Effect of Solid Particles on the Slurry Bubble Columns Behavior – A Review

A wide-ranging review is presented on the most focal aspects of gas-liquid-solid reactors to discuss the fresh headways towards the understanding of slurry bubble column reactors’ behavior. In more detail, in this critical review, published works’ findings concerning the effects of solid particles characteristics (size, concentration and density) on volumetric mass transfer coefficient, liquid-side mass transfer coefficient, gas-liquid interfacial area, gas hold-up and flow regime are deliberated. Besides, the effects of other pivotal parameters such as pressure, temperature, reactor size, height of liquid, gas distributor, density, and viscosity on the performance of slurry bubble column reactors are considered. Eventually, regarding the effects of each of the aforementioned parameters on the performance of reactor, logical conclusions are drawn.


Introduction
According to European Green Deal and in line with Paris Agreement, the European Union's aim is to be climate-neutral (which indicates achieving net-zero greenhouse gas emissions) by 2050. Aiming at climate neutrality is an opportunity and also a challenge to build a better future for all. Therefore, all sectors of the societies (ranging from petrochemical industry and mobility to forestry and agriculture) play their own pivotal roles. In the energy industry, more importantly, concepts for production of electrical energy must be focused on renewable sources such as solar and wind energy. A highly efficient way for storage of energy obtained from renewable sources is the production of oxygen and hydrogen via water electrolysis and then conversion of them to more valuable products such as methanol, as its suitable transport properties and high gravimetric energy density (20.2 MJ kg -1 ) make it a valuable fuel.
Todays, methanol is produced from synthesis gas (CO/H 2 ) in fixed bed reactors at elevated temperatures (200-270°C) and pressures (50-100 bar). Another sustainable route for the production of methanol is CO 2 hydrogenation. Because of a variety of advantages of slurry bubble column reactors (SBCRs) over fixed bed ones, such as higher heat transfer, yield, and the possibility of usage of nanosized catalysts, it would be beneficial to perform the exothermal synthesis of methanol using the SBCR. In general, these reactors have widespread applications in chemical, petrochemical and biochemical industries that present a variety of hydrodynamics, depending on the flow direction of phases and also type of discrete phases. In spite of their extensive applications, our knowledge about them is still not sufficient in some aspects because of diverse effective parameters that can affect the performance of a three-phase reactor. Additionally, individual studies in this field put the focus on a particular aspect of such reactors. Thus, this causes the scarcity of comprehensive works in this field that hampers our understanding of SBCRs.
Herein, the emphasis is put on slurry bubble column reactors (SBCR) in which solid particles are dispersed in the liquid phase by the liquid eddies induced by bubble movements. The absence of any moving parts like agitators and low maintenance cost have made the SBCRs one of the simplest multiphase reactors and suitable for various industrial processes like wastewater treatment, Fischer-Tropsch synthesis, and heavy oils' hydroconversion [1][2][3][4]. Besides axial dispersion coefficient and hydrodynamics, mass transfer coefficient and gas hold-up are important parameters for scale up and design of these reactors [5]. Such parameters are more critical when a mass transfer limited chemical reaction is considered to take place in the reactor. This review describes mass transfer, gas hold-up and flow regime of slurry bubble column reactors. -----

Reactor Types Distinction
Different researchers have proposed various criteria for distinguishing different types of three-phase reactors. For instance, based on the solid size and concentration, Yasunishi et al. [6] proposed to distinguish fluidized-bed reactors from slurry reactors. They stated that in slurry reactors, particle size is almost lower than 100 μm and its volumetric fraction is also lower than 0.1. In such a situation, bubble agitation causes solids to maintain a suspended state in the liquid phase. In the fluidized-bed reactors, on the other hand, particle size is mainly larger than 200 μm and solid concentration is between 0.2 and 0.6. In such a situation, gas and/or liquid phase supports solid particles to be dispersed. Despite some discrepancies among different classifications, it seems that there is a general agreement that heavier or/and larger solid particles are mainly used in fluidized beds compared to the slurry reactors. When very heavy and/or large particles are used in a column, the column is divided into two regions; dilute region in the upper part of the column and lower dense region in the bottom of it. These reactors are called fluidized-bed reactors. By decreasing the solid size and density, solid phase starts to disperse in the liquid phase and its concentration decreases exponentially alongside the column vertical axis. These types of reactors are called three-phase bubble columns. When small particles or/and low-density particles are used, the particles are dispersed uniformly in the column. These reactors are called slurry reactors (Fig. 1).
To establish criteria for the classification of these reactors, it has been confirmed that there are a variety of factors (such as gas and liquid velocity, viscosity, surface tensions, disperser unit, reactor size, and so forth) that can affect the axial dispersion of solid in a column among which solid size and difference between solid and liquid densities are the most important ones. To be more specific, although the operating condition in available experimental works are different, interestingly, if d p (r s -r l ) is plotted against d p for various studies on each types of reactor, the plotted data will be divided visibly in three different regions that each represents a specific type of reactor [7,8]. Therefore, the below rational criteria were proposed by Tsutsumi et al. [7,8] for the classification of three-phase reactors.
Slurry bubble column reactors: d p r s À r l ð Þ 0:22 ::: 0:3 Three-phase bubble column: 0:22 ::: 0:3 d p r s À r l ð Þ 1:0 Fluidized-beds: According to the aforementioned discussion, the behavior of three-phase reactors is mainly dependant on their types which are dictated by the solid axial distribution. Hence, understanding solid profile dispersion is crucial. In this regard, a myriad of researchers made noticeable efforts towards understanding of solid distribution based on the sedimentation-dispersion model which was proposed by Cova et al. [9] and Suganuma et al. [10]. Although this model is capable of describing solids' behavior, there are some discrepancies in the interpretation of the physical meaning of few parameters in this mode [11].
A mechanistic approach for solid distribution analysis can provide us with a fundamental understanding of three-phase reactors' hydrodynamics. Obviously, the solid dispersion is mainly dependant on the turbulence induced by bubbles' motion and their wakes entertainment [7,8,12]. In this regard, the wake shedding model tries to evaluate solid dispersion by focusing on wakes in the reactors. When a bubble is introduced into a reactor and starts to ascend, the wakes are developed immediately and moves with bubble with the same velocity. After a short distance, the wakes are shed in the slurry phase and deform. In this model, the reactor has three phases; gas, wake and slurry phase. For simplification, the following assumptions are considered in this model: -Wakes and bubbles ascend at the same speed -The hold-up of each phase is constant at any cross-sections of the reactor -No solid exchange between slurry and wake and phases except at the formation and shedding of wakes. -The wakes are shed from the bubble after a constant vertical distance (wake shedding length, l). Based on this model, the solid concentration along the reactor can be written as [7,8]: By equating the upward and downward mass flux of solid particles and some mathematical operations, the solid concentration along the reactor is obtained: Á e wake =e slurry À Á x ¼ C S; wake phase C S; slurry phase (8) In which C s0 is the slurry phase concentration at the bottom of the column. Different theoretical and empirical correlations have been proposed by researchers for calculation of each of the abovementioned parameters [13]. A comprehensive description of this model can be found in the work of Tsutsumi et al. [8] and Knesebeck et al. [14].
Bubble wakes, with creating the turbulence in the column, move liquid and solid inside the column and determine the reactor hydrodynamics. In fact, the liquid is carried by wakes at a higher velocity compared to the average liquid velocity and depending on the characteristics of particles, the solid particles can also be carried at equal, lower or higher velocity. Accordingly, the solid characteristics determine the type of reactor and its hydrodynamics. On the one hand, small particles with density near to that of liquid follow the bubble wake like tracers. In such a situation that normally occur in slurry bubble columns, particle concentration in the wake phase and slurry phase are almost the same (x = 1). On the other hand, when the particle size and differences between liquid and solid densities increase, due to the inertia, particles almost cannot follow the bubble wake and as a result, particle concentration in the wake phase decreases, compared to the previous case. Such situations are mainly observed in three-phase bubble columns. Furthermore, when the particle size and density increase further, the wake cannot carry the heavy particles and, thence, the concentration of particles in the wake phase approaches zero (x 0). By fitting the model to various experimental data, the values of x have been plotted by Tsutsumi et al. [7,8] against d p (r s -r l ) in Fig. 2. Based on Tsutsumi et al., the value of x for a system containing light and/or small particles cannot be greater than unity which means the solid concentration in the wake phase cannot exceed the solid concentration in the slurry phase. According to the available correlations [8,14], the value of b approach zero when x = 1. This means uniform distribution of solid particles in slurry bubble columns. Additionally, decreasing the x value as well as increasing the particle settling velocity cause the value of b to increase which leads to a substantial drop in particle concentration from bottom to the top of the column. Tsutsumi et al. [7,8] correlated the experimental data and proposed a correlations for x value: Slurry bubble column reactors: x ¼ 1 For three phase bubble columns, the following applys: and for fluidized beds: According to the discussed model, the solid distribution in different types of reactors is depicted in Fig. 1. As this review concerns experimental works in slurry columns, explaining other available models for investigation of three-phase reactors is out of the scope of this review. Nonetheless, a comprehensive study of models for investigation of three-phase reactors can be found in the work of Pan et al. [12] and Mühlbauer et al. [3] while the second one focuses on the advantages in computational fluid dynamics (CFD). Although considerable efforts have been made to quantify the solid dispersion in various three-phase reactors, further research is still required to determine the axial solid particle concentration for the design of the columns operated at different conditions.According to aforementioned description, the study of the performance of a slurry bubble column reactor needs adequate data on; -Liquid side and gas side mass transfer coefficient, interfacial area and enhancement factor. -Reaction kinetics and solid particles properties.        Monitoring of dissolved oxygen concentration Glass bead particle  are quantifying via equations in which gas hold-up plays a vital role. Furthermore, the gas hold-up also depends on the superficial velocity of gas that this dependency is different in various flow regimes in SBCRs. That is why a proper estimation of transition points is vital [65]. Todays, it is generally accepted that SBCRs can operate under three different flow regimes; heterogeneous (bubbly flow), transition and the heterogenous (slug flow and churn-turbulent flow) regimes that the first transition point sets apart the homogeneous and transition flow regimes and the second transition point, on the other hand, sets apart the transition and churn-turbulent regimes (Fig. 3). In depth description of each of them can be found in the literature [66][67][68][69][70][71][72]. It should be added that some flow regimes don't exist in some particular conditions. For instance, Orvalho et al. [27] reported that at low particle concentrations, all of the three regimes (homogeneous, transient and heterogeneous) exist for all of the initial height of the unsparged layer while at high particle concentration, only pure heterogeneous regime is observed. In the same vein, Rabha et al. [37], using an ultrafast electron beam X-ray tomography, understood that for low particle size (d p 100 μm) and low particle concentration (C s 0.03), the bubble size and flow regime are almost independent of the presence of particles while for larger solids and higher concentrations, the flow regime and bubble size are strongly dependent on the presence of particles. Additionally, Abdulrahman [30] reported that the slug flow does not exist in industrial SBCRs and there are just two flow regimes; bubbly and churn-turbulent flow regimes.
Using pressure fluctuation analysis, various methods have been employed for the determination of flow regimes in a slurry bubble column reactors such as fractal and chaos analysis [69], auto-correlation function [70], and statistical analysis [71]. Other methods are also available for determination of flow regime in SBCRs that are based on the gas hold-up measurement [72][73][74]. The methods that are based on the gas holdup measurement are not accurate enough because the difference between the slope of ''e g vs. U g '' curve is really small at the transition points. In fact, this curve slope changes slowly that make the identification of transition points obscure.
The flow regime map of water and dilute aqueous solutions is shown in Fig. 4. Different parameters such as sparger type, reactor size and liquid viscosity can strongly affect the transition border in Fig. 4. For instance, small column size stabilizes the gas plugs at higher gas superficial velocities which results in operating in the slug flow at higher gas velocities while larger columns trigger bubble column to operate under the churn turbulent flow regime. In this regard, according to Shah et al. [75], slug flow can occur at a really low gas superficial velocity in a highly viscous liquid. Also, a porous sparger with a pore size of lower than 150 μm can generate bubbly flows at U g = 0.05-0.08m s -1 while for a perforated plate with a hole diameter larger than 1 mm, bubbly flow is just possible at low gas superficial velocities. Accordingly, the boundaries between the flow regimes of Figure 4 are approximate [75]. Based on Fig. 4, obvi-ously, the flow regime depends heavily on the gas superficial velocity. In low gas velocities, the system flow regime is bubbly in which no bubble coalescences occur. In spite of extensive applications of SBCRs in different industries, many of the available regime maps lack the effects of solid particles. According to the available literature, particles with different properties can have different effects on the flow regime. In this part, some of the reliable studies on the effects of solids on the flow regime are discussed.
Regarding the detection of transition points, Chilekar et al.   deviation of pressure time series with gas superficial velocity. They concluded that the first transition point, the first largesize bubble (1.5 cm) is detected with a low occurrence frequency. In this situation, the pressure signal amplitude is small (136 Pa). In the transition regime, the large bubbles' occurrence frequency and their diameter increases with increasing the gas velocity noticeably. In this situation, pressure signal amplitude increases (413 Pa). At the second transition point, the size of large bubbles becomes constant (50 mm) and their occurrence frequency also reach an equilibrium. The pressure signal amplitude still increases till 565 Pa. Finally, in the churn flow regime, the pressure fluctuation amplitude increases to high values (980 Pa). Similarly, Li et al. [35] studied the flow regime in rectangular SBCRs in the presence of four different particles. They observed four flow regimes; discrete bubble flow regime, transition flow regime, bubble coalescence flow regime and strong turbulent flow regime. In the bubble coalescence regime, they observed that the bubbles have regular movements. Based on their observations, in this regime, small bubbles detached from the distributor rise in the central part of column and coalesce to form larger bubbles which move fast and deform irregularly. Therefore, in this regime, the number of small and large bubbles decreases and increases, respectively; that results in increment of bubble size distribution.
Regarding the effects of particles on the flow regime, it seems that there is a general consensus among the researchers on the decrement of gas superficial velocity of the transitions points with increasing the particle loading. In this regard, Li et al. [35] also reported that increasing the particle concentration and density result in decreasing the value of gas superficial velocity of the transitions points all. Decreasing the value of superficial gas velocity with increasing the solid concentration was also reported by a plethora of investigators like Mühlbauer et al. [20], Hooshyar et al. [44], Abdulrahman [30], Li et al. [38], and Mota et al. [42]. In this regard, Li et al. [38], using the differential pressure fluctuation analysis by Hilbert-Huang transform, reported the gas velocity at the first transition point (homogenous to transition) in the range of 0.058-0.069 m s -1 and the gas velocity at the second transition point is in the range of 0.156-0.178 m s -1 . Asil et al. [22] also reported that the flow regime changes from homogeneous to heterogeneous at the gas superficial velocity in the range of 0.0.43-0.08 m s -1 . The transition velocity from homogenous to heterogeneous flow regime was also reported as 0.03 m s -1 by Abdulkareem et al. [33]. Additionally, Rouhi et al. [39], for liquid height of H = 12D and solid concentration of 13 %, reported the transition velocity as 0.0298 and 0.0314 m s -1 using their own mathematical method and drift flux method, respectively. Regarding the effects of particle size, Li et al. [35] also reported that the particle size in the range of 48 to 150 μm cannot affect the flow map while increasing the particle size from 150 to 270 μm decreases the range of bubble coalescence regime and transition regime range. Rabha et al. [37] also reported that low particle size (d p 100 μm) and low particle concentration (C s 0.03 wt %) cannot affect the flow regime and bubble size while higher particle size and concentration strongly affect the flow regime and bubble size.
Other parameters also can affect the flow regime as well. Orvalho et al. [27] reported that increasing the initial height of the unsparged layer and solid concentration results in the destabilization of the homogenous flow regime. The same result (stabilizing and destabilizing effects of low and high concentrations of particles, respectively) was also gained in the Rouhi et al. [39] experiments. Abdulrahman [30] also reported that the transition velocity occurs at lower gas velocities with increasing the height of liquid. Rouhi et al. [39] pointed out that if the ratio of H/D in is higher than 5, increasing the liquid level does not affect the transition point significantly. In the same sense, Gheni et al. [31] reported that at low values of H/D in , such as 3, the small bubbles move straightly at the speed of 0.24 m s -1 . In such a situation, bubbles are spherical in the bottom of the reactor which creates homogenous flow regime and they are in a dynamic equilibrium at the top and middle of the reactor. For higher values of H/D in , like 4 or 5, vortices of bubbles appear and they bring almost more structure in the mixture field of velocity, although they do not behave regularly.
Regarding the behavior of liquid field of velocity, Li et al. [29] showed that the liquid velocity, which increases with increasing the gas superficial velocity, is influenced by the particle concentration slightly and is higher in the core of larger reactors compared to the smaller ones. Also, Lim et al. [43] claimed that the rising velocity of wakes and their equivalent sizes increases with increasing the liquid viscosity (1.0-50.0 mPa s), gas velocity (0.04-0.12 m s -1 ) as well as particle concentration (0-25 wt %). Lim et al. [43] also reported that the wakes' holdup and frequency increase with increasing the velocity of gas while they decrease with increasing the particle concentration and liquid viscosity. Similarly, Abdulah [25] reported that in cylindrical slurry bubble column (CSBC) and trapped slurry bubble column (TSBC), particles are distributed along the column longitude more uniformly for a higher value of gas velocity and particle concentration. It was also understood that the TSBC offers more uniform particles' axial profile compared to the CSBC that makes it suitable for environmental and bioreaction applications.

Gas Hold-up, Coalescence, and Breakup
Gas hold-up, which determines the transport phenomena of reactors, is a vital dimensionless parameter that is used for the design and scale-up of SBCRs. In fact, this parameter shows the fraction of reactor which is occupied by bubbles. In the same vein, the solid and liquid hold-ups also can be defined as an indication of the fraction of reactor that is occupied by solid phase and liquid phase, respectively. Owing to the importance of this parameter, a myriad of researchers has investigated it using pressure analysis and other available methods. Based on Li et al. [76], the static pressure drop along a bed height is written as: Here, ΔP, e, r, g, and ΔH are static pressure drop along the height of a reactor, hold up, density, gravitational acceleration and height difference between the transducers, respectively. Starting from Eq. (12) and by proper substitutions, the gas hold-up is written as: In which f L and f S are volume fraction of liquid phase and solid phase. Using this equation and measurement of static pressure between two points along the reactor's height, gas hold-up can be calculated. Calculation of the gas hold-up by measuring the pressure drop using a manometer or a transducer along the column is widely used by different researchers although other methods are also available for this aim. For instance, Sines et al. [26] studied the hold up of water, glass beads, and air in a SBCR using a novel technique called electrical capacitance volume tomography (ECVT) which has various advantages over the pressure gauge method; such as its ability to deliver non-invasive real-time direct measurements without making any assumptions about the column hydrodynamics. They concluded that their method is an acceptable method to be replaced with pressure gauge method for the study of threephase reactors hydrodynamics.
Rather than the overall hold-ups, the profile of gas hold-up is also important because of impacting the pressure variation and liquid recirculation which plays a vital role in mixing and mass and heat transfer [77]. The radial profile of gas hold-up depends on various parameters like liquid properties, superficial gas velocity, column size, operating pressure and temperature, sparger design and solid properties. In the following, the results of some important studies about the gas hold-up of SBCRs will be discussed.
Sehabiague et al. [36] studied the effects of pressure, temperature, gas velocity and solid density on the gas hold-up and bubble characteristics in a slurry bubble column. Mainly in systems containing a high concentration of helium, they reported that with increasing the solid concentration, the gas hold-up and mass transfer coefficient decreases and d 32 increases. They also reported that increasing the operating pressure inside the reactor and increasing gas density lead to gas hold-up increment and d 32 decrement. The same result was also reported by Shin et al. [46]. Sehabiague [36] also reported that increasing the temperature has effects similar to increasing the pressure excluding a system consist of N 2 -light F-T cut in which gas hold-up remains constant from 400 to 500 K. Additionally, Sehabiague et al. [36] concluded that increment of gas superficial velocity increases the gas hold-up and mass transfer coefficient while it can increase or decrease the bubble size. They understood that increasing the helium fraction in a system containing nitrogen and helium at a constant density has negligible effects on gas hold-up, mass transfer and d 32 . The gas hold-up and small bubbles' population for nitrogen bubbles in paraffin are greater than those of a system containing nitrogen and light F-T cut. For calculation of gas hold-up, they finally suggested: exp À1:2C s þ 0:4C 2 s À 4339d p þ 0:434X À Á (14) in which X equals to zero for a nonfoaming single-component liquid mixture and is also equal to unity for a foaming liquid mixture.
The presence of impurities, as it was mentioned, can alter the liquid phase properties and in turn, the gas hold-up. In this regard, Salvacion et al. [53] studied the effects of adding alcohol, particles and column diameter on the volumetric mass transfer coefficient and hydrodynamics in a gel suspended bubble column reactor. They concluded that the gas hold-up increases with adding alcohol to water. They correlated the results as: Bo À0:394 Mo À0:139 (18) In which the subscription zero refers to a system without solid particles.
Among the effects of different parameters, understanding the effects of solid concentration and size are of paramount importance. Based on the range of solid size and concentration, their influence on gas hold-up can be different. In order to evaluate the effects of solid particles on the interfacial area of gas and liquid phases, Pandit and Joshi [78] suggested four different regions that the first two regions are of interest to slurry bubble column reactors and the second two regions are of interest to fluidized bed reactors. The first region (A) is d p 100 μm and solid hold-up 0.6 vol %. They reported that in this region, solid particles tend to cover the bubble surface and prevent bubble coalescence that in turn results in smaller bubbles and increased specific area. Since the smaller bubbles have lower terminal velocity, in such a situation, solid particles cause the system to have a higher gas hold-up. Although some researchers reported an increment in specific contact area (and gas-holdup) [79], others even report its negative effects on the specific contact area (and gas-holdup) in this region [80]. Nonetheless, this region is of great importance for industries because many of the industrial slurry bubble column reactors generally operate with small particle sizes (below 100 μm) and low catalyst hold-up (below 0.6 %). The second region (B) is 100 μm d p 1000 μm at any solid loading and also d p 100 μm at C s 0.6 vol %. According to Pandit and Joshi [78], In this region, particles mainly contribute to the slurry viscosity, thus, the interfacial area increases by adding the solid particles. Despite this classification, some discrepancies emerged in the effects of solid particles on a and several classifications were also proposed among which the classification of Banisi et al. [81] is more reputable. Banisi et al. [81] suggest that the small concentration of small particles (d p 10μm and C s 0.6 vol %) as well as high concentrations of large particles (d p 2000 μm and C s 10 vol %) increases gas-liquid contact area and in turn, gas hold-up. Otherwise, the decreasing effects of solids on contact area are expected (e.g., high concentration of small particles, medium-sized particles at moderate concentration, low concentration of big particles). Fig. 5 depicts the classification of Banisi et al. [81]. At the low loading of small particles, the particles stick to the bubble surface and may hinder the bubble coalescence. Compared to a two-phase gas/water system, this results in smaller bubbles throughout the column. The smaller bubbles move slowly compared to the larger bubbles and that leads to higher gas hold-up. High loading of large particles, in the similar vein, cause bubble breakage and contribute to the slurry viscosity that finally leads to having smaller bubbles moving at lower velocity throughout the column that cause the column to operate with higher has hold-up. In the following, further results will be discussed in regard to the application of the classification.
Lakhdissi et al [23] studied the effects of particle concentration and size on the gas hold-up in an air-water-glass beads systems. Their experiments showed that at a constant solid concentration, increasing the solid size had no influence on the total gas hold-up at low solid concentrations (up to 3 % (v/v)) while increasing the solid size leads to decreasing gas hold-up at the higher solid particle's concentrations (5 % (v/v)). Additionally, at a constant particle size, increasing the particle concentration decreases the gas hold-up and this decreasing effect is more noticeable for larger solid sizes. They finally correlated their results as: in which E C is the collision efficiency which is affected by different factors like bubble surface mobility, flow regime and inertial forces.
In the same vein, Li et al. [50], Vandu et al. [49], Moshtari et al. [47], Hooshyar et al. [44], Ojima et al. [34], Sada et al. [61], Tyagi et al. [28], Li et al. [29], Asil et al. [22], Koide et al. [62], Sehabiague [36], and Orvalho et al. [27] concluded that increasing the solid concentration decreases the gas hold-up because of increasing the bubble coalescence and reduction of the number of small bubbles. Other researchers also reported almost the same effects with a slight difference. Götz et al. [32], for instance, concluded that the presence of solids increases the initial bubble size at the gas distributor and reported that low concentration of small solids reduces bubble coalescence, otherwise, the presence of particle increases the bubble coalescence. Likewise, Rabha et al. [37] reported that at low solid size and concentration (d p 100μm and C s 0.03 vol %), increasing the solid concentration does not affect the gas hold-up while at higher values of solid concentration and size, increasing the solid size and concentration decrease the gas hold-up. Additionally, Mühlbauer et al. [20] reported that in small bubble columns in which the wall effects are dominant, the gas holdup is almost independent of solid concentration while in a large column, increasing the solid concentration decreases gas holdup. Furthermore, Pino et al. [54] studied a reactor which was filled with foaming liquid and showed that increment of solid concentration decreases the gas hold-up in the foaming regime. And also, at a low gas superficial velocity that the liquid does not foam, solid particles with small size do not affect the gas hold-up while the presence of larger particles causes liquid to foam and increases the gas hold-up.
It should be noted that the contrary influence of increment of solid loading on the gas hold-up was also reported by a few researchers. For instance, Sun et al. [45] pointed out that increasing the particle concentration decreases bubble velocity and in turn, increases gas hold-up. Rabha et al. [40] concluded that with addition of particles, the local gas hold-up decreases owing to enhancing the bubble coalescence. On the other hand, for higher particle concentration, they concluded that increasing the solid content cause bubbles to break up and increase the gas hold-up. Ojima et al. [34] showed that the presence of hydrophilic solids causes bubble coalescence and this enhancement is saturated at a solid concentration of 0.45 vol %.
Regarding the effects of solid size on the gas hold-up, Rabha et al. [37], for instance, reported that at low values of solid size and concentration, the particle size cannot affect gas hold-up while at higher values of solid concentration and size, increasing the solid size decreases the gas hold-up. The same results were also reported by Lakhdissi et al. [23]. On the other hand, the experiments of Li et al. [50] revealed that increasing the solid size cannot affect the gas hold-up even for high concentrations of solid (up to 40 vol %). The same results were reported by Sines et al. [26]. Sada et al. [61] also reported that by increasing the particle size, the gas hold-up decreases and the dependency of gas hold-up on the solid size decreases for high solid concentrations. Furthermore, Pino et al. [54], for a reactor with foaming liquid, reported that at low gas superficial velocity, increasing the solid size increases the gas hold-up.  Accordingly, for evaluation of the effects of solid particles on the gas-holdup, it seems that the Banisi et al. [81] classification is acceptable in most of the cases. Various parameters, such as reactor size, operating condition and type of liquid and gas, can alter the boundaries of Banisi et al. [81] classification. Therefore, more in-depth researches are needed to develop this classification so as to be correct for all of the mentioned results.
In regard to the effects of reactor size on the gas hold-up, it has been confirmed by myriads of researchers that the reactor size does not affect gas hold-up on the proviso that the reactor is large enough [29]. Pino et al. [54], for instance, reported that the height of a column cannot affect gas hold-up noticeable when the ratio of column height to column diameter is between 6 and 12. Asil et al. [22] concluded that, in a reactor that the ratio of its height to its diameter is almost 20, increasing the static height of water increases the pressure drop and decreases the gas hold-up. Ojima et al. [34] also pointed out that if the hydraulic diameter of a column is higher than 150 mm, the effects of hydraulic diameter on the gas hold-up is meager. In the same vein, Rouhi et al. [39] reported that the liquid level has a very meager effect on gas hold-up at the low gas superficial velocities and after the transition point, the maximum gas hold-up is reduced with increasing the liquid level. In the experiments of Gheni et al. [31], the same results were also obtained. They reported that the influences of solid loading and column size on gas hold-up are meager compared to the effects of gas superficial velocity and the gas hold-up increases linearly with the gas superficial velocity up to 0.8 m s -1 and then levels off with more increment of velocity.
Concerning the effects of gas superficial velocity, it has been reported by Tyagi et al. [28], Moshtari et al. [47], Mühlbauer et al. [20], Li et al. [49], Sines et al. [26], Sun et al. [45], and Sehabiague [36] that gas hold-up increases with increasing the gas superficial velocity in SBCRs. Other Parameters like the sparger type can also affect the gas hold-up because the sparger type can affect the initial bubble size distribution. Götz et al. [32] reported that the gas spargers with low gas velocity per each hole produce smaller bubbles which results in a higher gas hold-up. As it was reported by Moshtari et al. [47] and endorsed by other pieces of literatures [82], a porous plate creates higher values of gas hold-up compared to a perforated plate. Asil et al. [22] also showed that the deployment of a perforated plate instead of a porous one increases the bubble size by almost 9 % which results in an almost 21 % decrement of gas hold-up. Abdulkareem et al. [33] also showed the better performance of a ring gas distributor compared to a plate gas distributor in the homogenous regime and various ratio of column height to its diameter.
It was reported by some researchers [36] that increasing the gas density increases the gas hold-up while some others [32,36] reposted that gas density has a meager effect on the gas hold-up. Götz et al. [32] also revealed that with increasing the density difference between liquid and solid, gas hold-up is reduced. Regarding the effects of liquid properties on the gas hold-up, Götz et al. [32] also indicated that the effects of liquid properties depend on the flow regime. In the homogenous flow regime, increasing the liquid viscosity has almost no effects on the gas hold-up while increasing the liquid viscosity and surface tension destabilize the homogenous flow regime. Almost the same results were also reported by Rabha et al. [40] that lower viscosity can stabilize a uniform bubble flow while a higher viscosity can destabilize the bubbly flow. Besides, Shin et al. [46] stated that the bubble size and frequency increase with increasing the liquid viscosity and these trends are more pronounced for higher column sizes. In Fig. 6, the results of Vandu et al. [49], Li et al. [50], and Parul et al. [28] is shown which are in accordance with the studied literatures in this section.
Götz et al. [83] collected 1992 reliable data from different literature for gas hold-up and correlated them using the least square method as below. Their correlation, in which the effects of phases' properties, reactor diameter, gas velocity and sparger design have been considered, is suitable for homogeneous and pseudo-homogeneous flow regimes. 1 þ K S1 r p Àr l r l 0:755 in which K 2 and K 4 (which can be read from Tab. 2) are constants for each type of sparger. K Surf is for surfactants which can be either 0 or 1 and also, K S1 is a constant for the solid's influence that can be read from the Tab. 3. Ar, Eo, Fr stands for Archimedes number, Eötvös number, Froude number. C SL is gas-free solid concentration by volume in the slurry. The GS is a dimensionless number that considers the effect of the hole diameter and number of holes. It can be calculated via:  in which a free is the free area of gas sparger and L c is its characteristic length. The above correlation is able to predict gas hold-up with the standard deviation of 17.8 % even in elevated temperature and pressure situations. The results of this correlation are in accordance with the results of different recent experimental works (Fig. 7). Although it is complicated and is almost hard to use, we would recommend it for the calculation of gas hold-up in slurry bubble column reactors.

Mass Transfer
Mass transfer coefficient is one of the momentous parameters for the design and scale-up of multiphase reactors. In a slurry bubble column reactor, a component in the gas phase needs to diffuse through the liquid and reach the catalyst active sites to react and then the reaction products need to travel back to liquid or gas phase, depending on the type of reaction. The reaction products that remain in the liquid phase can be separated by a simple distillation process. Therefore, four different resistances are on the way of reactants to reach the catalyst, react and come back: -The resistance in the gas phase.
-The resistance in the liquid phase at the interface of gas and liquid. -The resistance in the liquid phase at the interface of liquid and solid. -The resistance to reaction at the surface of catalyst.
Among the above resistances which are in series, most of the time, the second resistance is the rate-controlling one. Different theories were developed previously for describing mass transfer in a gas-liquid system. For instance, the two-film model for describing steady-state mass transfer was introduced by Lewis and Whitman [84]. Other models, additionally, like surface renewal and penetration model were proposed for describing unsteady-state mass transfer between liquid and gas phases [85,86]. Alper and Ö ztürk [87] and Alper et al. [88] claimed that the above models are unable to describe mass transfer in the presence of particles properly. Hence, the concept of gas liquid mass transfer enhancement by particles was introduced by them.
Solid particles cause enhancement phenomena by four different mechanisms. The hydrodynamic effect, which is the first mechanism, influences the boundary layer between liquid and gas. In fact, because of particles collision with the interface and the turbulence created by solid in the system, the solid particles presented in the liquid-gas interface decrease the boundary layer effective thickness. Additionally, solid particles cause liquid side mass transfer coefficient (K l ) to increase owing to the higher refreshment rate of liquid in the liquid-gas interface [89,90]. The shuttle effect, which is the second mechanism, was firstly introduced by Alper et al. [88]. It states that particles with a high specific area and porosity adsorb more gas and desorb it in the liquid that causes more gas transport and    increment of K l . Coalescence inhibition effect, which is the third mechanism, states that solids stick to the bubbles and prevent them from coalescence which results in higher specific area and higher volumetric mass transfer coefficient [91]. The reaction enhancement effect, which is the fourth effect, states that particles which are used as catalysts in a slurry bubble column reactor catalyze the reaction at the liquid-gas interface and increase the conversion of reaction as well as the mass transfer [92]. Different effects of the presence of particle on the performance of slurry bubble column are depicted by Fig. 8.

Liquid-Side Mass Transfer Coefficient at the Gas-Liquid Interface (K l )
Reaction with adsorption on and catalysis by solid particles can enhance the mass transfer from gas to liquid. This part focus on the influence of inert particles on mass transfer (K l ).
Respectively, the definition of K l based on the film theory and penetration theory are: and Inert solid particles can affect mass transfer coefficient via two distinct mechanisms. The first effect is lowering the effective diffusivity D A by means of reducing the available volume fraction of liquid for diffusion. For particles size in the order of film thickness or smaller, this effect can be considerable. The second effect is altering d L and t c by solid particles via changing the hydrodynamics in the vicinity of the gas liquid interface.
The pseudo-homogeneous-liquid approach is almost successful for systems in which the densities of liquid and gas are close to each other like the situation that is frequently encountered in bioreactors. For these types of systems, Kawase et al. [56] proposed a theoretical correlation for K l , by combining the Einstein-Li periodic viscous sublayer model and Highbie's penetration theory for the prediction of contact time t c . Their theory was derived for a system that behaves as a Bingham plastic, e.g., various fermentation systems that contain filamentous cells. For Newtonian (b = 0) liquid and non-Newtonian ones (b 0.7), they derived the contact time at the solid surface: After combining with penetration theory, K l can be derived as: For bubble columns, specific energy dissipation is calculated as: As Fig. 9 depicts, the accuracy of the above correlation has been tested for various solutions of CMC in large bubble columns but it seems that a decisive test for applicability of this correlation is also needed.
Regarding the effects of solids on liquid-side mass transfer coefficient, Schumpe et al. [58] concluded that the presence of solid particle increases mass transfer for both alumina and Kieselguhr particles on the proviso that the solid concentration is below 5 vol % Sada et al. [63], on the other hand, reported a decrease in mass transfer coefficient for all concentrations of Ca(OH) and MG(OH) 2 particles in 0.2 M NaOH in water. The results of Schumpe et al. [58] and Sada et al. [63] may have been affected by the size of column as none of their columns met the Wilkinson criteria. We are of the opinion that their experiments must be repeated in a larger column. Shah [55] reported that the large poorly wettable particles of polystyrene reduce K l . Although the size of these particles is larger than boundary film thickness considerable, it is possible that in this case (r p » r l ), solids dampen the turbulence in the vicinity of the interface. Lakhdissi et al. [21], on the other hand, pointed out that the presence of particles increases the liquid-side mass transfer coefficient. According to Fig. 10  Regarding the effects of operational conditions on the liquidside mass transfer coefficient, Chen et al. [41] found out that increasing the gas superficial velocity results in decrement of liquid-side mass transfer while as Fig. 10 depicts, increasing the gas superficial velocity increases the liquid-side mass transfer. As it is inferable from the above-named pieces of literatures, the effects of operational parameters and presence of particles on the liquid-side mass transfer coefficient are not fully understood yet and the available sets of data are scattered and contradictory excluding the pseudo-homogenous systems in which the effect of solid particles on mass transfer can be calculated by Eq. (25).

Gas-Liquid Specific Contact Area (a)
In addition to the knowledge of K l , in chemical reactions where enhancement occurs at the interface of gas and liquid, knowledge of specific contact area between gas and liquid, a, is important. The measurement techniques for contact area, which are explained in Beenackers et al. [82], and Chang et al. [93], and Oyevaar and Westerterp [94], includes chemical and physical methods. The physical methods, for calculation of interfacial area, include light reflection, photography, light scattering, real-time neutron radiography and γ-ray radiography. The light reflection and photography methods are suitable for transparent columns and low gas hold-up situations. The above-mentioned methods just reveal the contribution of bubbles to a while there are other techniques that are suitable for calculation of the contribution of interface ripple to a [95,96]. In chemical method, for the calculation of interfacial area, a swift chemical reaction is used. A review on the calculation of gas-liquid interfacial area is accessible in [97].
Owing to the importance of this parameter for the determination of heat and mass transfer rate, many scholars investigated it. Schönau [64] studied the influence of solid particles on gas hold-up and bubble size distribution. They also understood that the Sauter bubble diameter is independent of the solid hold-up, thus, for low and moderate gas hold-up, the interfacial area can be written as: The results of this study are also in good agreement with those of Schumpe et al. [58,59]. Yang et al. [98] investigated the mass transfer of CO and H 2 in a slurry bubble column reactor in industrial conditions. They reported that the interfacial area between gas and liquid increases with increasing the gas superficial velocity and pressure. The same results were also gained by Han et al. [24] and Chen et al. [41]. Yang et al. [98] also reported that the interfacial area between gas and liquid also decreases with the increment of particle concentration and temperature (Figs. 11 and 12). These results were also endorsed by Lakhdissi et al. [21]. Yang et al. [98] proposed the Eq. (28) for calculation of interfacial area between gas and liquid. It must be noted that it is valid for 3.6 10 6 Eu 1.

The Volumetric Liquid-Side Mass Transfer
Coefficient at the Gas-Liquid Interface (K l a) The volumetric mass transfer coefficient, because of giving valuable knowledge about liquid side mass transfer coefficient and contact area simultaneously, is one of the most momentous parameters for designing and scaling up of slurry bubble column reactors. The available methods for calculation of K l a are divided to physical and chemical methods. Among the physical methods for the calculation of volumetric mass transfer coefficient, the transient physical gas absorption (TPGA) technique is direct and simple. For calculation of mass transfer coefficient, Chang and Badie [99] developed a strong model in which the system's total pressure decrement is recorded and together with total volume and mole balances, the volumetric mass transfer coefficient is calculated for systems containing an extensive range of gases, liquids, and solids. This model improvement can be found in subsequent contributions [100]. In chemical method for calculation of volumetric mass transfer, a slow chemical reaction is used to obtain K l a. Lack of reliable reaction kinetics and difficulties in controlling the reaction temperature are the main problems of chemical methods. A review on chemical methods for calculation of K l a is available in [101][102][103]. By calculation of volumetric mass transfer (K l a) and gas-liquid interfacial area (a), the liquid side mass transfer coefficient can be calculated indirectly. It should be noted that a and K l a must be measured simultaneously under the same condition and hydrodynamics because the liquid side mass transfer coefficient is firmly dependent on the system turbulence.
In spite of a myriad of researchers in this field, there is not a universal agreement on the influence of various volume fractions of each type of solid particles on the mass transfer coefficient. Previous reviews on this topic can be found in [104,105]. If the viscosity of the liquid is high or the differences between solid and liquid densities is small, the slurry behavior resembles a pseudo-homogeneous phase. Hence, the volumetric mass transfer coefficient can be calculated using the effective viscosity of suspension which can be calculated using various available correlations [106]. In this regard, Ö ztürk et al. [57] found out that the presence of small concentrations of dense solid particles in low density and viscosity liquids affects the volumetric mass transfer considerably. Except for alumina in ligroin, all the results of their experiments were correlated as: in which zero indexes indicate the absence of solids while other conditions remain constant. This correlation is suitable for viscosity range of 0.54-100 mPa with a small mean error of 7.7 % The above results, which were achieved in organic solutions, are in accordance with the results of Schumpe et al. [58] for sodium sulfate solution and water in the same bubble column. They reported a decreasing function of volumetric mass transfer coefficient with effective viscosity. Schumpe et al. [58] reached higher values of K l for low concentrations of high-density solid particles. They proposed the below correlation which is valid for electrolyte and non-electrolyte solutions with effective viscosity between 1 to 100 mPa s.
Due to the enhancement of mass transfer, the volumetric mass transfer coefficient in systems with fine high-density particles and low viscosity liquids is higher compared to the predicted values by Eqs. (29) and (30). Additionally, non-wettable   solid particles may also reduce the value of volumetric mass transfer coefficient considerably. That's why Eqs. (29) and (30) should be used conservatively. Schumpe et al. [59] reported an extra decrement in volumetric mass transfer coefficient compared to Eqs. (29) and (30) for a system with non-wettable polypropylene particles in aqueous solutions of carboxymethylcellulose. They attributed it to surface blockage of the interface of gas and liquid by a Langmuir Hinshelwood type of adsorption of the non-wettable solid particles. It is interesting to note that K l a in a system with 5 mm activated carbon solid particles and aqueous solutions obey Eq. (29) although activated carbon sticks to the gas and liquid interface [58]. Probably, interface coverage by activated carbon, owing to activated carbon' large active area, does not block the interface like polypropylene particles. The mentioned correlations are more applicable to the homogeneous flow regime while the industrially momentous flow regime is heterogeneous. Sada et al. [61] were about to correlate the dependency of volumetric mass transfer and gas hold-up to the system properties in slug flow regime. They reported that the presence of solid particles has a meager influence on K l a and gas hold-up in electrolyte solutions compared to nonelectrolyte solutions. Additionally, by increasing the particle size and loading, the gas hold-up decreases and the dependency of gas hold-up on the solid size decreases for high solid concentrations. They concluded that in two-and three-phase bubble columns, the volumetric mass-transfer coefficient has a relationship with gas hold-up as: in which the gas hold-up can be calculated using Eqs. (32) and (33) for systems containing pure water in the absence and presence of solid particles, respectively. e G 10 À e G ð Þ 4 ¼ 0:046 U g (32) e G 10 À e G ð Þ 3 ¼ 0:019 U g U t 1=16 e s À0:125U À0:16 In the above correlations, C is a function of system properties and must be measured experimentally that results in many uncertainties.
For churn-turbulent flow regime and partially, for transition regime, Koide et al. [62] correlation has extensive applicability. They reported reductions in gas hold-up and volumetric mass transfer coefficient with the addition of suspended solid particles. These reductions are considerable in the transition flow regime and are less pronounced in the heterogeneous flow regime. Koide et al. [62] empirical correlations for gas hold-up and volumetric mass transfer in heterogeneous and transition flow regime are as below: Here, C is a constant that depends on the system properties (C = 0.364 for organic electrolytes aqueous solutions and C = 0.277 for water and also glycol/glycerol aqueous solutions). It would be really significant if the future studies could come up with the values of C for different liquids and predict the trend of C with the help of machine learning. Relations like those of Koide et al. [62] and Sada et al. [61] are not really applicable for systems containing liquids and solids with close densities, such as the reactors that are used in biochemical engineering, in as much as the single particle' terminal settling velocity U ts is going towards zero.
Sauer and Hempel [60] studied systems in which liquids and solids have close densities. They concluded that adding small light solids (r s 1300 kg m -3 ) to the system at low gas velocity (U g 0.04 m s -1 ) results in producing smaller bubbles and in turn higher gas hold-up. They also reported that the volumetric mass transfer coefficient decreases always by adding solid particles to the system because the increment in interfacial area is compensated by a larger decrease in liquid side mass transfer coefficient. Some of their results are depicted by Fig. 13. They correlate all of their results as follow: (46) here, Pe is the Peclet number and the constants C, n 1 , n 2 , and n 3 depend on the types of spargers that are available in Tab. 4.
The industrial reactors have a typical diameter between 2 to 6 m. Therefore, so as to take full advantage of experimental data obtained from lab-scale equipment, the effect of column size on its performance must be considered. Wilkinson [92] demonstrated that gas hold-up and mass transfer are almost independent of column size if the three below criteria are met although it may also depend on the physicochemical properties of the materials: -The diameter of reactor must be larger than 15 cm. -The ratio of reactor height to its diameter must be higher than 5. -The spargers' hole diameter must be larger than 1 or 2 mm.
Accordingly, the scale-up procedure in which a set of experimental data that was obtained in a small-scale apparatus is used, leads generally to overestimation of mass transfer, gas hold-up as well as interfacial area. Hence, it is strongly recommended to use large dimension pilot plants which meet the Wilkinson criteria for investigation of different aspects of slurry bubble columns. In the rest of this paper, the focus will be mainly on the studies that meet the Wilkinson [92] criteria.
Rather than solid properties' effects, other phases' properties, column size, operational parameters and presence of impurities can appreciably affect the volumetric mass transfer. In this regard, Salvacion et al. [53] studied the effects of adding alcohol, particles and column diameter on the volumetric mass transfer coefficient in a gel suspended bubble column reactor. They concluded that the addition of particles to the system decreases mass transfer coefficient. They also reported that, depending on the type and concentration of alcohol, the addition of alcohol can increase or decrease the volumetric mass transfer compared to that of pure water. They finally proposed the below correlation for calculation of volumetric mass transfer coefficient: K l a s l r l D AB g ¼ 12:9 Sc 0:5 Mo À0:159 Bo À0:184 e 1:3 g 0:47 þ 0:53 exp À41:4 P K * m l U S Re À0:5 Here, f s , Π ¥ , and U s stand for volumetric fraction of slurry, surface pressure and slip velocity, respectively.
Additionally, Dewes et al. [52] investigated volumetric mass transfer and gas hold-up in a slurry bubble column reactor changing the density of gas by a factor of up to 300 and they observed a strong effect of gas density on the mass transfer between gas and liquid. They concluded that the mass transfer increases strongly with increasing the gas density and they proposed: with m eff ¼ k 2800U g À Á nÀ1 (50) in which k is the fluid consistency index and n is an empirical constant varying from 0.18 to 1.
In a similar vein, Yang et al. [51,98] investigated the mass transfer of CO and H 2 in a slurry bubble column reactor in industrial conditions. They reported that the opertating conditions have strong effects on the interfacial area between gas and liquid and in turn, on volumetric mass transfer. The volumetric mass transfer coefficient increases by increasing temperature  Figure 13. Effects of high-density large particles on volumetric mass transfer against gas superficial velocity in air-water-solid systems (polyoxymethylene, r p = 1255 kg m -3 , d p = 2.8 mm, perforated plate; ion exchange resin, r p = 1060 kg m -3 , d p = 0.6 mm, sintered plate) Sauer and Hempel [60]. and decreases slightly by increasing the particle concentration. They also indicated that in the applied range of gas superficial velocity and pressure, the volumetric mass transfer does not change significantly. For calculation of the liquid side mass transfer coefficient in a system containing H 2 , they proposed: K l D in D AB ¼ 1:546 10 2 Eu 0:052 Re 0:076 Sc À 0:231 (51) in which D in is the column diameter and Eu is Euler number (P gauge /(r sl U g 2 ) and D AB is the gas diffusivity. This formula is valid for 3.6 10 6 Eu 1. 5 10 8 , 8 Re 340, 13 Sc 270.
Also, for calculation of the liquid side mass transfer coefficient in a system contain CO, they proposed:  [36] studied the effects of pressure, temperature, gas velocity and solid density on the hydrodynamics and volumetric mass transfer coefficient in a slurry bubble column. They reported that increasing the pressure and gas density, increases the population of small bubbles that results in higher volumetric mass transfer. Slurry concentration increment decreases the volumetric mass transfer in all the cases. They correlated the experimental data as: that in this equation, X equals to zero for nonfoaming singlecomponent liquid mixtures and also equals unity for foaming liquid mixtures. To sum up, regarding the effect of particle concentration on the mass transfer, it seems that most of the literature reported a decreasing trend of volumetric mass transfer with increasing the solid concentration. For instance, Han et al. [24], Salvacion et al. [53], Yang et al. [51], Sehabiague et al. [36], Koide et al. [62], Sada et al. [61], Ö ztürk et al. [57], and Schumpe et al. [58] reported that increasing the solid concentration decreases the volumetric mass transfer coefficient. Nevertheless, increasing or constant trends also were reported by other researchers. For instance, recently, Lakhdissi et al. [21] pointed out that at a constant solid size (71 and 156 mm), increasing the particle concentrations (from 1 to 5 %) has no effect on the volumetric mass transfer coefficient for all applied gas superficial velocity. Besides, they reported that increasing the solid size at a constant solid concentration has also no effects on volumetric mass transfer. In sum, in the heterogeneous flow regime, they concluded that the presence of particle has no effects on the volumetric mass transfer due to two opposite effects of particles; increasing the liquid side mass transfer coefficient and decreasing the interfacial area between gas and liquid. Additionally, Chen et al. [41] reported that the volumetric mass transfer decreases with increasing the particle concentration generally except for low solid concentrations which sightly increase mass transfer coefficient. Chen et al. [41] used small size particles (d p 10 μm) while the concentration of particles in their study ranges from zero to 30 vol %. Based on Banisi et al. [81], for particle size lower than 10 μm (like the study of Chen et al. [41]), if the concentration of slurry is lower than 0.6 vol %, solid cause the interfacial area to increase. Otherwise, solid decreases the interfacial area. Exactly the same trend was reported by Chen et al. [41] for volumetric mass transfer coefficient.
In Fig. 14, the volumetric mass transfer coefficient as a function of solid loading for hollow glass spheres (d p = 9.6 μm, r p = 1100 kg m 3 ) is depicted [107]. As it is portrayed, it is really interesting that as far as the solid loading is lower than 10%, the volumetric mass transfer coefficient is higher in three phase systems compared to the two phase systems (C S = 0). For solid loading in the range of 0 C S 10 vol %, increasing the solid loading causes the volumetric mass transfer to pass through a peak (increases and then, decreases). The rationale behind this phenomenon can be attributed to different impacts of solids. Firstly, small solid loading cannot alter the slurry viscosity significantly while it improves the turbulence and surface renewal in the liquid film which leads to higher liquid side mass transfer coefficient and finally, higher volumetric mass transfer coefficient. Secondly, the presence of particles in liquid film at the gas-liquid interface can hinder the bubble coalescence and contribute to the interfacial area. In the contribution of Banisi et al. [81], the gas-liquid interface is staying high as far as the solid concentration is too low (C S 0.6 vol %). When the solid concentration ranges from 0.6 to 10 %, although the interfacial area contributes negatively, the liquid side mass transfer stay high enough to compensate the negative effects of interfacial area on the volumetric mass transfer. Nonetheless, higher solid Figure 14. Volumetric mass transfer coefficient as a function of solid loading for hollow glass spheres (d p = 9.6 μm, r p = 1100 kg m -3 ) [107].
loading (C S 10 %) increases the slurry viscosity which in turn, reduces the mobility and liquid-side mass transfer. Furthermore, higher solid loading leads to coverage of bubble surface with particles that hinder gas diffusion (that leads to lower K l ) as a result of lowering the effective gas-liquid interfacial area.
Based on the studied literature, it seems that the classification of Banisi et al. [81], which was correct to predict the effects of solids on interfacial area and gas hold-up, is also partially correct to predict the effects of the presence of solids on volumetric mass transfer coefficient. As the increment or derement behavior of volumetric mass transfer coefficient with presence of particles hings on the behavior of interficial area and liquid side mass transfer coefficient, Banisi et al. [81] need a slight modification to be also correct for volumetric mass transfer.
Gas superficial velocity is also one of the most decisive parameter in determination of the reactors efficiency. It was reported by Sauer et al. [60] and endorsed by Abdulkareem et al. [33], Han et al. [24], Sehabiague et al. [36] and a plethora of other researchers that increasing the gas superficial velocity results in increasing the volumetric mass transfer coefficient. Chen et al [41] also found out the same result and reported that increasing the gas superficial velocity results in the increment of volumetric mass transfer and decrement of liquid-side mass transfer. The same claim was also made by Han et al. [24] that the changes in volumetric mass transfer is mainly due to the variation of interfacial area at different operating condition.
There are other pivotal parameters that can also affect mass transfer. For instance, the type of gas distributor can change the initial bubble size distribution and in turn, alters the gas hold-up and volumetric mass transfer coefficient. Abdulkareem et al. [33] showed that the mass transfer coefficient is higher for a ring distributor compared to a perforated plate. The findings of other researchers such as Moshtari et al. [47], Asil et al. [22], and Beenackers et al. [82] leave a seal of approval on the assertion that ring and porous distributors are favorable to perforated distributors from the perspective of mass transfer.
Regarding the effect of column size on K l a, various contradictory sets of data are available. For instance, Abdulkareem et al. [33] reported that the mass transfer coefficient increases with increasing the ratio of column height to diameter while Chen et al. [41] remarked that increasing the axial height of column cannot affect the volumetric mass transfer. For more literature on the effects of column size, consult the gas hold-up part of this work. In regard to the effect of column size, the claim of Ojima et al. [34], which is in accordance with Wilkinson [92] criteria, seems to be rational. They pointed out that if the hydraulic diameter of a column is higher than 150 mm, the effects of hydraulic diameter on the gas hold-up (and probably mass transfer) is meager. Abdulkareem et al.'s [33] setup does not meet this criterion and needs to be repeated in a larger column.
Operating conditions like pressure and temperature also can have a palpable impact on the volumetric mass transfer. Exempli Gratia, it was revealed by different researchers that increasing the pressure increases the volumetric mass transfer [24,36]. Regarding the effects of gas density and temperature, it was revealed and reported that increasing the gas density and temperature increases the volumetric mass transfer as well [36,52,98].

Conclusion
The headway made during the past decades in our knowledge of how solid particles affect a slurry bubble column has been truly impressive. As it was discussed in the previous sections, the hydrodynamics of slurry bubble columns as well as their mass transfer characteristics are extremely affected by a number of parameters such as reactor geometry, operating condition and each phase's properties. Regrettably, a majority of the available studies on SBCRs have been done under the ambient conditions in the presence of water, air and glass beads that makes us almost unable to take full advantage of these experimental data in real industrial processes such as Fischer-Tropsch processes. In this part, an attempt is made to summarize the aforementioned points on different facets of SBCRs to reach a clearer view of the effects of each parameter.
-Regarding the effects of particles on gas hold-up, the classification of Banisi et al. [81] is correct. Therefore, a small concentration of small particles (d p 10 μm and C s 0.6 vol %) as well as high concentrations of large particles (d p 2000 μm and C s 10 vol %) increases the gas-liquid contact area and in turn, gas hold-up. Otherwise (e.g., high concentration of small particles, medium-sized particles at moderate concentration, low concentration of big particles), a decreasing effect of solids on the contact area is expected. This classification can also be valid for volumetric mass transfer coefficient but it might need a slight modification. Based on the available data, in some liquids like aqueous solutions of 0.8 M Na 2 SO 4 , small solid loading cannot alter the slurry viscosity significantly while it improves the turbulence and surface renewal in the liquid film which leads to a higher liquid side mass transfer coefficient. In contrast, in other liquids like aqueous solutions of 0.2 NaOH, adding even a small concentration of particles lowers the liquid-side mass transfer. In both cases, higher solid loading increases the slurry viscosity and covered bubbles' surface which in turn, reduces the mobility, gas diffusion and liquid-side mass transfer. Obviously, it is the interaction between a and K l that determines the decreasing or increasing behavior of K l a. Therefore, according to the behavior of a and K l in different situations, it seems that adding a small concentration of small particles to some liquids can increase volumetric mass transfer considerably. -Increasing the density of gas cause bubbles to shrink which results in a higher gas hold-up. As the molecular weight increment is translated into gas density increment, it seems logical to expect increasing the gas molecular weight also increases the gas hold-up and volumetric mass transfer coefficient. The same trend was also reported by different researchers although some others are of the opinion that change in the gas molecular weight has neutral effects on gas hold-up and volumetric mass transfer coefficient. Furthermore, some others also reported a decrement in gas hold-up and volumetric mass transfer coefficient with an increment of gas molecular weight at low gas superficial velocity (< 0.05 m s -1 ). It seems that the effect of gas molecular weight is different in different flow regimes. Therefore, more research is also needed to recognize the operating conditions in which increasing the gas molecular weight decreases gas hold-up and volumetric mass transfer coefficient. -Increasing the liquid viscosity and surface tension increases the bubble size distribution which results in the decrement of gas hold-up and volumetric mass transfer coefficient. Increasing the liquid density results in the increment of volumetric mass transfer coefficient while its effects on gas hold-up are not really clear yet and different contradictory sets of data have been reported by researchers. -Increasing the pressure results in higher gas density and in turn, higher gas hold-up and volumetric mass transfer while the liquid side mass transfer stays almost constant. Increasing the temperature has been proven to increase the volumetric mass transfer coefficient although some researchers reported that increasing temperature leads to the gas holdup increment and the others reported decrement effects on the gas hold-up. Changing the temperature can alter gas density, liquid viscosity, liquid surface tension as well as diffusivity that it is the interactions between these parameters that determine the effects of temperature variation on gas hold-up. Therefore, it seems that more well-designed experiments are also needed to understand the effect of temperature on the gas-liquid contact area. -Increasing the gas superficial velocity leads to increment of gas hold-up and volumetric mass transfer coefficient while regarding the effects of gas superficial velocity on liquid-side mass transfer, the available sets of data are scattered and contradictory, to some extent. Additionally, for a continuous liquid phase in SBCRs, increasing the liquid velocity was found to decrease gas hold-up. -It has been confirmed by myriads of researchers that the reactor size does not affect gas hold-up on the proviso that the reactor is large enough. It is almost generally accepted that if the hydraulic diameter of a column is higher than 150 mm, and the ratio of column's height to its diameter is higher than 5 and the distributor's orifice diameter is larger than 1 or 2 mm, the column size cannot affect mass transfer coefficient and gas hold-up considerably. In order to use the experimental data for scaleup purposes, the mentioned criteria must be met. Regrettably, most of the available sets of data have been gained in small reactors which are of less value for scaling-up purposes. Generally, three different zones are identified in SBCRs. The zone near the sparger at the bottom of the reactor in which gas hold-up and mass transfer are strongly affected by gas distributor. The second zone is in the middle of the column which is called the bulk zone. The third zone is located at the top of a column in which the situation is complicated if the liquid foams. It is the bulk zone that determines the overall efficiency of a column and if the reactor is large enough (D H > 150 mm and H/D in > 5), the effects of the first and third zone are negligible. The distributor design can control bubble size distribution and gas hold-up not only in the first zone but also in the bulk zone. The gas spargers with low gas velocity per each hole produce smaller bubbles which results in a higher gas hold-up. It has been reported by various researchers that the mass transfer coefficient and gas hold-up are higher for a ring distributor compared to a perforated plate.
-It seems that the addition of a low concentration of small particles cannot affect the flow regime seriously while a higher loading of larger particles, by decreasing the gas superficial velocity of transition regime, affects flow regime seriously. Presented particles accumulate in the bubbles' wakes and increase the net mass that leads to a lower velocity of bubbles. -Based on Banisi et al. [81], adding a high concentration of large particles can increase the interfacial area. The effect of such situations on the liquid-side mass transfer is still ambiguous. In order to determine the behavior of the volumetric mass transfer coefficient in such a situation, more research is needed. Additionally, more carefully designed works are needed to broaden our horizons about how hydrophobic solid particles in hydrophilic liquids stick to the G-L interface and enhance mass transfer. -For the sake of the development of diverse industrial processes, gaining a deep insight into the SBCRs' hydrodynamics and mass transfer is pivotal. That is why quantification and measurement of these momentous parameters have remained an area of interest in both academia and industry. The design of slurry bubble column reactors for the lowtemperature Fischer-Tropsch process is one of the most important examples of SBCRs. Unfortunately, in this field, there is still some knowledge gap which is particularly related to the mass transfer and hydrodynamic parameters in elevated pressures and temperatures in the presence of different types of solids. All in all, there is an overwhelming need for more investigations to reach a further understanding of the intricate and complex behavior of SBCRs under various operating conditions. New measurement techniques, such as optical probes, high speed tomography, Tomo-PIV systems, needle probes, but as well as new possibilities for data analyses and processing such as machine learning and artificial intelligence may help to enable a better understanding from experimental side and support the CFD simulations to become a reliable tool for the design of SBCRs in the near future.