Economic and Control Performance of a Fluid Catalytic Cracking Unit

Article pubs.acs.org/IECR

Economic and Control Performance of a Fluid Catalytic Cracking Unit: Interactions between Combustion Air and CO Promoters Rui Wang, Xionglin Luo,* and Feng Xu Research Institute of Automation, China University of Petroleum, Beijing 102249, China ABSTRACT: The presence of CO combustion promoters significantly affects the heterogeneous CO combustion in the regenerator of a fluid catalytic cracking (FCC) unit. Neglecting the quantitative correlation between the heterogeneous CO combustion and the amount of added CO combustion promoters in the previous models makes it impossible to predict the steady-state and the dynamic behaviors of the system with respect to the CO combustion promoters. Therefore, an augmented dynamic model of an FCC unit with high-efficiency regenerator incorporating the quantitative correlation between heterogeneous CO combustion and the CO combustion promoters is developed, and the corresponding closed-loop dynamic responses are obtained. Since CO combustion in the regenerator is affected by both the combustion air flow rate and the CO combustion promoters, a sensitivity analysis of some important variables related to the combustion air flow rate and the amount of added CO combustion promoters is carried out and the overall operating map of the system is developed by selecting the conversion of the riser, the integrated absolute errors of the controllers, and the temperature rise between the dense bed and the outlet of the freeboard to represent the concerns of economics, control, and safety.

1. INTRODUCTION Fluid catalytic cracking (FCC) is one of the most important processes in a refinery to convert low-value heavy oil feedstock into more valuable lighter products, for example, naphtha, diesel, and liquefied petroleum gas. Therefore, the FCC unit is highly expected to operate near the optimal operating condition with respect to economics. However, the optimal operating condition determined by steady-state optimization does not always guarantee the control performance because of the complex physical dynamic nature. As a result, to evaluate the performance of the operating condition, both economics and control should be considered by using an appropriate dynamic model. During the past several decades, numerous articles on FCC mechanistic modeling have been presented to describe its transient behaviors,1−14 steady-state multiplicities,15−19 control analysis,9,10,20−27 and optimization strategies.28−31 A recent review presented by Pinheiro and co-workers32 has given a detailed introduction of these models. As opposed to the riser part of the FCC unit, the behavior of the regenerator part dominates both steady-state and dynamic behaviors of the system because the heat released by coke burning and CO combustion directly dominates the conversion of the riser, and the residence time of the catalysts in the regenerator is considerably longer than that in the riser. Therefore, coke burning and CO combustion in the regenerator are important with respect to the concerns of economics and control. The heat released by coke burning and CO combustion in the regenerator, on the other hand, is a strong function of the flue gas composition, which is also an essential concern of afterburning in the dilute phase (also known as the freeboard) of the regenerator since a high CO content in the flue gas under complete combustion or a high oxygen content under partial combustion results in a sharp temperature rise in the freeboard or cyclone. Afterburning can be a major problem: the amount of coke burned in the © 2013 American Chemical Society

regenerator is limited by the afterburning temperature constraint. This can detrimentally influence the conversion and throughput of the FCC process.33 To overcome this afterburning problem, most, if not all, FCC units throughout the world tend to use CO combustion promoters.34 However, most studies17,21,23,24,35 related to the control of the flue gas composition have considered using only the combustion air flow rate and have ignored the significant correlation between the flue gas composition and the amount of added CO combustion promoters. Furthermore, most commercial combustion promoter additives contain between 300 and 800 ppm of platinum, supported on alumina or mixed oxides,36 which may also affect the operating cost to a certain extent. Hence, the study of the steady-state and dynamic behaviors with various amounts of added CO combustion promoters is a fundamental step in the reduction of the consumption of CO combustion promoters containing noble metals. Several dynamic models of FCC unit have considered CO combustion in both homogeneous and heterogeneous phases. In the model proposed by Arbel et al.,3 the heterogeneous CO combustion is correlated with the CO promoter by introducing a factor xpt to represent the relative combustion rate. However, the quantitative correlation between the relative combustion rate and the amount of added CO combustion promoters is not mentioned. The model proposed by Secchi et al.8 thereafter adopts the same method to simulate the relative heterogeneous combustion rate, but even this model does not consider the above-mentioned quantitative correlation. Further, the models proposed by Ali et al.,4 Arandes et al.,5 Han et al.,6 and Hernandez-Barajas et al. 18 adopt the kinetics of the Received: Revised: Accepted: Published: 287

June 5, 2013 November 29, 2013 December 1, 2013 December 2, 2013 dx.doi.org/10.1021/ie401777n | Ind. Eng. Chem. Res. 2014, 53, 287−304

Industrial & Engineering Chemistry Research

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schematic diagram of the FCC unit with high-efficiency regenerator is given in Figure 1.

heterogeneous CO combustion proposed by Morley and de Lasa37,38 in the absence of the amount of added CO combustion promoters. Later, in the works of Fernandes et al.,12,13,19 the rate expression adopted for the CO heterogeneous combustion is obtained from a technical report by IFP and is also not quantitatively correlated to the amount of added CO combustion promoters. The models proposed by Jia et al.10 and Gupta et al.11 also considered the heterogeneous CO combustion, but the kinetics adopted is not quantitatively correlated to the amount of added CO combustion promoters. The kinetics of CO combustion in the presence of platinum as catalysts has been discussed considerably in some articles.39−43 However, most of these studies focus mainly on the reaction mechanisms under relatively low temperature and pressure conditions as compared to the conditions in the regenerator. Thus, these kinetic models cannot be directly incorporated into the modeling of the heterogeneous CO combustion in the regenerator. To investigate the kinetics of the heterogeneous CO combustion under the operating conditions of the regenerator in the FCC unit, Liu et al.44,45 performed a series of experiments and determined the kinetics of CO oxidation using new Pt/Al2O3 promoters from the industry. In addition, these authors determined the reaction orders of carbon monoxide and oxygen to be 1 and 0.5 when excess oxygen is used. In the reaction rate expressions proposed, the reaction rate is quantitatively and directly correlated with the amount of added CO combustion promoters. Later, Liu et al.45 studied the heterogeneous CO combustion kinetics over the Pt/Al2O3 promoters that had been running in the regenerator; they found that the reaction orders of CO and O2 are as the same as that in the case of new promoters. However, it was only 9.36− 13.26% of the activity of the new Pt/Al2O3 promoters, which was attributed to the hydrothermal deactivation by these authors. This work aims to incorporate the kinetic model of heterogeneous CO combustion that is quantitatively correlated to the amount of added CO combustion promoters into the mechanistic model of an FCC unit and to investigate the roles of the combustion air flow rate and the CO combustion promoters in coke burning and CO combustion in the regenerator. Moreover, after these investigations, an overall operating map of the system will be presented with respect to both economics and control. The rest of this paper is organized as follows: A brief introduction of the base model of an FCC unit with highefficiency regenerator is given in section 2. Section 3 describes the model development so as to incorporate the modeling of CO combustion and freeboard into the overall FCC unit model. Further, the closed-loop dynamic responses are discussed in section 3. In section 4, the impact of the interactions between combustion air and CO promoters on the economic and control performance is thoroughly discussed in order to determine the overall operating map of the system.

Figure 1. Schematic diagram of FCC unit with high-efficiency regenerator.

2.1. Reactor. The reactor can be divided into two main parts: a riser reactor where the cracking reactions occur and a stripper where the products and the catalysts are separated. 2.1.1. Riser. The riser in the base model is modeled as an adiabatic plug flow reactor neglecting axial back-mixing and radial diffusion. The mass and heat balance of the gas and the solid phases is carried out under the following assumptions: (1) There exist no mass and heat transfer resistances between the gas and the solid phases. (2) The yields of the products and the coke content of the spent catalysts are modeled as a pseudosteady state because the residence time of the gas and the solid phases in the riser is only 2−5 s, which is considerably shorter than that in the stripper and the regenerator. However, the dynamics of the reaction temperature is modeled since the heat capacity of the thermal insulating layer significantly affects the heat balance in the riser. (3) The pressure in the riser is uniform. The cracking kinetic model adopts a five-lump model as follows: rA

gas oil(A) → υADdiesel(D) + υAN naphtha(N) + υAG gas(G) + υACcoke(C)

(1)

rD

diesel(D) → υDN naphtha(N) + υDG gas(G) + υDCcoke(C) rN

naphtha(N) → υ NG gas(G)

(2) (3)

All the cracking reactions along with the catalyst deactivation reaction are first-order reactions. 2.1.2. Stripper. The stripper is modeled as a well-mixed tank with the assumption that no further reactions occur because the gases and the solids separate rapidly and efficiently. Hence, only the dynamics of the inventory is considered since it is an important variable for the control of the FCC unit. Moreover, the temperature rise between the outlet of the riser and the stripper is assumed to be constant. 2.2. Regenerator. The high-efficiency regenerator mainly consists of two parts: a combustor where the gases and the solids are fast-fluidized and a dense bed where the gases and the solids are only bubbling-fluidized. Since the high-efficiency

2. BASE MODEL OF FCC UNIT WITH HIGH-EFFICIENCY REGENERATOR The model adopted in this work is derived from the model of an industrial FCC unit with a high-efficiency regenerator under complete combustion as proposed by Luo et al.,46,47 Wei et al.48,49 Here, a short description of each part is given, and the details of this base model are given in the Appendix. A 288

dx.doi.org/10.1021/ie401777n | Ind. Eng. Chem. Res. 2014, 53, 287−304


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regenerator is generally designed with excess air to guarantee the fast fluidization in the combustor, the base model assumes that no CO exists in the regenerator in the presence of a substantial amount of CO combustion promoters. Thus, the reactions in the regenerator simply include the following: C + O2 → CO2 H+

1 1 O2 → H 2O 4 2

R es =

Ar =

(5)

dWrg1 dt

Z0 = 0.01205 exp[9.586(ε* − εa)]

(9)

18R es + 2.7R es1.687 Ar

(13)

= GCst + GCrg21 − GCrg1

GCrg1Θrg1 πDT2 Wrg1 4

= 7.8 × 10−4

(14)

exp(1 − Zi) Fr1.25 exp(1 − Zi) + 1

⎡ ⎤−0.42 G ⎢ Crg1 ⎥ ×⎢ 2 ut 0.21DT−0.45 ⎥ πD T ⎢⎣ 4 ρs ut ⎥⎦

(15)

where ut and Fr denote the terminal velocity of the catalyst and the Froude number calculated as follows: ut = Fr =

g (ρs − ρg MWg)dp 2 18μg

(16)

us − ut gdp

(17)

Hence, the combustor is modeled as a fast bed considering the axial back-mixing while neglecting the radial dispersion. In addition to the assumptions above, the model also supposes the hydrogen−carbon molar ratio η to be constant and neglects the impact of coke burning on the gas phase molar flow rate and physical properties. 2.2.2. Dense Bed. The dense bed of the high-efficiency regenerator differs considerably from the dense bed of a general counter-current regenerator because the air introduced to the dense bed of the high-efficiency regenerator only assures the incipient fluidization, which results in a shallow bed. Hence, the dense bed is modeled as a continuously stirred tank reactor (CSTR) in the base model. Apart from the assumptions above, the regenerated catalysts from the combustor is not assumed to contain any hydrogen because the reaction rate of hydrogen is higher than that of

(10)

The dimensionless numbers Ra, Res, and Ar shown in the equations above are as follows: Ra =

μg2

where GCst, GCrg21, and GCrg1 denote the spent catalyst circulation rate, catalyst recirculation rate and catalyst circulation rate at the outlet of the combustor, respectively. The catalyst circulation rate at the outlet of the combustor GCrg1 can be determined by the experiment of a cold-flow unit of fast fluidized bed proposed by Kato et al.54 and the empirical correlation is as follows:

(7) (8)

⎧ ⎡ ε ̅ − εa ⎤ ⎫ ⎪ 1 − exp⎣⎢ Z0(ε * −εa) ⎦⎥ ⎪ ⎬ Zi = 1 − Z0 ln⎨ ⎪ exp⎡ ε ̅ − ε * ⎤ − 1 ⎪ ⎭ ⎩ ⎣⎢ Z0(ε * −εa) ⎦⎥

d p3ρg MWg(ρs − ρg MWg)

(6)

ε* = 1.28897R a 0.029578R total −0.10645

(12)

where ρs and ρg denote the densities of the catalyst particles and the gas phase, respectively; dp represents the average diameter of the catalyst particles; μg indicates the viscosity of the gas phase; MWg denotes the average molecular weight of the gas phase; ug and us represent the superficial gas velocity and the catalyst velocity, respectively; Rtotal denotes the mass flow rate of catalysts; ε̅ = 1 − ρ̅/ρs indicates the average porosity; ρ̅ = Wrg1)/Θrg1 represents the average density of the combustor, and Θrg1 denotes the total volume of the combustor. The dynamics of the catalyst inventory in the combustor Wrg1 can be expressed as follows:

where Z denotes the normalized height of the combustor, Z = z/zT; zT is the total height of the combustor; and ε is the porosity at Z. εa and ε* represent the porosities of the bottom and the top of the combustor, respectively; and Zi and Z0 denote the positions of the inflection point and the characteristic length, respectively. These parameters can be determined from the plant data, and the empirical correlations of the base model can be described as follows:53 εa = 0.060422R a −1.4548R total1.2167

μg

(4)

Moreover, the base model assumes that only the separation of the flue gas and the catalysts occurs in the freeboard, which is not modeled. Further, the coke burning in the lift is neglected since the velocities of the gases and the solids are significantly high, resulting in a very short residence time. 2.2.1. Combustor. As opposed to the model developed by Fernandes et al.12−14,19 in which the back-mixing along the combustor and the dynamics of the inventory of the combustor are neglected because the upper part of the combustor where most of the combustion reactions take place is modeled as a plug-flow reactor while mass and energy equilibrium are considered to be reached instantaneously in the lower part, the base model considers the axial back-mixing along the combustor and the dynamics of the catalyst inventory of the combustor on the basis of the theory of fast fluidization. As to the fast fluidization in the combustor, the KuniiLevenspiel model50 is no longer suitable since the bubbles disappear in the bed. According to Li et al.,51,52 the porosity of the fast-fluidized bed is shaped as an “S” in the axial direction, which implies that the bottom of the bed is in a dense phase while the top is in a dilute phase. The porosity profile of the fast bed can be calculated as follows: ε − εa 1 ln = − (Zi − Z) ε* − ε Z0

d pρg (ug − us)

(11) 289



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carbon. Moreover, the product of coke burning is only CO2 in the presence of a considerable amount of CO combustion promoters, which is similar to the assumption of the combustor.

[ρs (1 − εrg1)Cps + ρg εCpg ] ∂Trg1 ∂zrg1

3. MODEL DEVELOPMENT OF THE FCC UNIT IN THE PRESENCE OF CO COMBUSTION PROMOTERS To investigate the CO combustion in the regenerator, a detailed CO combustion model is developed in this study quantitatively taking into account the CO combustion promoters. The freeboard of the regenerator is also modeled since the temperature rise in this region is the main predictor of CO afterburning. 3.1. CO Combustion in Regenerator. Since the coke deposited on the spent catalysts is supposed to be composed of carbon and hydrogen, the reactions in the combustor include the following: C+

CO + CO + H+

r2g

1 O2 → CO2 2 r2s

1 O2 → CO2 2

Vair,rg2(yi,inlet − yi,rg2 ) = GCrg1(Crg1|Z = 1 − Crg2)υij −

[ρs (1 − εrg2)Cps + ρg εrg2Cpg ] =

(20)

β = 11.06 × 10−3 exp(33750/(RT ))

+

⎛ −5.6 × 104 ⎞ 0.5 1.5 r2s = 2.19 × 106 exp⎜ ⎟c PtxproηPtyCO yO p 2 RT ⎝ ⎠ (24)

where cPt, xpro, and ηPt denote the content of platinum in the CO combustion promoters, which is 500 ppm on average; the amount of added CO combustion promoters (i.e., the concentration of CO promoters in the catalyst inventory); and the equilibrium activity of the CO combustion promoters, which is 11% on average, respectively. 3.1.1. Combustor. The gaseous species molar balance and heat balance in the combustor are modified from the base model as follows:

ρg εrg1

ρg εrg2

−

ρs (1 − εrg2) Wrg2

dTrg2 dt

[GCrg1Cps(Trg1|Z = 1 − Trg2)

ρs (1 − εrg2) Wrg2

GCrg1(Crg1|Z = 1 − Crg2)( −ΔH1) (28)

3.2. Modeling of the Freeboard. The temperature rise in the freeboard is a key variable related to CO afterburning. The solids in the freeboard of the high-efficiency regenerator are mainly composed of the catalysts that are not separated in the cyclone at the top of the combustor lift but not the catalysts from the dense bed since the dense bed of the high-efficiency regenerator is only operated near incipient fluidization. In contrast to the freeboard of the general counter-current regenerator, the presence of the catalysts is neglected, and the freeboard is modeled as a gaseous homogeneous plug-flow reactor in a pseudosteady state. The flue gas content mixing from the combustor and the dense bed at the inlet of the freeboard is calculated by the following equation:

(23)

dzrg1

g s υij[r2,rg2 + r2,rg2 ρs (1 − ε)]

g s + [r2,rg2 + r2,rg2 ρs (1 − εrg2)]( −ΔH2)

(22)

1.26 ⎛ −5.6 × 105 ⎞ 0.26 ⎛ p ⎞ ⎟ r2g = 5.56 × 1026 exp⎜ ⎟yCO yO ⎜ ⎝ RT ⎠ 2 RT ⎠ ⎝

ρg εrg1 dzrg1

(26)

+ Vair,rg2Cpg(Tg,inlet − Trg2) − Q loss,rg2]

Apart from the combustion kinetics of the carbon and the hydrogen remaining as the base model, the CO homogeneous combustion kinetics adopts the rate expression proposed by Wei et al.,56 while the CO heterogeneous combustion kinetic model is the one proposed by Liu et al.,44,45 as illustrated by eqs 23 and 24, respectively:

2

− Q loss,rg1

(27)

(21)

ρs (1 − εrg1)

2 ∂zrg1

3.1.2. Dense Bed. The gaseous species molar balance and heat balance in the dense bed are modified from the base model as follows:

(19)

(heterocombustion)

s = −νijrj,rg1

∂ 2Trg1

i = O2 , CO, CO2 ; j = 1, 2, 3

(homocombustion)

d2yi,rg1

+ (λs(1 − εrg1) + λg εrg1)

g s + [r2,rg1 + r2,rg1 ρs (1 − εrg1)]( −ΔH2)

where β denotes the intrinsic molar ratio of CO2/CO, which adopts the following correlation proposed by Xu et al.:55

− Dg

= −(R totalCps + R gCpg)

(18)

r3s 1 1 O2 → H 2O 4 2

R g dyi,rg1

∂t

s s ( −ΔH1) + r3,rg1 ( −ΔH3)]ρs (1 − εrg1) + [r1,rg1

r1s

2β + 1 β 1 O2 → CO2 + CO 2(β + 1) β+1 β+1

∂Trg1

yi,mix =

Vflue,rg1·yi,rg1|Z = 1 + Vflue,rg2·yi,rg2 Vflue,rg1 + Vflue,rg2

(29)

The gaseous molar balance can be expressed as follows: Rg

dyi,fb dz fb

= υir2g

i = O2 , CO, CO2

(30)

B.C.: yi ,fb |Zfb= 0 = yi ,mix

g νijr2,rg1

(31)

The heat balance can be calculated as follows:

ρg εrg1

i = O2 , CO, CO2 ; j = 1, 2, 3

R gCpg (25) 290

dTfb = r2g( −ΔH2) − Q loss dz fb

(32)


Industrial & Engineering Chemistry Research Q loss =

4k w ΔTw Dfb

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It can be seen that although the regulatory control can bring the controlled variables back to the setting points, the regulatory control of the decreasing CO combustion promoters is not as efficient as that of the increasing CO combustion promoters. Further, when the amount of added CO combustion promoters decreases to a certain low amount, like 0.002 as demonstrated by the simulation, the controllers tend to oscillate severely and take a long time to be stabilized which indicates that the original tunings of the controllers may no longer be suitable for the perturbation of such a decrease in the amount of added CO combustion promoters. The perturbation of the CO combustion promoters has a considerably more intense impact on the performances of the controllers than that of the combustion air flow rate, as indicated by Figures 2 and 3. This may be attributed to the fact that the high-efficiency regenerator is always operated with redundant combustion air, which may result in making the impact of the partial pressure of oxygen less important in the CO combustion. Moreover, the amount of added CO combustion promoters directly affects the CO combustion and the heat balance of the system while the combustion air flow rate only directly affects the fluidization and the catalyst circulation of the system and then indirectly affects the heat balance.

(33)

B.C.: Tfb|Zfb= 0 = Tmix

(34)

where Tmix denotes the temperature of the mixture of the flue gas from the combustor and the dense bed at the inlet of the freeboard. 3.3. Closed-Loop Dynamic Responses of the Augmented Model. The closed-loop dynamic responses of the augmented model with several step tests of the combustion air flow rate and the CO combustion promoters on the basis of the base case operating condition, as shown in Table 1, are Table 1. FCC Unit Base Case Operating Conditions variables

value

units

fresh feed flow rate, Ffresh HCO flow rate, FHCO slurry flow rate, Fslurry regenerated catalyst circulation rate, GCrg2 catalyst to oil ratio, COR combustion air flow rate, Vair,rg1 fluffing air flow rate, Vair,rg2 amount of added CO combustion promoters, xpro inventories, W (combustor/dense bed/stripper) reaction temperature, Triser combustor top temperature, Trg1|Z=1 dense bed temperature, Trg2 coke content of spent catalysts, Csc coke content of regenerated catalysts, Crg2 O2 content in flue gas, yO2,fb

85 12.75 7.25 507.7 4.84 49340 6658 0.004

t/h t/h t/h t/h wt/wt m3/h m3/h wt%

24/5/5 493 691.8 700.2 0.948 0.048 3.58

t °C °C °C wt% wt% mol %

CO content in flue gas, yCO,fb CO2 content in flue gas, yCO2,fb

0.24 13.70

mol % mol %

4. IMPACT OF THE INTERACTIONS BETWEEN COMBUSTION AIR AND CO PROMOTERS ON THE ECONOMIC AND CONTROL PERFORMANCE The results obtained from the closed-loop dynamic responses discussed above predict that the combustion air and the CO combustion promoters play different roles in the coke burning and CO combustion in the regenerator. The impact of the interactions between these two variables on the economic and control performance is, thus, promising with respect to a reduction of the cost of the system. 4.1. Sensitivity Analysis of the Process. To further investigate the impact of the combustion air flow rate and the CO combustion promoters on coke burning and CO combustion, a sensitivity analysis was carried out, as illustrated in Figure 4, for different combustion air flow rates and amounts of added CO combustion promoters on the basis of the augmented FCC unit model under regulatory control. As illustrated in Figure 4a, the regenerator temperature decreases as the combustion air flow rate increases; this is mainly because the increasing excess combustion air may decrease the residence time of the catalysts in the regenerator and function as a type of coolant to deteriorate the coke burning. On the other hand, from the viewpoint of the CO combustion promoters, the regenerator temperature increases with an increase in the amount of the added CO combustion promoters since more heat is provided by the CO combustion. Figure 4b shows the coke content of the regenerated catalysts in the dense bed and at the outlet of the combustor; here, it can be seen that the coke content tends to decrease to a certain level since the oxygen partial pressure increases with a considerable amount of excess combustion air although the regenerator temperature decreases in the meanwhile. The catalyst-to-oil ratio (COR) is directly controlled by the heat balance between the riser and the regenerator in the presence of the reaction temperature controller. It can be seen from Figure 4c that COR increases as the combustion air flow rate increases; on the other hand, it decreases as the CO combustion promoters increases. Moreover, the conversion in

obtained. The five controllers of the system are the regenerated catalyst slide valve, spent catalyst slide valve, recirculation slide valve, the steam injected to the wet gas compressor turbine and the flue gas slide valve controlling the riser temperature, catalyst inventory in the stripper, catalyst inventory in the dense bed, reactor pressure, and the pressure difference between the reactor and the regenerator. After the system was stabilized under the base case operating condition, the step tests of the combustion air flow rate were performed as illustrated in Figure 2, where the combustion air flow rate was first increased to 54 000 m3/h, which is the limit of the capacity of the air compressor at 2000 s, then decreased to 49 340 m3/h at 7000 s, and then decreased again to 44 000 m3/h at 12 000 s. It can be seen that the regulatory control can bring the controlled variables back to the setting points efficiently. Moreover, the dynamic responses of flue gas contents are illustrated in Figure 2d, which reveals that the CO combustion is significantly affected by the combustion air flow rate under the regulatory control. On the other hand, the CO combustion is directly affected by the amount of added CO combustion promoters. Hence, the step tests of the amount of added CO combustion promoters were performed as illustrated in Figure 3. The amount of added CO combustion promoters was first increased to 0.005 at 2000 s, then decreased to 0.004 at 7000 s, then decreased again to 0.003 at 12000 s and then finally decreased to 0.002 at 17000 s. 291



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Figure 2. Closed-loop dynamic responses of step tests of combustion air flow rate: (a) temperature, (b) pressure, (c) catalyst inventory, and (d) flue gas content.

the riser is directly determined by the temperature along the riser, COR, and the relative activity of the catalysts as indicated by eq A1. Hence, although the reaction temperature at the outlet of the riser is controlled, the conversion increases because of the relatively high COR and low coke content of the regenerated catalysts as illustrated in Figure 4d. As opposed to the behavior of the riser reactor, the CO combustion in the regenerator is illustrated in Figure 4e; here, it can be observed that the CO content at the inlet of the freeboard decreases to a certain level as the combustion air flow rate increases, and it decreases as the amount of added CO combustion promoters increase. On the other hand, the CO content at the outlet of the freeboard varies considerably more severely as the combustion air flow rate increases, which is mainly attributed to the fact the CO homocombustion in the freeboard is closely related to the oxygen content and the gas superficial velocity. 4.2. Operating Map with Respect to Economics and Control. From the sensitivity analysis and the closed-loop dynamic responses of the system above, it can be observed that both the combustion air flow rate and the CO combustion promoters significantly affect the economic and control performance of the process. Hence, the operating map with respect to the interactions between the combustion air flow rate

and the amount of added CO combustion promoters is studied further. Since the FCC unit is one of the main supplies of high-value oil products, the conversion of the riser reactor is an essential concern for most refineries. Therefore, the economic performance can generally be indicated by the conversion of the riser reactor, which is illustrated in Figure 5. As also indicated by Figure 4d, although both the combustion air flow rate and the CO combustion promoters affect the conversion, the impact of the combustion air flow rate seems to be more significant. This is mainly because the catalyst circulation rate at the outlet of the combustor (GCrg1) is directly correlated to the combustion air flow rate on the basis of the fluidization of the combustor as indicated by eq 15, which sequentially affects the COR that directly affects the conversion. Figure 6 illustrates the contour of the three catalyst circulation rates in the regenerator related to the combustion air flow rate and the CO combustion promoters, which are the catalyst circulation rate at the outlet of the combustor (GCrg1), regenerated catalyst circulation rate (GCrg2), and the catalyst recirculation rate (GCrg21). It can be seen that the catalyst circulation rate at the outlet of the combustor (GCrg1) is not related to the amount of added CO combustion promoters, and the catalyst recirculation rate (GCrg21) changes correspondingly when the combustion air flow 292



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Figure 3. Closed-loop dynamic responses of step tests of CO combustion promoters: (a) temperature, (b) pressure, (c) catalyst inventory, and (d) flue gas content.

rate varies since the inventory of the dense bed is controlled by the catalyst recirculation rate (GCrg21). After these responses, the regenerated catalyst circulation (GCrg2) varies correspondingly in order to maintain the reaction temperature. However, the regenerated catalyst circulation (GCrg2) is more sensitive to the CO combustion promoters, particularly when the combustion air flow rate is low, which is mainly because the coke combustion deteriorates significantly at low combustion air flow rates as indicated by the coke content in Figure 4b. This makes the heat provided by heterogeneous CO combustion much more important in sustaining the heat balance of the riser and regenerator. However, it is essential to identify that the magnitude of the regenerated catalyst circulation (GCrg2) is considerably smaller than that of the catalyst circulation rate at the outlet of the combustor (GCrg1) and the catalyst recirculation rate (GCrg21). As the conversion of the base case operating condition is close to 80, the conversion under 80 is then considered to be less economic, which should be avoided from the viewpoint of economics, as illustrated by the shaded region in Figure 5. On the other hand, to investigate the impact of the two variables on the control performance, the integrated absolute errors (IAE) of the five controllers are calculated on the basis of

a perturbation of a 5% step increase of fresh feed as illustrated by eq 35: IAE =

∫0

tf

|e(t )| dt

(35)

For the sake of brevity, only the contour of the IAE of the controller for the riser reaction temperature is illustrated in Figure 7, which shows that a relatively high amount of CO combustion promoters may be better at resisting the perturbation, while a considerably high or considerably low combustion air flow rate may be less resistant to the perturbation. As shown in Figure 3 in section 3.3, when the amount of added CO combustion promoters is close to 0.002, the performance of the controllers severely oscillates. Therefore, the contour of the IAE only considers the amount of added CO combustion promoters as low as 0.0025. With respect to the performance of the controllers, the operating region with IAE higher than 150 is considered to be difficult to control, as illustrated by the shaded region in Figure 7. Because of the changes in the catalyst circulation rate, the regenerator temperature in the dense bed changes correspondingly as illustrated in Figure 8. It can be seen that the contour of the regenerator temperature in the dense bed has a similar shape as that of the regenerated catalyst circulation rate but has 293



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Figure 4. Sensitivity analysis of combustion air flow rate and CO combustion promoters: (a) regenerator temperature, (b) coke content, (c) COR, (d) conversion, and (e) CO content.

the opposite trend in values to that of the regenerated catalyst circulation rate.

Since the augmented model concerns the amount of added CO combustion promoters, the CO contents in both the 294



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Figure 5. Contour of conversion in riser with respect to combustion air flow rate and CO combustion promoters.

Figure 7. Contour of IAE of the reaction temperature controller with respect to combustion air flow rate and CO combustion promoters.

Figure 6. Contour of catalyst circulation with respect to combustion air flow rate and CO combustion promoters.

Figure 8. Contour of temperatures in dense bed and freeboard with respect to combustion air flow rate and CO combustion promoters.

combustor and the freeboard are significant indices along with the temperature rise in the freeboard. From Figure 8, it can also be seen that the contour of the temperature at the outlet of the freeboard does not vary with the same trend as that of the regenerator temperature. This is mainly because CO combustion in the freeboard behaves very differently from that in the combustor and the dense bed in the presence of the CO combustion promoters as demonstrated by the contour of the CO contents in the flue gas at the outlet and the inlet of the freeboard in Figure 9. It can be seen that the CO content mixed at the inlet of the freeboard is significantly related to the amount of added CO combustion promoters and almost unrelated to the combustion air flow rate, which is in accordance with the analysis of Figure 4e. On the other hand, the CO content at the outlet of the freeboard is significantly affected by the regenerator temperature and the partial pressures of CO and O2 along with the residence time of the flue gas in the freeboard. From Figures 8 and 9, it can be seen that large amounts of CO combustion promoters can always guarantee a low temperature at the outlet

of the freeboard and a low CO content in the flue gas because of the already sufficiently low CO content at the inlet of the freeboard. However, in the range of a small amount of added CO combustion promoters, the impact of the combustion air flow rate on the temperature in the freeboard and the CO content in the flue gas turns equally significant. The temperature at the outlet of the freeboard increases and the CO content at the outlet of the freeboard decreases with a decrease in the combustion air flow rate, because the CO content at the inlet of the freeboard is relatively high and the gas residence time in the freeboard is relatively long, which result in more CO combustion. Basically, the temperature rise along the freeboard is used for predicting the CO afterburning in the freeboard. However, the temperature at the inlet of the freeboard in a high-efficiency regenerator usually differs from that of the general ones, because the combustion air injected into the combustor is directly transferred into the freeboard without any heat transfer in the dense bed, which may result in a lower temperature at the inlet of the freeboard than the regenerator temperature in 295



Article

Figure 9. Contour of CO content in the freeboard with respect to combustion air flow rate and CO combustion promoters.

Figure 11. Contour of composite operating map with respect to combustion air flow rate and CO combustion promoters.

the dense bed in some circumstances. Since most FCC units always monitor the regenerator temperature in the dense bed but not the temperature at the inlet of the freeboard, the temperature rise between the dense bed and the outlet of the freeboard is chosen to predict the CO afterburning in this study, as illustrated by the contour in Figure 10. Here, it is

probable optimal operating region lies in the upper left part of the map. In the probable optimal operating region, the higher the combustion air flow rate is, the higher is the conversion, the higher is the IAE of the controllers, and the higher is the temperature rise in the freeboard region. On the other hand, the more the CO combustion promoters are charged, the higher is the conversion, the lower is the IAE of the controllers, and the lower is temperature rise in the freeboard region. Although a higher combustion air flow rate and a larger amount of added CO combustion promoters will favor the economic and control performance of the system, the higher combustion air flow rate will consume more power of the air compressor and the larger amount of CO combustion promoters will consume more precious metals like platinum. Therefore, to achieve the optimized operating condition, the integrated design of economics and control of the system by dynamic simulation may be favored in the future. In this study, we have attempted to investigate the integral economic and control performance of an FCC unit with highefficiency combustor under the condition of nearly complete combustion in the presence of CO combustion promoters. This investigation can also be applied to account for the integral performance of the FCC units with other types of regenerators in the presence of CO combustion promoters under the condition of either nearly complete combustion or partial combustion.

Figure 10. Contour of temperature rise in the freeboard with respect to combustion air flow rate and CO combustion promoters.

5. CONCLUSIONS In this study, an augmented dynamic model of an FCC unit with high-efficiency regenerator is developed in order to quantitatively investigate CO combustion in the presence of CO combustion promoters. From the closed-loop dynamic responses of the step tests of the combustion air flow rate and the amount of added CO combustion promoters, it is observed that the perturbation of CO combustion promoters has a considerably more intense impact on the performances of the controllers than the combustion air flow rate because of the fact that the high-efficiency regenerator is always operated with redundant combustion air, which may result in making the impact of the partial pressure of oxygen less important in the CO combustion. The sensitivity analysis of certain important

observed that the temperature rise has a similar trend as that of the temperature at the outlet of the freeboard. Therefore, from the perspective of safety, the temperature rise is not supposed to be higher than 15 °C, which can guarantee the temperature of the flue gas entering the cyclone to be below 720 °C, as illustrated by the shaded region in Figure 10. Hence, to depict the operating map of the system, the conversion is selected for addressing the concern of economics, the IAE of the controllers is selected for addressing the concern of control, and the temperature rise between the dense bed and the outlet of the freeboard is selected for addressing the concern of safety. Figure 11 illustrates the overall operating map of the three concerns from which it can be seen that the 296



Article

⎡ ⎛ E ⎞ ∂Cca 1 ∂Cca + = ⎢υACkA0 exp⎜ − A ⎟ ∂t ST ∂X ⎝ RTra ⎠ ⎣⎢

variables related to the combustion air flow rate and the CO combustion promoters is then conducted to depict the overall operating map. Among these variables, the conversion of the riser, the IAE of the controllers, and the temperature rise between the dense bed and the outlet of the freeboard are selected for addressing the concerns of economics, control, and safety, respectively. According to the operating map, it is predicted that too low a combustion air flow rate may deteriorate the conversion of the riser reactor due to the consequent low regenerated catalyst circulation rate; on the other side, too few CO promoters may deteriorate the control performance due to the severe oscillation of the controllers no matter how much combustion air is introduced into the regenerator; further, to guarantee the safety of the operation by avoiding afterburning in the freeboard, neither too low combustion air flow rate nor too few CO promoters are suggested. Therefore, the probable optimal operating region lies in the upper left part of the operating map.

■

⎛ E ⎞ ⎤ + υDCkD0 exp⎜ − D ⎟yD ⎥pra ϕ ⎝ RTra ⎠ ⎥⎦

B.C.: Cca|X = 0 = Crg

⎛ E ⎞ dϕ = −k′ϕ0 exp⎜ − ca ⎟pra ϕ dt C ⎝ RTra ⎠

A.1. Riser

The riser is modeled as an adiabatic plug flow reactor neglecting the axial back-mixing and the radial diffusion. According to the mass and heat balance of the differential element of the riser, the following partial differential algebraic equations are deduced. The yields of the five lumps comprising the reaction mixture in the riser can be determined by the following mass balances: ∂t

+

⎛ FO ⎞⎛ ρOw ⎞ ⎟⎟ tC = STX ⎜ ⎟⎜⎜ ⎝ FO + Fw ⎠⎝ ρOi ⎠

⎛ E ⎞ dϕ = −kϕ0 exp⎜ − ca ⎟pra ϕ dX ⎝ RTra ⎠ ϕ|X = 0 = g (Crg2)

⎡ ⎛ E ⎞ ⎛ E ⎞ ⎤ rD = ⎢υADkA0 exp⎜ − A ⎟yA − kD0 exp⎜ − D ⎟yD ⎥pra ϕ ⎢⎣ ⎝ RTra ⎠ ⎝ RTra ⎠ ⎥⎦ ⎡ ⎛ E ⎞ ⎛ E ⎞ rN = ⎢υANkA0 exp⎜ − A ⎟yA + υDNkD0exp⎜ − D ⎟yD ⎢⎣ ⎝ RTra ⎠ ⎝ RTra ⎠

∂Tra 1 ⎛ 1 ⎞ ∂Tra ⎜ ⎟ + ST ⎝ 1 + Γ ⎠ ∂X ∂t ⎛ Λ ⎞ GCrg2 ⎟ [r ΔH + rDΔHDR + rNΔHNR = −⎜ ⎝ 1 + Γ ⎠ FO A AR

(A4)

⎡ ⎛ E ⎞ ⎛ E ⎞ rG = ⎢υAGkA0 exp⎜ − A ⎟yA + υDGkD0 exp⎜ − D ⎟yD ⎢⎣ ⎝ RTra ⎠ ⎝ RTra ⎠

− (υACrA + υDCrD)ΔHAA ]

yD |X = 0 = 0, yN |X = 0 = 0,

(A14)

B.C.:

(A5)

Tra|X = 0 = FO_iCpO_iTO_i + GCrg2CpsTrg2 + Cp wFwTw − FO_iΔHV_i

B.C.: yA |X = 0 = 1,

(A13)

where g(·) denotes the initial relative activity of the regenerated catalysts at the bottom of the riser which is correlated with the coke content on the regenerated catalysts. For the highefficiency regenerator, this initial relative activity was supposed to be unity. The reaction temperature followed the heat balance and can be expressed as follows:

(A3)

⎛ E ⎞ ⎤ exp⎜ − N ⎟yN ⎥pra ϕ ⎝ RTra ⎠ ⎥⎦

(A12)

B.C.:

(A2)

⎛ E ⎞ ⎤ − kN0 exp⎜ − N ⎟yN ⎥pra ϕ ⎝ RTra ⎠ ⎥⎦

(A11)

Hence, the deactivation function can be expressed as follows:

(A1)

where ⎛ E ⎞ rA = −kA0 exp⎜ − D ⎟pra ϕ ⎝ RTra ⎠

(A10)

Define the new reaction rate constant as follows: ⎛ FO ⎞⎛ ρOw ⎞ ⎟⎟k′ϕ0 k ϕ0 = S T⎜ ⎟⎜⎜ ⎝ FO + Fw ⎠⎝ ρOi ⎠

i = A(gas oil), D(diesel), N(naphtha), G(gas)

(A9)

where tC denotes the gas-solid contact time which can be correlated with the dimensionless riser length X as follows:

⎛ GCrg2 ⎞ 1 ∂yi =⎜ ⎟ri ,ra , ST ∂X ⎝ FO ⎠

+ υ NGkN0

(A8)

The coke deposited on the catalysts also includes CCR coke resulting from thermal decomposition, which is mainly not formed at a catalytic site apart from the catalytic coke, determined above. The catalyst deactivation function in the equations above is determined by the following equation with the assumption that the activation energy of deactivation of the catalysts equals the activation energy of coke formation:

APPENDIX: BASE MODEL DESCRIPTION

∂yi

(A7)

yG |X = 0 = 0

FO_iCpO_i + GCrg2Cps + Cp wFwTw

(A6)

i = fresh, hco, slurry

The catalytic coke resulting from catalytic cracking reactions can be calculated from the five-lump kinetic model as follows:

(A15) 297



Article

where Γ and Λ denote the heat capacity correction coefficient for the effects of thermal insulating layer and the reaction temperature, respectively:

R totalC ps + R gC pg ∂T ∂T =− ∂t ρs (1 − ε)C ps + ρg εC pg ∂z

ρL Ω LCpL

+

ρOi Ω ra

Γ= CpO +

GCrg2

( )C + ( )C Fw FO

ps

FO

pw

CpO +

GCrg2

( )C + ( )C FO

Fw FO

ps

pw

pyO ρs (1 − ε) ⎤ ⎛ E ⎞ 2 + kH0 exp⎜ − C ⎟H( −ΔHH)⎥ ⎝ RT ⎠ ⎦ ρ (1 − ε)Cps + ρ εCpg

(A17)

s

4k w ΔTw − DT[ρs (1 − ε)Cps + ρg εCpg ]

A. 2. Stripper

The dynamics of catalyst inventory is determined as follows:

dWst = GCrg2 − GCst dt

Pes =

β ⎡ + st ⎢FO_freshCCR O_fresh GCrg2 ⎢⎣

Peg =

⎞ ⎛ D1 yA |X = 1⎟CCR O_hco + ⎜FO_hco − FO D1 + D2 ⎠ ⎝ ⎤ ⎞ ⎛ D2 yA |X = 1⎟CCR O_slurry ⎥ + γ + ⎜FO_slurry − FO ⎥⎦ D1 + D2 ⎠ ⎝

ug =

ugZ T Dg (R totalCps + R gCpg)Z T λs(1 − ε) + λg ε

ρg ε

pyO CzT ρs (1 − ε) ⎤ 2 ⎥ ⎥⎦ R total

(A22)

+

ρg ε dz

dz 2

⎡k ⎛ E ⎞ − ⎢ C0 exp⎜ − C ⎟C ⎝ RT ⎠ ⎣ 12

⎛ E ⎞ ⎤ pyO ρs (1 − ε) kH0 exp⎜ − H ⎟H ⎥ 2 ⎝ RT ⎠ ⎦ 4 ρg ε

(A29)

(A30)

⎡ ⎞ ⎛ 2 R total ∂H ⎢ − ∂H + 1 ∂ H − k exp⎜ − E H ⎟ = H0 ⎜ RT ⎟ ∂t ρs (1 − ε)zT ⎢⎣ ∂Z Pes ∂Z2 ⎝ rg1 ⎠

⎛ E ⎞ R total ∂H ∂ 2H ∂H =− + Ds 2 − kH0 exp⎜⎜ − H ⎟⎟pyO H ∂t ρs (1 − ε) ∂z ∂z ⎝ RTrg1 ⎠ 2

2

(A28)

Rg

⎛ E ⎞ pyO CzT ρs (1 − ε) ⎤ ⎥ − k C0 exp⎜⎜ − C ⎟⎟ 2 ⎥⎦ RT R ⎝ rg1 ⎠ total

(A21)

d 2yO

(A27)

⎡ 2 R total ∂C ⎢ − ∂C + 1 ∂ C = ∂t ρs (1 − ε)z T ⎢⎣ ∂Z Pes ∂Z2

⎛ E ⎞ R total ∂C ∂C ∂ 2C =− + Ds 2 − k C0 exp⎜⎜ − C ⎟⎟pyO ∂t ρs (1 − ε) ∂z ∂z ⎝ RTrg1 ⎠ 2

+ Dg

(A26)

Hence, the mass and heat balances are described by the following equations after the normalization of the combustor height:

(A20)

The combustor of the base model is modeled as a fast fluidized bed considering the axial back-mixing while neglecting the radial dispersion. According to the mass and heat balance of the differential element of the combustor, the following partial differential algebraic equations are deduced (for the sake of conciseness, the subscript rg1 of each variable is omitted):

R g dyO2

(A25)

R total ρs (1 − ε)

us′ =

A.3. Combustor

0=−

(A24)

where

where Cca|X=1 denotes the catalytic coke at the outlet of the riser, βst is the ratio of the CCR of the feed converts to coke, and γ is the amount of unstripped hydrocarbon which depends on the stripping condition. As the temperature rise between the outlet of the riser and the stripper is assumed to be constant, the temperature at the outlet of the stripper is simply described as follows:

C

us′Z T Ds

Peh =

(A19)

Tst = Tra|X = 1 − ΔTst

g

Define gas and solid phase mass and heat Peclect numbers as follows:

(A18)

The coke deposited on the spent catalysts at the outlet of the stripper can be expressed as follows: Csc = Cca|X = 1

∂ 2T ρs (1 − ε)C ps + ρg εC pg ∂z 2

⎡ ⎛ E ⎞ + ⎢kC 0 exp⎜ − C ⎟C( −ΔHC) ⎝ RT ⎠ ⎣

(A16)

1

Λ=

λs(1 − ε) + λg ε

(A31)

2 ⎡k ⎛ E ⎞ 1 d yO2 0=− + − ⎢ C0 exp⎜ − C ⎟C 2 ⎝ RT ⎠ ⎣ dZ Peg dZ 12

dyO

2

+ (A23) 298

⎛ E ⎞ ⎤ pyO ρs (1 − ε)z T kH0 exp⎜ − H ⎟H ⎥ 2 ⎝ RT ⎠ ⎦ 4 Rg

(A32)



Article

⎧ R totalCps + R gCpg ⎪ ∂T 1 ∂ 2T ∂T ⎨ =− + [ρs (1 − ε)Cps + ρg εCpg ]zT ⎪ Peh ∂z 2 ∂t ⎩ ∂z −

⎡ ⎛ E ⎞ 4k w ΔTwzT + ⎢k C0exp⎜ − C ⎟C(−ΔHC) ⎝ RT ⎠ DT(R totalCps + R gCpg) ⎣

+ kH0

us − ut

Fr =

gdp

(A45)

A.4. Dense Bed

The dense bed is modeled as a CSTR taking into account the external diffusion of the gas phase, due to the comparatively low superficial gas velocity. The mass transfer rate in the gas film on the catalyst surface can be described as follows:

⎤ PyO2 ρs (1 − ε)z T ⎫ ⎪ ⎛ E ⎞ ⎬ exp⎜ − H ⎟H(−ΔHH)⎥ ⎪ ⎝ RT ⎠ ⎦ R totalCps + R gCpg ⎭ (A33)

rr = kD(pO ,rg2 − pO , i )

B.C.:

2

C|Z = 0 = C0′ +

1 ∂C Pes ∂Z

H |Z = 0 = H0′ +

1 ∂H Pes ∂Z

yO |Z = 0 = yO′ ,0 + 2

2

T |Z = 0 = T0′ +

1 dyO2 Peg dZ

1 ∂T Peh ∂Z

The combustion rate of carbon can be calculated by using the following equation under the partial pressure of O2 on catalysts pO2,i:

(A34)

rr = k CpO , i Crg2

(A35)

C0′ =

According to the two eqs A43 and A44, the partial pressure of O2 on catalysts pO2,i can be eliminated, and the combustion rate of carbon can be deduced as follows:

(A36)

(A37)

rr =

H0′ =

ηCscGCst (1 + η)(GCst + GCrg21)

yO′ ,0 = yO ,inlet = 0.21 2

H0′ =

2

2

1 kD

dCrg2 (A38)

dt

dt

(A48)

= (Crg1|Z = 1 − Crg2)

2

(A40)

dTrg2 dt

(A41)

GCrg1 Wrg2

−

=

2

prg2 yO ,rg2 2

1 kD

+

1 k CCrg2

(A49)

Crg1|Z = 1 − Crg2 12

(A50)

ρs (1 − εrg 2) [ρs (1 − εrg2)Cps + ρg εrg2Cpg ]Wrg2 [GCrg1Cps(T |Z = 1 − Trg2) + Vrg2CE(Tg,inlet − Trg2) + GCrg1(C|Z = 1 − Crg2)( −ΔHC) − k w ΔTwA rg2]

= GCst + GCrg21 − GCrg1

(A51)

(A42)

The catalyst inventory of the dense bed can be expressed as follows:

where GCrg1 denotes the catalyst circulation rate at the outlet of the combustor which can be determined by an empirical correlation: GCrg1Θrg1 πDT2 Wrg1 4

dWrg2

exp(1 − Zi) = 7.8 × 10−4 exp(1 − Zi) + 1 ⎡ ⎤−0.42 G ⎢ Crg1 ⎥ × Fr1.25⎢ 2 ut0.21DT−0.45 ⎥ πD T ⎢⎣ 4 ρs ut ⎥⎦

dt

(A52)

The pressure balance is essential for FCC unit to ensure the circulation of the catalysts between the riser and the regenerator. Because of the relatively low operating pressure, the pressure of each part is given by the ideal gas law:

(A43)

dp RT dN = dt V dt

g (ρs − ρg MWg)dp 2 18μg

= GCrg1 − GCrg2 − GCrg21

A.5. Pressure Balance

where ut and Fr denote the terminal velocity of the catalysts and the Froude number which can be calculated as follows: ut =

1 k CCrg2

0 = Vrg2(yO ,inlet − yO ,rg2 ) − Grg1

For the catalyst inventory in the combustor, the dynamics can be expressed as follows: dWrg1

+

(A39)

Cps(GCstTst + GCrg21Trg2) + Vrg1CpgTg,inlet Cps(GCst + GCrg21) + Vrg1Cpg

pO ,rg2

According to the mass and heat balances, the following differential equations are deduced:

+ Crg2GCrg21

GCst + GCrg21

(A47)

2

where C0′ , H0′ , y′O2,0 and T0′ denote the corresponding properties of the mixture at the inlet of the combustor and can be determined as follows: Csc G 1 + η Cst

(A46)

2

(A53)

A.5.1. Pressure in the Disengagement Vessel. The pressure in the disengagement vessel is given by

(A44) 299


Industrial & Engineering Chemistry Research dpraf

=

dt

Article

⎡ yD |X = 1 yN |X = 1 ⎪ y |X = 1 RTraf ⎧ ⎨⎢ G + + Vraf ⎪ MWN MWD ⎩⎢⎣ MWG + +

yA |X = 1 MWhco

yA |X = 1

D1 + D1 + D2 MWslurry

H+

− k fra praf (praf

Vflue = Vrg1 + Vrg2 +

(A54)

Vflue,v =

dt

dprgf dt −

dt

=

⎧ RTrgf ⎪ ηC G ⎨Vrg1 + Vrg2 + + sc Cst + Vpuri 4(1 + η) Vrgf ⎪ ⎩ prgf (prgf − patm )

2 (1.5789 × 10−4Cdγdrgf Zrgf )2 Trgf MWflueZ + k flue

+ static pressure of the dilute phase of the disengagement vessel + static pressure of the stripper + static pressure of the spent catalyst standpipe (A63)

(A55)

resistance = pressure at the top of the regenerator + static pressure of the dilute phase of the regenerator

y |X = 1 RTt ⎡ FO ⎢k fra,t pb (pb − pt − Δpt ) − D MWD Vt ⎣ ⎤ pt (pt − Δpsep ) ⎥ ⎦

+ static pressure of the lift + static pressure of the combustor + pressure drop of the slide valve + pressure drop caused by catalyst flow (A64)

(A56)

where

Pressure at the separator: dpsep dt −

=

static pressure of the stripping section =

RTsep ⎡ y |X = 1 FO ⎢k fra,sep pt (pt − Δpsep ) − N Vsep ⎣ MWN

Fw,st + Fw,pre + Fw,atmr 18

− k wgf (Vwg) psep

Wstg Ωst

(A65)

pressure drop of the spent catalyst slide valve

⎤ − pwgc,out ⎥ ⎦

=

(A57)

A.5.3. Pressure in the regenerator. Because of the effect of the considerably large amount of added CO combustion promoters, the reactions in the regenerator simply include the following: C + O2 → CO2

⎫ ⎪ ⎬ ⎪ ⎭

driving force = pressure at the top of the disengagement vessel

⎤ pb (pb − pt − Δpt ) ⎥ ⎥⎦

− k fra,sep

=

(A62)

Pressure at the top: dpt

2 (1.5789 × 10−4Cdγdrgf Zrgf )2 Trgf MWflueZ + k flue

A.5.4. Catalyst Circulation Rates. The catalyst circulation rates can be calculated through the relation that the driving force equals to the resistance. For the spent catalyst slide valve:

RTb ⎡ ⎢k fra p (p − p − Δp ) raf raf t fra Vb ⎢⎣

− k fra,t

prgf (prgf − patm ) (A61)

FO FO D1 D2 yA |X = 1 − y |X = 1 MWhco D1 + D2 MWslurry D1 + D2 A

−

(A60)

where Cd and γ denote the flow coefficient and the expansion coefficient, respectively. According to eq A50

Pressure at the bottom: =

ηCscGCst 4(1 + η)

On the other hand, the amount of flue gas released through the flue gas valve is calculated as follows:

⎫ ⎬ − pt − Δpfra ) ⎪ ⎭ ⎪

where D1 and D2 denote the recycle ratios for heavy cycle oil and slurry, respectively. A.5.2. Pressure in the Fractionator. The pressure in the disengagement vessel is not directly controlled. Instead, it depends on the pressure of the oil−gas separator at the overhead of the main fractionator. The products from the riser are directly introduced to the bottom of the main fractionator and are separated into slurry, heavy cycle oil, diesel, gasoline, gas and water from the bottom to the top of the fractionator. For the sake of simplification, the fractionator was divided into two parts: the top and the bottom divided from the middle of the fractionator between the side stream diesel and heavy cycle oil. Assuming that the pressure of each part was uniform and the effect of the cold reflux was negligible, the pressure of each part can be derived by using the following equations: dpb

(A59)

Hence, the amount of gas increases 1/4 mol per mole coke combusted, and the amount of flue gas produced can be calculated as follows:

D2 ⎤ ⎥FO D1 + D2 ⎥⎦

Fw,st + Fw,pre + Fw,atmr 18

1 1 O2 → H 2O 4 2

2 GCst

ρpipe,st (VstZst)2

× 9722.7

static pressure of the combustor =

(A66)

Wrg1g Ω rg1

pressure drop caused by catalyst flow =

(A58) 300

(A67)

1 k Cst

2 GCst

(A68)



Article

For the sake of simplification, the other static pressure of the vessels can be represented by a certain constant; that is,

GCrg2 =

K st = (static pressure of the dilute phase of the disengagement vessel

GCst =

K st − (prgf − praf ) + 9722.7 ρpipe,st (VstZst)2

+

−

resistance = pressure at the top of the regenerator

Ω rg1

+ static pressure of the dilute phase of the regenerator (A70)

+ static pressure of the lift + static pressure of the combustor + pressure drop of the recirculated catalyst slide valve + pressure drop caused by catalyst flow + pressure drop in the cyclone

+ static pressure of the dilute phase of the regenerator

(A80)

+ static pressure of the dense bed + static pressure of the regenerated catalyst standpipe

where (A71)

static pressure of the dense bed =

Resistance = pressure at the top of the disengagement vessel + static pressure of the dilute phase of the disengagement vessel + static pressure of the riser + pressure drop of the prelift zone

static pressure of the combustor =

+ pressure drop of the regenerated catalyst slide valve + pressure drop caused by catalyst flow + pressure drop caused by feed flow

=

where Wrg2g

Ω rg2

2 GCrg21

ρpipe,rg21(Vrg21Zrg21)2

Ω rg1

(A83)

The same simplification as that for the spent catalyst standpipe is considered here, and hence, the other static pressure of the vessels can be represented by a certain constant; that is,

× 9722.7 (A74)

K rg21 = static pressure of the recirculated catalyst standpipe

2 GCrg2

pressure drop caused by feed flow = k OGO2

1 2 GCrg21 k Crg21 (A84)

pressure drop of the regenerated catalyst slide valve

k Crg2

(A82)

× 9722.7

(A73)

1

(A81)

Wrg1g

pressure drop caused by catalyst flow =

Ω rg2

pressuredropcausedbycatalystflow =

Wrg2g

pressure drop of the recirculated catalyst slide valve (A72)

ρpipe,rg2 (Vrg2Zrg2)2

(A78)

(A79)

driving force = pressure at the top of the regenerator

=

1 k rg2

+

+ static pressure of the dense bed + static pressure of the recirculated catalyst standpipe

For the regenerated catalyst slide valve:

2 GCrg2

− k OFO2

+ static pressure of the dilute phase of the regenerator (A69)

Wrg1g

1 k Cst

static pressure of the dense bed =

Ω rg2

driving force = pressure at the top of the regenerator

Hence, the spent catalyst circulation rate is calculated as follows: Wstg Ωst

9722.7 ρpipe,rg2 (Vrg2Zrg2)2

Wrg2g

For the recirculated catalyst slide valve:

+ static pressure of the spent catalyst standpipe) − (static pressure of dilute phase of the regenerator + static pressure of the lift)

K rg2 − (prgf − praf ) +

− (static pressure of the lift + pressure drop in the cyclone)

(A75)

(A85)

(A76)

Hence, the recirculated catalyst circulation rate is calculated as follows:

The same simplification as that for the spent catalyst standpipe is considered here, and hence, the other static pressure of the vessels can be represented by a certain constant; that is,

K rg21 + GCrg21 =

K rg2 = (static pressure of the dilute phase of the regenerator

■

+ static pressure of the regenerated catalyst standpipe) − (static pressure of the dilute phase of the disengagement vessel + static pressure of the riser + pressure drop of the prelift zone) (A77)

Wrg2g Ω rg2

9722.7 ρpipe,rg21(Vrg21Zrg21)2

−

Wrg1g Ω rg1

+

1 k rg21

(A86)

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-10-89733277. E-mail: [email protected]. Notes

Hence, the regenerated catalyst circulation rate is calculated as follows:

The authors declare no competing financial interest. 301



■

ACKNOWLEDGMENTS

■

NOMENCLATURE

Article

Subscripts and Superscripts

This work is supported by the National Natural Science Foundation of China (21006127) and the National Basic Research Program of China (2012CB720500).

Symbols

A = area, m2 C = coke content of catalysts, % Cp = heat capacity, kJ/(kg·K) cpt = content of platinum in the CO combustion promoters, ppm dp = solid particle diameter, m D = diffusion coefficient, m2/s DT = combustor diameter, m e = absolute error E = activation energy, kJ/kmol F = mass flow rate, kg/s G = catalyst circulation rate, kg/s H = hydrogen content of catalysts, % k = rate coefficient of a reaction or mass transfer rate coefficient MW = molecular weight P = pressure, Pa Pe = Peclect number Q = heat, kJ/s r = reaction rate R = ideal gas constant, 8.314 kJ/(kmol·K) Rg = gas molar flux, kmol/(m2·s) Rtotal = catalyst mass flux, kg/(m2·s) ST = space time, s t = time, s T = temperature, K tC = contact time of gas and solid, s tf = simulation time, s u = superficial velocity, m/s V = gas flow rate, m3/s W = inventory, t X = dimensionless length of riser xpro = amount of added CO combustion promoters, % y = product yield or gas content, % z = combustor or freeboard length, m Z = dimensionless length of combustor or freeboard or valve position

■

atmr = atomization steam b = bottom of main fractionator C = catalyst ca = catalytic coke fb = freeboard fra = main fractionator g = gas phase h = heat i = in the pore of catalyst particle L = thermal insulating layer O = gas oil pre = prelifting steam ra = riser raf = riser roof rg1 = combustor rg2 = dense bed rg21 = catalyst recirculation from dense bed to combustor rgf = regenerator roof s = solid phase sc = spent catalyst sep = separator of main fractionator st = stripper t = top of main fractionator w = water or wall wgc = wet gas compressor

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Greek Letters

β = intrinsic molar ratio of CO2/CO ΔH = reaction enthalpy, kJ/kg or kJ/kmol ΔHAR = gas oil cracking heat, kJ/kg ΔHNR = naphtha cracking heat, kJ/kg ΔHDR = diesel cracking heat, kJ/kg ΔHAA = coke adsorption heat, kJ/kg ε = Porosity ϕ = catalyst relative activity η = hydrogen−carbon molar ratio, H/C ηPt = equilibrium activity of CO combustion promoters λ = thermal conductivity, W(m·K) μ = viscosity, kg/(m·s) Θ = volume of combustor, m3 ρ = density, kg/m3 or kmol/m3 ν = stoichiometry coefficient Ω = cross-sectional area, m2 302



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