application conditions of cement material in a geotechnical well construction field is much different from that in the civil construction area. When pumping the prepared cement slurry into the downhole annulus, the transition state development in the setting and hardening process has to meet several engineering demands such as having a long enough pumpable time to place the slurry as desired, quick gel strength evolvement to facilitate the prevention of formation gas/liquid intrusion as much as possible, and fast mechanical strength advancement to resume afterward operation as soon as possible. Therefore, to verify these properties and figure out the transition state regimes in the lab are significant to the successful cementing job. This is also applied to the magnesia blended Portland cement system. So, three aspects corresponding to the aforementioned properties will be illustrated as follows as thickening time, transition time, and wait-on-cement (WOC) time respectively.

The fluid loss reflects the relative effectiveness of a cement slurry to retain its water phase when exposed to a differential pressure condition with a filter medium (e.g. geological formation). Too much fluid loss/filtrate means the cement slurry undergoing dehydration which will cause a series of quality issues of cement sheath (micro-annuli, bonding issue, etc.,). Some researchers pointed out that the incorporation of magnesia particles into Portland cement will increase the slurry’s fluid loss quantity (Brandl et al., 2014). Other studies also used such a testing method to evaluate the possible impact of magnesia introduction into Portland cement (Ghofrani and Plack, 1993; Hammad and Altameini, 2002). The testing procedures and requirements can also be found in (API, 2013). As for the static fluid loss test, the prepared slurry will be poured into a specially designed cell with the 325 mesh screen mounted at the bottom. After applying a 1,000 psi differential pressure and opening the bottom valve, the accumulated fluid volume filtered out within 30 min will be measured and doubled as the fluid loss if without the gas blow through.

Rheology properties of cement slurry directly influence the efficiency of slurry placement and displacement rate of drilling fluid (Shahriar and Nehdi, 2012; Tao et al., 2019). In the field, it also impacts the pumpability and mixability of the cement slurry. The specific experimental procedure has been included in (API, 2013). Three parameters (plastic viscosity, yield point strength, and gel strength) are employed to describe several fundamental properties of cement slurry during the pumping process. Plastic viscosity affects the flow regime of cement slurry. The turbulent flow regime and viscous property of flowing cement slurry are both beneficial to enhance the displacement rate of drilling fluid. Hence, the proper plastic viscosity gained means the compromised result between these two factors which is desired under certain operation conditions (Murtaza et al., 2019). Yield point strength always correlates with the anti-setting capability of cement slurry. Higher yield point strength indicates that the cement slurry shows a lower tendency to settle down its solid particles with relatively better vertical homogeneity. The gel strength reflects how easy to activate/resume the flowing state of cement slurry after keeping it static for a while. Relative lower gel strength facilitates the commence of the pumping process and lowers the requirements of cementing pump devices. Some researchers have pointed out the values or studies these rheological properties regarding magnesia blended oil well cement (Ghofrani and Plack, 1993; Hammad and Altameini, 2002; Srivastava et al., 2018; Jafariesfad et al., 2020).

In recent years, an applicable modeling program has been developed which can be used to analyze the stress evolution and pre-stress situations during the cement paste hydration under different simulated downhole surrounding conditions (Onaisi et al., 2017, 2019). The core equations of their modeling methods are listed below. δ σ r f = 2 λ f + G f A f − 2 G f B f r 2 − α f E f 1 − ν f C δ σ θ f = 2 λ f + G f A f + 2 G f B f r 2 + α f E f 1 − ν f ( C − δ T ) δ σ z f = 2 λ f A f − α f E f 1 − ν f δ T (6) δ σ r c a s = 2 λ c a s + G c a s A c a s − 2 G c a s B c a s r 2 − α c a s E c a s 1 − ν c a s C δ σ θ c a s = 2 λ c a s + G c a s A c a s + 2 G c a s B c a s r 2 + α c a s E c a s 1 − ν c a s ( C − δ T ) δ σ z c a s = 2 λ c a s A c a s − α c a s E c a s 1 − ν c a s δ T (7) δ σ r c = 2 λ c + G c A c − 2 G c B c r 2 − 3 K b c δ ε e x p − b c δ P p o r e − α c E c 1 − ν c C δ σ θ c = 2 λ c + G c A c + 2 G c B c r 2 − 3 K b c δ ε e x p − b c δ P p o r e + α c E c 1 − ν c ( C − δ T ) δ σ z c = 2 λ c A c − 3 K b c δ ε e x p − b c δ P p o r e − α c E c 1 − ν c δ T (8) C = 1 r 2 ∫ r i r ρ δ T ∂ ρ (9) ∂ T ∂ t = D c a s ∂ 2 T ∂ r 2 + 1 r ∂ T ∂ r ∂ T ∂ t = D f ∂ 2 T ∂ r 2 + 1 r ∂ T ∂ r ∂ T ∂ t = D c ∂ 2 T ∂ r 2 + 1 r ∂ T ∂ r (10) 2 λ cas + G cas A cas − 2 G cas r i c a s 2 B cas = − δ P p o r e 2 λ c a s + G c a s A c a s − 2 G c a s r o c a s 2 B c a s − 2 λ c + G c + M c b c 2 A c + 2 G c r o c a s 2 B c = α c a s E c a s 1 − ν c a s C c a s − 3 K b c 1 + M c b c K s c δ ε exp + M c b c γ c δ ξ c − 3 α m c δ T r o c a s A c a s + B c a s r o c a s − r o c a s A c − B c r o c a s = − 1 + ν c a s 1 − ν c a s α c a s r o c a s C c a s 2 λ c + G c + M c b c 2 A c − 2 G c r h o l e 2 B c − 2 λ r + G r A f + 2 G r r h o l e 2 B f = 1 − 2 M c b c 2 α c E c 1 − ν c C c + 3 K b c 1 + M c b c K s c δ ε exp − M c b c γ c δ ξ c − 3 α m c δ T r h o l e A c + 1 r h o l e B c − r h o l e A f − 1 r h o l e B f = − 1 + ν c 1 − ν c α c r h o l e C c r o b A f + 1 r o b B f = − 1 + ν c 1 − ν c α c r o b C f (11) where, subscripts of f, c, cas, ob, hole, ocas, icas refer to the surrounding formation, cement paste/slurry, casing, the outer boundary of formation, the outer diameter of casing, the inner diameter of casing respectively; subscripts r, θ, and z denote radius direction, circumferential direction, and borehole axial direction respectively; σ means stress; λ and G are Lame coefficients; r is the radius from wellbore center; α refers to the linear thermal expansion coefficient; E denotes the elastic modulus; ν is the Poisson’s ratio; ρ means density; T denotes temperature; K _b is the bulk incompressibility modulus; ɛ _exp denotes the expansion strain; b denotes Biot coefficient; P _pore is the pore pressure inside of cement specimen; γ is the pore pressure-hydration coupling parameter; ξ _c is the cement hydration degree; Eqs. 6–8 are the stress-strain equilibrium equations of casing, cement paste/sheath, and formation; Eq. (10) are the temperature profile in casing, cement, and formation; Eq. (11) can be used to calculate the intermediate parameters of A and B.

Based on the assumptions from their work (Onaisi et al., 2017, 2019) and by applying some laboratory measurements and homogenization techniques, all the specific directional-based stresses and strains components can be obtained. Radial tensile crack development and debonding scenarios can be analyzed by using the Mohr-Coulomb criterion Onaisi et al. (2017).

Given the directional stresses, strains, and other parameters shown in Eqs (6)–(11), the main equations governing the coupling effect regarding cement paste/sheath between pressure, stress, strains (shrinkage or expansion) can be acquired with such equations: δ σ m e a n = K b c δ ε v s − 3 K b c δ ε l exp − b c δ P p o r e δ P M c = − b c δ ε m e a n − 3 1 − b c δ ε e x p − γ c δ ξ c + δ m w ρ w γ c = ρ w + ρ c a s R w c − H ρ w + ρ c a s W / C ε i s h δ ϕ = γ c − ϕ 0 R w c − H W / C δ ξ c (12) where subscripts of c and w refer to cement and water respectively; R w c − H is the mass ratio of water to cement grains consumed by hydration reaction; W/C denotes the water to cement ratio by mass; ɛ _ish means the cement internal shrinkage; ϕ refers to the porosity in cement paste/sheath; ϕ ₀ refers to the initial porosity in cement paste/sheath.

T-CemInt model is a hydration modeling method that mainly focuses on the mechanical and relevant volumetric properties of cement paste hydration. The cement sheath integrity is not only about mechanical characteristics, but also including hydraulic features. Bois et al. proposed a crossing check method on a cement plug by use of cement mechanical integrity (CMI) and cement hydraulic integrity (CHI) models (Bois et al., 2019). Although they didn’t give the complete set of equations, the hypotheses, physical case configurations, and specific parameters have been illustrated in their paper. The novelty of their work is the introduction of the porous media idea into the existed hydration modeling and taking into account the surrounding formation fluids exposure scenarios.

Formulated on the hypotheses and configurations (Bois et al., 2019), coupling analysis was conducted between the fluid pressure variation (hydraulics) and the solid-matrix stiffness (mechanics) at the micro-annulus area with introducing CHI simulation techniques. Some insightful conclusions were acquired as:

• The most probable integrity risk comes from the micro-annulus formed at the second cementing interface (interface between cement plug and wellbore formation). Other failure risks such as compression or tension exist but at much lower possibilities.

In order to investigate the influence of pre-stress status caused by the expansion (e. g. mineral brucite formation) on the cement matrix mechanical integrity, Patel et al. used the Finite Element Modeling (FEM) method and acquired some perceptive findings (Patel et al., 2019). Their work included two parts: 1) the effect of different pre-stress conditions on the mechanical integrity of set cement; 2) sensitivity analysis between them. Their physical model included three parts as the inner liner, the intermediate cement sheath, and the outer casing unit. The loading condition only covered the wellbore pressure imposed on the inner liner. The cementing interface between liner and cement sheath was the study interest. For the sake of conducting the FEM simulations, they validated their FEM model by comparison with the analytical calculation (based on the thick-walled concentric cylinder model) results of radial and hoop stress under different wellbore pressure conditions. They found that the compressive pre-stress is dominated by and proportional to the linear expansion while it impacted the cement sheath mechanical integrity only marginally. The expansion would benefit mitigating the radial cracking probability by compensating the hoop stress with compressive pre-stress status. However, some further studies need to be conducted on the shear stress failure risk in terms of the expansion-induced pre-stress.

First of all, the reactivity of MgO matters in the hydration process of magnesia blended Portland cement. Talking about this means it hardly bypasses the SSA. The positive correlation between them is evident (Shand and Jin, 2020; José et al., 2020). Higher SSA means higher reactivity of MgO particles (Jin and Al-Tabbaa, 2020). This also illustrates the importance of calcination conditions during the manufacturing of MgO. The impact of calcination temperature and residence time have similar impacts to the calcination of magnesia precursors, not only magnesite or dolomite but also brucite. Usually, beyond the critical decomposition temperature, 350°C for brucite, 500°C for dolomite or magnesite, lower temperature with shorter residence time (15–25 min) will produce a higher specific surface area of MgO (ref Figure 7). Hence, the calcination temperature of producing caustic magnesia commonly is between 400°C and 1,000°C (Unluer and Al-Tabbaa, 2013). For example, 52 years ago (Smithson and Bakhshi, 1969), already pointed out that the calcination temperature and residence time dominate the particle size and crystalline content of produced MgO from precursors. When calcined below 500°C, MgO particle size can be less than 10 nm; above 1,000°C, MgO particle size can reach more than 100 nm. This range varies among different pieces of literature, probably because of the different contents of impurities of precursor materials.

Another factor is the crystal structural features. On account of the coordination number of the Mg atom/ion, it is impossible to fabricate the perfect crystal structure of MgO even it is the simplest form of crystalline-like halite. In more detail, the surface defects can be depicted from plane view and 3D view. In the two-dimensional view, the surface of MgO is always born with defects such as steps, kinks, vacancies, adatoms, and fissures (Sushko et al., 2002). In the three-dimensional view, the existence of apexes/corners/edges of cryptocrystalline plus the coordination unsaturation of Mg atom/ion magnifies the defect severities. These defects become the front of hydration because they provide the vulnerable zone for ion exchange and corresponding water molecule chemisorption (Shand, 2006f).

The pH value of solution media plays a vital role in the dissolution and hydration of MgO (Shand, 2006f; Fruhwirth et al., 1985). Some pH-dependent rate-controlling processes can be summarized as follows (at room temperature): M g O + H 2 O → pH > 7 M g 2 + + 2 O H − (13) M g O + 2 H + → pH < 5 M g 2 + + H 2 O (14)

The process of Eq. (14) is the proton attack at the crystal structure of MgO and hereafter the desorption of cation Mg²⁺ and hydroxyl anion, especially at the defect spots. However, the process regarding Eq. (13) is the adsorption of hydroxyl anion at the defect spots and desorption of cation Mg²⁺ and hydroxyl anion from the crystal surface. Pure proton diffusion probably happens in the case of the pH as between 5 and 7.

Besides the impacts of reactivity of MgO and pH surroundings on the dissolution and hydration of MgO, the exposure of MgO with H₂O molecule simultaneously occurs as the chemisorption of H₂O. This adsorption is part of dissolution and afterward hydration. How easily the chemisorption emerging relies also on the characteristics of the defects of the cryptocrystalline of MgO as mentioned above. In a word, less crystal defect means the lower tendency of water molecule chemisorption (Onishi et al., 1987; Peng and Barteau, 1990).

The hydration process can be regarded as several steps: water molecule reaction with MgO surface layer to produce Mg (OH)₂, dissolution of such Mg (OH)₂, and exposure of fresh solid MgO particle surface for hydration proceeding. Nevertheless, the solubility of Mg (OH)₂ is very limited which makes the removal of Mg (OH)₂ “coating” very slow (Smithson and Bakhshi, 1969; Fruhwirth et al., 1985; Khangaonkar et al., 1990). On the other hand, the reactivity of magnesia depends strongly on its particle size and crystal defects. Lower calcination temperature with shorter residence time makes the calcined magnesia with smaller particle size and more crystal defects. Therefore, these characteristics facilitate the magnesia hydration progressing more readily.

When we discuss the expansion behavior and properties of magnesia blended cement, it is inevitable to mention its rival—shrinkage. What the shrinkage issue deteriorates and what this may cause are mostly the aspects that the expansion behavior needs to cope with.

Shrinkage issue is an intrinsic feature and issue accompanied by hydration of cement material. At present, this issue can be categorized into several types: chemical shrinkage, self-desiccation (autogenous shrinkage), and thermal shrinkage.

• Chemical shrinkage arises from the fundamental property of cement hydration which means the hydration products occupy less volume than the reactants (Sant et al., 2006; Scrivener et al., 2016). Some estimated chemical shrinkage value may be around 6.25 ml/100 g BWOC (by weight of cement) (Baumgarte and Thiercelin, 1999).

Why is addressing the shrinkage issue important? It will benefit the well integrity more or less which mainly arises from cement sheath mechanical properties like bonding strength at cementing interfaces, internal tensile strength, stress condition, elastic properties, etc.,.

First of all, shrinkage will increase the probability of debonding incidents at both of the cementing interfaces. Micro-annulus is probably caused by certain shrinkage issues which could induce formation fluid migration and sustained casing pressure (SCP) (Reddy et al., 2009). Besides the SCP phenomenon, the micro-annulus issues can usually be validated with the loss or weak response of CBL (cement bond log) and VDL (variable density log) logging at wellsite (Baumgarte and Thiercelin, 1999; Gowida et al., 2018). Although formation fluid migration (especially gas migration) has been categorized into three types (Stiles, 2006) which all demanded bundle of cement slurry/sheath properties (Ravi et al., 2002; David; Stiles, 2006; Williams et al., 2011; Shadravan et al., 2014; Jafariesfad et al., 2017a), the volume stability is always on the list.

Secondly, shrinkage is always coupled with cement pore pressure decrease during the hydration process. With the hydration going on, the original cementitious clinker materials will react with water to produce certain products, mostly as C-S-H gel/phase. This hydration will cause a chemical shrinkage phenomenon which results in the porous matrix and capillary effect during cement setting. The solution media in the pores contributes to the pore pressure. This plays a critical role in the initial internal stress condition of the set cement sheath which further connects internal cracking issues (Onaisi et al., 2017; Zhang et al., 2019). Pore pressure variation indicates two meaningful factors for shrinkage mitigation/expansion activation:

• Water supply. If the cement sheath was under drained conditions, it would get the water supply from the surroundings. This scenario refers to the downhole cementing contacting with water-bearing formation. Since some of the expansive additives activate their expansion through their hydration reactions, the water supply (between internal pore structure and formations) matters in two senses: how much the expansive additive is hydrated and how much pore solution residue there is. Lack of water supply with on-going hydration and condense matrix formed in the pores will make the pore pressure drop below the surrounding pressure.

Expansive cement, as one of the effective measures mitigating or addressing the shrinkage and self-cracking issues, has become the study topic for over one century. In this work, the term expansive cement refers to the PC mixed with the expansive agents. The aim of using this material is to counter the shrinkage effect and realize the controlled volume expansion to maintain its volume consistency in the construction area and the primary sealing capability in the downhole annular space. Self-healing cement is a synonym of expansive cement under some circumstances (Zhang et al., 2020). Enhanced autogenous healing can be facilitated through non-encapsulated additions such as magnesia. Aside from this, if micro-cracks/internal cracks formed after the cement set, the microencapsulated healing technique can be the remedial candidate. The core materials include mineral expansive additives like magnesia (Mao et al., 2020).

On the crystal growth based pathways, magnesia mixed cement has also been successfully applied in the geological well fields because of its higher tolerance to high temperature (Ghofrani and Plack, 1993; Nelson and Drecq, 1990; Appah and Reichetseder, 2002), lower water consumption (Nagataki and Gomi, 1998), controllable hydration (Mo et al., 2010; Jafariesfad et al., 2016), lower hydration enthalpy (Ghofrani and Plack, 1993), and lower carbon dioxide leaching tendency (Section 6.3). Moreover, the blending of reactive MgO with PC does not interact with each other to produce the new hydration products except their hydration products (brucite and C-S-H gel), respectively (Vandeperre et al., 2008). However, regarding hydration kinetics, the blending of magnesia with PC behaves differently from each other (Thomas J. et al., 2014). Magnesia hydration will be substantially retarded while the PC hydration will behave as usual. One possible reason can be attributed to the pore solution chemical conditions such as pH value variation, different ionic components (silicate ions, aluminate ions). Some other researchers, (Brandl et al., 2014), gave another version of magnesia’s impact on PC hydration. They commented on two side-effects of magnesia on PC hydration: 1) acceleration of PC hydration and setting; 2) increment of fluid loss of cement slurry.

Along with shrinkage mitigation, soundness is another important factor that needs to be considered. ASTM standards requires that the maximum expansion extent should be 0.8% (ASTM International, 2019a). However, some studies have shown that under certain magnesia dosages (<5%), there is no evident observation of unsoundness phenomena (Moradpour et al., 2013).

Mitigating shrinkage issue is not only significant to the volume stability of set cement matrix itself but is also vital to some other key properties such as flexibility. As (Jafariesfad et al., 2017a) mentioned, increasing the flexibility of the set cement matrix is to improve the ratio of tensile strength versus Young’s modulus or as σ _t /E. Fibers (micro-fiber, nano-fiber) and nano-particles are usually incorporated into the cement formulation regarding this aim. Besides this, coupled with high resistance to reciprocated loading regimes during well production processes and low shrinkage properties is preferred. For instance, shale gas development always requires volumetric fracturing after well completion which demands the cement sheath with good bonding properties and flexibility. Some researchers (Williams et al., 2011) pointed out that some quantitative expansion ratios such as between 0.2% and 0.5% should be met to reduce the SCP (sustained casing pressure) as much as possible.

As we know, the hydration of cement paste/slurry always proceeds with the induction period at the beginning time. From the study results of (Ogawa and Roy, 1982), the bulk volume variation also undertook the process from the chemical shrinkage (the extent rested on the formulation of cement slurry) to the gradual expansion. Besides this, the expansion rate and hydration degree of the sample also behaved higher when the curing temperature was higher. Meanwhile, these two values also reached a plateau earlier than the lower curing temperature samples. Apart from the reactivity of magnesia affecting its hydration rate, the aging conditions such as curing temperature also impact its hydration rate. Therefore, the question of how to realize the optimum expansion from magnesia hydration corresponding with the hydration progress of Portland cement already aroused some researchers’ interests. In 1993, Reza Ghofrani et al. pointed out this issue in their study of the expansion effect from dead-burnt magnesia (calcined at 1,400°C) and lime (calcined at 1,400°C) on neat Portland cement slurry under atmospheric and HPHT (high-pressure, high-temperature) conditions (Ghofrani and Plack, 1993). The choice of these two oxide expansive additives should depend on the downhole temperature. The calcium oxide (calcined at 1,400°C) is fit for the temperature of less than 70°C. And the magnesium oxide (calcined at 1,400°C) is fit for the case of higher temperature up to 175°C. In addition, the shear bond strength (at the cementing interfaces) was improved by the bulk expansion, and the permeability of the hardened cement sample was decreased on account of the in-situ expansion in the pore matrix of set cement. Jafariesfad et al. (Jafariesfad et al., 2017b) investigated the impact of magnesia with different reactivity (70–260 nm in average particle size) on the expansion and tensile strength of some oil well cement slurry. They employed near ambient aging conditions (40°C, atmospheric pressure) to cure their cement specimens. Based on their results, it is promising to obtain the acceptable tuning between shrinkage compensation and sustained mechanical strength of cement sheath by manipulating the reactivity of magnesia.

The carbonation of magnesia or magnesium hydroxide originally arose from the purification of MgO (Doerner et al., 1946; Sheila et al., 1991; Shand, 2006e). During the carbonation process, the chemisorption of CO₂ with the MgO crystal surface probably happens as reaction Eq. 15. The lattice oxygen in MgO crystal is essentially prone to attract acidic molecules such as CO₂ to produce surface C O 3 2 − (Ochs et al., 1998). C O 2 ( i n t e r f a c e ) + O ( i n t e r f a c e ) 2 − → C O 3 ( i n t e r f a c e ) 2 − (15)

At the same time, because of the co-existence of H₂O, MgO, and CO₂, the following reactions/processes also will take place under atmospheric pressure (CO₂ partial pressure) and ambient temperature conditions (20°C) (Fernández et al., 1999): C O 2 ( g a s ) + H 2 O ( l i q u i d ) → C O 2 ( a q u e o u s ) (16) C O 2 ( a q u e o u s ) ↔ C O 2 ( i n t e r f a c e ) (17) M g O ( s o l i d ) + H 2 O ( l i q u i d ) → M g ( O H ) 2 ( s o l i d ) (18) C O 2 ( i n t e r f a c e ) + M g ( O H ) 2 ( s o l i d ) + ( n − 1 ) H 2 O ( l i q u i d ) → M g C O 3 ⋅ n H 2 O ( s o l i d ) (19) M g C O 3 ⋅ n H 2 O ( s o l i d ) + C O 2 ( i n t e r f a c e ) ↔ M g ( i n t e r f a c e ) 2 + + 2 H C O 3 ( i n t e r f a c e ) − + ( n − 1 ) H 2 O ( l i q u i d ) (20) M g ( i n t e r f a c e ) 2 + + 2 H C O 3 ( i n t e r f a c e ) − ↔ M g ( a q u e o u s ) 2 + + 2 H C O 3 ( a q u e o u s ) − (21)

Processes 16 to 21 will occur when there is enough dissolved CO₂ in the solution. Through these reactions, more carbon will be trapped in magnesium bicarbonate compounds. However, if the dissolved CO₂ decreased or the temperature of the solution increased, the magnesium bicarbonate compounds would precipitate magnesium carbonate compounds (e.g. hydromagnesite) and produce CO₂ from the solution. One example can be illustrated as the following reaction Eq. 22: 5 M g ( H C O 3 ) 2 ( a q u e o u s ) → M g 5 ( C O 3 ) 4 ( O H ) 2 ⋅ 4 H 2 O ( s o l i d ) ↓ + 6 C O 2 ( gas ) ↑ (22)

This decarbonization process will proceed as the dehydroxylation reactions with regards to solubility decreased trend (ref. to Supplementary Table S5 in the Supplementary Material) as follows (Langmuir, 1965; Davies and Bubela, 1973) Eq. 23: M g C O 3 ⋅ 5 H 2 O Lansfordite → 10 ° C M g C O 3 ⋅ 3 H 2 O Nesquehonite → 55 ° C M g 5 ( C O 3 ) 4 ( O H ) 2 ⋅ 4 H 2 O Hydromagnesite (23)

Even though the above carbonation mechanisms were obtained from the leaching magnesia pulp, the fundamental reactions are also applicable to the magnesia/brucite carbonation in terms of the carbon dioxide capture and sequestration (also abbreviated as CCS). Extensive studies have been conducted on this hot topic especially in the latest decades because of the greenhouse effect issue (Zhang et al., 2017). Among these works, some of them focused on the carbonation of civil binder materials including brucite, magnesia cement (no PC content), and magnesia blended cement (with PC content) under ambient conditions (normal temperature, ambient CO₂ partial pressure). Others targeted the carbonation of magnesium silicate mineral and magnesia blended cement with respect to high-temperature, high-pressure (CO₂ partial pressure) conditions. Meaningful findings extracted from these works will shed light on the CO₂ geological sequestration and relevant geotechnical well constructions.

Some studies targeted the carbonation of neat brucite (between CO₂ gas and brucite solid) (Béarat et al., 2002). The dehydroxylation, carbonation, and rehydroxylation mechanisms were investigated under different CO₂ partial pressure, different temperatures, and different morphological factors. Several insights of the dehydroxylation/carbonation of brucite are as follows:

• Carbon dioxide (CO₂) pressure and temperature have vital roles in the carbonation process of brucite.

More investigations have been carried out on the enhanced carbonation of reactive magnesia blended cement materials under ambient temperature/pressure and different CO₂ concentrations. The experimental details summary can be found from one table including five sub-tables (Supplementary Tables S7–S11) of the Supplementary Material. Since portlandite would be formed after Portland cement hydration, some researchers studied the carbonation mechanism when portlandite and brucite co-exist in suspension (Silva et al., 2009). Inclusion of magnesium carbonate phase into calcium carbonate system can improve the strength property by means of introducing magnesium hydroxide into calcium hydroxide slurry exposed to CO₂ carbonation curing. The Mg/Ca ratio of the initial mix determines the strength performance variation. The CO₂ pressure and curing duration impact the strength property differently based on the initial Mg/Ca ratio. The magnesium-bearing carbonate contents [(Ca,Mg)CO₃ and MgCO₃⋅3H₂O] are favored with higher CO₂ pressure and longer carbonation curing duration.

Based on the results from (Hopkinson et al., 2008), when suspending magnesia into some solution (CaCl₂) at a mol ratio of 5:1, the transition phase (transitory magnesium hydrate carbonate, MgCO₃⋅2H₂O) can be formed in the transformation process from nesquehonite to hydromagnesite and depends strongly on the curing period, the porous aqueous solution chemical composition, and the in-situ crossings of supersaturation limits. Meanwhile, the geochemical response, from dissolution to precipitation process between calcite and transitory hydromagnesite phases, can accelerate the transition from nesquehonite to hydromagnesite.

Dung and Unluer found the positive effects of hydration agent (HA) and dispersant agent (DA) on accelerated carbonation of reactive magnesia suspension (Dung and Unluer, 2016): the HA (e.g. HCl) can improve the conversion from magnesia to brucite in both rate and amount aspects; the DA [e.g. (NaPO₃)₆] can delay the precipitation of brucite and facilitate its direct carbonation in pore solution. These two agents facilitate the afterward HMCs [hydrated magnesium carbonates, nesquehonite—MgCO₃⋅3H₂O, hydromagnesite—4MgCO₃⋅Mg(OH)₂⋅4H₂O, dypingite—4MgCO₃⋅Mg(OH)₂⋅5H₂O] formation and the micromorphology variation (denser matrix, larger HCMs crystal size), which in turn benefits the compressive strength gain in the short term (28 days), e.g., 115% and 58% higher than the control mix with ambient carbonation and accelerated carbonation respectively.

In terms of ternary magnesia cement (reactive magnesia, PFA—pulverized fly ash, natural aggregates like sand and gravel) (Unluer and Al-Tabbaa, 2014), the carbonation and afterward mechanical performance development is dependent on such factors as water/cement ratio (w/c ratio), CO₂ concentration, curing duration, RH (relative humidity), and wet/dry cycling frequency. They are influenced by each other. PFA addition is beneficial to the carbonation rate and extent of this system. Shorter carbonation duration prefers lower w/c ratio mix and vice versa. CO₂ concentration has an optimal value in terms of maximum carbonation extent because the higher CO₂ concentration of 20% is reflected by the similar mechanical property compared with the lower CO₂ concentration of 10% regardless of other conditions. At the same time, the effective access of water and CO₂ are both important to optimal carbonation. The impact of RH on the carbonation does not behave linearly but rather the RH of 78% outperformed all the other RH conditions within the scope of this work.

As for the hybrid reactive magnesia blended Portland cement (reactive magnesia, Portland cement, supplementary cementitious material like PFA or GGBFS), accelerated carbonation can promote the HCMs (hydrated magnesium carbonate such as dypingite, hydromagnesite, lansfordite, etc.,) and nesquehonite formation inside cement matrix and also improve the compressive strength compared with the atmospheric carbonation cured samples (Liska et al., 2008; Panesar and Mo, 2013). The natural carbonation on these mixes progresses very slowly even after more than 196 days of curing (Liska et al., 2008). The hybrid reactive magnesia blended Portland cement with substantial replacement of Portland cement with SCMs (as for PFA, > 50% PFA and > 25% reactive magnesia in mass ratio; as for GGBFS, PC:MgO:GGBFS = 1:2:2) can obtain equivalent or even better mechanical properties (e.g. compressive strength, toughness, stiffness) after enhanced carbonation curing (ambient temperature, ambient pressure but with > 20% CO₂ concentration, and longer aging duration) (Vandeperre and Al-Tabbaa, 2007; Panesar and Mo, 2013). This was attributed to the forced carbonation facilitating the formation of a denser matrix resulting from more nesquehonite in-situ formation from brucite which hence enhances the mechanical behavior and microstructure of reactive magnesia-aggregate systems (Liska et al., 2008). Water content (including original w/c ratio and relative humidity), CO₂ content, and porosity influence the carbonation efficiency even under enhanced carbonation conditions because these parameters control the diffusion of CO₂ into the cement matrix and the accessibility of water molecules to the intermediate magnesium bearing compounds (brucite, nesquehonite, hydrated magnesium carbonate). Maximum carbonation always takes place under moderate CO₂ concentration and medium relative humidity conditions (Vandeperre and Al-Tabbaa, 2007; Liska et al., 2008; Panesar and Mo, 2013).

Although the above carbonation experiment studies are relevant to ambient temperature and pressure conditions, the findings show us the high potentials of using reactive magnesia as one of the primary cementitious materials when we proceed with CO₂ geological sequestration and CO₂ EOR (enhanced oil recovery) operation due to: 1) mitigating the calcium leaching issues from Portland cement, 2) and the better performance as mechanical properties, permeability, and bonding strength derived from magnesium carbonates transformation (Shand, 2006b; Liska and Al-Tabbaa, 2012; Dung and Unluer, 2017; Ruan and Unluer, 2017). Therefore, other researchers have extended the investigations pertaining to high-temperature and high-pressure surroundings. H a ̈ nchen et al. (Hänchen et al., 2008) studied the supersaturation solution composed of NaCO₃ and MgCl₂ in equilibrium with CO₂. The nesquehonite, hydromagnesite, and magnesite would precipitate under the supersaturation conditions with respect to nesquehonite, brucite, and hydromagnesite respectively. Carbonation temperature and pressure dominate the type of precipitation. Nesquehonite would be formed with regards to the ambient condition (25°C, 1 bar of CO₂ partial pressure). Magnesite would be the final phase when the carbonation is cured at high-temperature (120°C) and no matter the CO₂ partial pressure. During these processes, hydromagnesite would be formed temporarily.

Frost et al. inspected the thermal stability of artinite [MgCO₃⋅Mg(OH)₂⋅3H₂O], dypingite [4MgCO₃⋅Mg(OH)₂⋅5H₂O], and brugnatellite (MgCO₃⋅2H₂O) by use of the DTA method (Frost et al., 2008). The dehydration temperature for these three compounds is 219°C, 213°C, and 247°C respectively. In addition, the decarbonization temperature is within the range of 350°C–355°C. These results provide reference not only to the CO₂ geosequestration with magnesium-bearing minerals but to the reactive magnesia blended Portland cement studies.

Qakofu et al. studied the magnesite formation under low temperature (35°C and 50°C) and high CO₂ partial pressure (90 and 110 atm) conditions (Qafoku et al., 2015). They found that the formation of magnesite through an aqueous solution medium would progress very slowly even with the supercritical CO₂ phase. However, in the long-term view (56 days for 50°C case and 135 days for 35°C case), the intermediate nesquehonite and hydrated magnesium carbonate would transform into magnesite finally.

Srivastava et al. investigated the resistance performance of dead burnt magnesia (calcined at 1,250°C) incorporation into Class H oil well cement under high-temperature (107°C) and high-pressure (16.4 MPa, 41 MPa) conditions lasting for 14 days (Srivastava et al., 2018). Apart from the expansion effect, magnesia has the potential to improve the carbonic resistance of oil well cement sheath granted that the formulation of magnesia blended Portland cement should be designed with care to realize the synchronized hydration between magnesia and PC. In terms of carbonic acid resistance and degradation prevention of PC material, lower temperature and CO₂ partial pressure are both desired. However, from another viewpoint, these aging conditions would not favor the formation of magnesium-bearing carbonates.