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공학박사학위논문

Modeling, simulation, structural analysisand feed characterization of a fluid

catalytic cracking process

FCC공정의모델링,시뮬레이션,시스템구조분석및공급물정의

2018년 2월

서울대학교대학원

화학생물공학부

김성호

Modeling, simulation, structural analysisand feed characterization of a fluid

catalytic cracking process

지도교수이종민

이논문을공학박사학위논문으로제출함

2018년 1월

서울대학교대학원

화학생물공학부

김성호

김성호의박사학위논문을인준함

2018년 1월

위 원 장 이원보 (인)

부위원장 이종민 (인)

위 원 남재욱 (인)

위 원 이창준 (인)

위 원 이웅 (인)

Table of Contents

Table of Contents v

List of Figures vii

1 Introduction 1

1.1 Fluid catalytic cracking process . . . . . . . . . . . . . . . . . . . . . 1

1.2 Structural Analysis of Systems . . . . . . . . . . . . . . . . . . . . . . 3

1.3 FCC feed characterization with plant data . . . . . . . . . . . . . . . 4

1.4 The scope of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Modeling and simulation of a fluid catalytic cracking (FCC) process 7

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Modeling of the Riser reactor . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Modeling of the feed inlet zone . . . . . . . . . . . . . . . . . 8

2.2.2 Reaction zone . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Regenerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.1 The dense bed phase . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 The dilute phase . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Steady-state simulation results . . . . . . . . . . . . . . . . . . . . . . 25

2.6 Dynamic response analysis . . . . . . . . . . . . . . . . . . . . . . . . 26

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Structural observability analysis of FCC plant system 41

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2 Graph-theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.1 Concept of graph theory . . . . . . . . . . . . . . . . . . . . . 42

3.2.2 Modeling of FCC plant systems through graph and directed graph 43

3.3 Structural analysis of modeling releationships . . . . . . . . . . . . . 44

v

3.3.1 Structuring the modeling relationships of a system . . . . . . . 44

3.3.2 Attempt to solve the entire modeling relationships simultaneously 45

3.3.3 Finding an output-set assignment . . . . . . . . . . . . . . . . 45

3.3.4 Completing the assignment - Finding optimal place for addi-

tional measurements . . . . . . . . . . . . . . . . . . . . . . . 46

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4 FCC feed characterization with plant data 55

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Experimental data on basic properties of petroleum fractions . . . . . 56

4.2.1 Boiling point and distillation curves . . . . . . . . . . . . . . . 56

4.3 Conversion of various distillation data . . . . . . . . . . . . . . . . . . 58

4.3.1 Riazi-Daubert method . . . . . . . . . . . . . . . . . . . . . . 59

4.3.2 Daubert’s method . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4 Conversion of various process data to distillation curve . . . . . . . . 61

4.5 Validation of the results . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.6 Conversion of the measured process data into model constants . . . . 70

4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5 Concluding remarks 75

Appendix A Nomenclature 77

Bibliography 83

vi

List of Figures

1.1 Flow diagram of FCC process . . . . . . . . . . . . . . . . . . . . . . 3

2.1 The feed inlet zone and mixing unit . . . . . . . . . . . . . . . . . . . 10

2.2 Steady-state result compared to plant data(1) . . . . . . . . . . . . . 27





2.7 Dynamic response of the model to a 10% increase of the air flow rate(1) 32




2.11 Dynamic response of the model to a 10% increase of the catalyst cir-

culation flow rate(1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 36







3.1 Examples of undirected, directed and closed graph . . . . . . . . . . . 50

3.2 Example of a system in form of a directed graph. . . . . . . . . . . . 51

vii

3.3 Occurrence matrix of the sample system . . . . . . . . . . . . . . . . 52

3.4 An example of assigning an output to the un-assigned equation . . . 53

3.5 Occurrence matrix of the FCC process . . . . . . . . . . . . . . . . . 53

3.6 Occurrence matrix of the FCC process with 5x5 complete set . . . . . 54

3.7 Fully complete occurrence matrix of the FCC process . . . . . . . . . 54

4.1 True boiling-point curve of various crude oils . . . . . . . . . . . . . . 57

4.2 Comparison of ASTM–D86 curve and converted TBP curve(1) . . . . 64

4.3 Comparison of ASTM–D86 curve and converted TBP curve(2) . . . . 65

4.4 History of API gravity data from the plant in this study . . . . . . . 68

4.5 PFD of the FCC process on Aspen HYSYS V8.4 . . . . . . . . . . . . 69

4.6 The mathematical model result with correlated TBP compared to As-

pen HYSYS V8.4 (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.7 The mathematical model result with correlated TBP compared to As-

pen HYSYS V8.4 (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

viii

Abstract

Modeling, simulation and state

observation based on structural

analysis of a fluid catalytic

cracking process

Sungho Kim

School of Chemical and Biological Engineering

The Graduate School

Seoul National University

This thesis presents a mathematical approach on modeling the fluid catalytic

cracking(FCC) process and its application including systematic analysis and feed

characterization.

Fluid catalytic cracking (FCC) is one of the most important refinery processes. It

is used for cracking high molecular weight hydrocarbon feedstocks to smaller, valuable

molecules. The existing FCC plant in the refinery consists of a reaction unit which

is followed by the fractionation unit that separates the reactor effluent into the final

products. The reaction unit is composed of the riser and the regenerator therefore are

ix

x

modeled separately and interconnected. Meanwhile, The process disturbance or faults

have a serious impact on process operation, product quality, safety, productivity and

process economy if undetected. However, measuring all state variables of a complex

FCC process is usually impossible or impractical. What is more realistic is to estimate

the state variables based on a finite set of measurements. Furthermore, we nave less

accessibility on physical properties of the feed in the FCC process. Since direct

measurement on the operating plant is not realistic because of both cost and time,

alternative methods that provides complete description of FCC process feeds from

measured process data is highly demanded.

At first, reaction kinetics were developed to describe the reactor effluents and

thermodynamic phenomena in the reactor. Empirical correlations that describe the

reaction kinetics with model parameters were built. Also, an approach to apply the

yield function for the kinetic model of the riser was made. Lastly, hydrodynamics,

mass balance and energy balance equations of the riser reactor and the regenerator

were considered to complete the modeling. Steady-state simulation results and dy-

namic responses to the change of process variables were simulated by the process

model and compared to the plant data. The results showed good agreement with the

measured data from the plant.

After the modeling, a systematic analysis was performed to identify the structural

observability of the system using the model and process design data. The reactor

and regenerator unit in this system were divided into six nodes based on their func-

tions and modeling relationships were built based on nodes and edges of the directed

graph. Output-set assignment algorithm was demonstrated on the occurrence matrix.

It was found that only a part of the system was fully observable and the states in

the regenerator was not observable with current measurement sets. Optimal loca-

tions for additional measurement were suggested by completing the whole output-set

assignment algorithm of the system.

Finally, to estimate unmeasured properties of feed mixture, a correlation method

relating properties of mixture were investigated. Various correlation methods between

xi

complex petroleum properties were found from literature and interconnected to find

the distribution function. The correlation model was validated by comparing the

reaction results from model with another results from the chemical process simulator.

The comparison showed slightly disagreed expectation result for LPG and LCO. It

is assumed that uncertainties about catalyst in the reactor and process model in the

simulator have caused this difference. Considering that point, we conclude that the

correlation model exhibits an acceptable agreement with the results of Aspen HYSYS

V8.4. The proposed approach provided insights into the FCC process and was found

to be a suitable technique for process design, operation and even more applications

such as optimization.

Keyword: Fluid catalytic cracking, discrete lumped group, process modeling,

structural observability analysis, Feed characterization

Student number: 2013-30984

Chapter 1

Introduction

1.1 Fluid catalytic cracking process

Fluid catalytic cracking (FCC) is one of the most important refinery processes. It is

used for cracking high molecular weight hydrocarbon feedstocks to smaller molecules

which boil at relatively lower temperatures. In the refinery plant from this study,

heavy vacuum gas oil (HVGO) feed is converted to off-gas, liquefied petroleum gas

(LPG), whole crack naphtha (WCN), light cycle oil(LCO) and clarified oil (CLO).

LPG and WCN are usually the primary products. About 45% of naphtha in the world

is produced by FCC [1]. The existing FCC plant in the refinery consists of a reaction

unit which is followed by the fractionation unit that separates the reactor effluent into

the final products. The reaction unit is composed of the riser and the regenerator.

A simplified process flow diagram of FCC in our study is shown in Fig 1. HVGO is

fed to the bottom of the riser after it is dispersed through a nozzle system. After

dispersion, the feed vaporizes upon contact with the hot catalyst coming from the re-

generator. Dispersion of the feed provides more heat transfer which in turn increases

the efficiency of feed vaporization. Some amount of lift steam is also added to provide

1

2

drag force to catalyst particles. Steam and the vaporized feed lift the catalyst parti-

cles upward through the riser. In the riser, vaporized hydrocarbons crack to smaller

molecules on the catalyst surface. In addition to the cracking reactions, some amount

of coke is deposited on the catalyst surface which reduces the catalysts activity. At

the riser exit, deactivated catalyst particles are separated and transferred back to the

regenerator ‘whereas the vaporized hydrocarbons are sent to the fractionation unit

where they are separated into the end products. In the regenerator, the coke on the

catalyst in burned with air and fresh hot catalyst is transferred back to the riser inlet.

In the riser, hydrocarbon compounds are converted to smaller molecules which boil

at lower temperatures. There is a number of chemical species in the reaction system.

Each species involves in the cracking reactions of hydrocarbons. In order to model

such complex mixtures, Quann and Jaffe [2] presented a structure oriented lumping

approach which takes the molecular structure into account. However, industrial ap-

plication of SOL is difficult since the analysis of petroleum fractions at the molecular

level is still limited. Complexity of detailed models has motivated the development of

simpler lumped models. In the discrete lumping approach [3], the mixture is assumed

to be composed of pure pseudo-components that are characterized by an intrinsic

property such as average Normal Boiling Point (NBP). In the discrete lumping liter-

ature, most studies prefer to use a small number of PCs to facilitate modeling and to

reduce the number of unknown kinetic constants. In early studies [4][5] the reaction

medium is represented by 3 lumps (feed, gasoline and light gases, coke). Limited

flexibility of these models has motivated the introduction of additional lumps. In

some studies, coke and light gases are considered as separate lumps [6][7][8]. Later

studies also include diesel as another lump [9][10][11]. Vargas et al. used a 6-lump

3

Figure 1.1: Flow diagram of FCC process

model and estimated parameters from refinery data [12]. In some detailed studies

10-lump models are used [13][14][15]. Gupta [3] developed a new kinetic model con-

sidering a large number of lumps. It is assumed that each pseudo-component gives

two other pseudo-components in one single cracking reaction step. They estimate

the kinetic constants using a probability based empirical approach that considers all

feasible reactions.

1.2 Structural Analysis of Systems

Knowing the internal state of a complicated system is important in many applications

such as process modeling, control and state estimation. However, measuring all state

variables is usually impossible or impractical. More realistic way is to estimate the

state variables based on a finite set of measurements. The notion of system observ-

ability characterizes whether a given set of measurements is adequate to estimate any

4

state of the system. For linear time invariant systems, if the rank of the observability

matrix is equal to the dimension of the state space model, then the system is ob-

servable [16]. For non-linear dynamic systems diverse local observability definitions

can be considered, for example using Lie derivatives [17]. In addition to analyzing

observability for a given set of measurements, it would also be useful to systemati-

cally determine minimum set of measurements which makes the system observable,

especially for large-scale complex systems. By analyzing the model structure we can

infer the minimum number of measurements and the possible choices to choose.

Structural observability is a fundamental property that provides a necessary con-

dition for system observability, and often it may also be sufficient for many complex

chemical systems [17][18]. Structural observability analysis can be done using graph-

theoretic techniques and modeling relationships. Under some assumptions, unknown

disturbances and parameters can be estimated by augmenting the system with them

as state variables with relationships, making it necessary to check the observability

of the augmented system.

Structural observability analysis via graph theory offers a visual means to pinpoint

measurements need to be estimate states, or to detect which cannot be estimated with

the provided system[19].

1.3 FCC feed characterization with plant data

One of the most important tasks in petroleum refining and related chemical pro-

cesses in the reliable values of properties for hydrocarbons and their mixtures of the

oil.[20][21] They are important from the design to operation, optimization and fault

diagnosis. Ideally, these FCC processing would relate feed composition to product

5

yield and qualities for any operating conditions. However, during operation of an

industrial petrochemical plant, crude oil from several reservoir is combined before

process and recycled flows are mixed, making plant operators difficult to know its

properties. Besides, real-time measurement of the process state for the plant is un-

realistic in both cost and time[22]. The industry developed method to correlate feed

properties with the plant data.

There are three major trends in the area of FCC feed characterization. They

are; 1. parametric models which include important feed properties in mathematical

models without adding additional knowledge about the effect of each property on the

process [24][25]; 2. lumping models in which different hydrocarbons are lumped into

groups to characterize the feed [13][14][26]; 3. ”single event” kinetic representations

of the feed which adopt a mechanistic description of catalytic cracking based on the

mechanisms of traditional reactions [27][28].

Parametric models are easily adopted in industrial plant operations as they in-

clude process properties which are able to be easily measured. However, this method

depends on empirical model and can be applied to a specific process.

On the other hand, lumping models can provide more insight about how feed

effects the cracking reactions. However, the model require various data which is not

convenient to measure during operation or even in complex experiment in laboratory.

Single-event kinetic modeling is more advanced and make kinetic parameters that

are independent of the feed property. The analysis of the feed is made by liquid

chromatography or mass spectrometry.However, this method still requires complex

analysis and is far from practical use yet.

6

Another approach that using a boiling point test based on distillation analy-

sis to analyze pseudo-components in the hydrocarbon feed have received attention

recently.[39] With the boiling point distribution known, the prediction of the com-

plete distributions for various properties of a C7+ fraction is possible using the bulk

properties of the mixture and a distribution model.

In this study we combine the correlations available in the literature for petroleum

characterization and classification to develop a system of equations for most complete

description of FCC process feeds from measured process data and find a fraction

distribution of the feed in this study.

1.4 The scope of thesis

This thesis present various research including modeling, simulation, systematic struc-

tural analysis and feed characterization of FCC plant with plant data.

In chapter 2, a mathematical model of a FCC plant is introduced. Steady-state

results and dynamic response of the plant to change of process variables are demon-

strated.

Chapter 3 presents structural analysis of the system. For structural analysis,

we divide the system into partitions based on their functionality and define set of

modeling relationships. Then output-set assignment algorithm is performed.

Chpater 4 represent feed characterization of the FCC plant with the measured

process data. It uses experimental data from literature and thermodynamic correla-

tions to characterize unknown process feed. The expected results are compared with

results from a commercial chemical process simulator.

Finally, in chapter 5, the conclusion and contribution of this research are discussed.

Chapter 2

Modeling and simulation of a fluidcatalytic cracking (FCC) process

2.1 Introduction

This chapter presents a dynamic process model for a FCC plant. This model includes

the riser reactor and the catalyst regenerator. These units are modeled individually

and then connected for investigating dynamic response.

In this study, we suggested that when the j-th pseudo-component cracks it can

form all the lighter pseudo-components with different yields. Specifically, a yield

function p(i,j) that specifies the amount of the i-th pseudo-component formed from

cracking of the j-th PC is suggested. The yield function parameters are set from

measured data and it is assumed that the results of yield function approximate the

real distribution. To predict the amounts of the WCN, LCO, CLO, LPG and off-

gas in the feed and the final products, an empirical model is developed by making

use of temperature cut-points (TCPs). This eliminates the need for any rigorous

fractionation unit model to calculate the product distribution. In this way effect of

the riser and the regenerator operating conditions on the product can be predicted.

7

8

The catalyst regenerator is modeled to calculate the heat supplied to the riser

reactor from the combustion reaction. Possible combustion reaction pathways are

suggested. Mass and energy balance equations are built for each elementary reac-

tion. Parameters of the model are estimated by the weighted least-square estimation

method. Steady-state model results and dynamic responses of the model to a step

increase of process conditions are demonstrated.

2.2 Modeling of the Riser reactor

The riser unit is divided into the feed inlet zone and the reaction zones. Stripper zone

is not considered and spent catalyst is assumed to be completely separated from the

product rapidly.

2.2.1 Modeling of the feed inlet zone

At the bottom of the reactor the residue feed is mixed with steam and hot catalyst.

The feed is spread in the inlet zone and vaporized by heat from hot catalyst and

steam. Major input and output streams of the feed inlet zone are shown in Fig 2.1.

It is commonly considered in the literature that mixing and vaporization occurs in

a small fraction of the riser.[29][30] Therefore, the mixing zone is considered to have

uniform temperature and hydrodynamic features. Also, cracking reaction does not

occur in this zone.[1]

Under this assumptions, a steady-state energy balance for the feed inlet zone is:

9

∫ Tmixzone

Tregen

˙Mcat × Cp,catdT =N∑i=1

∫ TB,i

THVGO

Mi × Cp,liquid,idT +N∑i=1

∆Hvap,i

+N∑i=1

∫ Tmixzone

TB,i

Mi × Cp,gas,idT +

∫ Tmixzone

Tsteam

Msteam × Cp,steamdT

(1)

In Equation 1, the left hand side is heat from regenerated catalyst particles. On

the right hand side, the first term is the energy that needed to increase the temper-

ature of the mixture to their boiling points. The second is heat of vaporization of

hydrocarbons. And the third is heating of the mixtures to the zone temperature.

The last term is the energy from the steam. Heat capacity and heat of vaporization

are obtained from literature[20] and Aspen HYSYS, a commercial chemical process

simulator. In this chapter, variation of mixture composition under same API gravity

is not considered and identical physical properties were assumed for identical API

gravity. Further investigation of this uncertainty is performed in the chapter 4.

The velocity of the gas leaving the feed inlet zone is calculated from the ideal gas

law with Tmixzone from Equation 1.

vg =MHVGO ×R× TmixzoneMW × P × Ariser

(2)

2.2.2 Reaction zone

In the reaction zone, vaporized hydrocarbon feeds and catalyst particles flow along

the reaction zone where the cracking reactions occur. At the riser exit, deactivated

catalyst particles are separated from the mixture and sent to the catalyst regenerator.

Vapor hydrocarbons are sent to the fractionation unit where they are separated into

10

Figure 2.1: The feed inlet zone and mixing unit

products. The riser is a two-phase(vapor-solid) reactor. However, the amount of solid

phase is very small and both phases are assumed to be perfectly mixed. Therefore

the reactor is modeled as a single-phase model.

Hydrodynamics

The pressure drop in the riser reactor is governed by acceleration of particles and

gravitational forces. It is calculated by[31][32]:

11

∂P

∂z= −((1− ε)ρcat + ερg)g −

∂

∂z((1− ε)ρcatv2cat + ερgv

2g

(3)

where the void fraction ε is given by

(1− ε) =˙Mcat

vcatρcatAriser(4)

The catalyst velocity is calculated from

∂vcat∂z

= CD3

4

ρg × (vg − vcat)2

dcatρcatvcat+

(ρg − ρcat)gρcatvcat

(5)

CD is the drag coefficient, Dcat is the average diameter of the catalyst particles,

ρcat and ρg are density of the catalyst and the gas phase. Assuming the same velocity

for gas and catalyst reduces the computational load and would not change the results

significantly.

Mass balance

The cracking reaction rate depends on many factors including feed and catalyst prop-

erties. Bollas defined a feed index to relate paraffinic, olefinic and aromatic content

of the feed to rate constants based on empirical correlations[39]. Ginzel studied the

influence of feed quality on cracking performance[40]. These studies showed that

limited knowledge of chemical composition for complex feed can provide only the

part of qualitative understanding of reaction kinetics. In our case, pre-exponential

factor Ai and the activation energy Ei are defined as a function of normal boiling

12

point(NBP)[41]. This method can use available boiling point data which is most

representative of oil fractions in our model.

The pre-exponential factor and activation energy of the ith pseudo-component are

defined as a function of normal boiling point(NBP) as:

Ai = β ×NBP µi

(6)

EA,i = E1 − (E2 ×NBP i) (7)

Then the rate constant for each pseudo-component is calculated from:

ki = Aie(−EA,i/RT ) (8)

Equation (6) is in the form of a power law since materials with higher boiling point

have higher cracking rate constants[42][43]. Equation 7 is proposed based on experi-

mental data from literatures that activation energy tends to be higher for materials

with lower boiling points[44][45][46].

In the kinetic model from earlier studies each pseudo-component is cracked into

two other pseudo-components in a single reaction. In our model when a pseudo-

component cracks, it makes all the lighter pseudo-components with different reaction

yield. The yield function p(i, j) represents the amount of the ith pseudo-component

formed form the cracking of the j th component.

Building a yield function of an operating plant is very difficult since the reactions

are highly dependent on feed content, operating conditions and many other unknown

13

process factors[47]. Besides, refinery data is limited since direct measurement cannot

be performed at the reactor riser which makes the analysis of the intermediate prod-

ucts. Hernandes used a beta distribution function to avoid similar problems[48]. Also,

there are studies which demonstrated that a temperature and composition profile ex-

ists along the riser reactor[31][48][49][50]. The product distributions of paraffinic and

olefinic petroleum feedstocks are presented in Nace’s work[43]. The product distribu-

tion of a specific petroleum cut is also presented in other studies[51]. Thus, starting

from the riser inlet, the yields of cracking reactions to intermediate products should

be in significant, and those intermediate products should be consumed by secondary

reaction.

Based on those studies, a yield function was constructed to calculate the products

distribution from a specific pseudo-component.

p(i, j) =1

P Tj

√λP ×NBP j

2π ×NBP 3i

e−λP×NBPj

2(µp×NBPj)2NBPi(NBP i−(µp×NBP )2)

(9)

where P Tj is the normalization factor of yield functions so that

∑ji=1 p(i, j) = 1:

P Tj =

j−1∑i

√λP ×NBP j

2π ×NBP 3i

e−λP×NBPj

2(µp×NBPj)2NBPi(NBP i−(µp×NBP )2)

(10)

p(i, j) for each pseudo-components that have different NBPs are presented in figure.

In the riser reactor, along with cracking reactions, some portion of hydrocarbons

is deposited on the surface of solid catalyst due to coking. Coke deposition on the

catalyst surface causes significant deactivation of catalyst. The amount of coke gener-

ated should be predicted accurately to calculate deactivation of the catalyst and the

reaction rate in both riser reactor and regenerator. In lumped-kinetics method, coke

14

is considered as a separate lump. The coking speed is affected by feedstock, operat-

ing conditions, catalyst type and reactor design[52]. In several studies most of the

coke formation occurs early in the riser[53][54]. It is found that catalyst to oil ratio

is positively correlated with coke formation[54]. Heavy and aromatic hydrocarbons

increase coking tendency[55]. We introduced a coking tendency parameter (ϕ) in our

model. For every cracking reaction, ϕ fraction of the reactant is converted to coke.

To characterize the composition of petroleum mixture, a boiling point curve is

commonly used as a standard. The curve can be obtained from ASTM-standard

laboratory test in which distilled volume fractions of the sample are described as a

function of temperature. [20] Chemical process software such as Aspen HYSYS can

be used as an alternative to plot the curve. In our case, the boiling point of HVGO,

WCN, LCO and CNO are defined as operating temperature of the fractionation unit

which separates the cracked product. It is not possible to sample and perform a

similar analysis on the product output before the fractionation due to safety and

other technical difficulties. Instead, we modeled the fractionation unit with same

operation condition in HYSYS which shows similar separation performance and found

saturation temperature of each pseudo-component.

The following steady-state mass balance equation applies to the ith pseudo-

component at any axial position, z:

∂(Mi)

∂z= −ki ×

Mi

vg× (1− ε)× ρcat × Φ

+N∑n>i

p(i, n)× (1− ϕ)× kn ×Mn


(11)

where Mi is the mass flow rate of ith component; ki is the cracking rate constant

15

(m3/kg cat h) of ith component and Φ is the catalyst activity coefficient. The first

term in the right hand side means cracking of ith component into smaller components;

the second is the formation of that component from cracking of larger molecules. The

yield function p(i,n) determines the amount of the ith pseudo-component formed

from cracking of the nth component. For each reaction, ϕ fraction of the reacting

material is converted to coke instead of other pseudo-component.

The overall mass balance between the inlet and outlet of the riser reactor gives:

N∑i=1

Mi + C = MHVGO + C0 (12)

where C0 is the coke flowrate (kg/h) in the catalyst from the regenerator to the

feed inlet zone of reactor. The coke mass flowrate leaving the reactor is

C = MHVGO −N∑i=1

Mi + C0 (13)

Catalyst activity depends on the coke fraction on the catalyst surface since coke is

the physical reason for deactivation. An exponential type deactivation model is used

in this study. [31] Catalyst activity coefficient is defined by

Φ = e−α(C/Mcat) (14)

where CMcat

is the coke fraction on the catalyst.

Energy balance

We built a steady-state energy balance equation for axial position, z:

16

∂(M × Cp,avg × T + Mcat × Cp,cat × T )

∂z=

N∑i=1

∆Hi × ki ×Mi


(15)

where Cp.avg is the average heat capacity of all pseudo-components in the reactor

and δHi is the heat of cracking of ith pseudo-component. The heat of cracking of the

ith pseudo-component is calculated from [3]:

∆Hi = Hc,coke × ϕ+i∑

j=1

p(i, j)× (1− ϕ)×Hc,j −Hc,i (16)

where Hc.coke is the heat of combustion of coke; Hc,i is the heat of cracking of ith

pseudo-component. Due to difficulty of measuring the heat of combustion directly in

the plant, we use a power-law type equation to relate heat of combustion to NBP.

As mentioned in above, identical physical properties were assumed for identical API

gravity. Heat of combustion can be calculated by the Aspen Properties simulator

with detailed feed characterization which is performed in the chapter 4.

Hc,i = ac ×NBP bci

(17)

where ac and bc are adjustable parameters.

Hc.coke is considered to be a function of API gravity of the feed, which is the only

measurable state of the feed flow in this study.

Hc,coke = acoke × APIHVGO + bcoke (18)

17

When the temperature cut-point[33] used in the process are known, they can be

used to calculate the amounts of the final products and can be compared to the

amount of product flows in the fractionator process after the reactor. If the model

and the measured data fits, the final products amounts are predicted exactly by the

model. Therefore we have to compute the cut-points from the data.

Let P(NBP) be a polynomial that relates the NBP to the corresponding cumulative

mass of reactor riser effluent. They should satisfy those constraints:

p(NBP h) = M (19)

p(NBP l) = 0 (20)

where M is the total mass flowrate of the pseudo-components at the riser and

NBPCLO and NBPoffgas are the highest and the lowest boiling point temperatures

in each pseudo-component. 4 cut-points should be calculated for 5 products which

exists in this model. The cut-points are calculated from:

minθ

4∑i=1

(P (θi)−i∑

j=1

Mi,p)2 (21)

where θ is the vector of 4 cut-points which defined as

θ = [θoffgas−LPG θLPG−WCN θWCN−LCO θLCO−CLO] (22)

18

P(θi) is the total mass which boils up to the temperature θi; Mi,p is the amount of

i)th product from the plant. For instance, θoffgas−LPG is the cut-point temperature

between offgas and LPG. Like:

P (θoffgas−LPG) = Moffgas (23)

P (θLPG−WCN) = Moffgas +MLPG (24)

2.3 Regenerator

In the regenerator coke on catalyst surface is burnt to increase the catalyst activity.

The air is fed to the bottom of the regenerator and reacts with the coke and other pol-

lutants on the catalyst. Since combustion reactions are very exothermic, regenerated

catalyst is transferred to the riser reactor, mixed with the feed at a high temperature

and provides heat for the endothermic reactions in the riser reactor.

We assumed that the regenerator has two physical phases: solid dense bed and

vapor dilute phase. These phases are modeled respectively.

2.3.1 The dense bed phase

The dense bed is the lower part of the regenerator where a higher concentration of

catalyst particles exists. As air flows through the dense bed, coke and other pollutant

react with oxygen in the air. Although there may be a little catalyst concentration

and temperature gradient in the dense bed[35][34], flowing air flow mixes catalyst bed

19

Reaction Reaction Heat of reaction

I C + 1/2O2

kC,CO−→CO ∆HC,CO

II C +O2

kC,CO2−→ CO2 ∆HC,CO2

III CO + 1/2O2

kC,CO2,c−→ CO2 ∆HCO,CO2

IV CO + 1/2O2

kC,CO2,c−→ CO2 ∆HCO,CO2

V H2 + 1/2O2

kH2,H2O−→ H2O ∆HH2,H2O

Reaction Reaction rate expression

I rC,CO = kC,CO( Mcat

VDensebed× Y regencoke

MW coke)a1× (PO2)

a2

II rC,CO2 = kC,CO2(Mcat

VDensebed× Y regencoke

MW coke)a3× (PO2)

a4

III rC,CO2,c = kCO,CO2,c × Mcat

VDensebed× (PCO)a5 × (PO2)

a6

IV rC,CO2,h = kCO,CO2,h × (PCO)a7 × (PO2)a8

V Instantaneous reaction speed

Table 2.1: Catalyst regeneration reactions and rate expression in the regenerator unit

and the gradient become negligible. Therefore, to make our model simpler, we have

modeled the dense bed as a single-phase, well-mixed reactor. Primary reactions, rate

expression and heat of reactions are presented in Table 2.1

Mcat (kg) is the total catalyst mass holdup in the dense bed. We assume that

the catalyst holdup is kept constant by manipulating the valves on the regenerated

catalyst circulation. VDensebed is the volume of the dense bed; Y RegenCoke is the coke mass

fraction of the catalyst in the dense phase; MWcoke is the molecular weight of coke.

PCO and PO (bar) are the partial pressures of CO and O2. CO combustion reaction

occurs through both catalytic and homogeneous paths. The reaction mechanism is not

fully defined due to complex catalyst influence, uncertainty of reaction medium and

hydrodynamics issues. In the literature different reaction mechanisms and numerical

values for the reaction orders and kinetic parameters have been proposed[14][34][36].

20

Among the reactions, burning of H2 does not influence the kinetics of the regener-

ator by its concentration because the reaction is so fast that it is assumed to occur

instantenously[37] However, the thermal effects from the reaction are significant be-

cause of its high combustion energy[38]. Expressions for the rate constants are given

as:

kC,CO =βce−Eβ/RTkc0e

−Ec0/RT

βce−Eβ/RT + 1

kC,CO2 =βce−Eβ/RT

βce−Eβ/RT + 1

kC,CO2,C = k3c0e−E3c/RT

kC,CO2,h = k3h0e−E3h/RT

(1)

Approximate values of parameters in these expressions are available in the litera-

ture. [14]

Unlike the riser reactor, the dynamics of the dense bed phase are significant due

to its large catalyst mass holdup. The approximate residence time of the catalyst in

the dense bed is about 5–10 min, which is much longer than 5–10 seconds in the riser

reactor. The mass balance for the coke is given by

Mcat

MW coke

d

dt(Y regen

coke ) = McatY Risercoke

MW coke

− McatY Regencoke

MW coke

− (rC,CO + rC,CO2)VDensebed (2)

where (rC,CO + rC,CO2) is the combustion rate of coke.

The gaseous species have a residence time about 5 seconds in the dense bed. There-

fore, we have assumed pseudo-steady state for the gaseous phase in the regenerator.

The mass balance for CO in the dense phase is:

21

−MCO,DensetoDilute + rCOVDensebed = 0 (3)

-MCO,DenseToDilute is the molar flowrate of CO that leaves the dense phase. rCO is

calculated from:

rCO = kC,CO(Mcat

VDensebed× Y regen

coke

MW coke

)a1

× (PO2)a2

−kCO,CO2,c ×Mcat


a6 − kCO,CO2,h × (PCO)a7 × (PO2)a8

(4)

From material balance for CO2,

−MCO2,DensetoDilute + rCO2VDensebed = 0 (5)

where rCO2 is

rCO = kC,CO2(

Mcat

VDensebed× Y regen

coke

MW coke

)a3

× (PO2)a4

−kCO,CO2,c ×Mcat


a6 − kCO,CO2,h × (PCO)a7 × (PO2)a8

(6)

H2 generated during the reaction is converted to H2O instantly and leaves the

dense bed phase. Flow rate of the H2O is:

MH2O,DensetoDilute = McatYrisercoke

Y riserH2

MWH2

(7)

where Y cokeH2

is the H2 fraction in coke. Similarly, material balance for O2 is given

by

22

MO2,in − MH2O,DensetoDilute − McatYrisercoke

Y cokeH2

2MWH2

+ rO2VDensebed = 0 (8)

rO2 = −kC,CO × (Mcat

VDensebed

Y regencoke

MW coke

)a1

× (PO2)a2 − kC,CO2 × (

Mcat

VDensebed

Y regencoke

MW coke

)a3

× (PO2)a4

−kC,CO2,c ×Mcat


a6 − kC,CO2,h × (PCO)a7 × (PO2)a8

(9)

MO2,in is the molar flow rate of O2 into the dense bed from the fresh air and

MO2,DenseToT ilute is the molar flow rate of O2 that leaves the dense bed phase.

The energy balance for the dense bed is:

d

dt((Mcat +MO2 +MN2 +MCO +MCO2 +MH2O)× Cp,avg × Tregen) =

(MO2,in × Cp,O2 × Tair + MN2,in × Cp,N2 × Tair + Mcat × Cp,cat × Triser)[−(MO2,DensetoDilute × Cp,O2 × Tregen + MN2,DensetoDilute × Cp,N2 × Tregen

+Mcat × Cp,cat × Tregen)

][−(MCO,DensetoDilute × Cp,CO × Tregen + MCO2,DensetoDilute × Cp,CO2 × Tregen

+MH2O × Cp,H2O × Tregen)

]

+QR,DensebedVDensebed + McatYrisercoke

Y cokeH2

MWH2

∆HH2,H2O

(10)

where Tregen is the dense phase temperature, Tair is the air temperature, and

QR,Densebed is the heat released per unit volume from combustion reactions of catalyst

which calculated from:

23

QR,Densebed = kC,CO(Mcat

VDensebed

Y regencoke

MW coke

)a1

(PO2)a2∆HC,CO+

kC,CO2(Mcat

VDensebed

Y regencoke

MW coke

)a3

(PO2)a4∆HC,CO2+

kCO,CO2,cMcat

VDensebed(PCO)a5(PO2)

a6∆HCO,CO2+

kCO,CO2,hMcat

VDensebed(PCO)a7(PO2)

a8∆HCO,CO2

(11)

2.3.2 The dilute phase

Contrary to the dense phase, the amount of catalyst particles in the dilute phase is

negligible. Therefore, solid coke nor catalyst does not exist in the dilute phase. The

dilute phase is assumed to be pseudo-steady state since the velocity of the gaseous

phase is very high. The dilute phase is modeled as an one-dimensional adiabatic plug

flow reactor in which CO is burnt homogeneously and other reaction is neglected.

The material balance of CO, CO2, O2 at an axial position z is given by:

d

dz(MCO) = −kCO,CO2,h × (PCO)a7 × (PO2)

a8Aregen (12)

d

dz(MCO2) = −kCO,CO2,h × (PCO)a7 × (PO2)

a8Aregen (13)

d

dz(MO2) =

1

2kCO,CO2,h × (PCO)a7 × (PO2)

a8Aregen (14)

The energy balance of the dilute phase is given by:

24

− d

dz

MO2 × Cp,O2 × T + MN2 × Cp,N2 × T+

MCO × Cp,CO × T + MCO2 × Cp,CO2 × TMH2O × Cp,H2O × T

+

kCO.CO2,h × (PCO)a7 × (PO2)a8 ×∆HCO.CO2 × Aregen = 0

(15)

2.4 Parameter estimation

The parameters of the model were estimated by the weighted least square estimation

method. The weighted sum of squared errors (WSSE) between measured data and

model prediction was defined as the objective function and minimized.

WSSE(P ) =n∑i=1

m∑j=1

(yij − yij)TWij(yij − yij) (1)

where n is the number of data points, m is the number of measured variables (seven

in this study), yij is the measured value of variable j at time i, and yij is the calcu-

lated value of variable j at time i from the model. For the riser reactor, measured

plant variable include the product amount, temperature and pressure of product and

catalyst. Even though we cannot measure the composition of the reactor product

flow, we assume that product flow rate from the main fractionator after the reactor is

same as that of the reactor product flow. For the regenerator, measured variables are

the temperature of dense and dilute phase. The weighting factor, Wij, was defined

to assign more weights to measured variables with less variances and to balance the

scales among measured variables as

Wij =1

σijλj(2)

25

where σij is the standard deviation of the measurement variables and λj is a scaling

factor for normalizing the measurement variables as

λj =

∑ni=1 |yij − yij|∑ni=1 |yijr − yijr |

(3)

where yijr is the measured variable used as a reference variable and yij is the mean

value of the measurement variables. The standard deviation σij is calculated after

normalizing the measured data.

The following parameters should be estimated:

[α β βc µµp λp φ ac bc acoke bcoke kc0 ]

[E1 E2 Eβ Ec0 E3c E3h K3c0 K3h0](4)

The optimization problem to minimize WSSE was solved using the statistics tool

in Matlab.

2.5 Steady-state simulation results

The constructed model of the FCC was tested for various steady-state operating

condition and feed. The main results which we are interested of the riser reactor are

the flow rate of products and other process variables; the pressure and temperature

at the riser exit. From the regenerator model we can gain expected temperature

of dilute gas phase and dense solid phase. The result was compared to measured

data from an operating FCC plant. The model simulation results and corresponding

plant data are shown in Fig 2.2, Fig 2.3 and Fig 2.4. Although there are little

discrepancies between the simulation results and measured data, it was observed that

the simulation data points have similar trends. Values of R2 of the result are 0.9313,

26

0.8808, 0.9639, 0.8605, 0.8806 for each pseudo-component group and 0.9808, 0.9539,

0.9734, 0.9896, for riser temperature, riser pressure, dilute phase temperature and

dense phase temperature.

Table 2.2 shows the results of parameter estimation of the model. Parameters

which are not listed in table 2.2 are considered to be constant and taken from the

literature.

Due to lack of feed property data in construction of the model, NBP and tem-

perature cut-points are considered as constant values. To solve this problem, further

study about estimating feed property with available process data is required.

2.6 Dynamic response analysis

Dynamic analysis of the model helps understanding the interactions between the

operation of the riser reactor and the catalyst regenerator. Fig 2.5, Fig 2.6 and Fig

2.7 show dynamic response of the model to an 10% increase of the air flow rate. The

amount of air flow determines the combustion reaction in the regenerator. When

more air is supplied, more combustion reactions occur, and more heat is generated.

Consequently, the temperature of dense and dilute phase in the regenerator increases.

A relatively hotter catalyst is transferred to the riser and increases temperature of

the riser reactor. This high temperature causes more cracking reaction occur in the

riser reactor. The amount of heavier products (CLO and LCO) decreased while the

amount of the lighter product (Offgas and LPG) increased.

Next we studied the effect of increased catalyst circulation rate by 10%. When

the catalyst circulation rate is increased, more energy is transferred to the riser re-

actor and the riser temperature is suddenly increased. As the cracking reactions are

27

(a) Off-gas

(b) LPG

Figure 2.2: Steady-state result compared to plant data(1)

28

(a) WCN

(b) LCO


29

(a) CLO

(b) Temperature of the riser reactor


30

(a) Pressure of the riser reactor

(b) Temperature of dense bed


31

(a) Temperature of the dilute phase


endothermic, the cracking reactions occur more often in this condition. However, as

the riser and the regenerator temperature began to decrease, the flow rate of heavier

components became favored. The amounts of the light products increased slightly

because of the increased catalyst flow rate in the riser reactor. The results are shown

in Fig.2.8, Fig 2.9 and Fig 2.10.

All the simulated dynamic responses showed similar trend with plant data.

2.7 Conclusion

Using the discrete lumped group method, The FCC process systems are investigated

to develop a process model for an fluid catalytic cracker. This model predicts the

product yield and other process states under steady-state and dynamic conditions.

32

(a) Off-gas

(b) LPG

Figure 2.7: Dynamic response of the model to a 10% increase of the air flow rate(1)

33

(a) WCN

(b) LCO


34

(a) CLO



35

(a) Temperature of dense bed

(b) Temperature of dilute phase


36

0 5 10 15 20 25 30

Time (min)

4300

4350

4400

4450

4500

4550

4600

Response

Off-gas (kg/h)

(a) Off-gas

0 5 10 15 20 25 30

Time (min)

1.15

1.16

1.17

1.18

1.19

1.2

1.21

1.22

Response

×104 LPG (kg/h)

(b) LPG

Figure 2.11: Dynamic response of the model to a 10% increase of the catalyst circu-lation flow rate(1)

37

0 5 10 15 20 25 30

Time (min)

2.78

2.8

2.82

2.84

2.86

2.88

2.9

Response

×104 WCN (kg/h)

(a) WCN

0 5 10 15 20 25 30

Time (min)

4340

4360

4380

4400

4420

4440

4460

4480

4500

4520

4540

Response

LCO (kg/h)

(b) LCO


38

0 5 10 15 20 25 30

Time (min)

9300

9350

9400

9450

9500

9550

9600

9650

9700

9750

Response

CLO (kg/h)

(a) CLO

0 5 10 15 20 25 30

Time (min)

520

525

530

535

540

545

550

Response

Riser temperature (K)



39

0 5 10 15 20 25 30

Time (min)

670

675

680

685

690

695

700

705

710

Response

Dense phase temperature (K)

(a) Temperature of dense bed

0 5 10 15 20 25 30

Time (min)

690

695

700

705

710

715

720

725

730

735

Response

Dilute phase temperature (K)

(b) Temperature of dilute phase


40

Empirical correlations that describe the reaction kinetics with model parameters are

built. A yield function for the kinetic model of the riser is constructed and applied to

the model. Also, an approach to estimate the fraction of products using temperature

cut-point is suggested. Using this model, steady-state simulation results and dynamic

responses to change of process variables are presented.

Chapter 3

Structural observability analysis ofFCC plant system

3.1 Introduction

Evaluation of the performance, control, and optimization of a chemical plant are

based on knowing about current state of the plant. The process disturbance or faults

have a serious impact on process operation, product quality, safety, productivity and

process economy if undetected. However, measuring all state variables is usually

impossible or impractical. What is more realistic is to estimate the state variables

based on a finite set of measurements[56]. The notion of observability means whether

a given set of measurement is adequate to estimate the state of the system. For

linear time-invariant systems, if the rank of the observability matrix is equal to the

dimension of the system, then the system is observable. [57] For nonlinear systems

local observability definitions can be used, such as Lie derivative.[17] In addition to

analyzing observability for a given set of measurement, it is necessary to systematically

find the minimum set of measurements which makes the system observable. By

analyzing the model, we can find the minimum set of measurements and the possible

41

42

choices. In this study, we studied our FCC model with graph theory and modeling

relationships to analyze structural observability of the process and find out which

part of the plant is unobservable. Based on the result, we propose optimal place for

adding sensors for recovering observability of the system.

3.2 Graph-theory

3.2.1 Concept of graph theory

A graph G is defined by G = (V(G),E(G),ψG) consisting of a non-empty set V(G)

of vertices, a set E(G) which is a set of edges, disjoint from V(G) and an incidence

function ψG. The incidence function ψG can be neglected in our study. An edge

connects two nodes vi and vj (vi, vj ∈ V (G)) is denoted by (vi, vj) and vi and vj are

called adjacent nodes.

A graph may be directed or undirected. Directed graph D is an ordered (V(D),E(D),ψD)

consisting of an non-empty set V(D) of vertices and a set E(D), which is disjoint from

V(D). Let an edge ei =( vi, vj) ∈ E, then vi is the initial vertex and vj is the final-

vertex, gives (vi, vj) ≡ vi → vj. In directed graphs, edges are marked with directed

lines while in undirected graphs it is not. On the other hand, for undirected graphs,

(vi, vj) and (vj, vi) are same.

A path is a sequence of edges connected on after another. A path has an initial

node and a final node. Number of edges in a path is called the length of the path. A

graph is simple if any path in the graph have no loops nor node appearing more than

once. If a path has identical initial and final nodes, it is called a close path.

A cycle is a closed path with no node appearing more than once except the initial

43

and the final nodes. A set of cycles such that no two cycles have any common nodes

are a cycle family. In a cycle family if paths from vi to vj and from vj to vi exits then

vi and vj are strongly connected.

3.2.2 Modeling of FCC plant systems through graph and di-

rected graph

Our FCC model consists of the riser reactor and the catalyst regenerator. Each

unit can be divided further into three nodes based on their functions. The riser

reactor consists of the feed inlet zone, reaction zone and stripping zone. Although

the stripping zone was not modeled in our study since the catalyst is separated from

the product rapidly and completely, we need process state of the location to find

out accuracy of our model and the results. Meanwhile, the catalyst regenerator is

divided into the dilute gas phase where the spent catalyst are fed and CO is burnt,

surface between dilute/dense phase bed where mass and energy are transferred, and

the dense solid phase bed where the coke on catalyst surface is burnt and the catalyst

returns to the riser reactor. For each functional node, several sensors are installed in

the plant. However, not all kinds of sensors are available for every location, making

further defining of nodes impossible.

A directed graph consisting these nodes is generated and shown in Figure 3.2.

44

3.3 Structural analysis of modeling releationships

3.3.1 Structuring the modeling relationships of a system

Structural analysis of modeling relationship is a way to find controllability and ob-

servability of a complex system by using a graph theory and output-set assignment

method. Traditional method to find controllability or observability requires exact

state-space model. Unfortunately, it is unrealistic to construct the state-space model

of a complicated chemical processes such as FCC reactor due to complex reaction

mechanisms and limited system measurements. However, if we have a system associ-

ated with input-output relationships, we can analyze the system to find whether the

system is controllable or observable.

To perform structural analysis of modeling relationships, we have to identify all

nodes, connections between the nodes, inputs and outputs of the system and identify

what system variable we can measure. Fig 3.2 is an example of a system with input-

output relationships.

From input-output relationships and directed graph, set of modeling relationships

are defined in a form of:

f1(x1, x3) = 0

f2(x1, x2, x3) = 0

f3(x2) = 0

(1)

For these relationships, output-set assignment can be found. From the third

relationship, x2 can solve f3, which denoted as (x2; f3). It is unnecessary to solve the

equation algebraically. If we have exact solution of a relationship, then the variables

45

xi can be used as a process state when building occurrence matrix. (x1; f1) and (x3;

f2) can be found from the relationships in the same manner.

These assignments are translated into an occurrence matrix. Functions are placed

at row and state variables are in column. Assignments are marked in the correspond-

ing position in the matrix.

3.3.2 Attempt to solve the entire modeling relationships si-

multaneously

If all of the modeling relationships or the occurrence matrix could be solved simulta-

neously, the system is said to be completely observable and completely controllable.

Before starting the sequential analysis of the system, we attempted to solve the mod-

eling relationships of the system simultaneously. However, any analytical solution of

the modeling relationships could not be found. Besides, the maximum structural rank

of the occurrence matrix is 9, which indicates the occurrence matrix is a structurally

singular matrix and the output-set from the matrix is incomplete. In this case, the

structural rank of a occurrence matrix is equal to the maximum possible number of

output-set assignment which can be made for the matrix.

3.3.3 Finding an output-set assignment

Let us begin searching at a position in the occurrence matrix where the equation

can be solved spontaneously. Check every function in which the solved variable is

included. Than find another function which become solvable with previous result.

Repeat this searching until solve every function. If a solvable function cannot be

found during the process, stop searching and gather complete set into diagonal form.

46

Functions and system variables which found assignment are complete output set,

while those without assignment are incomplete output set.

This results gives answer to the question whether each node of graph model is

observable. If any node, location or process state variable of the system is found to

be in the complete output set, then it is systematically observable. However, if it is

in the incomplete output set then the state is unobservable.

The output-set assignment is not unique. If no complete output-set can be found

for a set of modeling relationships, then there exist structural problems with the set

of modeling relationships, which means a subset of modeling relationship is over-

specified or under-specified.

3.3.4 Completing the assignment - Finding optimal place for

additional measurements

To complete the assignment, we can assume that we know additional variable which

was unassigned and continue the algorithm. In the example, we assume that we

know the variable x8. We assign it as an output of f1 and relax the assignment

of the current output variable(x3). Then we continued with the algorithm until an

unassigned equation is assigned by other state variable. By completing the assignment

the location of optimal measurement could be found.

3.4 Results

The procedure described above is demonstrated on the FCC plant in this study.

From input-output relationships and directed graph, set of modeling relationships

47

are defined as:

For the system variables in the riser reactor,

f1(x1, x2, x8) = 0

f2(x2, x3) = 0

f3(x3, x4, x5) = 0

(1)

For the variables in the catalyst regenerator,

f4(x5, x6, x9, x11) = 0

f5(x6, x7, x11) = 0

f6(x7, x8, x9) = 0

(2)

For the whole system,

f7(x1, x4, x9, x10) = 0

f8(x1) = 0

f9(x4) = 0

(3)

For these relationships, output-set assignment was found by constructing the oc-

currence matrix in Figure 3.5.

The assignment could start from both f8-x1 and f9-x4 as they have only one

variable related. f8-x1 was selected for the sake of simplicity. Then the algorithm

was repeated for x2, x3 and x5. However, it is found out that for FCC plant system

in this study not every function was solvable with given modeling relationship and

measurements. Assigned nodes and variables are gathered to create the diagonal form

and make 5x5 complete output-set.

This result shows that five system variables and three nodes are identified to

be observable and controllable. The result is shown in Figure 3.6. Comparing the

48

result to the directed graph it is found that whole nodes and edges in the reactor are

completely observable. However, in the catalyst regenerator, most of edges were not

controllable or observable. This is because of lack of measurement in the regenerator

and poorly designed modeling relation.

By completing the output assignment the optimal location of additional measure-

ment is suggested in Figure 3.7. To complete the assignment, some of additional

system variables which was unassigned, x6-x10, are assumed to be measured addi-

tionally. By this assumption, the assignment algorithm could be continued at any

unmeasured variable. It is found that gas effluent and regenerated catalyst which is

cycled to the feed inlet zone in the reactor are the most optimal location for addi-

tional measurement. Completing output assignment of the entire system with single

additional measurement was infeasible in this modeling relationships.

3.5 Conclusion

In this chapter, structural analysis of the fluid catalytic cracking process is performed

to find observability of the FCC system. A directed graph was drawn to construct

modeling relationships of the system. The reactor and regenerator unit in this sys-

tem are divided into six nodes based on their functions. The modeling relationships

were built based on nodes and edges of the directed graph. Output-set assignment

algorithm was demonstrated on the occurrence matrix which is made of modeling

relationships. The results of this chapter show that only a part of the system is fully

observable and the states in the regenerator is not observable without measurements.

However, it is also suggested that with additional state measurements, these unob-

servable states can be observed. Optimal locations for additional measurement are

49

suggested by completing the whole output-set assignment algorithm of the system.

50

(a) An undirected graph

(b) A directed graph

(c) A closed graph

Figure 3.1: Examples of undirected, directed and closed graph

51

Figure 3.2: Example of a system in form of a directed graph.

52

Figure 3.3: Occurrence matrix of the sample system

53

Figure 3.4: An example of assigning an output to the un-assigned equation

Figure 3.5: Occurrence matrix of the FCC process

54

Figure 3.6: Occurrence matrix of the FCC process with 5x5 complete set

Figure 3.7: Fully complete occurrence matrix of the FCC process

Chapter 4

FCC feed characterization withplant data

4.1 Introduction

In this study we combine the correlations available in the literature for petroleum

characterization and classification to develop a method for most complete description

of FCC process feeds from measured process data and find a fraction distribution of

the feed in this study.

There are three major trends in the area of FCC feed characterization. They

are; 1. parametric models which include important feed properties in mathematical

models without adding additional knowledge about the effect of each property on the

process [24][25]; 2. lumping models in which different hydrocarbons are lumped into

groups to characterize the feed [13][14][26]; 3. ”single event” kinetic representations

of the feed which adopt a mechanistic description of catalytic cracking based on the

mechanisms of traditional reactions [27][28].

Parametric models are easily adopted in industrial plant operations as they in-

clude process properties which are able to be easily measured. However, this method

55

56

depends on empirical model and can be applied to a specific process.

On the other hand, lumping models can provide more insight about how feed

effects the cracking reactions. However, the model require various data which is not

convenient to measure during operation or even in complex experiment in laboratory.

Single-event kinetic modeling is more advanced and make kinetic parameters that

are independent of the feed property. The analysis of the feed is made by liquid

chromatography or mass spectrometry.However, this method still requires complex

analysis and is far from practical use yet.

Another approach that using a true boiling point (TBP) test based on distillation

analysis to analyze pseudo-components in the hydrocarbon feed have received atten-

tion recently.[39] With the true boiling point distribution known, the prediction of

the complete distributions for various properties of a C7+ fraction is possible using

the bulk properties of the mixture and a distribution model.

4.2 Experimental data on basic properties of petroleum

fractions

4.2.1 Boiling point and distillation curves

Pure compounds have a single value for the boiling point. However, for mixtures like

crude oil and residue oil in FCC process, the temperature at which vaporization occurs

varies from the boiling point of the most volatile component to the boiling point of

the least volatile component. Therefore, boiling point of a mixture is represented by

boiling points of the components in the mixture. For a petroleum mixture of unknown

57

Figure 4.1: True boiling-point curve of various crude oils

composition, the boiling point is presented by a curve of temperature vs fraction of

vaporized mixture.

The temperature range in this curve is boiling point range. The the lowest boiling

point is initial boiling point and the highest boiling point of the mixture is the final

boiling point. We can assume that compounds in the mixture have boiling point

between them and roughly estimate the number of carbon atoms of hydrocarbons

compounds. The boiling point curve provides a look into the composition of feedstocks

58

and products about petroleum processes. There are several method of measuring and

reporting boiling points.

ASTM–D86 is one of the simplest and oldest method of measuring boiling points of

petroleum fractions. It is conducted mainly for products such as naphthas, gasolines,

kerosenes, gas oils and other similar petroleum products. However, this test is not a

consistent and reproducible method.

ASTM–D2887, simulated distillation (SD) method is performed by using gas chro-

matography. This method is much precise and reproducible. Also, this method is

applicable for a wider range of temperature than ASTM–D86 method.

However, these measurement cannot present actual boiling point of components

in the mixture. Actual true boiling point(TBP) is the idealized temperature cuts for

a petroleum mixture. Atmospheric TBP data can be obtained through distillation

of a petroleum mixture using a distillation column with high reflux ratios. However,

measuring TBP data is more difficult than ASTM–D86 or ASTM–D2887 data in

terms of both cost and time. In our study, normal boiling point(NBP) and boiling

point curve is used as index for temperature of hydrocarbons in the feed and the

product.

4.3 Conversion of various distillation data

There were several attempt to develop empirical methods for converting ASTM distil-

lations to TPB from the 20th century. [59][60][61][62] These correlations were based

on experimental data from literature. In the 1980s Riazi-Daubert method were de-

veloped analytical method for conversion of distillation curves based on the general

59

correlations for hydrocarbon properties. [63] Another conversion methods were de-

veloped at 1990s through modifying Riazi-Daubert correlations.[64] These are most

recommended correlations in today and used in other references.

In this study, four ASTM–D86 curve data from an industrial FCC plant is con-

verted to TBP curve to apply on the process model.

4.3.1 Riazi-Daubert method

Riazi-Daubert methods are based on the generalized correlation for property estima-

tion of hydrocarbons.

ASTM–D86 to TBP

If distillation data in form of ASTM-D86 is available, we can convert this data into

TBP.

T (desired) = a [T (available)]b × SGc (1)

where T (available) is the available distillation temperature data at a specific vol%

distilled and T (desired) is the desired distillation data for the same vol% distilled.

SG is the specific gravity of fraction at 15.5◦C. For this particular type of conversion

regarding TBP curve, c becomes zero for all vol%[20] and the equation reduces to

TBP = a [ASTMD86]b (2)

where both TBP and ASTM–D86 temperatures are in kelvin. Constants a and b

at various points along the distillation curve are given in Table 4.1

60

V ol% a b ASTM D86 range0 0.9177 1.0019 20–32010 0.5564 1.0900 35–30530 0.7617 1.0425 50–31550 0.9013 1.0176 55–32070 0.8821 1.0226 65–33090 0.9552 1.0110 75–34595 0.8177 1.0355 75–400

Table 4.1: Correlation constants for Riazi-Daubert method with ASTM–D86

4.3.2 Daubert’s method

Daubert’s method is a different correlation that convert ASTM–86 and ASTM–2887

data to TBP. [64]In these methods, first conversion should be made at 50% point and

then the difference between two cutpoints are correlated. In this method, ASTM–

2887 data can be converted to TBP without converting to ASTM–86 as was in Riazi-

Daubert method.

ASTM–D86 to TBP

This equation is used to convert an ASTM–D86 data at 50% point into TBP 50%

point temperature data.

TBP (50%) = 255.4 + 0.8851 [(ASTM −D86(50%)− 255.4]1.0258 (3)

Once the 50% point data is calculated, Eqn.() is used to determine the difference

between two cut-points.

61

i Cut point range A B1 100–90 0.1403 1.66062 90–70 2.6339 0.75503 70–50 2.2744 0.82004 50–30 2.6956 0.80085 30–10 4.1481 0.71646 10–0 5.8589 0.6024

Table 4.2: Correlation constants for Daubert method with ASTM–D86

Yi = AXBi (4)

where Yi is the difference in TBP temperature between two cut-points, Xi is the

difference in ASTM–D86 temperature between same cut-points. Constants A and B

are given in table 4.3.

To determine the TBP temperature at any vol% distilled, we begin calculation

with 50% TBP temperature and add or substract the proper temperature difference

Yi to find temperature at target Vol%.

In this study, four available distillation data from an industrial FCC plant is

converted to TBP curve using these two methods. Figure 4.3, Figure 4.4 and Table

4.3 shows the conversion results and comparisons.

4.4 Conversion of various process data to distilla-

tion curve

Unfortunately, real-time measurement of the distillation curve from every feed is un-

realistic. Thus, another method to describe the mixture property is highly demanded.

62

Test method Vol % Data #1 Data #2 Data #3 Data #4ASTM–D86(K) 0 368.5 387.9 371.1 369.1

10 625.5 662.4 663 622.930 735.9 782.4 784.2 734.150 792.4 843.7 820 792.670 832.2 895.2 855.6 836.190 880.7 911.4 900.9 941.4

TBP(K) 0 338.5 360.7 339.9 340.210 605.5 646.6 640.6 600.830 725.9 776.5 770.9 72150 797.4 856 820.5 800.870 847.2 918.7 865.4 855.690 905.7 945.2 920.3 960.6100 948.9 988.2 998.7 992.9

Table 4.3: Conversion results from ASTM–D86 to TBP data

A mathematical function that describes intensity of amount of a carbon number or

molecular weight of compounds with NC ≥ 6 is called as a probability density func-

tion(PDF). The PDF can be obtained form a distribution function that describes how

various components are distributed in a mixture. [65]

Several distribution functions have been utilized for calculations related to the

petroleum mixture. Among the distribution functions which can be found in the

literature, 25 methods were chosen to be analyzed in Sanchez’s work.[66] The selected

distributions in the literature is listed in Table 4.4. Well-known but not included in

the list are Turkey-Lambda, Cauchy, and F distributions. They are seldom used to

model empirical data and they lack of a convenient analytical form of the PDF.

According to the literatures, the following observations were made:

• Four-parameter distribution functions offer the best fitting capability.

• Some of the three-parameter distribution functions can fit distillation data with

63

Eqn. Function Parameters1 α (normalized) 22 α 43 β 44 Bradford 35 Burr 46 χ 37 Fatigue life 38 Fisk 39 Frechet 310 folded normal 211 Γ 212 generalized extreme value 313 generalized logistic 314 Gumbel 215 half normal 216 Jhonson SB 417 Kumaraswamy 418 log-normal 219 Nakagami 320 normal 221 Riazi 322 Student’s t 323 Wald 224 Weibull 325 Weibull extreme 4

Table 4.4: Probability Distribution Functions Used in literatures

64

(a) Data #1

(b) Data #2

Figure 4.2: Comparison of ASTM–D86 curve and converted TBP curve(1)

good accuracy: the Weibull and Γ distributions.

• Two-parameter distribution functions exhibited poor fitting capability

Using four-parameter distribution functions is ideal for curve fitting and vali-

dation. However, Since we have only one available measured data (API gravity),

four-parameter distribution functions are unavailable. Instead, three-parameter dis-

tributions with proper assumptions can be applied. In the literature[66], Weibull, χ

and Γ distribution function are reported to show good accuracy. Three distribution

functions are used respectively in the algorithm and compared to evaluate accuracy.

The population density function in terms of molecular weight for this distribution

65

(a) Data #3

(b) Data #4

Figure 4.3: Comparison of ASTM–D86 curve and converted TBP curve(2)

model is:

F (M) =(M − η)α−1exp(−M−η

β)

βαΓ(α)(1)

where α, β and η are three parameters which can be determined by experiment.

When α < 1, the population density function becomes suitable for gas condensate

system. For values of α ≥ 1, the system shows behavior of heavier components as α

increases. However, if the experiment is not available, 1 and 90 for α and η can be

used as a default constant. [65]

The average molecular weight of the mixture(i.e., M7+) is:

66

M7+ = η + αβ (2)

which can be used to estimate parameter β.

The Weibull function with three parameters is defined in forms of PDF and cu-

mulative distribution function(CDF) as

PDF =C

B[(y − A)/B]C−1exp(−[(y − A)/B]C)

CDF = 1− exp(−[(y − A)/B]C)

(3)

The χ function is defined as

χ = 1− Γ(C

2,[(y − A)/B]2

2) (4)

The gamma function, Γ(α) is defined as

Γ(x) =

∫ ∞0

tx−1e−tdt (5)

which gives Γ(1) = 0 when α = 1.

The density function given in Eqn. 1 can be reduced to simpler form with the

assumption mentioned above.

F (M) =1

M7+ − ηexp(− M − η

M7+ − η) (6)

By integrating Eqn 4. between molecular weight boundaries of M−n and M+

n , xm,n,

mole fraction of SCN group n can be calculated.

67

xm,n = −exp( η

M7+ − η)×

⌈exp(− M+

n

M7+ − η) − exp(

M−n

M7+ − η)

⌉(7)

To use this characterization method, API gravity which is measured from the

plant in this study should be transformed to other property such as molecular weight

of C+7.

API gravity can be converted to specific gravity directly by:

SG =141.5

APIgravity + 131.5(8)

An extensive analysis was made was made on basic characterization for C+7 frac-

tions of wide range of crude oils were made [67]. In the analysis, following versatile

equation was found to be the most suitable for various properties of crude oils.

P ∗ = (A

Bln(

1

x∗))

1

B(9)

where P is a any property distribution including specific gravity, P ∗ is P−P 0

P 0 , and

x∗ is 1 − xc. Parameter A and B can be determined by experiments, or by using

literature data [67]. The parameter A can be calculated by experimental correlation:

SG∗average = 0.619A1/3SG

(10)

and B can be assumed to be a constant, 3. The distribution model of the mixture

can be estimated by reversing the specific gravity distribution we obtained.

68

Figure 4.4: History of API gravity data from the plant in this study

Figure 4.4 shows history of API data from the industrial plant in this study. Data

points of the steady state among the plenty of the measured data were selected and

used. The time when the data was selected is marked with red boxes.

For measured data from the industrial plant, distribution functions for cumulative

TBP curve are produced.

Converted TBP curve data seem to be very similar. That is because the API

gravity data which is measured from the plant is very close to each other since the

operating condition did not change drastically during the operation. Besides, other

fluid properties were not available nor considered in conversion algorithm. Therefore,

we need additional validation of the conversion results using other process data such

as temperature and pressure of the FCC reactor unit to guarantee the reliability of

the results.

69

Figure 4.5: PFD of the FCC process on Aspen HYSYS V8.4

4.5 Validation of the results

The reliability of the models with three distribution functions should be validated

with experimental data. However, real-time measurement for the industrial plant is

not available as mentioned in the previous chapter. Instead, the accuracy of the feed

property models were validated by comparing the reaction result using the mathe-

matical model which is built in this study with a steady-state result from a process

simulation software, Aspen HYSYS V8.4.

The default FCC reactor model in the software is used. The TBP curve data from

oil manager and petroleum assay with same API gravity in Aspen HYSYS is entered

to a feeder block for every 10◦C. The Peng-Robinson equation of state is employed

for this system. The naphtha hydro-treater unit in this model is deactivated to avoid

unnecessary reactions in the hydro-treater and preserve the distribution curve data

from the feeder block to the FCC block. The unit size, operating conditions and other

specifications at the same time were used for the design of HYSYS FCC model.

Table 4.5 shows that the Weibull distribution function and gamma distribution

function showed similar accuracy while the χ function was a little inaccurate. Hence,

70

Eqn. R2(Off − gas) R2(LPG) R2(WCN) R2(LCO) R2(CLO)Weibull 0.951 0.934 0.946 0.939 0.929

χ 0.948 0.930 0.941 0.9.7 0.927γ 0.953 0.937 0.946 0.941 0.933

Table 4.5: Comparison of validation results from three distribution functions

the gamma distribution function is selected to be used for the correlation model in

our study since data and assumptions parameters for the gamma distribution is much

available.

Fig 4.7 and Fig 4.8 presents the result of simulation distribution . The comparison

showed slightly disagreed expectation result for LPG and LCO. It is assumed that

uncertainties about catalyst in the reactor have caused this phenomenon. Process

catalyst coefficient can be calculated, but it is not known what kind of the catalyst

it is and kinetic constants in the reaction rate may vary. Considering that point, we

conclude that the correlation model exhibits an acceptable agreement with the results

of Aspen HYSYS V8.4.

4.6 Conversion of the measured process data into

model constants

In chapter 2, physical properties like heat capacity and heat of combustion are con-

sidered as constant since the model was incapable of identify different mixture com-

position within the feed flow. As the feed is characterized using the measured process

data, the heat capacity and the heat of combustion can be estimated by Lee-Kesler

correlation or API standard correlation depending on measuring environment.[68][69]

71

When 145K < T < 0.8TC

CLP = a(b+ cT )

a = 1.4651 + 0.2302Kw

b = 0.306469− 0.16734SG

c = 0.001467− 0.000551SG

(1)

For Tr < 0.85

CLP = A1 + A2 + A3T

2

A1 = −4.90383 + (0.099319 + 0.104281SG)KW +4.81407− 0.194833KW

SG

A2 = (7.53624 + 6.2147610KW ) · (1.12172− 0.27634

SG) · 10−4

A3 = −(1.35652 + 1.11863KW ) · (2.9027− 0.70958

SG) · 10−7

(2)

Aspen Properties and HYSYS software with workbook are used for calculation

of these properties in the modeling and validation. Since the correlated distillation

curve varied little, the heat capacity and heat of combustion are considered to be

almost unchanged.

4.7 Conclusion

This chapter provided an method to estimate unmeasured properties of feed mixture

and tested with measured data from an industrial plant and to validate the algorithm.

For the estimation, various correlation methods between complex petroleum proper-

ties were found from literature and interconnected to find the distribution function.

The results were validated by being compared with the results from Aspen HYSYS

72

V 8.4 under same operating condition. The proposed approach can provides insights

of complex feed in the petrochemical process without performing costly and time-

consuming experiment. This study can be improved to consider some attributes that

may be important but not available in this study. It is probable that with wide range

of plant data before the our FCC plant, we can improve the prediction performance

and help better understand the properties of feed flow.

73

(a) Off-gas

(b) LPG

(c) WCN

Figure 4.6: The mathematical model result with correlated TBP compared to AspenHYSYS V8.4 (1)

74

(a) LCO

(b) CLO

Figure 4.7: The mathematical model result with correlated TBP compared to AspenHYSYS V8.4 (2)

Chapter 5

Concluding remarks

This thesis presents a mathematical approach on modeling the fluid catalytic crack-

ing(FCC) process and its application including systematic analysis and feed charac-

terization. For this purpose, we study a FCC process in various ways.

Reaction kinetics should be defined to describe the reactor effluents and thermo-

dynamic phenomena in the reactor. Empirical correlations that describe the reac-

tion kinetics with model parameters are built. Also, an approach to apply the yield

function for the kinetic model of the riser is made. Lastly, hydrodynamics, mass bal-

ance and energy balance should be considered. Steady-state simulation results and

dynamic responses to the change of process variables are simulated by the process

model and compared to the plant data. Then based on the model and process de-

sign data, a systematic analysis is performed to identify the structural observability

of the system. The reactor and regenerator unit in this system are divided into six

nodes based on their functions and modeling relationships are built based on nodes

and edges of the directed graph. Output-set assignment algorithm is demonstrated

on the occurrence matrix to find that only a part of the system is fully observable

and the states in the regenerator is not observable with current measurement sets.

75

76

Optimal locations for additional measurement are suggested by completing the whole

output-set assignment algorithm of the system. A correlation method to estimate

unmeasured properties of feed mixture are suggested and tested to validate the algo-

rithm. Various correlation methods between complex petroleum properties are found

from literature and interconnected to find the distribution function. The proposed

approach can provides insights into the FCC process and will be a suitable technique

for process design, operation and even more applications such as optimization.

Based on this research, some of future works can be considered. First, mode

detailed systematic analysis can be performed to analyze structural observability and

controllability of the system. In this research, the system is divided into only 6

nodes regarding their functions. However, by defining more detailed system, we can

make use of much more measured data to improve accuracy of our model. Also,

we did not study about control problems of the FCC process. Further systematic

analysis would help this topics. The next is to evaluate more detailed correlation

model for characterizing the feed property. In this study only existing theories were

combined to find any improved correlation between available measurements and the

feed property. However, with more insight with thermodynamics and petrochemicals,

a new conversion method may be developed.

78

Appendix A

Nomenclature

ε = The void fraction

ρcat = The bulk catalyst density kg/m3

ρg = The gas density, kg/m3

θ = The temperature cut poin, K

Φ = The catalyst activity coefficient

ϕ = The coking tenency

Ai = The pre-exponential factor of ith pseudo-component, kJ/mol

Ariser = The crosssectional area of the riser, M2

Aregen = The crosssectional area of the regenerator, M2

BP i = The boiling point of ith pseudo-component, kJ/kG

C = The coke mass flowrate, kg/h

C0 = The coke flowrate at the riser inlet zone

CD = The drag coefficient

EA,i = The activation energy of ith pseudo-component, kJ/mol

Hc,coke = The heat of combustion of coke, kJ/kg

79

Hc,i = The heat of combustion of ith pseudo-component, kJ/kg

∆H i = The heat of cracking of ith pseudo-component, kJ/kg

∆HC,CO = The heat of combustion in reaction I, kJ/mol

∆HC,CO2 = The heat of combustion in reaction II, kJ/mol

∆HCO,CO2 = The heat of combustion in reaction III and IV, kJ/mol

∆HH2,H2O = The heat of combustion in reaction V

∆Hvap,i = The heat of vaporization of ith pseudo-component, kJ/kg

MCO = The molar flow rate of CO (mol/h)

MCO2 = The molar flow rate of CO2 (mol/h)

MO2 = The molar flow rate of O2 (mol/h)

MN2 = The molar flow rate of N2 (mol/h)

MHVGO = The molar flow rate of the feed (mol/h)

MH2O = The molar flow rate of H2O (mol/h)

MCO,DensetoDilute = The molar flow rate of CO leaving the dense bed (mol/h)

MCO2,DensetoDilute = The molar flow rate of CO2 leaving the dense bed (mol/h)

MN2,AirtoDense = The molar flow rate of N2 from theair to the dense bed (mol/h)

MH2O,DensetoDilute = The molar flow rate of H2O leaving the dense bed (mol/h)

MO2,DensetoDilute = The molar flow rate of O2 leaving the dense bed (mol/h)

MO2,in = The molar flow rate of O2 from the air to the dense bed (mol/h)

Mcat = Total catalyst holdup in the dense bed (kg)

Mi = The mass flow rate of ith pseudo-component (kg/h)

M = The mass flow rate of pseudo-components (kg/h)

Mcat = The mass flow rate of catalyst (kg/h)

80

Msteam = The mass flow rate of steam (kg/h)

MW = The average molecular weight (kg/mol)

MW i = The molecular weight of ith pseudo-component (kg/mol)

MW coke = The molecular weight of coke (kg/mol)

MWH2 = The molecular weight of hydrogen (kg/mol)

N = The number of pseudo-components

NBP = The normal boiling point (K)

P = Pressure (bar)

PCO = The partial pressure of CO (bar)

PO2 = The partial pressure of O2 (bar)

QR,Densebed = heat released per volume due to combustionreactions in the dense bed (kJ/m3)

QR,Dilutebed = heat released per volume due to combustionreactions in the dilute phase (kJ/m3)

R = Ideal gas constant

TB,i = the boiling point temperature of ith pseudocomponent (K)

T = Temperature (K)

TDilute = the temperature of dilute phase(K)

Tmixzone = the temperature of feed inlet zone

THVGO = the temperature of liquid feed (K)

Tregen = the temperature of the dense phase regenerator (K)

Tsteam = the steam temperature (K)

VDensebed = The volume of the dense bed (m3)

81

Y Risercoke = the coke weight fraction on catalyst from the riser reactor to regenerator

Y Regencoke = the coke weight fraction on catalyst from the regenerator to riser reactor

Ycoke = the coke weight fraction on catalyst

Y CokeH2 = the H2 weight fraction in coke

Cp,O2 = the heat capacity of oxygen (kJ/mol K)

Cp,N2 = the heat capacity of nitrogen (kJ/mol K)

Cp,CO = the heat capacity of CO (kJ/mol K)

Cp,CO2 = the heat capacity of CO2 (kJ/mol K)

Cp,H2O = the heat capacity of H2O (kJ/mol K)

Cp,cat = the heat capacity of catalyst (kJ/mol K)

Cp,avg = the average heat capacity (kJ/mol K)

Cp,gas,i = the heat capacity of ith pseudo-component in gas phase (kJ/mol K)

Cp,liquid,i = the heat capacity of ith pseudo-component in liquid phase(kJ/mol K)

Cp,steam = the steam heat capacity(kJ/mol K)

dcat = catalyst particle diameter(m)

g = gravitational acceleration (m/s2)

ki = the cracking rate constant of ith pseudo-component (mol/m3h)

kC,CO = the reaction rate constant in reaction I (1/bar h)

kC,CO2 = the reaction rate constant in reaction II (1/bar h)

kCO,CO2,c = the reaction rate constant in reaction III (mol/kgcathbar2)

kCO,CO2,h = the reaction rate constant in reaction IV (mol/hbar2)

kH2,H2O = the reaction rate constant in reaction V

p = the yield function

82

rC,CO = rate of reaction I (mol/m3h)

rC,CO2 = rate of reaction II (mol/m3h)

rC,CO2,c = rate of reaction III (mol/m3h)

rC,CO2,h = rate of reaction IV (mol/m3h)

vcat = the velocity of the catalyst in riser reactor (m/h)

vg = the gas velocity in riser reactor (m/h)

wi = the weight fraction of the ith pseudo-component

z = the axial position (m)

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