In this section, the four homogeneous models described previously were used to com- pare the vaporization times of typical FCC feedstock with the simplified model of Buchanan (1994) which was used particularly for analysing the gas-oil droplet vaporization. Due to the fact that gas-oil vaporization data are scarcely available, data reported in Buchanan’s (1994) work were taken as a reference to compare with the other model predictions.
Due to the complex compositions, the reported physical properties of the vacuum gas oil (VGO) may vary significantly.
Besides droplet diameter, knowledge of appropriate slip velocity is critical in compu- ting the droplet Reynolds number correctly for heat transfer modelling purpose. It is perhaps a very challenging task to satisfactorily estimate slip velocity between an evaporating droplet and surrounding gas in an FCC riser environment. In a real scenario, the slip velocity would fall in a range depending on the droplet size distribution produced from the atomizer. In a typical FCC riser, the feed droplets are atomized at velocity of 30-50 m/s (Buchanan, 1994;
Gao et al., 2001; Mirgain et al., 2000). During liquid jet break up from feed nozzle, the slip velocity of droplets being produced from the circumference of the jet is possibly higher due to turbulent shearing effect however the slip velocity of droplets in the centre of jet plume may decelerate to the terminal settling velocity (Buchanan, 1994). It was further shown in his work that the effect of slip velocity on vaporization time is more pronounced when droplet diameter is large and the effect is rather less when droplet size is smaller.
Table 3.2 lists physical properties data of the gas, liquid and solid phases obtained from the work of Buchanan (1994). The operating conditions of the FCC riser are provided in Table 3.3. Due to the absence of riser flow rate data in Buchanan’s (1994) work, these data were sourced from the work of Nayak et al. (2005) to compute individual phase volume frac-
Chapter 3 62 tions. Regarding the droplet size in FCC riser, a large range was noted in various reported studies i.e. from 30 - 500μm (Mauleon & Courcelle, 1985); 30–3000 μm (Buchanan, 1994);
100-400àm (Mirgain et al., 2000), and 500àm (Nayak et al., 2005). In this study, the droplet size data were taken from the work of Mauleon and Courcelle (1985) since presumably they used industrial scale data in their study and also the upper bound of the droplet size distribu- tion is close to the other reported data.
Besides droplet diameter, knowledge of appropriate slip velocity is critical in compu- ting the droplet Reynolds number correctly for heat transfer modelling purpose. It is perhaps a very challenging task to satisfactorily estimate slip velocity between an evaporating droplet and surrounding gas in an FCC riser environment. In a real scenario, the slip velocity would fall in a range depending on the droplet size distribution produced from the atomizer. In a typical FCC riser, the feed droplets are atomized at velocity of 30-50 m/s (Buchanan, 1994;
Gao et al., 2001; Mirgain et al., 2000). During liquid jet break up from feed nozzle, the slip velocity of droplets being produced from the circumference of the jet is possibly higher due to turbulent shearing effect however the slip velocity of droplets in the centre of jet plume may decelerate to the terminal settling velocity (Buchanan, 1994). It was further shown in his work that the effect of slip velocity on vaporization time is more pronounced when droplet diameter is large and the effect is rather less when droplet size is smaller.
Table 3.2 FCC feed (vacuum gas oil) liquid and vapour properties in a typical FCC riser (Buchanan, 1994)
Thermal conductivity
k, (W/mK)
Viscosity à, (Ns/m2)
Density ρ, (kg/m3)
Heat capacity Cp (J/kgK)
Molecular weight M
(kJ/kgK)
Diffusion coefficient D (m2/s)
Latent heat LV (J/kg)
gas (G) 0.062 1.4 x 10-5 3.6 3180 120 2.6 x 10-6 -
Chapter 3 63
liquid (L) 0.100 8.0 x 10-4 610 2760 320 6.7 x 10-9 222,000
Catalyst
particle (P) 0.167 - 1400 1130 - - -
Table 3.3 Operating conditions of a typical FCC riser (Buchanan, 1994; Nayak et al., 2005) Operating parameters Unit Value
Riser temperature K 922K
Riser pressure bar 3
Saturation temp. of gasoil feed K 700
Feed preheat temperature K 561
Catalyst to oil ratio (CTO) - 8
Gasoil flow rate kg/s 480
Atomizing steam (wt% of feed) - 5%
Steam density kg/m3 0.89
Steam viscosity Pa.s 2.71x10-5
Slip velocity (gas and droplet phase) m/s 6.1 Slip velocity (solid and droplet phase) m/s 6.1 Liquid volume fraction εL - 2.14%
Solid volume fraction εp - 7.46%
Gas volume fraction εG - 90.4%
The variation in slip velocity would also affect the corresponding Reynolds number.
Using the range of slip velocity suggested by Buchanan (1994) from 5 – 10 m/s and feed droplet diameter from 30 μm to 500 μm, a Reynolds number range from 5 to 163 was ob- tained. However, acknowledging the fact that there is great uncertainty in estimating a proper slip velocity which depends on the droplet size, we rather chose to use a constant slip velocity
Chapter 3 64 of 6.1 m/s also used in Buchanan’s (1994) work. The aforesaid range of Reynolds number confirms the applicability of using (Ranz & Marshall, 1952b) correlations for estimating Nu and Sh number in all models presented in this study which is reportedly valid for Reynolds number up to 1000 (Macklin, 1964).
Figure 3.4 compares the temporal change of diameter and temperature for a 300àm droplet predicted by the four homogeneous models with the data reported by Buchanan
(1994) referred as “Buc (1)” in the subsequent figures.
Figure 3.4a presents times predicted by the four different models for complete vapori- zation of the feed droplet which are around 104.8 ms, 120.0 ms, 161.2 ms and 155.6 ms pre- dicted by the ITC, AS, FTC and ETC model respectively. Considering Buchanan’s data as a base case (t = 77.3 ms), the deviation in other model predictions ranges from 36 % to more
Chapter 3 65 than 100 %. Among others, the ITC model could be seen matching well with the base case data.
Figure 3.4 Transient change of FCC feed droplet diameter predicted by four different homo- geneous models - ITC, AS, FTC & ETC compared with the base case of Buchanan [Buc (1)].
Conditions are: dd0 = 300 àm, dp = 65 àm, Td0 = 561 K, TB = 700 K, TG = Tp = 922K (a).
Conditions are: dd0 = 300 àm, dp = 65 àm, Td0 = 561 K, TB = 700 K, TG = Tp = 922 K (b).
All models could be seen predicting the temperature profile almost reaching satura- tion temperature consistently. This trend is unlike previous temperature predictions (Figure 3.3a & b), where the saturation temperature could not be reached even towards the end of droplet lifetime; and is a consequence of using Eq. (3.21) for estimating carrier gas thermo- physical properties. In the case of gasoil, Eq. (3.22) was used which enabled the saturation temperature to be reached. However, this prediction could not be validated due to lack of any published data.
Table 3.4 shows the different vaporization times predicted by the five different mod- els for gas oil droplet size ranging from 30 àm to 500 àm at riser temperature TG = 922 K, and initial droplet temperature Td0 = 561 K. The vaporization time ranges from 1.54-393.6 ms and
Chapter 3 66 when compared to the base case of Buchanan, it indicates that towards the higher droplet siz- es, disagreement with the other model predictions in general is more. This could be attributed to the implicit assumption of infinite thermal conductivity used in the modelling analysis of Buchanan, and for this reason, ITC model prediction is close to Buchanan’s data while all other models predict much higher vaporization time. Of only few data available on the vapor- ization of feed droplet, Mauleon and Courcelle (1985) reported vaporization time in the range of 3.0-400 ms to attain 90 % vaporization of feed droplet for initial droplet size ranging from 30-500 àm. Acknowledging the fact that model predictions depend critically on the thermo- physical properties of the FCC feed type, associated compositions and operating conditions, present model predictions reasonably agree well with the measurements reported by Mauleon and Courcelle (1985). The agreement with the published data could be considered towards indirect validation of the present model predictions at least from the perspective of droplet size reduction. In the present study, the feed droplet vaporization times computed using ho- mogeneous models were found to fall in the first half second of the total residence time (1.54- 393.6 ms) which is well within the typical residence time of industrial risers reported to be in the range of 1.5-4.0 s (Buchanan, 1994). However, considering the physical complexities in- volved in the vaporization process, and recognizing inability of a single model to capture all the physics involved in an appropriate manner, all the model predictions should be regarded in a qualitative way.
Table 3.4 Droplet vaporization times (ms) for different size of FCC feed droplets predicted by homogeneous models (operating conditions are: dp = 65 àm, Td0 = 561 K, TB = 700 K,
TG = Tp = 922 K) Droplet diameter (àm)
30 50 100 300 500
Buc (1) 1.538 3.713 14.79 77.35 166.93
Chapter 3 67 ITC 1.956 4.812 15.88 104.76 247.4
AS 2.350 6.080 20.08 120.00 275.4 FTC 2.373 5.868 20.79 161.20 393.6 ETC 2.309 5.803 20.54 155.58 383.6