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Improvements in Petroleum Refinery Planning: 1. Formulation of Process Models Omar J. Guerra† and Galo A. C. Le Roux*

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Department of Chemical Engineering, University of S~ao Paulo, Av. Prof. Luciano Gualberto trav.3, 380, CEP 05508-900, S~ao Paulo-SP, Brazil ABSTRACT: Optimization of the production planning is crucial for the economic success of a petroleum refinery. Nevertheless, it is a difficult task, because of the large scale of the system and the complexity of the processes involved. Part 1 of this series of two papers addresses the formulation of process models for petroleum refinery planning. First, a generic formulation of nonlinear refinery planning model is adopted from the literature. Subsequently, the formulation of nonlinear empirical models for crude distillation units (CDUs) and a fluid catalytic cracking (FCC) unit is addressed. These empirical models were successfully validated using rigorous process simulators. Finally, the results from model validation showed that the accuracy of model predictions is as good as the current empirical process models reported in the literature, while the empirical process models proposed in this work overcome the limitations of both linear and nonlinear empirical models for CDUs and FCC units previously developed by other authors. Part 2 [Ind. Eng. Chem. Res. 2011, DOI: 10.1021/ie200304v] involves the implementation of nonlinear empirical process models in the petroleum refinery planning.

1. INTRODUCTION For many years, production planning problems in petroleum refineries have been addressed using the linear programming (LP) technique.1 This technique is based on delta-base process models (linearization of nonlinear process behavior at a particular set of operating conditions). Nevertheless, the linear process models are not suitable for refinery process modeling, since refinery processes involve both physical operations (phase separations, blending operations, etc.) and chemical operations (cracking reactions, hydrotreating reactions, etc.) that are characterized by their nonlinear nature. Because of this fact, the results (operating plans) from production planning models based on the linear programming technique can be unreliable. Furthermore, the recent advances in computer hardware and optimization algorithms allow the implementation of nonlinear process models in the production planning models. Moreover, Moro et al.2 quantify the impact of the adequate usage of refinery planning tools based on nonlinear process models in a potential increase of ∼6 000 000 US$/yr in the profitability for a typical refinery with operational capacity of 169.8 kbpd/day. Consequently, nowadays, different petroleum companies such as BP, ECOPETROL, ExxonMobil, and PETROBRAS have decided to develop their own refinery planning tools (based on nonlinear process models), instead of using commercial tools (based on the linear programming technique) such as the Process Industry Modeling System (PIMS) or the Refinery and Petrochemical Modeling System (RPMS). In this paper, nonlinear empirical models for crude distillation units (CDUs) and fluid catalytic cracking (FCC) units are proposed and validated. The empirical model for CDUs was based on the empirical procedure proposed by Watkins,3 using HYSYS (a rigorous process simulator) for model validation. In addition, the empirical model for a FCC unit was based (formulation and validation) on rigorous simulations carried r 2011 American Chemical Society

out in a FCC process simulator from PETROBRAS. Finally, the predictions from the empirical models developed in this work were compared with those obtained using empirical models from the literature.

2. REFINERY PLANNING Being profitable in petroleum refining depends on using systems and tools that enable the right people/functions to make the right decisions at the right time.4 These decisions are taken at different hierarchical levels (advanced control, real-time optimization, production scheduling, production planning, and strategic planning) and over different time horizons (seconds, minutes, days, weeks, months, and years), using phenomenological or empirical process models. The model accuracy, the computational effort to solve it, and the profit scale for each decision level can be represented as shown in Figure 1. As can be seen in this figure, the profit scale is inversely proportional to the model accuracy and the effort to solve it. In addition, there is an interaction between each two adjacent hierarchical levels; for example, the planning model provides the production plan for the scheduling model, and this provides the production program and the feasibility of the production plan from the planning level. According to Kreipl and Pinedo,5 the interaction between the planning and the scheduling levels may be intricate, because, in the planning model, the feedstock supply and the final product demand and production are considered as average values for the entire time horizon, whereas, in the scheduling model, the operation is considered to be a sequence of activities and the Received: February 12, 2011 Accepted: July 22, 2011 Revised: July 8, 2011 Published: July 22, 2011 13403

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Figure 1. Hierarchical structure of the decisions in a petroleum refinery.

Figure 2. Process unit structure.2

feedstock supply and the final product demand and production vary along the time horizon. Recently, several works have been reported about the integration between planning and scheduling in order to reduce the discrepancies in the results from these two models.6
8 Moreover, in order to provide accurate estimation of product yields and properties in the planning model, it is necessary to ensure an adequate modeling of the refinery process. Several works have been reported that are related to the implementation of nonlinear empirical process models in the refinery planning,2,9,10 because of the limitation of linear models to reproduce the refinery process behavior under any particular set of operating conditions. Moro et al.2 presented a general framework for the formulation of nonlinear refinery planning models, which will be described below. 2.1. Nonlinear Planning Model. According to Moro et al.,2 the topology of a refinery can be defined as a set of process units interconnected by mixers and splitters; the structure of each process unit is described in Figure 2. In general, the streams from one or more units (u0 ∈Uu) that can be sent (at a flow rate Fu0 ,s,u) as a feed to unit u are defined by the set su = {s1,s2,..,sn}. These streams are mixed together to obtain the total feed FFu to the unit u.

The set USu0 ,u contains all streams from the unit u0 that can be sent as a feed to the unit u; similarly, the set SUs,u contains all units u0 that can receive (as a feed) the stream s from the unit u. All streams existing in the entire refinery are characterized by the set of properties p = {p1,p2,..,pm}, the relevant properties for the feed to unit u are defined by the set PIu, while the relevant properties for each product stream s from this unit are defined by the set POu,s. In addition, the variables PAu,p and PCu,s,p denote the property values for the feed and each product streams s in the unit u, respectively. The set SOu contains all product streams from unit u, the yield and properties for the product stream s∈SOu can be function of a set of operational variables Ou = {o1, o2,..,ok}. The value for each operational variable is denoted by the variable Vo,u. The units that can be fed by external streams (i.e., distillation units) are defined by the set Uf, as well as the units that produce final products are defined by the set Up, these units can be represented as mixers. For convenience, the feed streams to each unit u∈Uf are considered to be product streams from a hypothetical unit r. Based on the sets and variables defined above, the mathematical model for the refinery planning can be written as follows: 13404

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Table 1. Mixing Rules and Property Indicesa property or property index

notation

addition base

cetane index

CTI

volume

motor octane numberb

MON

volume

index correlation

reference

research octane numberb

RON

volume

specific gravity

SPG

volume

API gravity

API

weight

Conradson carbon residue (wt %)

CCR

weight

sulfur (wt %)

SUL

weight

pour point index (pp = pour point (F)) smoke point index (smp = smoke point (mm))

PPI SPI

volume volume

PPI = 316200 exp{12.5 ln[0.001(PP + 459.67)]} SPI =
362 + [2300/ln(SMP)]

Li et al.11 Li et al.11

viscosity index (ν = kinematic viscosity (cSt))

VII

volume

VII = log10(ν)/(3 + log10(ν))

Riazi12

a

b

The mixing rules are a volumetric average, if the addition base is volume, or a weight average, if the addition base is weight. The mixing rule for these properties is a simplification used in this work, usually these properties have a nonlinear mixing rule.

Objective function: max Profit ¼

∑

u ∈ Up




Cpru 3 FF u


∑

u∈U

∑

∑

u ∈ Uf s ∈ USr, u

Crms 3 Fr, s, u ð1Þ

Copu 3 FF u

subject to FF u ¼

∑

∑

u0 ∈ Uu s ∈ USu0 , u

"u∈U

Fu0 , s, u

ð2Þ

PAu, p ¼ fu, p ðFu0 , s, u ju0 ∈ Uu ;s ∈ USu0 , u , PCu0 , s, p ju0 ∈ Uu ;s ∈ USu0 , u ;p ∈ PI u Þ

" u ∈ U, p ∈ PI u

ð3Þ

FPu, s ¼ hu, s ðFF u , PAu, p jp ∈ PIu , Vo, u jo ∈ Ou Þ " u ∈ U, s ∈ SOu

ð4Þ PCu, s, p ¼ gu, s, p ðPAu, p jp ∈ PI u , Vo, u jo ∈ Ou Þ " u ∈ U, s ∈ Su , p ∈ POu, s

ð5Þ

∑

u0 ∈ SUs, u

Fu, s, u0 ¼ FPu, s

FF u g Demandu

∑

u ∈ Uf

" u ∈ U, s ∈ SOu " u ∈ Up

Fr, s, u e Supply s

up FF lo u e FF u e FF u up PAlo u, p e PAu, p e PAu, p

Vo,lou e Vo, u e Vo,upu

" s ∈ USr, u "u∈U " u ∈ U, p ∈ PI u " u ∈ U, o ∈ Ou

FF u , Fu0 , s, u , FPu, s ∈ Rþ ; PAu, p , PCu, s, p , Vo, u ∈ R

ð6Þ ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ ð12Þ

Equation 1 defines the objective function (maximize the total profit (US $/day)) for the refinery planning model in terms of sales revenue (blending units, u∈Up), raw material purchase costs (units that can process external streams, u∈Uf), and operating costs. The terms Cpru, Crms, and Copu denote the

unitary product prices, raw material costs, and operating costs respectively. These costs and prices are not necessarily constants. For example, the product prices can be a function of a key property (in the case of gasoline, the octane number can be the key property) and the operating costs can be a function of operational variables (for more details, see Part 2 of this work [Ind. Eng. Chem. Res. 2011, DOI: 10.1021/ie200304v]). Equation 2 denotes the mass balance for the feed mixer in each process unit. Equation 3 represents the total feed properties as a function of the properties and flow rate of each individual feed stream to the unit. The function fu,p denotes a mixing rule for the property p; this mixing rule can be on a volume basis (i.e., density, olefins (vol%), etc.) or a weight basis (i.e., sulfur content (wt %), nitrogen content (ppm), etc.). Nevertheless, many properties involve highly nonlinear mixing rules (i.e., pour point, flash point, viscosity, etc.); in this case, the linear blending indices (volumebased or weight-based) can be used, the mixing rules and property indices used in this paper are described in Table 1. Equation 4 represents the flow rate of each product stream as a function of operational variables Vo,u|o∈Ou and flow rate and properties of total feed to the unit. Similarly, eq 5 represents the properties of product streams PCu,p|p∈PIu as a function of operational variables Vo,u|o∈Ou and properties of the total feed to the unit. Equation 6 denotes the mass balance for each product stream s from each unit. Inequality 7 denotes the lower bounds on product demands for blending units (u∈Up); it will be assumed that product demand is flexible in the sense that it is given by a hard lower bound and a free upper bound. Similarly, inequality 8 denotes the upper bounds on raw material supply. Inequality 9 represents the operational capacity for every unit in the refinery. Inequality 10 denotes the specifications for the final product streams (u∈Up), as well as the possible feed specification for the process units (uˇUp). In addition, inequality 11 denotes the lower and upper bounds for the operational variables in each process unit. These limits generally are subject to design conditions. Finally, expression 12 denotes the domain of the variables used in the formulation of the refinery planning model. The mathematical model for the refinery planning described above results in a nonlinear planning model and can be solved using nonlinear programming (NLP) optimization algorithms such as sequential linear programming (SLP), generalized reduced gradient (GRG), sequential quadratic programming (SQP), and interior point (IP). These algorithms have been implemented in some NLP solvers, such as CONOPT, IPOPT, 13405

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Figure 3. Simplified distillation processes.

KNITRO, MINOS, and SNOPT, which are available in many modeling systems (AIMS, AMPL, GAMS, and MINOPT).

3. CRUDE DISTILLATION UNITS Crude distillation units (CDUs) are the most important process units in a refinery, because they perform the separation of crude oil in many fractions (naphtha, kerosene, diesel oil, atmospheric residue, vacuum gas oils, etc.) that are processed in the downstream units (FCC units, delayed coking unit, etc.) or sent to the blending system to form final products. Consequently, the overall economical performance of a refinery is directly impacted by the operation of the CDUs. The crude distillation process occurs in two sections: in the first one (denoted as atmospheric distillation), the operating pressure is set close to atmospheric pressure. In the second section (denoted as vacuum distillation), the operating pressure is set to vacuum pressure (generally in the range of 50
100 mmHg). Prior to the distillation processes, the crude oil is desalted using water (to prevent corrosion problems) and heated to provide the adequate conditions for the separation. In Figure 3, a simplified distillation process is presented. The yields and properties of the different fractions from the distillation process depend on the type of crude processed (heavy, medium, or light) and the operating conditions (heater outlet temperature, reflux ratio, etc.). 3.1. Overview of Empirical Models for Crude Distillation Units. The empirical models for CDUs reported in the literature

include the swing cut model,13 the adherent recursion model,14 and the Weight Transfer Ratio (WTR) model.15 The swing cut model is the most commonly used of these models. Normally, the swing cut model is implemented in commercial planning tools such as RPMS and PIMS, basically due to its simplicity. On the other hand, the swing cut model is more inaccurate than the adherent recursion and WTR models. In the swing-cut model, the TBP (true boiling point curve) cut point between each two

adjacent fractions is optimized using a pseudo-cut called a swing cut (a virtual cut between each two adjacent fractions) with constant properties. The size of each swing cut is defined as a certain volume percentage or weight percentage of the overall crude fed to the CDU (i.e., 5 wt% for the swing cut naphtha/ kerosene, according to Zhang et al.13). Optionally, the size of each swing cut can be defined as a certain TBP range (i.e., 50 F, according to Trierwiler14). In the case that more than one crude oil can be fed to the CDU, the flow rate of each swing cut from all crude oils are pooled and the resultant stream is distributed between the corresponding two adjacent fractions. The major limitation of the swing cut model is that the properties for each swing cut are considered constants across its TBP range, while the property distribution across the TBP ranges are known to be highly nonlinear. Consequently, the swing cut model fails to represent the highly nonlinear behavior of distillation processes. The adherent recursion model addresses this limitation, using an iterative procedure between a LP planning model and a rigorous process simulator (HYSYS, PRO/II, etc.). In this procedure, the LP planning model is used to optimize the TBP cut points and the solution at each iteration (new cut points) is used by the rigorous process simulator to provide updated yields and properties for the CDU fractions. The main limitation of the adherent recursion is the long computational time required for the convergence of the iterative procedure, because of the use of a rigorous process simulator. Finally, in the WTR model, the CDU operating modes are used to determine the maximum and minimum yield of each fraction over the TBP curve of the crude oil fed to the CDU; these values are fixed as upper and lower bounds for the yield of each fraction from the CDU. In addition, the properties of CDU fractions are expressed as a nonlinear function of their respective mid-volume transfer ratio. The TBP cut points are optimized using the yield of CDU fractions as decision variables constrained 13406

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Figure 4. Typical TBP distillation curve.

Figure 5. Typical sulfur distribution curve.

by the mass balance and the maximum and minimum yields obtained from the operating modes. Therefore, this model can represent the highly nonlinear behavior of distillation processes. Nevertheless, as in the petroleum industry, it is very usual that the CDU is able to process more than one crude oil; the implementation of the WTR model requires additional tedious procedures to estimate the TBP curve of the crude oil mixture fed to the CDU. 3.2. Empirical Model for CDUs. The necessary characterization information of each crude oil must be available in the refinery (i.e., from laboratory databases) in order to developed a meaningful empirical model for CDUs. There are two types of characterization information normally used for crude oil evaluations: the crude oil distillation curve (TBP) and the crude oil property distribution curves. The TBP curve is the relationship between the distillate temperature and the cumulative volumetric fraction distilled in a standard distillation column. The standard test method for the experimental estimation of the TBP is ASTM D2892 (at atmospheric pressure) for fractions with boiling points below 400 C and the ASTM D1160 (at reduced or vacuum pressure) for fractions with boiling points above 400 C. For distillate products, standard method ASTM D86 is generally used. Distillation curves obtained by the ASTM D1160 and ASTM D86 standard test methods can be converted into TBP curves using the method described by Riazi.12 A typical TBP curve is presented in Figure 4. On the other hand, the properties (API density, sulfur (wt %), etc.) of distillate products can be expressed using the property distribution curves, which represent the relationship between the crude oil properties and the mid-volume transfer ratio (Mid-Vol (%)) of the fraction distilled.3 A typical sulfur (wt %) distribution curve is presented in Figure 5. The TBP curve and the property distribution curves for each crude oil (available in the refinery) are the necessary characterization information for the empirical model developed in this work. In many cases, the distribution curve for a given property can be unavailable in the refinery. In that case, the distribution curve can be predicted from the TBP curve and the distribution curve for other property (density, viscosity, molecular weight, etc.) using empirical correlations.12 In addition to the crude oil characterization information, the set of decision variables is another important aspect to be defined in the formulation of the empirical model for CDU. This set should be related to the operating variables that significantly affect the process behavior for a given feedstock characterization. The TBP cut points between adjacent fractions are probably the operating variables that have the greatest impact on the CDU operation.

The definition of the TBP cut point between adjacent fractions is illustrated in Figure 6. In this figure, the temperature T100 L represents the final TBP boiling point for the light fraction (EBPL) and the initial TBP boiling point for the heavy fraction (IBPH) is represented by the temperature T0H. As can be seen in Figure 6, the TBP cut points are defined as the average temperature between the EBPL and IBPH (Tcut = 0.5(T100 L
T0H)). In addition, the degree of separation between two adjacent fractions is given by the difference between EBPL and IBPH (T100 L
T0H). This degree of separation depends upon the efficiency of the distillation column. The detailed procedure for the estimation of the TBP cut points is presented in Figure 7. As shown in this figure, the TBP cut points can be estimated from ASTM D86 100% (the temperature corresponding to the 100 vol % on the ASTM D86 distillation curve) product specifications and the degree of separation given by the Gap (5
95) ASTM (the temperature difference between the ASTM 5 vol % boiling point of the heavier product and the ASTM 95 vol % boiling point of the adjacent lighter product). The product yields and properties are strongly affected by changes in TBP cut points. Furthermore, they are commonly used in the CDU operation to control the adequate separation efficiency in the distillation column, as well as the product specifications. For this reason, the TBP cut points are chosen as decision variables in the proposed approach. The ASTM D86 specifications are defined for each refinery, and the Gap (5
95) can be set by heuristics or estimated using a rigorous process simulator (HYSYS, PRO/II, etc.). In that case, many scenarios must be defined by varying the operating conditions and the feedstock characterization in order to evaluate the variability of each degree of separation; the Gap (5
95) ASTM between each two adjacent fractions should be reported as the average value for all of the scenarios. Usual values (recommended by Watkins3) for the ASTM D86 boiling point range (IBP and EBP) of CDU fractions and the Gap (5
95) ASTM are presented in Tables 2 and 3, respectively. In this work, ranges of 260
275 F and 650
700 F will be considered for the EBP of gross overhead and heavy distillate, respectively; in other case, the values from Table 2 will be used. The volumetric yield of each CDU fraction can be estimated as a function of the TBP cut points. For example, the volumetric yield (vol %) of heavy naphtha for a given crude oil is estimated as the difference between the cumulative volume percent corresponding to the two adjacent TBP cut points (heavy naphtha/ light distillate and gross overhead/heavy naphtha TBP cut points). In addition, the Mid-Vol (%) value of each fraction is 13407

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Figure 6. Definition of TBP cut point between adjacent fractions.3

Figure 7. Procedure for the estimation of TBP cut point between adjacent fractions.3

estimated using its volumetric yield and the actual cumulative volume percentage. 3.2.1. Mathematical Model. The mathematical formulation of the empirical model for the CDUs is based on the process unit structure presented in Figure 2. It is considered that the refinery has only one CDU, and this is the only unit that processes crude oil (Uf = {CDU}). Nevertheless, the model can be easily implemented if there is more than one CDU in the refinery. The model was formulated on a volumetric basis (volumetric balances are very common in the petroleum industry), then all of the flow rates are given in volumetric units. The set USr,CDU = {s01 ,s0 2,...,s0 k} defines the crude oils (at a flow rate Fr,s0 ,CDU) that can be fed into the CDU, and the total feed flow rate to the CDU is represented by the variable FFCDU. The product streams from this unit are defined by the set SOCDU = {s1,s2,...,sn}. In addition, the variable FPCDU,s denotes the total flow rate of each product stream from the CDU, and the contribution of each crude oil to the total flow rate of each product stream is represented by the variable FDs,s0 . In general, the product streams from the CDU can be characterized by the set of properties POCDU = {p1,p2,...,pm},

while the relevant properties for each product stream are defined by the set POCDU,s⊆POCDU. The variables PCCDU,s,p and PDs0 ,s,p represent the property values of the product streams and the contribution of each crude oil to the property values of each product stream from the CDU, respectively. The units that can process product streams from the CDU are defined by the set SUs,CDU. The operating variables in the CDU are defined by the set of TBP cut points between adjacent fractions OCDU = {Ts1,s2,Ts2,s3,...,Tsn
1sn}. In addition, the variable VTsi,si+1 ,CDU denotes the value of each operating variable in the CDU. The crude oils are characterized by the TBP curve (TBPs0 ) and the property distribution curves (PROp,s,). The variable VDs0 ,Tsi ,si+1 represents the volume percent vaporized of crude oil s0 for each TBP cut point and the variable Mid_Vols,s0 represents the mid-volume transfer ratio for product streams from the CDU. Finally, based on the sets and variables described above, the mathematical model for the CDUs can be written as follows: VDs0 , Tsi , siþ1 ¼ TBPs0 ðVTsi , siþ1 , CDU Þ " s0 ∈ USr, CDU , Tsi , siþ1 ∈ OCDU

ð13Þ 13408

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Table 2. Suggested ASTM Boiling Ranges for CDU Fractionsa Operating Mode product

a

max naphtha

max light distillate

gross overhead (GO)

250
275 F (EBP)

250
275 F (EBP)

250
275 F (EBP)

heavy naphtha (HN)

400 F (EBP)

325 F (EBP)

325 F (EBP)

light distillate (LD) heavy distillate (HD)

375
600 F (IBP
EBP) 575
675 F (IBP
EBP)

300
600 F (IBP
EBP) 575
675 F (IBP
EBP)

300
550 F (IBP
EBP) 525
675 F (IBP
EBP)

Data taken from ref 3.

∑

Table 3. Suggested Gap (5
95) ASTM for Adjacent Fractionsa adjacent fractions

a

max heavy distillate

u0 ∈ SU s, CDU

Gap (5
95) ASTM (F)

gross overhead/heavy naphtha (GO/HN)

20
30

heavy naphtha/light distillate (HN/LD)

25
50

light distillate/heavy distillate (LD/HD)

0
10

heavy distillate/bottom residue (HD/BR)

0
10

VTlosi , s

FF CDU ¼



1 " s0 ∈ USr, CDU VDs0 , Ts1 , s2 100
 ð15Þ 1 ð100
VDs0 , Tsn
1 , sn Þ " s0 ∈ USr, CDU ¼ Fr, s0 , CDU 100 ð16Þ

FDs1 , s0 ¼ Fr, s0 , CDU

∑

" s ∈ SOCDU

FDs, s0

Mid _ Volsi , s0 ¼ VDs0 , Tsi
1 , si þ 0:5ðVDs0 , Tsi , siþ1
VDs0 , Tsi
1 , si Þ "si jTsi , siþ1 ∈ fTs2 , s3 , Ts3 , s4

,..., Tsn
2 , sn
1 g, s0 ∈ USr, CDU

Mid_Vols1 , s0 ¼ 0:5VDs0 , Ts1 , s2

" s0 ∈ USr, CDU

Mid_Volsn , s0 ¼ 100
0:5VDs0 , Tsn
1 , sn

ð17Þ

ð18Þ ð19Þ

" s0 ∈ USr, CDU ð20Þ

PDs0 , s, p ¼ PROp, s0 ðMid_Vols, s0 Þ " s0 ∈ USr, CDU , s ∈ SOCDU , p ∈ POCDU, s

ð21Þ PCCDU, s, p ¼

1 FPCDU, s

∑

s0 ∈ USr, CDU

" s0 ∈ USr, CDU

∑

s0 ∈ USr, CDU

PDs0 , s, p FDs, s0 " s ∈ SOCDU , p ∈ POCDU, s

ð22Þ

ð25Þ

Fr, s0 , CDU

ð26Þ

up

ð27Þ

FF loCDU e FF CDU e FF CDU

FF CDU , Fr, s0 , CDU , VDs0 , Tsi , siþ1 , FDsi , s0 , Midvolsi , s0 , FCDU, s, u0 ,

ð14Þ

s0 ∈ USr, CDU

e VTsi , siþ1 , CDU e VTsi , siþ1 , CDU " Tsi , siþ1 ∈ OCDU

up

 1 FDsi , s0 ¼ Fr, s0 , CDU ðVDs0 , Tsi , siþ1
VDs0 , Tsi
1 , si Þ 100 "si jTsi , siþ1 ∈ fTs2 , s3 , Ts4 , s5 , :::, Tsn
2 , sn
1 g, s0 ∈ USr, CDU

FPCDU, s ¼

ð23Þ

up

iþ1 , CDU

Fr, s0 , CDU e Fr, s0 , CDU




FDsn , s0

" s ∈ SOCDU

ð24Þ

Data taken from ref 3.




FCDU, s, u0 ¼ FPCDU, s

FPCDU, s ∈ Rþ ; PDs0 , s, p , PCCDU, s, p , Vo, CDU ∈ R

ð28Þ

Equation 13 defines the volume percent vaporized (in units of vol %) of each crude oil as a function of the TBP cut points (in this work, the TBP curves are represented using a third-order polynomial function). The contribution of each crude oil to the total flow rate of each product stream is described by eqs 14, 15, and 16, while the total flow rate for these products is obtained using eq 17. In addition, the mid-volume transfer ratio for product streams can be estimated according to eqs 18, 19, and 20. The contribution of each crude oil to the property values of each product stream is expressed by eq 21; in this work, the property distribution curves were represented using a fourth (or less)-order polynomial function. Furthermore, the properties of product streams are estimated using eq 22 if the mixing rule of the property is based on volume. In the case of properties with a mixing rule based on weight, the flow rate in eq 22 should be given in mass units (the property indices shown in Table 1 can be used for properties with highly nonlinear mixing rules). Equation 23 denotes the volumetric balance at the product splitters. Inequalities 24 and 25 denote the constraints for operating variables and crude oil supply, respectively. Equation 26 represents the volumetric balance at the feed mixer (crude oil mixer) of the CDU. The operating capacity is defined by inequality 27. Finally, the expression described by eq 28 denotes the domain of the variables used in the formulation of the empirical model for CDUs. 3.2.2. Model Validation Using HYSYS. The empirical model for the CDUs was validated using rigorous process simulations (based on TBP data and pseudo-components) carried out in Aspen HYSYS v7.0, using Peng
Robinson as the fluid package. Three case studies were evaluated using two different crude oils: Tia Juana Light and Arabian Heavy. The configuration of each case study is presented in Table 4. The main products from the 13409

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Table 4. Case Studies for CDU Model Validation Feed Flow Rate (kbpd) crude oil

Case A

Case B

Case C

Tia Juana Light (API = 31.6)

60

70

80

Arabian Heavy (API = 27.4)

40

30

20

total

100

100

100

predictions using the empirical model was e4.10 vol %. This absolute error can be reduced to be e0.51 vol % via the addition of bias factors to the empirical model predictions, as described in eq 29. These bias factors were calculated as an average of the empirical model errors, with respect to the rigorous simulation. FPCDU, s ¼

molecular weight

Case A

Case B

Case C

29.65

30.06

30.48

234.0 kg/kmol

230.2 kg/kmol

226.4 kg/kmol

Table 5. Product Specifications Specification product

ASTM D86, 100%

Gap (5
95) ASTM

gross overhead

275 F (135.0 C)

heavy naphtha

325 F (162.8 C)

25 F

light distillate

600 F (315.6 C)

35 F

heavy distillate

700 F (371.1 C)

10 F

bottom residue

FDs, s0 þ BiasðsÞ

 FF CDU " s ∈ SOCDU

CDU Feed Properties

API density

∑

s0∈ USr, CDU

5 F

CDU are: gross overhead, heavy naphtha, light distillate, heavy distillate, and bottom residue. The specifications for CDU products and the degree of separation between adjacent fractions are presented in Table 5. The data shown in Table 5 should be interpreted as follows: the Gap (5
95) ASTM between gross overhead and heavy naphtha is equal to 25 F. The configuration of the CDU in HYSYS includes a preflash column, a crude oil heater, and a distillation column. The preheated crude oils are mixed and fed to the preflash column at 450 F and 75 psia. In the preflash column, light components are removed from the crude oil (mixed crude oil) in order to reduce the energy consumption in the crude oil heater. The heavy product (bottom product) from the preflash column is fed to the crude oil heater, where it is heated to the appropriate column feed temperature. According to Watkins,3 the column feed temperature should be in the range of 650
700 F in order to avoid thermal cracking. In this work, the column feed temperature was set to 700 F. In addition, the distillation column includes a main column with 29 theoretical stages, three pumparounds, three side-strippers, a condenser, and a reboiler (see Figure 8). The distillation column has 13 degrees of freedom (see Table 6), while the empirical model developed in this work has only 8 degrees of freedom (4 ASTM D86 100% and 4 Gap (5
95) ASTM). This is because the empirical models are more simplified than the rigorous process models. For example, the energy balance is not included in the empirical model for CDUs developed in this work. The CDU was simulated for all of the case studies using both the rigorous process simulator model (the HYSYS model) and the empirical model developed in this work. In the empirical model, the TBP cut points were estimated using the procedure described in Figure 7, using the specifications presented in Table 5. The comparison of product yields is shown in Table 7. As can be seen in this table, the absolute error in the yield

ð29Þ

Equation 29 is a modification of eq 17; the sum of the bias factors should be equal to zero, because of the volumetric balance in the product splitters. In the work of Li et al.,15 the yield predictions from the WTR model were compared (using three case studies) with rigorous simulation carried out in Aspen Plus version 11.1; the absolute error in the yield predictions was determined to be less than or equal to 1.3, 3.2, 3.07, 2.67, and 3.06 wt % for the gross overhead (GO), heavy naphtha (HN), light distillate (LD), heavy distillate (HD), and bottom residue (BR), respectively. Finally, based on the results from model validation, it can be concluded that the empirical model for CDU developed in this work is adequate for the simulation of the CDUs.

4. FLUID CATALYTIC CRACKING (FCC) UNIT Fluid catalytic cracking (FCC) is the most important conversion process in a refinery. In this process, heavy fractions (atmospheric gas oil, vacuum gas oil, cocker gas oil, etc.) are converted into light and more-valuable fractions (ethane, ethylene, propylene, butylenes, iso-butane, n-butane, naphtha, etc.). FCC naphtha becomes a gasoline blending stock. According to Robinson,16 the FCC units produce more than half of the world’s gasoline. Light olefins (particularly propylene and butylenes) and iso-butane are alkylated (in the alkylation unit) to produce highoctane hydrocarbons for the gasoline pool. In addition, ethane and ethylene are used as petrochemical feedstock to produce a variety of products. The FCC units consist of a riser reactor, a regenerator, and a product separation system (see Figure 9). In the riser, the fresh feed is mixed with the regenerated catalyst to provide the necessary conditions for the cracking reactions. In the regenerator, the combustion air provides the necessary oxygen for the catalyst regeneration by burning of the coke in the spent catalyst from the reactor. In addition, the cracked products from the reactor are obtained separately in the fractionator. The FCC feed composition has a direct impact in the process behavior. For example, the reactivity increases according to paraffins > naphthenes > aromatics. Therefore, paraffinic feeds produce more naphtha (with less octane number) than naphthenic and aromatic feeds for the same set of operating conditions. Olefins are not the preferred feed to an FCC unit, because they often polymerize to form undesirable products, such as decanted oil and coke. The typical olefin content of FCC feed is