**1. Introduction**

Unconventional hydrocarbon reservoirs are different from their conventional counterparts in the sense that they require distinctive operations for recovery that differ from normal practices deployed for conventional reservoirs. The main reason for this is the ultra-low permeability of the rock formation, which hinders the ease of flow of hydrocarbons towards the well, but other factors such as the reservoir fluid properties also impact flow mechanisms. Examples of unconventional reservoirs are gas hydrates, oil shales, gas shales, tight-gas sandstones, tight-gas limestones, heavy oil and tar sandstones, and coalbed methane reservoirs [1–7].

As the term implies, heavy oil and tar reservoirs are those that contain viscous and dense oils. About a third of the total world oil and gas reserves consist of the heaviest range of hydrocarbons, yet they are mostly overlooked due to the perceived high costs and difficulties associated with its production [5]. Although reservoir properties including pressure, permeability and porosity are important measures of its behaviour, the fluid density and viscosity determine the approach used for production [5]. Heavy oils and tars are generally high in density and viscosity. Density is a measure of how much mass is contained per unit volume. The standard unit of measurement adopted in the oil and gas industry, especially in the United States, is the degree of American Petroleum Institute (API) gravity. A lower API value indicates a higher density and vice versa. Normally, oils below 20o API gravity are defined as heavy which may be as low as 4o for bitumen with high tar content [3, 5]. Oil viscosity, on the other hand, defines its resistance to gradual shear or tensile deformation when subjected to shear or tensile stress respectively. A viscous fluid exhibits resistance to shear stress and, thus, its flow is reduced where shear stresses are applied. Oil viscosity has an inverse relationship with temperature; it varies greatly by becoming less viscous as temperature increases. The flow rate of reservoir fluids is a key parameter and because of the direct link between viscosity, temperature and the ease of flow, oil viscosity is considered to be more important than oil density during production [3, 5]. Thus, viscosity, rather than density is used as a measure of the heaviness of oil. Under reservoir conditions, heavy oils have viscosities >100 cp [3]. Apparently, there is no direct correlation between density and viscosity, largely due to the influence of temperature. Low-density oils in shallow reservoirs, where the temperatures are cooler, may have higher viscosities in comparison to oils at hotter deep reservoirs.

Oil shale is a fine-grained sedimentary rock richly composed of organic matter [8], in the form of kerogen [2]. Kerogen is a solid mixture of organic compounds and is the primary source of hydrocarbons from oil shale. This type of hydrocarbon is referred to as shale oil, which is unconventional and different from tight oil naturally present in shales and ultra-low permeability sandstones, carbonates and siltstones [9]. Kerogen, also known in some instances as total or bitumen-free organic matter, consist of more than 80% organic matter; however, a major proportion of this is not readily soluble in ordinary organic solvents under moderate conditions [2]. Therefore, it is more challenging to extract in comparison to crude oil from conventional reservoirs because of high costs and negative environmental impacts [10]. To remove shale oil from oil shales, it is imperative to decompose the insoluble organic matter with heat. This is achieved by thermal dissolution, hydrogenation or pyrolysis [11–13]. The three methods require very high temperatures.

Tight oil is light crude oil found in shales and very low permeability and low porosity sandstones, carbonates and siltstones [9]. Although the term is sometimes used interchangeably with shale oil normally contained in oil shales (e.g., [9, 14]), there are distinctions. As at 2015 the world's technically recoverable tight oil from shale formations was estimated at 418.9 billion barrels (bbl). A large proportion of this amount is located at United States (78 bbl), Russia (75 bbl), China (32 bbl), Argentina (27 bbl), Libya (26 bbl), United Arab Emirates (23 bbl), Chad (16 bbl), Venezuela (13 bbl) and Mexico (13 bbl) [15]. Typical porosity and permeability of tight oil formations are below 12% and 0.1 mD respectively, though a broader definition of tight oil reservoirs can generally refer to those with very low porosity and permeability [9]. The low- porosity and permeability characteristics furthers the need to stimulate tight oil reservoirs for successful production.

Worldwide, the commercial production of unconventional hydrocarbons is in constant increase. This supplements supply from conventional reservoirs resulting in an overall increase in hydrocarbon production globally and a decrease in prices [16].

### *Production from Unconventional Petroleum Reservoirs: Précis of Stimulation Techniques… DOI: http://dx.doi.org/10.5772/intechopen.106318*

This inverse relationship between oil production and oil prices is illustrated in Monge *et al*. [14], where an increase in U. S. oil production from the shale oil boom drives down *West Texas Intermediate* (WTI) oil prices.

Other forms of unconventional gas resource are gas hydrates and coalbed methane reservoirs. Gas hydrates are crystalline ice-like forms of water with a structured molecular framework joined together to create cavities such that gas molecules, which are mostly methane, are trapped within it [17]. Other entrapped guest gases include ethane, isobutene and propane [18]. Natural gas hydrates were only discovered a few decades ago and 98% of deposits occur in upper sedimentary layers underneath the seafloor [7]. It is extensively spread in oceans and polar areas with a reserve that is 10 times greater than global conventional gas [18]. The creation and stability of gas hydrates rely on the properties of both the water and composition of gas, temperature and pressure [18, 19]. The formation of gas hydrate is exothermic, which implies the release of heat during this stage. On the other hand, heat is required for dissociation of hydrates [18–20]. The dissociation of hydrates is an endothermic process relying on the surrounding heat. Gas hydrates are stable at high pressure and low temperature conditions; therefore, depressurisation is an effective means of inducing the release of gas from hydrate deposits [20–22].

Coal seams are dark-banded deposits of coal trapped between layers of rock. They differs from conventional gas reservoirs in terms of their pore structure, porosity, permeability, fluid flow mechanism, gas-water relative permeability and other reservoir characteristics [23]. Coal is both heterogeneous and anisotropic; it is characterised by a dual porosity comprising a porous matrix with micro pores enclosed by a larger scale medium of cleats, which constitute the macro pores [23–25]. Coal porosity and permeability is mostly defined by the micro pores and macro pores, respectively [23]. Usually, water permeates coal seams, which helps to retain the adsorbed gas on the coal surface [25]. Coal seams are unconventional reservoirs containing a variety of gases including methane, hydrogen, ethane, nitrogen and carbon dioxide [26]. It contains a significant proportion of methane, which is more easily extracted in comparison to some of the other gas constituents (e.g., hydrogen and nitrogen). This is due to the reduced affinity coal has for methane. The concentration of methane in the gas content can be as high as 99.95% [27]. The chemical composition of coalbed methane—also known as coal seam gas—is the same as natural gas obtained from conventional reservoirs. The gas is contained in three ways: adsorbed on the surface of micro pores; in a free state in macro pores, i.e., the natural fractures (cleats) within the coal material; and dissolved in the formation water [23, 25, 28].


**About the Editor**

**Fangxin Fang** is a senior research fellow at Imperial College London and executive manager of the data assimilation laboratory at the Data Science Institute, Imperial College London. She leads research on advanced computational tools and data science technologies that can help us to manage a safe, comfortable and healthy environment. She has over 25 years of experience in data assimilation and mathematical modelling technologies. Her main original contributions centre on cutting-edge techniques of predictive modelling (machine learning and data assimilation techniques, reduced-order modelling, adaptive observation), where the work is at the forefront of data-centric modelling. The applications are mainly focused on ocean, atmospheric, multiphase flows, and environmental problems. Fang and her group first applied deep learning techniques to real-time spatiotemporal prediction of nonlinear fluid flows. Applications of advanced data-centric modelling techniques will be renewable energy, weather prediction, pollution forecasting, and hydraulic and coastal engineering.

### *Editorial* **Numerical and Data-Driven Modelling in Coastal, Hydrological and Hydraulic Engineering**

**Fangxin Fang**

#### **1. Introduction**

This special issue aims at exploring advanced numerical techniques for real-time prediction and optimal management in coastal and hydraulic engineering. Numerical simulations of fluid dynamics have been indispensable in many applications relevant to physics and engineering.

*Multiscale physical modelling:* The grand challenge in modelling complex physical phenomena is to predict their characteristics and evolution with adequate accuracy and reliability. This has remained an open scientific problem for decades, unsurprisingly given the extreme disparity in the length- and time-scales involved, spanning several orders of magnitude. For example, climate modelling involves both basin scale and smaller scale features such as boundary currents, mixing, chemical interactions and transport, overflows, and mesoscale eddies. Over traditional structured mesh models, the use of adaptive unstructured meshes provides several profound and widely acknowledged advantages [1]. These include: the ability to conform accurately and efficiently to complex domain geometries (for example, bathymetry, a complex cityscape); the ability to dynamically adapt mesh resolution to improve the accuracy of model results, to capture detailed dynamics, or follow the physical processes.

*Data assimilation*—incorporating information from experiments and observations to reduce uncertainties in numerical prediction [2,3]. To achieve a predictive capability, numerical modelling often needs to be linked with experiments/monitoring. Data assimilation is a versatile methodology for estimating model uncertainties (parameters, model error, initial and boundary conditions, etc.). A variety of approaches have been used to facilitate data assimilation and include statistical interpolation methods, nudging data assimilation, Kalman filter, Ensemble Kalman filter, and variational (adjoint) methods. Optimal monitoring location is the key in data assimilation. Targeted observations represent a subcategory under adaptive observations where data collection is optimized to improve a particular forecast aspect (e.g., energy, health impact). The targeting approach incorporates dynamical information from numerical model predictions to identify when, where, and what types of observations would provide the greatest improvement to specific model forecasts at a future time [4]. Such targeted observations are important as they will allow the most effective use of available monitoring resources.

*Data-driven modelling:* Numerical models have benefited from the availability of high-resolution spatio-temporal data due to recent advances in measurement techniques [5], which make the studies of more complex flows possible. However, the computational cost involved in solving complex problems is intensive, which still precludes the development in these areas. Recently, data-driven modelling has gained popularity in rapidly predicting nonlinear fluid flows. Various studies have shown that machine learning methods have potential for capturing non-linear subgrid processes. Reichstein et al. [6] suggest that future models should integrate physical-based modelling and machine learning approaches. Such combination will be the optimal way by which physical modelling results can provide

**Citation:** Fang, F. Numerical and Data-Driven Modelling in Coastal, Hydrological and Hydraulic Engineering. *Water* **2021**, *13*, 509. https://doi.org/10.3390/w13040509

Received: 5 February 2021 Accepted: 12 February 2021 Published: 16 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

dynamic understanding from the governing equations, while data-driven modelling results may find some patterns that are not expected from physical modelling.

The Special Issue of Water journal comprises five original papers covering the aspects of the above-mentioned challenges. Overall, the authors focused on different topics, such as, multiscale modelling [7], data assimilation [8], adaptive observation [9], machine learning [10], and application [11].

#### **2. Author Contributions**

Juznetsov et al. [7] presented the results with a new 3D unstructured mesh finite volume coastal model, FESOM-C [12]. Over existing structured mesh models, FESOM-C with hybrid meshes (quadrilaterals and triangles) is geometrically flexible and allows the resolution of the mesh to be varied (within reasonable limits) in both the horizontal and vertical, letting the mesh contour complex coastlines. Variable horizontal resolution enables the use of coarser meshes in open sea regions but more refined ones in shallow areas to resolve important small-scale processes such as wetting and drying, sub-mesoscale eddies, or sub-mesoscale dynamics of steep coastal fronts. In this work, the FESOM-C model was applied to an area of the south-eastern North Sea and its performance was evaluated by comparing the results against observations. With use of mixed unstructured meshes, the salinity and temperature gradients, as well as frontal dynamics, can be captured well.

Du et al. [8] explored the capability of ensemble Kalman filter (EnKF) in its applications. EnKF has its potential for efficient use on parallel computers with large-scale geophysical models. EnKF techniques are widely used in operational modelling. The EnKF is based on a Monte Carlo approach, using an ensemble of model representations to build up the necessary statistics [13]. A background error covariance is computed using an ensemble of forecasts, with the current analysis ensemble serving as initial conditions. However, the introduction of perturbations into background variables may break the physical conservation law. One of challenges in EnKF is how to maintain the physical features of variables after inducing the initial perturbations. To address this issue, Du et al. [8] proposed a multivariate balanced initial ensemble generation method based on the multivariate empirical orthogonal function (MEOF) method. The Local Ensemble Transform Kalman Filter in combination with the MEOF based balanced perturbation scheme was applied for improving accuracy of atmospheric general circulation modelling. The study case was the six-hour model forecast from 1 January to 31 March 2004. The prognostic model variables were temperature, surface pressure, wind velocity, and specific humidity. The results obtained from their work suggested that the ensembles integrated from the initial ensemble generated from the MEOF-based perturbations maintain a much more reasonable spread and more reliable horizontal correlation than those from the randomly perturbed initial fields.

Fattorni and Brandini [9] presented their recent work on adaptive observation strategy. Due to expensive field-deployed resources, there is a need to optimally place observations that will maximally improve the accuracy of numerical solutions at forecast times. The optimal observation network could be adapted for a wide range of forecasting goals, and it could be adapted either by allocating existing observations differently or by adding observations from programmable platforms to the existing network. Fattorni and Brandini [9] proposed the observation strategies based on singular value decomposition (SVD). In their work, SVD was used for identifying the areas where maximum error growth occurred, and a correlation analysis was used to limit redundant observations. The case study was Double Gyre, a well-known idealized case to reproduce the seasonal and interannual oscillations of the large-scale circulation in the ocean, useful for the climate system predictability. The results indicated that optimal observation strategies can provide effective and efficient data assimilation for improving predictive accuracy.

He et al. [10] explored the potential of deep learning techniques in emulating the process-based Martinez Boundary Salinity Generator in simulating downstream salinity boundary for the Sacramento–San Joaquin Delta of California, United States. In their work, the multilayer perceptron, long short-term memory network, and convolutional neural network-based models were used. The training datasets were from 1991 to 2002 while validation datasets were from 2003 to 2014. The results obtained in this work showed that deep learning neural networks can provide competitive or superior results compared to the process-based model, especially during extreme (i.e., wet, dry, and critical) years.

Lastly, Gao et al. [11] presented their study of transport time scales (TTS) for a Hyper-Tidal Estuary. The water exchange processes and transport time scales are important factors in governing tracer transport, water quality, and the ecosystem of the basin [14]. The study site chosen in this work was the Severn Estuary, one of the largest estuarine basins in the UK, with typical spring and neap tidal ranges of 13.5 m and 6.5 m, respectively. The aim of this study was to investigate the residence and exposure times of the Severn Estuary in parallel, and to characterize the transport time scales for a hyper-tidal estuary. The results obtained from their work suggested that for all flow and tide conditions, the exposure times are significantly greater than the residence times. That is, there is a high possibility for water and/or pollutants to re-enter the Severn Estuary after leaving it on an ebb tide. The fractions of water and/or pollutants re-entering the estuary for spring and neap tide conditions are very high, with 0.75–0.81 for neap tides, and 0.79–0.88 for spring tides.

In conclusion, this special issue presents recent studies on numerical and data-driven modelling and applications to atmosphere, ocean, coastal, and hydrological engineering.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**1. Introduction**

Rubber is one of the most important polymer materials playing an essential role in dynamic applications like tires, belts, diaphragms, and seals. Rubber products are continuously subjected to repeated cyclic deformation, according to the service conditions. In most areas, due to the working conditions like rubbing, abrading, chunking, and tearing the product undergoes mechanical failure very easily. Such failure mainly occurs due to continuous friction, wear, abrasion, and crack formation. Friction and wear often occurs when two surfaces contact each other [1]. Movements between the two contacting surfaces cause cutting or damage of the rubber surface, usually known as abrasion [2]. The continuous cutting of the soft rubber material generates small cracks, which propagates faster when the rubber product is subjected repeatedly to dynamic working conditions. The mechanical performance of rubber composites depends on several material parameters like type of elastomers, type of filler, filler content, filler size and structure, state of filler dispersion, interaction between polymer and filler, type of plasticizer, and the nature of crosslinks and its density [3]. Natural rubber is one of the main rubbers used in truck tire applications due to its excellent self-mechanical reinforcement and crack growth resistance, which are attributed to its strain induced crystallization behavior [4,5]. Incorporation of fillers like carbon black and precipitated silica into the natural rubber further improves the reinforcement characteristics. In recent years, novel nanofiller systems such as layered silicates, carbon nanotubes, or graphene nanoplatelets have been emerging, which, due to their nanoscale and

their special aspect ratios, o ffer reinforcements beyond carbon black or silica [6–12]. Non-crystallizable rubbers like styrene butadiene rubber and acrylonitrile butadiene rubber have no self-reinforcement behavior. Therefore, the rubbers display poorer tear strength and crack propagation characteristics. These synthetic rubbers do not have the ability to crystallize during mechanical deformation [13]. Technically, for such non-crystallizable rubbers, the reinforcement is mainly enhanced only via a proper selection of fillers [14–16].

Carbon blacks are the major class of reinforcing materials for rubbers fulfilling the requisite properties for more than a century due to its ability to o ffer outstanding mechanical performance [17,18]. However, in the last few decades, precipitated silica is emerging as a potential candidate and has partially or fully replaced carbon black, mainly due to lower rolling resistance and improved wet grip properties in tire applications despite sensitively varying tear strength values and crack resistance properties [16,19]. However, poor nano/microscale dispersion and interaction with rubber is one of the critical issues encountered with silica and is strongly influencing the failure properties of rubber products. However, these issues have been overcome through multi-stage mixing and by incorporating suitable silane coupling agents. Scientifically, several assumptions are believed about the rubber product failure when rubbers are subjected to the mentioned severe working conditions. Some of them are: (1) molecular chains attempt to move in the stressed direction, causing chains slippage and reorientation, (2) crosslinks, entanglements, and filler particles hinder chain motion, which leads to a state of tension and local chain scission occurs, (3) scission of single polymer chain transfers the load to the neighboring chains, which propagates and the cumulative e ffect produces microvoids, and, lastly, (4) the microvoids grow to from microcracks, which is an irreversible process and these microcracks propagate and, ultimately, cause product failure [19].

For the current study, silica filled rubber composites are prepared by two di fferent methods. First, commercial precipitated silica is directly incorporated into the rubber and next silica particles are generated inside the rubber by the sol-gel method [20]. More details concerning the preparation of sol-gel silica inside the rubber could be found in our earlier work [21]. The volume fraction of silica in both nanocomposites is the same and is confirmed through thermogravimetric analysis [21]. The particle morphology (size and structure), crosslink density, and state of silica dispersion of the prepared SSBR composites are entirely di fferent. The synthesis of in-situ silica in the polymer matrix leads to trapping of polymer chains inside the silica aggregates as well as strong linkage of the polymer molecules at the silica surface. This can be considered as additional network nodes and is responsible for enhanced reinforcement of the rubber without a silane coupling agent. Usage of silane results in a further increase of the physical properties of the composites with in-situ silica due to improved silica-rubber interaction. Incorporation of a masterbatch containing in-situ silica particles leads to commercial precipitated silica to (a) enhanced silica dispersion, (b) possible higher silica loading in the elastomer matrix without impairing its processability, (c) the possibility to control and customize the particle size, and (d) energy-e ffective processing due to easy incorporation of the filler particles.

The main interest is to study how the filler size, structure, and crosslink density of the two di fferent silica filled vulcanizates contribute to friction, abrasion, and crack propagation properties.


*Article* **Research on the Mechanical Performance of Carbon Nanofiber Reinforced Concrete under Impact Load Based on Fractal Theory**

**Wei Xia 1,\*, Jinyu Xu 1,2 and Liangxue Nie 1**

**Abstract:** The research is focused on the dynamic compressive strength, impact toughness and the distribution law of fragmentation size for the plain concrete and the carbon nanofiber reinforced concrete with four fiber volume contents (0.1%, 0.2%, 0.3% and 0.5%) under impact load by using the *Φ*100 mm split-Hopkinson pressure bar. Based on the fractal theory and considering the micropore structure characteristics of the specimen, the impact of the strain rate and the dosage of carbon nanofibers on the dynamic mechanical performance of concrete is analyzed. According to the results, both the dynamic compressive strength and the impact toughness increase continuously with the improvement of the strain rate level at the same dosage of fiber, showing strong strain rate strengthening effect; at the same strain rate level, the impact toughness increases gradually with the increase in the fiber dosage, while the dynamic compressive strength tends to increase at first and then decrease; the distribution of the fragmentation size of concrete is a fractal in statistical sense, in general, the higher the strain rate level, the higher the number of fragments, the lower the size, and the larger the fractal dimension; the optimal dosage of carbon nanofibers to improve the dynamic compressive strength of concrete is 0.3%, and the pore structure characteristics of carbon nanofiber reinforced concrete exhibit obvious fractal features.

**Keywords:** carbon nanofiber reinforced concrete; impact load; dynamic compressive strength; pore structure characteristics; fractal dimension


*3.1. Austenite Nucleation*

Figure 3 shows the morphologic changes from room temperature to the preset temperature of 860 ◦C. Some particles were present on the surface of the sample, and these dark particles were (Fe, Cr, Mn)3C precipitates (Figure 3a) determined by the following results. Due to the increased amount of Cr and Mn, (Fe, Cr, Mn)3C precipitates dominated in the as-received steel treated by hot rolling and subsequent air cooling. When the temperature was increased to 548.7 ◦C, some corrugated folds appeared on the sample surface. These folds correspond to the grain boundaries of the initial ferrite (pearlite), which gradually emerged under the effect of thermal etching (Figure 3b). As the temperature increased to 701.6 ◦C, another corrugated fold gradually covered the grain boundaries of the existing ferrite (Figure 3c). Additionally, this corrugated fold became more and more clear and gradually formed the grain boundaries of polygonal grains as the temperature rose to 827.7 ◦C (Figure 3d) and 862.9 ◦C (Figure 3e). It was inferred that the corrugated fold at 701.6 ◦C was an austenitic grain boundary, that is, the Ac1 temperature (the beginning temperature at which the pearlite transforms to austenite during the heating process) was about 701.6 ◦C when the steel was reheated at 5 ◦C/s. The measured Ac1 temperature of this experimental steel was about 658 ◦C using a thermal simulated test, a little lower than that obtained via in situ observations. The measured Ac1 temperature was obtained with a very slow heating rate (about 0.1 ◦C/s), and the Ac1 temperature increased with the increase in the heating rate (5 ◦C/s). Moreover, austenization process of the sample finished more quickly at a higher heating rate. The austenization process completed at 862.9 ◦C (Figure 3e), but the grain boundary morphology of the initial microstructure remained. Meanwhile, the visible (Fe, Cr, Mn)3C precipitates became clearer and their size increased.

Austenite transformation is related to the nucleation rate and the growth rate, and can be expressed as Equations (1) and (2) [30,31]:

$$N = f\_{N} \exp\left(-Q\_{N}/K\Delta T\right) \tag{1}$$

$$G = f\_G \exp\left(-Q\_G / K\Delta T\right) \tag{2}$$

where *N* is the nucleation rate, *G* is the growth rate, *QN* and *QG* are the nucleation and growth activation energies, respectively, *fN* and *fG* are the impact factors between structure and nucleation with growth, respectively, and Δ*T* is the superheat. This equation reveals that the superheat increases with the increase in the heating rate, which increases the nucleation and growth rates of the austenitic transformation. Therefore, the rate of austenitic

transformation increased significantly, the time required from initial austenization to complete austenization was greatly reduced, and thus the required phase transition interval was correspondingly reduced. In addition, the transformation of steel during continuous heating is equivalent to the accumulation of countless isothermal transformations. The relationship between the isothermal incubation period and the transition temperature can be established using Scheil's superposition principle [32]:

$$\sum\_{i=1}^{i=n} \frac{\Delta t}{A\_i} = 1 \tag{3}$$

**Figure 3.** Morphology variations from room temperature to 860 ◦C. (**a**) 25.5 ◦C, before heating; (**b**) 548.7 ◦C, initial grain boundaries appeared; (**c**) 701.6 ◦C, austenization began; (**d**) 827.7 ◦C, obvious austenite grains; (**e**) 862.9 ◦C, the preset quenching temperature.

Differential Equation (4) is obtained when Δ*t* is small enough.

$$\int\_{t=0}^{t=t\_n} \frac{dt}{A(T)} = 1\tag{4}$$

where Δ*t* and *dt* are the transformation time at temperature *T* and *Ai* and *A*(*T*) are the corresponding incubation periods. The relationship between the incubation period and the transition temperature is shown in Equation (5):

$$\int\_{T\_1}^{T\_s} \frac{dt}{A(T)} = \int\_{T\_1}^{T\_s} \frac{1}{A(T)} \cdot \frac{1}{\frac{dT}{dt}} \cdot dT = \int\_{T\_1}^{T\_s} \frac{1}{A(T)} \cdot \frac{1}{v} \cdot dT = 1\tag{5}$$

The relationships between the transformation rate, *C*, transformation beginning and ending temperatures, *Ts* and *Tf*, and the heating rate, *v*, are interpreted by Equations (6) and (7), where the transformation volume is *f*.

$$
\sigma = \frac{df}{dt}, \upsilon = \frac{dT}{dt} \tag{6}
$$

$$\int\_{t=0}^{t=t\_n} \frac{df}{dt} dt = \int\_{T\_s}^{T\_f} \frac{df}{dt} \cdot \frac{dT}{v} = \int\_{T\_s}^{T\_f} \frac{\mathbb{C}}{v} \cdot dT = 1 \tag{7}$$

where *T*1 is the equilibrium temperature and *tn* is the time to the transformation ending temperatures *Tf*. This equation proves that with the increase in the heating rate, both the initial temperature and the end temperature of the phase transition increase. In addition, the dissolution and diffusion of carbonitrides is inevitable during the austenization process of experimental steel, and atoms migrate between phases through the diffusion mechanism. With the increase in the heating rate, the diffusion of carbon and alloying elements at the equilibrium temperature decreases, thus increasing the austenitic transition temperature. In the process of continuous heating, with the increase in temperature, the diffusion coefficient and diffusion rate of atoms increase greatly, so the driving force of the austenite phase transformation is enhanced.

The morphological variations from room temperature to 1160 ◦C are displayed in Figure 4. Some (Fe, Cr, Mn)3C particles appeared on the sample surface (Figure 4a) and corrugated folds appeared at 550.4 ◦C (Figure 4b). Another corrugated fold gradually covered the grain boundaries of the existing ferrite structure at 704.7 ◦C (Figure 4c). The corrugated fold became more and more clear and gradually formed the grain boundaries of polygonal grains at 828.4 ◦C (Figure 4d). The Ac1 temperature was basically the same as that in specimen reheated to 860 ◦C. This is because the heating processes of the two samples were the same before heating to 860 ◦C. However, when the sample was reheated to 1160 ◦C (Figure 4e), more large-sized grains appeared and the grain boundaries became sharper and clearer. In addition, the number of clearly visible (Fe, Cr, Mn)3C particles increased significantly, and they gradually became more coarse. This can be explained by the gradual dissolution of some invisible finely dispersed (Fe, Cr, Mn)3C particles at 1160 ◦C. The austenite grain boundary mobility increased, quickly resulting in the coarsening of austenite grains. The increased amount of visible (Fe, Cr, Mn)3C particles was attributed to the ripening of more micro/nano (Fe, Cr, Mn)3C particles at high temperatures. Compared with the sample quenched at 860 ◦C, the austenite grains quenched at 1160 ◦C clearly coarsened. Figure 5 shows the (Fe, Cr, Mn)3C particles in the specimen quenched at 1160 ◦C by TEM and the related energy spectrum. (Fe, Cr, Mn)3C particles was a compound of cementite (Fe3C) with other alloy elements. A few microalloy elements such as Ti, V, and Mo were captured due to their increased solvation at higher temperatures. In addition, apparent quenching dislocations were observed in the lath martensite.

**Figure 4.** Morphology variations from room temperature to 1160 ◦C. (**a**) 23.2 ◦C, before heating; (**b**) 550.4 ◦C, initial grain boundaries appeared; (**c**) 704.7 ◦C, austenization began; (**d**) 828.4 ◦C, obvious austenite grains; (**e**) 1160.7 ◦C, the preset quenching temperature.

**Figure 5.** (**a**,**b**) TEM images and (**c**) energy spectrum showing (Fe, Cr, Mn)3C particles at 1160 ◦C.

#### *3.2. Austenite Growing*

Figure 6 shows the morphologic changes from 1~10 min with a time interval of 1 min when the quenching temperature was 860 ◦C. Compared with the morphology after just reaching the preset temperature, the grain boundaries of austenite grains were clearer after 1 min (Figure 6a). This is because the grain boundary grooves are more easily exposed after longer thermal etching. In addition, the austenite grain boundaries were narrow and straight with a grain boundary angle of 120◦. Some local small grains gradually merged into large ones, as shown in the rectangle in Figure 6f,j. In addition, the austenite grain boundaries expanded and migrated to form large grains, as shown by the pink arrows in Figure 6d,j. The gradual merging of small grains and the migration of some grain boundaries indicated a unconspicuous growth process and trend.

During the thermal holding process, a fog-like substance shown by the oval in Figure 6c appeared. The fog-like substance gradually turned black, and then subsequently disappeared. This dark mist is the vapor of alloying elements, which tends to steam outward from the steel matrix when reheated. A similar phenomenon was also reported in the research of Lan et al. [33]. Manganese (Mn) volatilization was determined by a simultaneous thermal analysis, and they clarified that Mn tended to migrate to the substrate surface and volatilize when the temperature was high enough. In addition to the clearly visible precipitates at the beginning of reheating, many fine (Fe, Cr, Mn)3C particles also appeared in the austenite grains during thermal holding, as shown in Figure 6d. These fine (Fe, Cr, Mn)3C particles gradually appeared as some of the unprecipitated (Fe, Cr, Mn)3C particles matured and emerged. The (Fe, Cr, Mn)3C particles matured during thermal holding, as shown in Figure 6j.

The morphologic variation in a time interval of 10 min from 20~60 min at the quenching temperature of 860 ◦C is exhibited in Figure 7. The coarsening of (Fe, Cr, Mn)3C particles was more obvious, and there were more areas where small grains merged into large grains. In addition, twins could be observed in austenite grains (Figure 7a). The existing fog-like steam gradually volatilized and disappeared during thermal holding, while it appeared in other areas. This may be explained by the uneven distribution of some alloying elements such as Mn. In addition, austenite grain coarsening was obvious during thermal holding, in which the proportion of small grains decreased gradually. Moreover, and the intramural twins were more clearly visible (Figure 7e). The intracrystalline twins can be considered as annealing twins [34]. There were more alloying elements in the experimental steel, which significantly reduced the stacking fault energy. Compared with ordinary carbon steel, intracrystalline twins are more likely to occur in alloyed steels. The appearance of twins segregated and refined the grains, thus increasing the resistance of dislocation movement and strengthening the steel.

**Figure 6.** Morphologies during thermal holding at 860 ◦C from 1~10 min. (**a**) 1 min; (**b**) 2 min; (**c**) 3 min; (**d**) 4 min; (**e**) 5 min; (**f**) 6 min; (**g**) 7 min; (**h**) 8 min; (**i**) 9 min; (**j**) 10 min.

**Figure 7.** Morphologies during thermal holding at 860 ◦C from 20~60 min. (**a**) 20 min; (**b**) 30 min; (**c**) 40 min; (**d**) 50 min; (**e**) 60 min.

Figure 8 presents the morphologic evolution from 1~10 min at the quenching temperature of 1160 ◦C. The austenite grains were much clearer after holding at 1160 ◦C for 1 min (Figure 8a) as a result of continuous thermal etching. The migration of grain boundaries was obvious during holding, as shown in Figure 8a,b (blue arrow 1) and Figure 8b,c (blue arrow 2). Part of the original grain boundaries gradually faded away during grain boundary migration, and the old ones were gradually filled in. In addition, except for the outward expansion of grain boundaries, small grains were partitioned by surrounding large grains, as shown in the oval in Figure 8d. Alloy element steam, as shown in Figure 7c, also appeared in the specimen reheated to 1160 ◦C. In addition, many annealing twins traversing or occupying the whole grain were captured in the austenite grains. (Fe, Cr, Mn)3C particles ripened during the holding process, as shown in Figure 8j. The gradual appearance of fine (Fe, Cr, Mn)3C particles was attributed to (Fe, Cr, Mn)3C ripening at 1160 ◦C, which was captured by limited magnification. Compared with the grain morphology at 860 ◦C for 20~60 min, the grain size was obviously coarsened at 1160 ◦C, and there were many dense fine (Fe, Cr, Mn)3C particles inside the grains.

The coarsening of austenite grains at 1160 ◦C is related to the redissolution of (Fe, Cr, Mn)3C particles. Firstly, the atomic size of Cr/Mn/Ti is very different to Fe, which causes a certain solute atomic dragging effect. Reconcentration of a large number of solute atoms such as Cr, Mn, vanadium (V), and titanium (Ti) at the grain boundaries or subgrain boundaries could prevent the migration of grain boundaries and thus inhibit recrystallization. In addition, (Fe, Cr, Mn)3C particles were preferentially precipitated at the grain boundaries and dislocation lines, pinning the austenite grain boundaries and hindering the growth of austenite grains. Grain boundary migration caused austenite grain growth. The surface energy increased when the grain boundaries contacted the (Fe, Cr, Mn)3C particles. Only when the thermal activation energy was greater than the increased surface energy were the (Fe, Cr, Mn)3C particles cut or bypassed by the grain boundary. Therefore, the (Fe, Cr, Mn)3C particles significantly slowed down the formation of austenite and prevented the growth of grains. Similar observations were made in the work of G. Khalaj et al., where they established a model to predict the austenite grain size in Nb/Ti microalloyed steel [35]. Since the solute concentration around small particles was greater than those around large particles, the solute atoms spread from small particles to large particles, resulting in the redissolution of small particles and the growth of larger particles. Therefore, the fine precipitates gradually redissolved and continuously formed large size carbonitride particles when the holding time was long enough at 1160 ◦C.

**Figure 8.** Morphologies during thermal holding at 1160 ◦C from 1~10 min. (**a**) 1 min; (**b**) 2 min; (**c**) 3 min; (**d**) 4 min; (**e**) 5 min; (**f**) 6 min; (**g**) 7 min; (**h**) 8 min; (**i**) 9 min; (**j**) 10 min.

Figure 9 displays the morphologic changes with a time interval of 10 min from 20 to 60 min at 1160 ◦C. Dense, small (Fe, Cr, Mn)3C particles formed in the austenite grains. This signifies that the coarsening of (Fe, Cr, Mn)3C particles was more obvious compared to that during the holding time of 10 min. In addition, the grain boundaries of small-size austenite were gradually absorbed by the surrounding large-size austenite. In addition, apparent twins were observed in austenite grains (Figure 9a). Furthermore, austenite grain coarsening still occurred during holding from 20 to 60 min, in which the proportion of small grains further decreased. The intra twins were more clearly visible (Figure 9e) because of the larger austenite grains.

**Figure 9.** Morphologies during thermal holding at 1160 ◦C from 20~60 min. (**a**) 20 min; (**b**) 30 min; (**c**) 40 min; (**d**) 50 min; (**e**) 60 min.

## *3.3. Grain Size*

Figure 10 summarizes the grain size and growth rate of austenite at different quenching temperatures. Enough grains were present to ensure an improvement in the accuracy of the statistical process. Grains less than half the average size grain were not counted, and grains larger than half the average size grain were considered. There was little difference in the austenite grain size during the reheating stage before the preset quenching temperatures. However, the austenite grain size at 860 ◦C was always smaller than that at 1160 ◦C. Figure 10b shows the growth trend of austenite grains with time at 860 ◦C. The growth process was relatively slow, and the obvious coarsening of austenite grains was complete after holding for about 30 min. The growth process of austenite grains was very rapid and intense, and the coarsening of austenite grains was completed within 10 min at 1160 ◦C. Austenite grain growth rate curves at different quenching temperatures were obtained through the first derivative (Figure 10d–f). The austenite grain growth rate was significantly faster at 1160 ◦C. In addition, when the quenching temperature was 1160 ◦C, the maximum austenitic growth rate appeared at the holding time of ~3 min, whereas it occurred at ~30 min at 860 ◦C.

**Figure 10.** (**a**–**c**) Grain size and (**d**–**f**) growth rate of austenite from formation to thermal holding at different quenching temperatures.

It can be concluded that the austenite grains coarsened in a short time and the coarsening rate was higher at 1160 ◦C. This is because the austenite grain boundary migration ability was increased at a higher temperature. The atomic diffusion process was more rapid, and part of the grain boundary faded and disappeared more easily. In addition, many small dispersed (Fe, Cr, Mn)3C particles redissolved and ripped, which led to a significant decrease in the migration ability of austenite grain boundaries. Furthermore, the growth rate began to decrease gradually when austenite grains coarsened extensively. This was because the energy for grain growth can no longer be provided as the heating temperature was unchanged, and the redissolution and breaking of the (Fe, Cr, Mn)3C particles was basically resolved. Consequently, the pinning effect of (Fe, Cr, Mn)3C particles on austenite grain boundaries was stabilized, so the austenite coarsening gradually weakened.

#### *3.4. Martensite Transformation*

The above-mentioned austenite grain growth rules indicated that the austenite grain size greatly varied at different quenching temperatures. It has been pointed out that the austenite grain size affected the martensitic transformation temperature and the phase transformation behavior of supercooled austenite during cooling. Figure 11 shows the martensitic transformation during cooling in the sample quenched at 860 ◦C. Lath martensite appeared, as shown by the blue arrow in Figure 11a, when the temperature decreased to 369.2 ◦C. This martensite was primary martensite, also called fresh martensite (FM). The martensitic phase transition point (Ms) of the sample was about 369.2 ◦C, while the Ms temperature of this steel was determined to be 340 ◦C via a thermal simulation experiment. The effective Ms was obtained via a thermal simulation experiment through the overall volume expansion effect of the martensitic transformation, while in situ observation determined the Ms just according to the temperature at which the martensite appeared in one certain grain. Generally speaking, the Ms determined by in situ observations is higher than that reflected in thermal simulation experiments. This is because the martensitic transformation does not start at the same time in all grains, although the nucleation and growth of martensite explosively proceeded following this. In addition, martensite nucleated from the grain boundary and grew in between grains until stopping at the grain boundary. More and more lath

martensite explosively appeared as the temperature decreased, and most lath martensite traversed the entire grain. Furthermore, some lath martensite was found to nucleate and grow from the twins (Figure 11b). Since the formed martensite stimulated the nucleation of the surrounding untransformed austenite, the austenite nucleated and grew in parallel after this trigger. Therefore, the lath martensite grew in a parallel manner in some austenite grains. The lath martensite appeared simultaneously with an angle of 60◦ at 267.5 ◦C. In addition, some lath martensite simultaneously formed parallel to each other. More FM was observed as the temperature continued decreasing accompanied by secondary martensite (SM). SM refers to martensite with slightly thin laths formed around FM, which appeared at a certain angle with FM (Figure 11c). More and more surface reliefs due to martensitic transformations gradually appeared at the PAG boundaries (Figure 11d). Most martensite stopped growing when they encountered grain boundaries, and some martensite met each other, which also stopped the growth of lath martensite (Figure 11e). The nucleation and growth of martensite were very weak when the temperature approached room temperature. Most martensite transformations finished within 13 s, and the rate of martensitic transformations gradually slowed down. However, the distortion caused by martensitic transformations prevented martensitic transformations in the surrounding austenite. Small parts of the regions were retained as residual austenite, in which the sharing of elements such as carbon in ferrite to residual austenite was mainly completed (Figure 11f). The growth rate of lath martensite was relatively fast, but the growth rate of longitudinal lath martensite was faster than that of lateral lath martensite. Although the martensitic transformations explosively proceeded, the martensitic transformations were not simultaneous. Martensitic transformations selectively started in PAGs, but this selective process was very short. Nevertheless, the temperature of the sample may remain unchanged or even slightly increase during the cooling process since martensitic transformations release more latent heat of transformation. Therefore, isothermal martensite formation was inevitable. This latent heat caused by martensitic transformations was also one of the reasons for the selective initiation of martensitic transformations. The supercooling degree became smaller at a constant or slightly increased temperature; thus, martensitic transformations were inhibited. In addition, the selective initiation of martensitic transformations was also related to the distortion caused by martensitic transformations. Martensitic transformations in untransformed austenite were strongly inhibited by the surrounding martensitic transformations.

The martensitic transformation of the sample quenched at 1160 ◦C is displayed in Figure 12. The martensitic phase transition point, Ms, was about 310.0 ◦C (Figure 11a), which was lower than that in the sample quenched at 860 ◦C (369.2 ◦C). The Ms temperature should be higher in a larger austenite. However, the results of in situ observations of martensitic transformations were extraordinary. The possible reason for this is that the martensitic transformations observed by the in situ method were local to the sample surface, with a limited view field. An unobserved view field may have shown the martensitic transformations at a relatively higher temperature. In addition, it is difficult to unify the different starting temperatures of martensitic transformations due to the uneven composition caused by the evaporation of alloying elements. It was accidentally observed that lath martensite grew through grain boundaries in Figure 12c. These newly formed grain boundaries were relatively straight. In addition, some lath martensite nucleated and grew from the twins. The reason why the twins acted as martensitic nuclei was that martensitic transformations require structural and energy fluctuations. As a kind of crystal defect, twins provide a large defect energy which meets the structural and energy fluctuation requirements. Increasingly more FM and SM gradually appeared with the decrease in temperature, in which the SM appeared at a certain angle to FM. Most martensite transformations finished within 2.25 s, and the rate of martensite transformations slowed down. However, the distortion caused by martensite transformations inhibited the martensite transformations in surrounding austenite (Figure 12j). Martensite growth was a nondiffusion interfacial cooperative pushing process, and the martensite specific volume was larger than that of austenite. Therefore, elastic deformation was caused, accompanied by volume expansion, during the martensite

phase transition. Additionally, then a large distortion energy formed, which hindered further martensite transformations.

**Figure 11.** Martensite transformations of supercooled austenite quenched at 860 ◦C. (**a**) 369.2 ◦C, martensite appeared; (**b**) 274.6 ◦C, martensite increased; (**c**) 267.5 ◦C, martensite nucleated and grew at the twins; (**d**) 264.9 ◦C, SM and surface relief; (**e**) 260.5 ◦C, martensitic lath collisions; (**f**) 102.2 ◦C, martensitic transformation stopped and residual austenite formed.

Martensitic transformations in the same sample did not appear at first in large-sized grains but appeared in the PAGs in a seemingly chaotic manner. This may be explained by the differences in the size, composition, and defect density in PAGs, which led to the selectivity of martensite nuclei. In addition, the grains were coarser due to a higher quenching temperature; thus, the driving force of martensitic transformations was greater. Additionally, the migration rate of phase interfaces increased accordingly, so the martensitic transformations were faster.

Figure 13 shows the martensitic transformation of supercooled austenite at different quenching temperatures, which is a summary based on in situ observations. Martensite nuclei did not occur simultaneously during the quenching process of supercooled austenite, but selectively proceeded and increased in batches in some areas. This nucleation pattern divided untransformed austenite into multiple regions. In different regions, the size of firstly formed martensite (fresh martensite) was large and the size of subsequent martensite (secondary martensite) was small. This is because the shape of martensite depends on the stress field between the nucleated lath martensite and other martensitic nuclei. The parent austenite presented obvious different grain sizes at different quenching temperatures. In addition, the size and volume fraction of the coarse (Fe, Cr, Mn)3C particles in the matrix increased with the quenching temperature.

**Figure 12.** Martensite transformation of supercooled austenite quenched at 1160 ◦C. (**a**) 310.0 ◦C, martensite appeared; (**b**) 304.7 ◦C, martensite increased; (**c**) 303.5 ◦C, martensite traversed grain boundaries; (**d**) 302.1 ◦C, martensite increased and appeared at 60◦ angles; (**e**) 300.9 ◦C, martensitic packet; (**f**) 299.6 ◦C, SM increased; (**g**–**i**) 298.4 ◦C, explosive martensite; (**j**) retained austenite.

**Figure 13.** Schematic diagram of martensitic transformations of supercooled austenite at (**a**) 860 ◦C and (**b**) 1160 ◦C.

Martensitic nucleation and growth in different parent austenite grains did not affect each other in the early stage of martensitic transformations, during which less martensite formed. The martensitic transformations gradually increased as the temperature decreased, and the martensitic laths restricted each other. In general, there were three types of martensitic nucleation. Firstly, martensite nucleated along the PAG boundaries and grew in between the grains until stopping when it collided with other lath martensite or grain boundaries. In addition, martensite nucleated at annealing twins, which had lattice defects and provided better structural and energy fluctuations. Moreover, martensite nucleated at the preformed lath martensite and grew in the austenitic grains at about 60◦ or 120◦ to form new lath martensite. The lath packet exhibited two types: parallel laths (0~2◦) based on the preformed laths and martensitic laths at 60◦ or 120◦ in the other direction stimulated by the preformed laths, finally forming triangle, parallelogram, or hexagon morphologies. The formation of SM laths also strongly inhibited the martensitic transformations of the surrounding untransformed austenite and promoted the formation of residual austenite.

#### **4. Conclusions**

**Author Contributions:** Methodology, Z.L., Q.Y., Y.Z. and S.L.; Formal analysis, S.X. and S.L.; Investigation, Z.L., Q.Y., Y.Z. and G.X.; Resources, S.X.; Data curation, Y.Z.; Writing—original draft, Z.L.; Writing—review & editing, Q.Y., S.X. and G.X.; Visualization, G.X.; Supervision, Z.L.; Funding acquisition, Q.Y. and S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** National Natural Science Foundation of China (no. 52004193), China Postdoctoral Science Foundation (no. 2022M710596), and the Joint Foundation of Nature Science Foundation of Hubei Province (2022CFD078).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.

**Acknowledgments:** The authors gratefully acknowledge the financial support from National Natural Science Foundation of China (no. 52004193), China Postdoctoral Science Foundation (No. 2022M710596), and the Joint Foundation of Nature Science Foundation of Hubei Province (2022CFD078).

**Conflicts of Interest:** The authors declare no conflict of interest.