In gas-solid fluidised bed, solid particles come into contact with a gaseous flow with a range of velocities which is dependent on the applications. In fluidised bed granulation, liquid coating materials are sprayed as atomised droplets into a particle bed and vaporisation of the liquid film takes place when droplet are in contact with the granules (T.-J. Wang et al., 2001).
In petrochemical operations, fluidised bed plays important roles in fluid coking and fluid cat- alytic cracking unit. In fluid coking process, bitumen or heavy petroleum fractions are inject- ed as atomised liquid into a fluidized particles bed; interaction between the hot coke particles and liquid droplets enable the quick vaporisation followed by cracking to yield distillate products from the coker feeds (Gray et al., 2001; McMillan et al., 2005).
In fluidized catalytic cracking risers, droplets are injected in to a gas-solid flow in- cluding hot steam and catalysts which are preheated well above the boiling temperature of the
Chapter 2 12 feedstock. Vaporisation of the feedstock is then completed through heat received from both hot steam flows and catalysts when droplets are in contact with the catalyst particles. The commonly used approaches describing the droplet vaporization process under these condi- tions are homogeneous mode wherein droplets receive heat only from the surrounding hot gas, and heterogeneous mode wherein vaporization process involves direct collision between droplet and hot solid particles. Numerous studies have been conducted on homogeneous va- porization of droplets involving both mono and multi-component droplets especially in rela- tion to the spray combustion in internal combustion engines and liquid fuelled burners which is reflected in the recent studies of Sazhin (2014) and Sirignano (2010). A review of the rele- vant literature on homogeneous vaporisation is presented later in section 2.2.
Although critical, a large number of studies reported on the numerical simulations of FCC riser apparently ignore the feed vaporization phenomenon because of instantaneous na- ture of the process (Gan et al., 2011; Gao et al., 1999; Lopes et al., 2011; Wu et al., 2010).
Some other studies include rather simpler vaporization models without considering the drop- let-particle interactions in their numerical modelling (Behjat et al., 2011; Gan et al., 2011;
Gao et al., 1999; Lopes et al., 2011; Wu et al., 2010). Possibly, the complex nature of such interactions in the feed vaporization zone coupled with simultaneous heat and mass transfer process appears to be quite challenging to formulate the suitable physical models to include in the numerical modelling studies. A summary of typical numerical studies which include simple vaporisation approaches was presented in Table 2.1 to reflect the status of the droplet vaporization process modelling under film boiling conditions.
Chapter 2 13
Table 2.1 Typical numerical studies including the droplet vaporisation under film boiling regime, particularly in FCC riser and fluid coker oper- ating conditions
Authors Feed vaporization approach Theologos and
Markatos (1993)
Instantaneous Theologos et al.
(1997)
Distillation curve (ASTM D-1160) of a typical Hellenic Aspropyrgos Refinery feedstock was used to deter- mine hydrocarbon temperature as a function of the mass fraction of vaporized feedstock.
Theologos et al.
(1999)
Vaporization rate was calculated using droplet size and vaporization time from data of Mauleon and Courcelle (1985)
Gao et al. (1999) Instantaneous
I.-S. Han et al. (2000) The feed vaporization section is modelled as pseudo heat transfer system in which two streams (catalyst and feed) join. The catalyst temperature after feed vaporization is calculated by the energy balance assuming adia- batic operation, and the vapour temperature is calculated by the Antoine equation.
Gao et al. (2001) Vaporization was calculated by dividing mass of single droplet by fixed vaporization time (0.2 s). (simplified d2 law) Both sensible heat transfer and latent heat transfer were considered.
Gupta and Subba Rao (2001)
Sensible heat transfer between solid and liquid and latent heat transfer between gas and liquid considered Bowman et al. (2002) The model was based on the fundamental physics of stationary single droplet vaporization and then modified
for large groups of droplets in a convective environment using correlations.
S.-L. Chang and Zhou (2003)
The model was based on the fundamental physics of stationary single droplet vaporization and then modified for large groups of droplets in a convective environment using correlations.
Gupta and Subba Rao (2003)
Sensible heat transfer between solid and liquid and latent heat transfer between gas and liquid considered
Chapter 2 14
X. Wang et al. (2004) Droplet vaporization in gas phase was considered. Droplet-solid heat transfer was accounted indirectly by in- corporating a modified Nusselt number which accounted for influence of vapour and solid particles.
Fernandes et al.
(2007)
Instantaneous. The change in feed enthalpy during vaporization was calculated using a multi-variable empirical correlation involving feed temperature, Watson characterization factor, and API gravity.
Wu et al. (2010) Instantaneous Lopes et al. (2011) Instantaneous
Behjat et al. (2010) Vaporization of droplets was considered to occur in gas following three different stages – inert heating, vapori- zation and boiling. The reduction in heat transfer coefficient from droplet to gas phase due to presence of the vapour film around the droplet was accounted.
Gan et al. (2011) Instantaneous
Behjat et al. (2011) Vaporization of droplets was considered to occur in gas following three different stages – inert heating, vapori- zation and boiling. The reduction in heat transfer coefficient from droplet to gas phase due to presence of the vapour film around the droplet was accounted.
Pougatch et al. (2012) Two mechanisms of liquid spreading in the fluidized bed were considered: first, by random motion of particles, and second, by liquid exchange during a collision. Interfacial heat transfer between droplet and gas phase was obtained through the use of the Nusselt number correlation by Ranz and Marshall correlation.
J. Chang et al. (2012) Fixed droplet diameter was considered and droplet vaporization time considered to be proportional to square to droplet diameter
Ahsan (2015) Instantaneous vaporization of the feed droplets which are in contact with the hot catalyst particles was consid- ered. The resulting heat transfer involves removal of both latent heat of vaporization and sensible heat from the hot catalyst and vapour thus formed remains in thermal equilibrium with the catalyst particles.
Q. Yang et al. (2016) Complete vaporisation assumed just after injection John et al. (2017) Instantaneous
Li et al. (2017) Instantaneous
Chapter 2 15 Only very few studies have focused on the detailed droplet-particle interaction mech- anism and the subsequent vaporisation approaches (Buchanan, 1994; Martin, 1990; Mirgain et al., 2000; Mitra, 2016; Nayak et al., 2005) which are discussed below.
Martin (1990) was possibly the first time to propose two different heterogeneous heat transfer mechanisms in FCC riser. In the first mechanism, it was assumed that feed droplets are larger than the catalyst particles and direct contact heat transfer at particle surface area occurs through the thermal conduction during collision. In the second mechanism, Lei- denfrost effect was assumed to occur during the collision of feed droplet and catalyst particle which prevents direct contact between the droplet and hot particle due to presence of a thin vapour film at the droplet-particle contact area. No quantification in terms of physical model- ling of these mechanisms however was reported.
Later on, in the same line of thought, Buchanan (1994) proposed two physical models of the heterogeneous vaporization process to represent the two limiting cases of heterogene- ous heat transfer process during droplet-particle collision: (i) infinitely fast heat transfer be- tween droplets and particles where the entire heat was assumed to be transferred instantane- ously from the catalyst particle to the feed droplet during collision; (ii) hard sphere model where a pair of droplets and particles was assumed to undergo an elastic collision due to presence of a thin vapour film (Leidenfrost effect) at the solid-liquid contact area. No physi- cal collision model however was proposed and the presence of solid catalyst particles was accounted through modification of Reynolds number in the expression of Ranz-Marshall cor- relation (1952) for convective heat transfer by inclusion of solid volume fraction.
In these two cases analysed by Buchanan (1994), the thermal history of a droplet was divided into two distinct phases: heat-up and vaporization. In the first phase, droplet is heated from initial temperature to its boiling temperature without vaporization; and during the sec-
Chapter 2 16 ond phase, only the vaporization was assumed to occur without any change in temperature.
Total vaporization time was therefore calculated by summing up the heating and vaporization time. These two limiting cases i.e. (i) and (ii) also set the maximum and minimum possible heat transferred to droplets during collisions with catalyst particles hence the minimum and maximum possible vaporization time respectively.
Contrary to the theory proposed by Martin (1990) and Buchanan (1994), Mirgain et al. (2000) argued that Leidenfrost effect possibly does not occur during droplet-particle colli- sion in FCC riser primarily because of high Weber number (We> 5000) of the injected drop- lets. They reasoned since the critical We number for droplet breakup is reported to be ~ 80 in Leidenfrost regime (Wachters & Westerling, 1966), droplet must break upon interactions with particles under the FCC operating conditions. It is critical to know if feed droplets could be vaporised completely within the typical residence time in riser. The residence time in an industrial scale FCC riser is usually defined as the time since the feed is injected into the bot- tom of the riser reactor until the product vapours come out at the top of the riser. This resi- dence time includes time for both feed vaporization and subsequent cracking reactions.
Mirgain et al. (2000) critically analysed the effect of homogeneous and heterogeneous heat transfer modes on the vaporization time in FCC riser and showed that within the typical resi- dence time in a riser, complete vaporization of the feedstock is not possible without including the heterogeneous mode which accounts for the enhanced heat transfer coefficient. Three dif- ferent droplet-particle collision mechanisms were proposed between a liquid-covered and a liquid free catalyst particle: (i) two particle stay bonded by the liquid film (ii) liquid film is shared between the two particles and (iii) liquid film is completely transferred to the other particle. These interactions mechanisms provide realistic insights to heterogeneous vaporiza-
Chapter 2 17 tion mechanisms although no physical model was suggested to incorporate these scenarios into the heat transfer expression.
Inclusion of collision in heterogeneous vaporization involving a large droplet and a small particle was first described by Nayak et al. (2005). In his phenomenological model, the collision between the droplet and particle was accounted for by an adjustable parameter which represents the ratio of vapour volume generated during collision to the volume of a solid particle. Different values of this adjustable parameter were used in their study and a value of 14 was observed to match well with the vaporization time suggested in the early work of Buchanan (1994). Although phenomenological in nature, the model actually incorpo- rated the collision interactions and presented the heterogeneous vaporization process in a more effective way.
Recently Mitra et al. (2016) showed that in a droplet-particle system in film boiling regime (particle temperature 250 to 350 oC), Leidenfrost effect is limited to only up to a range of impact Weber numbers. Beyond this range (We ~ 34 to 146), a clear transition from rebound to disintegration regime was noted. The observed transition indicates that direct con- tact between droplet and particle is inevitable when relative velocity exceeds a threshold val- ue. Also shown was the effect of impact Weber number on the droplet-particle contact time which exhibited a decreasing trend with increasing Weber number up to the transition thresh- old and then indicated much less dependency on the Weber number once the droplet under- goes disintegration. The above discussion shows that limited research is indeed available on the droplet-particle interaction mechanisms related to vaporisation of feed droplets in multi- phase systems like FCC units. There are different modelling approaches reported which may provide different vaporisation times and a comprehensive comparison of these models is es- sential to identify an operation window. Also, there is a pressing need to develop more phys-
Chapter 2 18 ics based models as opposed to empirical correlations that capture the underlying mecha- nisms of phase interactions for more complete description of the multiphase vaporisation pro- cess. Section 2.2 and 2.3 review the two important aspects of droplet vaporisation process - convective (homogeneous mode) and conductive (heterogeneous), respectively, to provide an adequate background of the problem undertaken in this study.