Producción de urea por carbonatacion de amoniaco

8/18/2019 Producción de urea por carbonatacion de amoniaco

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A D UAL A PPROACH FOR M ODELLING AND O PTIMISATION OF I NDUSTRIAL U REAR EACTOR : S MART T ECHNIQUE AND G REY B OX M ODEL

Sohrab Zendehboudi, 1* Gholamreza Zahedi, 2 Alireza Bahadori, 3 Ali Lohi,4 Ali Elkamel1 and Ioannis Chatzis 1

1. Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G12. Chemical & Biological Engineering Department, Missouri University of Science & Technology, Rolla, Missouri 65409

3. School of Environment, Science and Engineering, Southern Cross University, Lismore, NSW, Australia 4. Department of Chemical Engineering, Ryerson University, Toronto, Ontario, Canada M5B 2K3

Urea has the highest demand among all solid nitrogenous fertilisers within the agriculture industry. In this paper, a mathematical model andan Articial Neural Network (ANN) technique are proposed for the simulation and optimisation of the urea plant in an industrial petrochemicalcompany. The developed mathematical model consists of complex vapour–liquid equilibria for the NH 3 –CO2 –H2 O–(NH 2 )2 CO system in thermo-dynamic and reaction frameworks. The smart technique (e.g. ANN) considers the CO 2 conversion in terms of temperature and the molar ratios of NH3 /CO 2 and H 2 O/CO 2 in the liquid phase. The ANN predictions were compared with the real data and results obtained from the mathematicalmodel. An acceptable agreement was attained between deterministic methods. Through implementation of a systematic sensitivity analysis, itwas found that a temperature of 191 ◦ C, a pressure of 132 atm and a NH 3 /CO 2 ratio of 2.7 are the optimum process conditions for the ureaproduction. It is concluded that the developed ANN (or connectionist) technique is an efcient tool for modelling complex phase equilibria with

reaction in the industrial urea plant.

Keywords: urea plant, simulation and optimisation, connectionist technique, ammonium carbamate, thermodynamics model

INTRODUCTION

N itrogen-based fertilisers are the most broadly producedkinds of fertilisers. [1–3] Among them, urea is the mostimportant product whose consumption is increasing sig-nicantly in the agriculture industry. In addition, urea is widelyused as a raw material in producing many chemical compounds

including plastics, chemical solutions, adhesives and medicaldrugs. [2–4] Urea or carbamide is an organic compound withthe chemical formula (NH 2 )2CO. The German chemist, FriedrichWohler (1828), produced urea by reacting silver isocyanate withammonium chloride. [5–7] The synthesis of this organic materialfrom an inorganic compound made a great impact on the devel-opment of organic chemistry. The industrial production of ureais based on the reaction of ammonia (NH 3) and carbon dioxide(CO2) at high pressure and temperature to form ammonium car-bamate, which is consecutively dehydrated into urea and water.Both the exothermic carbamate reaction and the endothermic ureaformation reaction often happen in the urea reactor of the indus-trial plants. [7–10] The reactor is designed such that its volume is bigenough for the desired urea production. In most of the technolo-gies developed for urea synthesis, the main reaction takes place inthe liquid phase under pressure ranging from 13 to 25 MPa; while,the reactor temperature is between 170 and 200 ◦ C.[6,7,10] Moreover,the recent reactors are operated as adiabatic in practice. [1,7,10]

Transport phenomena (e.g. heat and mass transfer) betweenexisting phases and the kinetics of urea reaction govern thebehaviour of the urea reactor. Therefore, the conversion of car-bamate into urea is not only controlled by the equilibriumconstraints of urea reaction as traditionally believed, but also bythe uid dynamics contributing into the reactor operation. [7–10]

The widespread urea synthesis technologies were addressedby several researchers. [1,3,10] These different technologies of urea

production mainly contrast on how urea is separated from theraw materials and how NH 3 and CO 2 are recycled back to thereactor. [5,11 ,12] The urea technologies include total or partial recy-cle of unconverted CO 2 and NH 3 in order to remove the restrictionsapplied by chemical equilibrium on conversion of the raw materi-als to urea. Modications of the production technologies are oftenfocused on enhancement of CO 2 conversion, optimisation of heatrecovery and reduction in the utility consumption. Despite the factthat modelling and simulation of the urea process is well treatedin the literature, there are still various key aspects to be explainedin the numerical modelling of such a complex process. [7,13–15]

For instance, developing an accurate thermodynamics model isnecessary in order to predict the compositions of reactants andproducts with high precision at different temperatures and pres-sures during the urea production process. Also, it is worthy topropose a reliable tool (e.g. intelligent methods) for fast, lowcost and effective assessment of urea reactors in the absence of adequate experimental or/and commercial data. Gorlovskii andKucheryavyi [16] developed an empirical equation after analysingthe urea conversion data reported by several authors. [16–18] The

proposed correlation provides an accurate way to relate conver-sion of CO 2 in the form of urea to H 2O/CO 2 mole ratio whichis used in the current study. [16–18] However, very few researchworks have been published on biuret (NH 2CONHCONH 2) for-mation, the major undesired by-product in the urea production

∗ Author to whom correspondence may be addressed. E-mail address: [email protected]. J. Chem. Eng. 92:469–485, 2014©2013 Canadian Society for Chemical EngineeringDOI 10.1002/cjce.21824Published online 26 April 2013 in Wiley Online Library(wileyonlinelibrary.com).

| VOLUME 92,MARCH 2014 | | THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING | 469 |


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process. [16–18] Since biuret is toxic to plants, its content in fertilis-ers has to be kept as low as possible. Therefore, this by-productshould be considered in a comprehensive numerical modelling of urea synthesis, as well. This will help controlling the operationalconditions of the urea reactor to lower the concentration of biuretin the product stream.

The importance of urea production demands for energy con-servation and environmental control mandates are the mainmotivations to model and optimise the urea production reactor.This paper addresses main aspects of an industrial urea plant

in terms of process engineering perspectives. The mathematicalmodelling of the urea synthesis is complicated due to the for-mation of ammonium carbamate, an intermediate product andthe uid dynamics. A mathematical model and an Articial Neu-ral Network (ANN) system are developed in this study basedon the thermodynamics and synthesis frameworks for the ureareactor in the industrial plant of Shiraz Petrochemical Companyin South of Iran. This study utilises the MATLAB TM and AspenPlus softwares for modelling simulation of the Stamicarbon CO 2process operating in the Petrochemical Company. A comprehen-sive Pressure/Volume/Temperature (PVT) study was carried outusing the Aspen Plus package in this paper. UNIQUAC model andthe modied Peng–Robinson (PR) equation of state (EOS) havebeen used to calculate the equilibrium conditions of the liquidand gas phases, respectively, for this rather complicated system.Following the mathematical modelling and the sensitivity analy-sis, an ANN system was used to forecast the CO 2 conversion andthermodynamic behaviour in the chemical reactor. The CO 2 con-version was considered as a function of temperature, NH 3 /CO 2and H 2O/CO 2 molar ratios. The optimisation of the urea reactorwas lastly performed using the ANN technique.

UREA PRODUCTION PROCESS VIA STAMICARBON METHOD

There are several commercialised processes proposed for urea pro-duction such as Stamicarbon process, Snamprogetti Process, Chaoprocess and Uchino process. [7,9,10] Stamicarbon method is one of

the most common processes for urea production designed andcommercialised by a Dutch company. [1,2,7] This type of process isrecognised as an acceptable and a fast growing process for pro-ducing urea. [1,7] In this production method, usually the generatedcarbamate from ammonia and carbon dioxide enters the reactorto produce urea in the form of a closed total recycle.

In general, the urea plant consists of three key parts: reactor,stripper and condenser. First, carbamate is produced in the con-denser and then it returns to the reactor through the gravitationalforce. The tubular reactor is equipped with some trays for effec-tive mixing of the phases. The inlet CO 2 is injected with someair to cover the wall of the reactor in order to prevent corrosionin the system. Figure 1 shows the block diagram of the processdescribed.

The process used in the urea production plant of Shiraz Petro-chemical Company is based on the Stamicarbon method. Theresidence time in the reactor (about 28.5 m height and 2.5 mdiameter) is about 30–40 min. In order to prevent the back mix-ing phenomenon and improve dispersion and contacting betweenphases, the reactor is equipped with eight sieve trays. However,these trays cannot eliminate the back mixing problem completelyand the reactor behaviour is far from an ideal Continuously StirredTank Reactor (CSTR). On the other hand, the reactor cannot beconsidered as a plug ow reactor, since the material streamsthrough the reactor are not in a plug ow movement. This is thereason to model the reactor in the form of some CSTRs in series.

THEORY OF UREA SYNTHESIS

Frejacques [8] proposed one of the early time kinetic models for thechemical reaction of urea production; a reversible reaction for theurea synthesis in the form [1,8] :

2NH 3(l) + CO2(l) ↔ NH2CONH 2(l) + H2O(l) (1)

This model was widely accepted among researchers up to1952. [1] Thereafter, it was found by other researchers that the ureaproduction is a two-step reaction: synthesis of ammonium carba-mate (NH 4COONH 2), and then conversion of carbamate to waterand NH 2CONH 2 .[7,12 ,19] Thus, the reactions are stated as:

2NH 3(l) + CO2(l) ↔ NH4COONH 2(l) (2)

NH4COONH 2(l) ↔ NH2CONH2(l) + H2O(l) (3)

Lemkowits [20] considered two conversion extents for the abovereactions and also determined Henry’s constants for CO 2 and NH 3in the reaction mixture based on experimental data. A number of empirical correlations were proposed in the literature to calculatethe equilibrium mole fractions of the components in the reac-tion mixture system. [12 ,20] However, most of the studies have been

conducted within limited ranges of pressure and temperature.

MATHEMATICAL MODELLING OF UREA SYNTHESISREACTOR

Efciency or performance of a chemical reactor depends mainlyon the rate of reactions, rates of mass and heat transfer andintra-particle phenomena. Also, phase-equilibrium affects themagnitudes of the components’ concentrations in the reactor.During the last few decades, attempts were made to explain theeffects of non-ideality of the processes on reactor performance.The mixing process is commonly evaluated considering two mainmechanisms: molecular mixing or micro-mixing, and bulk mixingor macro-mixing. [21,22] This study focuses on the second approach.The urea reactor is split into CSTRs in the proposed mathemat-ical model. The modelling section includes thermodynamic andchemical synthesis frameworks.

Although, there are some similar studies [10,12] in the litera-ture which address the thermodynamic behaviour of the mixturecontributed in urea production process, the following main dif-ferences exist between the current research and previous studiesreported in the literature:

- Biuret production has not been considered in most of the previ-ous studies; while, the current study includes the reaction rateof biuret formation.

- The Equation of States (EOSs) selected in the previous studiesusually give the equilibrium data with some errors that arisefrom inaccurate mixing rules and ignorance of cross associationbetween components present in urea production process. How-ever, this paper addresses these shortcomings that lead to moreaccurate thermodynamic results.

- Since there are always some uncertainties related to reactionrates, EOS and non-ideality of the reactor, it would be valuableif a robust tool such as ANN and fuzzy logics is tried to captureall those uncertainties, even in the lump form, while predictingprocess behaviour of a chemical engineering equipment in anindustrial plant. An efcient smart technique is employed hereand no such investigations on industrial urea reactors are foundin literature.

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Figure 1. Block diagram of urea production process via Stamicarbon method. [2]

Thermodynamics BasisIn general, thechemical reactions which are noticeable in the ureasynthesis conditions are as follows [7,12 ,23] :

CO2(l) + 2NH 3(l) ↔ H2NCOO− + NH+4 (4)

CO2(l) + NH3(l) + H2O(l) ↔ HCO−3 + NH+4 (5)

H2NCOO− + NH+4 ↔ NH2 CONH2(l) + H2O(l) (6)

2NH 2CONH2(l) ↔ NH2CONHCONH 2(l) + NH3(l) (7)

The chemical reactions involved in the urea synthesis occur inthe liquid phase. The liquid phase contains the components andions including, H 2O (1), NH 3 (2), CO 2 (3), NH +4 (4), HCO

−3 (5),

H2NCOO− (6), H 2NCONH 2 (7) and H 2NCONHCOH 2N (8).The volatility of urea (H 2NCONH 2) and biuret

(H 2NCONHCOH 2N) is very low, and the ions are not ableto depart from liquid phase to vapour phase, thus only H 2 O (1),NH3 (2) and CO 2 (3) are present in the vapour phase, meaning itis necessary to consider vapour–liquid equilibria (VLE) of thesethree components with chemical reaction for this mathematicalmodelling, simultaneously.

The VLE system is expressed with the following equations:

CO2(g) ↔ CO2(l) (8)

NH3(g) ↔ NH3(l) (9)

H2O(g) ↔ H2O(l) (10)

It is proved that the rates of reactions (4) and (5) are higher thanthose of reactions (6) and (7). [6,7,10] Therefore, it is assumed herethat reactions (4) and (5) are at equilibrium conditions and equi-librium conversions can be considered for those reactions whilereactions (6) and (7) do not reach the equilibrium state. Thus,particular rates for reactions (6) and (7) are required in order toperform accurate numerical computations. The rate of reaction(6), R, is expressed as follows [14 ,19 ,20 ,24] :

R = kC T x6 −1

K x,6

x7x1x4

(11)

k = A exp

− E

RT ; A = 2.5 × 10− 8

s− 1

; E = 100kJ mol− 1

(12)

where k is the reaction constant, K x, 6 is the equilibrium constant of reaction (6) (refer to the Chemical Equilibrium of Urea SynthesisSystem Section), E is the activation energy, xi is the mole fractionof liquid component ( i), and T and R are the temperature anduniversal gases constant, respectively.

Formation of biuret is taken into account for this mathemat-ical method. The reaction of biuret production is endothermic.This slow chemical reaction occurs when the reaction mixturecontains a high concentration of urea and a small concentrationof ammonia at elevated temperatures. [25–27] In the case of biuret



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formation, the equation of reaction rate suggested by Shen [27] is:

RBiuret = kC 2T (x7,0 − x7)2 (13)

where k is the reaction constant, and x7,0 is the initialmole fractionof urea in the liquid phase. The parameters in Equation (13) arepresented as [27 ,28] :

k = A exp− E

RT ; A = 2.1 × 107 m 3 mol − 1 s− 1 ;

E = 8.5 × 104 kJ mol − 1 (14)

In order to numerically perform any simulations of the ureasynthesis reactor, it is necessary to have a robust and adequatethermodynamics model for the H 2O–CO2–NH 3 –urea system. Inthis study, the UNIQUAC model proposed by Sander [29] was usedto predict the activity coefcients of the components in the liquidphase.

According to the phase equilibria, the fugacity of each compo-nent ( f i) in all phases is the same at equilibrium conditions asshown in the following expression [21,22,30] :

f ˛i = f

ˇi = · · · = f i (15)

where ˛ , ˇ and illustrate the phases (e.g. gas, liquid and solid).This study includes just gas and liquid phases.

Based on Equation (15), the following fugacity relationship canbe written for phase equilibrium of H 2 O and NH 3 components(i = 1,2) in gas and liquid phases [21,22,30] :

xi i (T, x )f 0i (T, P = 0)expvi P RT

= Pyi i (T,P,y ) (16)

i(T, x ) is the activity coefcient of component ( i) that is a func-tion of temperature ( T ) and liquid composition ( xi). f 0i is the pureliquid reference fugacity of component i, depending on temper-ature. vi is the liquid molal volume of component i. i (T , P ,y)represents the fugacity coefcient of component i that is a func-tion of temperature ( T ), pressure ( P ) and mole fractions of gaseouscomponents ( yi ). It should be noted here that temperature andpressure are in the ranges of 442–456K and 131.5–133 atm alongthe reactor height. Therefore, the above parameters are differentfor various control volumes considered in the simulation runs asthe compositions of liquid and gas phases vary with height, aswell.

The phase equilibrium equation for CO 2 (i = 3) is also writtenas [21,22 ,30] :

x3 3(T, x ) H 3,1(T, P sat1 )expv∞3 ( P − P

sat1 (T ))

RT = Py3 3(T,P,y )

(17)

An expression for activity coefcient (ln i), which is valid fornon-polar substances, was suggested by Sander. [29]

The UNIQUAC model presents the activity coefcient in threedifferent terms [29 ,30] :

ln i(T, x ) = ln Ci (x) + ln Ri (T, x ) + ln

DHi (T, x ) (18)

where ln Ci (x)and ln Ri (T, x ) are the combinatorial and resid-

ual parts of the activity coefcient, respectively. These parameters

depend on temperature and concentrations of the components inliquid phase. ln DHi (T, x ) is the Debye–Huckel contribution to theactivity coefcient which is dened differently for ionic and non-ionic components. This part is a function of mole fractions of themixture components and temperature.

The temperature dependence of ammonia’s fugacity ( f 02 (T )) atzero pressure is expressed by the following equation [21,22 ,30] :

ln f 02 (T ) = A1T

+ A2 ln T + A3T + A4 (19)

In Equation (19), the units for f 02 and T are MPa and K, respec-tively.

The constants of Ai in Equation (19) for calculation of the NH 3fugacity are as follows:

A1 = − 2.5141 × 103 ; A2 = 0.28417;

A3 = − 2.5759 × 10 − 3 ; A4 = 14 .6460

The Henry’s constant of CO 2 in H 2O, H3,1 , is determined asfollows [21,22,30] :

ln H 3,1(T ) =− 2.6560 × 10 3

T − 3.5050 × 10 − 1 ln T

+ 6.2316 × 10 − 3 T + 18 .1575 + B3,1 (20)

where B3,1 represents the interaction between components H 2Oand CO 2 . The expression for B3,1 is given by the followingequation [22 ,30] :

B3,1 = 18 .1575 − 1.12 exp −2623 .7

T (21)

Equations (15)–(20) are used in the mathematical modelling tocalculate PVT data for the gas and liquid mixtures. These thermo-dynamic equilibrium relationships are solved with mass balanceand energy balance equations, simultaneously. It is important to

note that most of the parameters in these equations are functionsof compositions of the gas and liquid phases that are differentfor each element and must be computed accordingly, consideringthermodynamics and chemical equilibrium at various tempera-tures and pressures. Further information about the parameters inEquations (15)–(20) can be found in Appendices A and B, andthese references. [29–32]

It should be also noted here that PVT study of the mixture wasmostly conducted using the Aspen Plus software. The cross asso-ciation effects due to polar–polar interactions between H 2O andCO2 molecules which were not considered in the previous stud-ies, is taken into account in the current work. The EOS used forthe gas phase in this study is cubic-plus-association (CPA) EOSfor water-containing systems that include combination of the PREOS and the thermodynamic perturbation theory for the physicalinteractions and the hydrogen bondingof water molecules, respec-tively. Considering cross association between various moleculesand association between water molecules results in obtainingphysical properties of the mixture and the mole fractions of thecomponents with high accuracy. Technical reader is encouragedto study Firoozabadi, [31] and Li and Firoozabadi [32] for more infor-mation.

CSTRs in Series ModelTo simulate the reactor performance, it is necessary to derivethe corresponding mathematical equations. Since the reactor



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Figure 2. Schematic of the element considered for reactor simulation.

behaviour is non-ideal, the kinetic model proposed here is basedon n number of CSTRs in series. In this model, the cylindricalreactor is divided into n tanks and the material and energy bal-ance equations are written for each tank as a volumetric element(see Figure 2). Finally, the conversion distribution and also tem-perature prole are determined through solving the governingequations of n -CSTRs, simultaneously.

Subscript J denotes the element number and superscripts l andg denote liquid phase and gas phase, respectively. Using the mate-rial balance for the element J , the mass conservation equation iswritten as follows:

F J,i−

F J − 1,i =

V

7

r = 4 ˛r

i Rr

J J =

1, 2, 3, . . . , n (22)

F J,i is the molar ow rate of the component i in both liquid andgas phases in the element J . V is the volume of each element(the total volume of the reactor is about 140m 3 , thus the volumeof each element is calculated by dividing the reactor volume tothe number of the elements), ˛ r i is the stoichiometric coefcientof component i in reaction r , Rr J is the reaction rate and n is thetotal number of elements or CSTRs. Although, the urea productionreaction takes place in the liquid phase, the total volume of thereactor ( V ) should be taken into account in Equation (22), sincethe reaction rates of urea and biuret (e.g. Equations 11 and 13)are expressed in terms of C

T which is the total concentration of

the components in the mixture. On the other hand, Equation (22)includes molar ow rates of both liquid and gaseous componentsin the reactor. Hence, considering only liquid volume in the massbalance equation gives wrong results while modelling the ureasynthesis process.

The energy balance of the reactor can be written as follows:

[Rate of Energy Input] = [Rate of Energy at Outlet]

+ [Rate of Energy Consumption]

− [Rate of Energy Generation] (23)

9

i= 1

F l J,i ¯ H l

J,i +3

i= 1

F g J,i ¯ H g

J,i −9

i= 1

F l j − 1,i ¯ H l

j − 1,i −3

i= 1

F g J − 1,i ¯ H g

J − 1,i = Q̇ J

(24)

The reactor is operating adiabatically, therefore Q̇ J would beequal to zero.

In Equation (24), ¯ H l J,i and ¯ H g

J,i are partial enthalpies of compo-nent i in the element J for the liquid and gas phases, respectively.xi also denotes the mole fraction of component i.

In the urea reactor, there are liquid and gas phases such thatthey contact with each other along the reactor height and then aremixed on the reactor trays. As seen in the equations of mass andenergy balances, there are several terms including the propertiesof the components in each phase to compute the reactor efciencyand concentration distribution. In addition, the rates of chemicalreactions (e.g. Equations 11 and 13) include mole fractions of thecomponents in liquid phase as well as equilibrium constants of the reactions in the mixture. Therefore, an appropriate thermody-namics model for the system (H 2O–CO2–NH 3–urea) was selectedto determine the values of the terms explained above. More infor-mation about thermodynamic and synthesis frameworks aregivenin Appendices A and B.

Chemical Equilibrium of Urea Synthesis SystemAs explained earlier, reactions (4) and (5) play the most impor-tant role in the chemical equilibrium of the components at theconditions that the urea synthesis takes place:

The equilibrium constant as a function of temperature isobtained for the above two reactions as follows [21,22 ,25] :

ln K r (T ) =C 1,r T

+ C 2,r ln T + C 3,r T + C 4,r (25)

The coefcients values of Equation (25) for the chemical reac-tions are presented in Table 1.

The equilibrium constant is dened as shown below [21,22 ,30] :

K r (T ) = K x,r (x) K ,r (T, x ) (26)

For instance, K x,r (x) and K ,r ( ) for Equation (5) or r = 5 arepresented in the forms of the following expressions:

K x, 5 =x4x5

x1x2x3(27)

K ,5 = 4 5

1 2 3(28)

For reaction (4), the similar relationships are written for K x,r and K ,r .

The required equations to predict the reactor behaviour arethree thermodynamic equilibrium equations for three compo-nents (NH 3 , CO2 and H 2 O), eight molar balance equations for

Table 1. The values of coefcients in Equation (25)

Parameters

Function (ln K r ) 10 − 3 × C 1 ,r 102 × C 2 ,r 103 × C 3 ,r C 4 ,r

r = 4 9.9068 7.4296 − 5.3985 − 20.222r = 5 8.8226 0.8404 1.8736 − 21.6135



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all eight components involved in the urea synthesis process, andone energy balance equation. The unknown parameters are molarow of all components (eight variables) in the liquid phase, molarow of gaseous components (three variables) including NH 3 , CO2and H 2O and temperature of the output system (one variable). Allequations of the reaction rate and chemical equilibrium in theform of supplementary equations are included in the mole bal-ance relationships of the components. The input data are alsomolar ow of the input chemicals, reactor volume, temperatureand pressure. It should be also noted that the pressure is kept

constant during the process.The governing equations to obtain unknown variables are as

follows:

(1) Three equations for the phase equilibrium of H 2O (1), NH 3(2), CO 2 (3): f

gi = f

li ; i = 1, 2, 3.

(2) Eight equations for the material balance:

F J,i − F J − 1,i = V 7

r = 4

˛ r i Rr J

J = 1, 2, 3, . . . , n and i = 1, 2, . . . , 8

As mentioned earlier, there are seven reactions (Equations4–10) in the urea system; however, three of them (Equa-tions 8–10) just show thermodynamic equilibrium for CO 2 ,NH3 and H 2 O, respectively. In fact, four main reactions inthe urea process include formation of ammonium carbamate(e.g. Equation 4), reaction between all three main compo-nents (e.g. Equation 5), formation of urea (e.g. Equation 6)and formation of biuret (e.g. Equation 7).

(3) One equation for the energy conservation: Equation (25) or(24).

(4) Two supplementary equations for chemical equilibrium of reactions (4) and (5).

In order to calculate the unknown parameters explained above,the numerical modelling was performed using the MATLAB TM andAspen Plus software packages in this study. It is important to notethat all thermodynamic and physical properties of the individualcomponents and the mixture were computed for each certain set of T , P , and compositions usingthe Aspen Plus software and then thedata obtained at this stage were exported into a MATLAB programthat was written to perform modelling of the urea reactor througha synthesis framework. The framework dened in the program isbased on the analogy of CSTRs in series that is combined withthermodynamic section at each simulation run.

ARTIFICIAL NEURAL NETWORK

ANN is a robust technique which is able to capture and rep-resent complex relationships between inputs and outputs. ANNhas been developed from the information processing mechanismsof the brain. [33–36] The theory of ANN was developed initiallyby McCulloch and Pitts. [36] Over the last few years, ANN hasbeen broadly employed for numerous applications such as pro-cess control, behaviour prediction, model recognition and systemclassication. An ANN model is composed of a large number of interconnected neurons which can be considered as a comput-ing engine that receives inputs, processes them in a hidden layerand then generates an output. The main advantage of ANN sys-tems in contrast with conventional methodologies is that theydo not need the intricate nature of the process under study. The

Figure 3. A simple structure of an ANN with one hidden layer.

key shortcoming of ANNs is that they normally act as a ‘black-box’, not capturing important aspects related to the physics of themodelled phenomenon or process. However, a systematic math-ematical model is proposed in the present study to support theresults of the ANN model and also describe the complex dynam-ics of urea reactor in a proper manner. Figure 3 depicts a simplearchitecture of an ANN with one hidden layer. The numbers of neurons and hidden layers depend on the complexity and nonlin-earity of the problem. Each neuron is connected to the input andoutput by a corresponding weight. Inputs to each neuron are mul-tiplied by their corresponding weights. After that, the products aresummed up, and the sum is processed using a nonlinear transferfunction to obtain an output. [33–35] Initial values of weights arerandomly assigned by employing uniform or Gaussian distribu-tion. The weights are modied through a training process untilthe error between the actual output and the predicted output isminimised. There are number of different neural network struc-tures, and learning algorithms (e.g. back propagation (BP) andmultiple layer perceptron (MLP)) for the ANN technique. [33–35]

The BP method is recognised as one of the most general learningalgorithms that modify the weights from the output layer backto the input layer at each iteration until the mean squared error(MSE) meets the tolerance specied for the problem. [33–36] The BPalgorithm adjusts the weights using the gradient descent principlewhere the change in the weight is proportional to the error gradi-

ent with a negative sign.[33–35]

The performance of theANN modelis nally checked by introducing new and independent datasetsto the trained model. Additional details on the ANN technique canbe found in these references. [33–36]

Five important stages are usually required to design an ANNmodel. These steps described in brief are as follows:

(1) Data collection : The rst stage is collecting and preparingdata. As noted in this study, the experimental and real data fortemperature, NH 3 /CO 2 , H 2O/CO 2 , and conversion percentageare collected from the literature.

(2) Data preprocessing : After the required data are collected, nor-malising and randomising the data are necessary to attain



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reasonable and unbiased results. Data normalisation shouldbe done due to large differences between magnitudes andunits of various variables contributing in the ANN model.

(3) Network construction : The designer should determine thenumber of hidden layers, the number of neurons in eachlayer, transfer function in each layer, training function, weightlearning function and performance function at this stage.

(4) Training phase : The weights are adjusted at this stage as anacceptable match is obtained between the real data and pre-dicted outputs.

(5) Testing phase : Examining the performance of the developedANN model is the last. Unseen data (the data that have notbeen employed in the training stage) are considered for thetesting stage. Statistical parameters such as the coefcient of determination ( R2), and the MSE are calculated using theANN predictions in order to assess the performance of theANN system quantitatively and make sure whether there isany particular trend in the performance of the ANN model.

OPTIMISATION METHOD

Our purpose in the optimisation phase of this study is to obtain aseries of optimum input parameters to minimise a certain per-formance indicator. However, there are generally a number of uncontrollable and unmeasurable factors in a real process to makeit complicated to achieve our goal. It is assumed that the meanof these disturbances approaches to zero. Also, the average valueof a certain input variable in a long duration is considered as thereal steady input for a given parameter. Based on the assumptionstaken, the performance index is related to the mean values of theinput parameters. Then, a set of optimal averages of the inputvariables is searched to solve the optimisation problem.

The optimum stochastic objective function ( I ∗) is given by:

I ∗ = f ( F [u (t )] , w (t ) , v ( t ) , t ) (29)

where w(t ) and v(t ) are the random disturbances of process whose

average are zero. u ( t ) is the random input variable. F [u (t )] is themean value of u ( t ) at steady state condition. For the sake of sim-plicity, the objective function, I ( t ), is considered as the output of the ANN network, y(t ).

I ( t ) = y(t ) (30)

To minimise the average value of the stochastic objective func-tion ( I ( t )), the solution of the optimal problem can be obtainedthrough the following relationships:

∂F [ I ( t )]∂F [u (t )]

= 0 at F ∗[u (t )] (31)

The mean values of the input parameters are updated as below:

F [u (t )] = − ∂F [ I ( t )]∂F [u (t )]

(32)

Here, is a positive step size.The optimum values of the system input variables are taken

into account as the optimal set points for the important variablesin the controllers of a given process. It should be noted here thatthe steepest descent method is employed to do the optimisationcomputations.The optimisation framework using ANN is depictedin Figure 4.

Figure 4. A schematic of optimisation procedure via ANN.

Stochastic process referred in this study considers measuring orcollecting the input and output variables (they may have uncer-tainties) contributing in the urea production. It is recommendedthat the important parameters are identied based on the physicsand mathematical modelling of the urea process. These data areusually collected from the literature and/or real plants and thenemployed in the smart or predictive tools such as ANN system.In fact, the grey-box model introduced in this study for the ureaproduction is a comprehensive study with logical formulationsin terms of mass conservation, energy conservation and thermo-dynamic behaviour. However, the main concerns regarding themodel include uncertainties with reaction rates, mixing rules of the EOS and non-ideality of reactor. The ANN model is examinedto lower the effect of the uncertainties on the predicted results.On the other hand, running the simulation program with compli-cated nonlinear equations is generally time-consuming and costly.To overcome this problem, the smart method is used in this study.The ANN model is able to optimise the urea production and alsopredict the behaviour of urea reactor with different scales. It alsoassists engineers to scale-up and/or improve the process througha quick and reliable manner.

RESULTS AND DISCUSSION

As highly exothermic reaction of carbamate formation takes placemainly at the interface among the liquid and gas phases, heat andmass transfer from the interface to the bulk of the phases appearsto be an important feature while modelling the process behaviourof the urea synthesis reactor. In addition, the uid dynamic (e.g.size of bubbles and rise rate) may play an important role in thereactor performance. However, considering these aspects requiresdetailed operational data (e.g. pressure variation and concentra-tion prole) and more information about the internal parts (e.g.tray). Providing all required data is a time-consuming and fairlycostly task. This is the main reason that ANN is applied in thisstudy to take into account all uncertainties through employingadaptive parameters in the network.

In order to validate the mathematical and ANN models devel-oped for urea synthesis reactor, the results predicted by the modelsare compared to theactual data of theureasynthesis reactor in Shi-raz Petrochemical Company. It should be noted here that typicalindustrial operating conditions (real data) of the urea plant havebeen collected from the process control room by the rst author of this paper. Furthermore, the introduced models are employed toinvestigate the effects of temperature, and ow rates of H 2O, NH 3and CO 2 on the conversion percentage. At last, the optimisationprocess is carried out to obtain the optimal conditions that leadto a higher conversion in the urea reactor.

Results of this study show that the proposed modelling method-ology is a practical approach in analysing the plant performance



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Table 2. Predicted results and industrial data for molar ow rates inthe liquid phase

Flow rate (kmol/day)

Components in liquid phase Predicted Actual

NH3 (input) 116 180 117 356NH3 (output) 79 580 80 082CO2 (input) 38 330 41 334CO

2 (output) 18 410 20 163

H2 O (input) 18 700 18 383H2 O (output) 45 660 45 344Urea (input) 170 208Urea (output) 25 490 26 609

and improving plant operation such as energy saving, highconversion and identication of bottlenecks. Furthermore, themethodology is a solid base for further optimisation efforts anddeveloping on-line control systems for the urea reactor.

Mathematical MethodIn this study, the simulation part conducted by employing theAspen Plus and MATLAB softwares covers the condenser, stripperand reactor parts, since the governing mass and energy equationsare similar for these three important elements (governing equa-tions for the condenser and stripper are given in Appendix C).Starting mathematical modelling from the condenser, chemicaland thermodynamic equilibrium relationships are applied to thispart when temperature andmolar ratios of NH 3 /CO 2 and H 2O/CO 2are the known variables for this phase of simulation. The realdata and the results obtained from the mathematical approach areshown in Tables 2 and 3 for both liquid and gas phases involvedin the urea reactor of the commercial plant. A good agreementis observed between the model outcomes and the actual processdata.

The results of this numerical computation in more details areillustrated in Figures 5–10. The amount of the produced urea inthe reactor versus the input H 2O moles is presented in Figure 5.As shown in the gure, the amount of produced urea will decreasewhen the ow rate of the water introduced into the reactorincreases. This is because the water phase acts as a by-product inthe system of the urea synthesis reaction. Therefore, it improvesthe reaction (see Equation 6) in the reverse direction of urea

Table 3. Modelling results and industrial data for ow rates in the gasphase

Flow rate (kmol/day)

Components in gas phase Predicted Actual

NH3 (input) 32 129 32 381NH3 (output) 15 422 13 433CO2 (input) 10 440 10 794CO2 (output) 4620 4249H2 O (input) 1660 1687H2 O (output) 750 726N2 (input) 1387 1387N2 (output) 1387 1387O2 (input) 213 213O2 (output) 213 231

Figure 5. Effect of ow rate of water introduced into the reactor on theamount of urea produced.

production according to the Le Chatelier’s principle, while the

amount of produced water increases.Figure 6 shows the temperature distribution along the height

of reactor. An increasing trend for temperature is predicted ver-sus the height of reactor. This behaviour is acceptable since theurea production reaction (combination of reactions (4) and (6))is generally exothermic.

The ow rates of the components of the reaction mixture forvarious points within the reactor are shown in Figure 7. As seenin the gure, the ow rates of NH 3 and CO 2 will decline versus thelength of the reactor as the temperature increases. This increase intemperature enhances the urea reaction and consequently causeshigh consumption of NH 3 and CO 2 in the process system. Follow-ing the same logic, reverse patterns for H 2O and urea components(as main products) are observed in Figure 7.

As expected, the amounts of the products increase from thebottom to top of the reactor, while a reduction in the ow rates of the reactants contributing in the production of urea is observed.Also, there is a good agreement between the simulation resultsand the commercial reactor data, as depicted in Figure 7.

Figure 6. Temperature prole in the urea reactor according to thesimulation results and the commercial plant data.



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Figure 7. Flow rates of the mixture components over height of thereactor based on the modelling outputs and the real data.

According to the synthesis model chosen for this study, the realreactor is divided into n-CSTRs (or backmix reactors) in seriesin a way that the total volume of them is equal to that of thereal reactor. First, low number (e.g. one or two) of CSTRs inseries is selected to simulate the non-ideality behaviour of the realreactor. Then, the material and energy balance equations are writ-ten for each tank as a volumetric element. Finally, the conversiondistribution and also temperature prole are determined throughsolving the governing equations of n-CSTR’s, simultaneously. If the temperature and CO 2 conversion (the amount of urea pro-duced) from the modelling part are very close to the real data,then the rst guess about the number of CSTRs is correct; oth-erwise, the number of the backmix reactors is changed and the

same computation will be carried out. This procedure will pro-ceed until a good agreement between the modelling outputs andthe actual data is observed.

Figure 8 shows the effects of the number of CSTRs on the pre-dicted conversion of CO 2 to urea for the output stream of the ureareactor at the real operating conditions. As shown in Figure 8,the performance of the reactor increases as the number of CSTRs

Figure 8. Reaction conversion versus number of CSTRs.

Figure 9. Effect of the feed temperature on the reactor height whilehaving the same conversion for all heights.

increases. However, there is a characteristic number of CSTRs at

about n = 12 after which no signicant change was experiencedin the magnitude of conversion. Therefore, 12 CSTRs can simulatechemical reaction and thermodynamic behaviour of thisnon-idealreactor of urea production. Moreover, the results illustrated inFigure 8 convey this massage that the eight sieve trays placedin the reactor are not able to maintain complete mixing. It shouldbe noted here that the number of stages would be equal to thenumber of trays in the case of perfect mixing.

In fact, only real temperature and CO 2 conversion at the reactoroutlet are required to calculate the number of CSTRs while mod-elling the non-ideality of the urea reactor. However, more realdata including temperature and CO 2 conversion of the inlet andmiddle points of the reactor are added to Figure 8 in order tohave a better comparison between the real data and theoreticalresults. The method proposed by Stamicarbon Staff [2] for measur-ing the compositions is to install N/C measurement devices onvarious locations (e.g. inlet, middle part and outlet) of the reac-tor. In this technique, the samples taken from the urea reactor rstpass through a sampling process (e.g. cooling, pressure reducingand ushing). Then, they are analysed by the density meter, GCand HPLC to determine the mixture compositions and N/C ratio.All these sampling and measuring parts are placed in a cabinet,known as N/C measurement system.

Figure 10. Conversion of CO 2 to biuret versus temperature of reactor feed.



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As mentioned earlier, the number of trays employed in the realreactor is 8 considering that an efciency of 65–75% for each traywas reported by Stamicarbon Staff [2] and Dente et al. [6] The gasand liquid passing through the reactor mix with each other anduniform concentrations and temperature are attained on each tray.Thus, it is reasonable to simulate the actual reactor in the formof 12 CSTRs based on the tray efciency. Also, the modellingsimulation conducted in this study shows that the output tem-perature will not be suitably matched with the real temperatureof the reactor outlet if greater numbers of CSTRs are consid-

ered for simulation of the real urea reactor. On the other hand,a number of CSTRs higher than 12 moves towards the plug owrestraining behaviour within the error of control instruments andalso sampling and laboratory methods. In addition, an acceptableagreement between the real data and the results obtained from thesynthesis and thermodynamic implies that 12 CSTRs can approxi-mate the reactor behaviour in terms of concentration back-mixingand residence time distribution (RTD).

Based on the numerical investigation conducted here, if the feedwith the higher temperature is provided for the synthesis reactor, itwould be possible to lower or prevent producing biuret in the exitstream. In this case, if the temperature of the production streamis controlled well, the same conversion can be attained using ashorter reactor (see Figure 9). A trade-off between energy costfor heating and the manufacturing cost for the reactor is veryimportant to make an economical decision in this situation.

As noted before, the urea synthesis becomes more complicatedby the production of biuret that should be kept at a low level,since it unfavourably inuences the growth of various plants.The current modelling simulation addresses the effects of vari-ous parameters such as feed temperature and reactor length onthe amount of biuret produced in the urea plant. The effect of feed temperature on the conversion of CO 2 to biuret is illustratedin Figure 10. Although, an increase in temperature increases theCO2 conversion to urea, it may cause producing a by-productcalled biuret. Figure 10 clearly depicts that as the temperatureincreases beyond 440 K; the favourable conditions for advanc-

ing the reaction of biuret formation would be achieved, leadingto production of higher amount of biuret in the product stream.Thus, controlling condenser and reactor pressures, which affectthe temperature of the feed and product streams considerably,is inevitable in the urea synthesis loop through setting a properprocess engineering strategy. The distribution of biuret producedalong the height of the urea reactor is demonstrated in Figure 11.This gure was obtained based on the operating conditions (e.g. P = 131.5atm) of the real urea reactor. The conversion of CO 2 tobiuret is increased as the reaction mixture goes up along the reac-tor height and obtains higher temperatures. Again, it is conrmedthat a strong dependency exists between the pressure, tempera-ture and the reactor height. Therefore, it is necessary to nd theoptimal conditions as the conversion percentages of CO 2 to ureaand biuret have the maximum and minimum values, respectively.According to both Figures 10 and 11, a reasonable match is noticedbetween the simulation results and the real data, indicating theappropriateness of the mathematical modelling employed in thisstudy. It is important to note that N/C measurement devices areinstalled on the reactor to obtain the biuret ow rate.

The mathematical model sensitivity to variations in NH 3 /CO 2and H 2O/CO 2 ratios in the urea synthesis unit is presented here. InFigure 12, the equilibrium conversions predicted by this numeri-cal modelling are compared with the experimental data reportedby Gorlovskii and Kucheryavyi. [16] As seen in Figure 12, it can beconcluded that the proposed thermodynamics model could predict

Figure 11. Variation of biuret production rate in the commercial plantwith reactor height.

the phase behaviour of the mixture contributing in the urea syn-thesis in the industrial plant, considering the average relative errorfor equilibrium conversion is about 6.7%. Therefore, the presentstudy clearlyprovides an accurate t of the real/experimental datapublished in open sources. [16–18]

ANN MethodBased on the phase rule, the degrees of freedom ( F ) for the ureasystem are determined by:

F = C − + 2 (33)

where C is the number of independent components and is thenumber of phases.

In our case, the number of phases is two and the independentcomponents are three, including ammonia (NH 3 ), carbon dioxide(CO 2) and water (H 2O) in the liquid phase. Therefore, F = 3 for thesystem under study. According to the literature, these three inde-

pendent parameters are usually temperature, and the molar ratiosof NH 3 /CO 2 and H 2O/CO 2 . [7,9,10] Thus, the ANN model considered

Figure 12. Conversion percent of CO 2 to urea at 445K under equilibrium conditions. A comparison between the modelling outputsand the experimental data of Gorlovskii and Kucheryavyi. [16]



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these three independent variables as input parameters. Input datawas normalised before starting the ANN modelling to avoid anyfalse inuence of factors with higher order of magnitude. Datanormalisation was performed using Equation (34) as follows:

X =x − (( xmax + xmin ) / 2)

(( xmax − xmin ) / 2) (34)

where xmax and xmin are the highest and lowest values of vari-able x, respectively. The ANN model was trained using 125experimental and/or commercial plant data taken from thesereferences. [1,6,7,10] The training dataset was selected randomlyfrom the available urea synthesis data (85% of the whole data),covering a temperature range of 435–485 K, NH 3 /CO 2 range of 2.0–6.5 and H 2O/CO 2 range of 0.1–1.4. The back-propagationmethod was used to modify the weights until the MSE becameless than 0.005. MATLAB ® software version 7 from Mathworks,Natick, Massachusetts was employed for the ANN modelling. TheLevenberg–Marquardt optimisation algorithm was the BP tech-nique selected for training the neural network. The algorithm isthe fastest BP algorithm in MATLAB ® toolbox. Hyperbolic tangentsigmoid and linear functions were the transfer functions for thehidden and the output layers, respectively. The performance of

the ANN model was tested by 17 new and independent datasets.Any ANN model contains one input layer, one output layer andone or more hidden layers. According to the universal approxima-tion theory, one hidden layer with a sufcient number of neuronscan model any set of input/output data to a reasonable degreeof accuracy. [37] Thus, one hidden layer was selected in the ANNmodel developed in this study. Table 4 shows the performance of neural network models with various numbers of neurons in a sin-gle hidden layer. The performance of the network was tested bycalculating the coefcient of determination ( R2), mean absolutepercent error and maximum/minimum absolute percent errorsfor both training and testing datasets. It should be noted herethat R2 is a statistic parameter which gives information on good-ness of t in a model. In regression analysis or tting of a model,

the R2 coefcient is a statistical measure of how well the modelline approximates the real data points. An R2 of 1.0 indicates themodel line perfectly ts the data. The following equation showsthe mathematical denition of R2[38 ,39] :

R2 =

n

i=(yPi − ȳ

M)2

n

i= 1(yMi − ȳM)2

(35)

where yM and yP represent the measured and predicted out-put parameter (e.g. CO 2 conversion percentage), respectively. ȳM

stands for the average of the measured yi data.R2 was found higher than 0.998 for neural networks with 4

and higher numbers of hidden neurons. High values for meanand maximum percent errors were obtained when the number of neuron was less than 4. Increasing the number of neurons from 2to 8 lowered the mean percent error by 93% from 66.4% to 4.5%.The maximum and minimum absolute errors for thenetwork witheight neurons were 17% and 0.01%, respectively. Increasing the

number of neurons from 8 to 10 increased the maximum abso-lute percent error of the training and testing phases by 31% and44%, respectively. Thus, the optimum ANN model was found tohave one input layer with three neurons, one hidden layer witheight neurons and one output layer with one neuron (refer toTable 4).Higher numbersof hidden neurons were avoided in orderto prevent overtraining of the ANN model. This important pointshould be considered while performing the training phase in ANNsystems. [33–36]

As seen in Figures 13 and 14, a comparison between predictedand measured CO 2 conversion to urea at training and testingphases for the ANN model was conducted in this study. It is clearfrom Figures 13 and 14, the outputs of the model simulated withANN exhibit an acceptable agreement with the actual data of theurea reactor and also the experimental data available in the liter-ature. The references for the data used in the ANN model includethe following studies and/or documents. [1,6,7,10]

Optimisation StudyIt is assumed that the input and output variables are randomparameters for the process under study. The urea reactor includesa feed stream that has a gaseous phase and a liquid phase contain-ing ammonia and carbon dioxide. The mole ratio of NH 3 to CO2 inthe feed is A(t ). The temperature of the feed is established by thepressure of the boiler stream P f ( t ) in the ammonium carbamatecondenser. This plant has liquid and gas outputs at the bottom andtop of the reactor, respectively. It is a reasonable assumption thatthe load of the plant remains constant. [1–3] However, the valuesof P f ( t ) and A(t ) regularly change with noise.

Regardless of economical considerations, an optimal operatingcondition is usually determined to maximise the conversion of CO2 . It is known in the commercial urea plant that the systempressure has the lowest value when the operating load is notchanged. [1,2,4] In this case, the conversion of CO 2 to urea is at itshighest level. Thus, the minimum system pressure, P ( t ), is cho-sen as the objective function. There are two main manipulating

Table 4. Performance of ANN with various numbers of neurons in one hidden layer

Training dataset Testing dataset

Max. abs. Min. abs. Mean abs. Max. abs. Min. abs. Mean abs.Neuron no. R2 % error % error % error R2 % error % error % error

2 0.995 1475 0.40 66.4 0.997 275 0.99 67.13 0.995 1358 0.13 90.8 0.996 425 1.21 86.64 0.999 341 0.00 33.7 0.997 171 0.34 34.85 0.998 603 0.01 27.8 0.999 150 0.65 46.36 0.998 372 0.27 33.5 0.997 127 0.43 34.07 0.999 291 0.00 21.3 0.996 177 3.94 30.48 0.999 17 0.01 4.5 0.998 15 0.17 9.49 0.999 31 0.00 5.7 0.994 56 13.41 14.010 0.999 44 0.00 5.0 0.995 45 0.35 10.4



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a

b

Figure 13. Measured versus predicted CO 2 conversion using the ANNmodel: (a) training, and (b) testing.

variables to the system pressure, namely, proportion of ammoniaand carbon dioxide in feed, A(t ), and the boiler stream pressure, P f ( t ).

Having A(t ) and P f (t ) as the input variables, and P (t ) as theoutput variable, a BP neural network was employed. The networkcomprises one input layer (two input neurons), one hidden layer(three hidden neurons) and one output layer (one output neuron)as shown in Figure 15.

From the urea plant in Shiraz Petrochemical Company, severalsample patterns in terms of steam pressure ( P f ), NH 3 /CO 2 (A) and

system pressure ( P ) were collected every 30 min. The process dataare given in Table 5 for sample number ( k ) = 1, 2, . . . ,60.

The initial weights equal to one are selected in the neural net-work. Also, the learning step is set on 0.05. The error function isgiven as follows:

e =12

60

k = 1

( P (kT ) − P ( k̂ )) 2 (36)

where P (kT ) and P ( k̂ ) are the sample output and the networkoutput, respectively. It was found that about 440 iterations are

a

b

Figure 14. Performance of the developed ANN model based on R2 : (a)training phase, and (b) testing phase.

Figure 15. Optimisation network for urea reactor.

required to attain the error value close to zero. Then, 15 aver-age value patterns (( F [ A(t )], F [ P f ( t )]), F [ P ( t )]) are considered totrain this network. After 55 iterations, the error function satis-es the desire condition. Once the training phase is completed,some of new sample patterns are picked to examine the generali-sation potential of the learned network. This part gives acceptableresults. To do the optimisation task, the steepest descent methodis used to solve the problem. The conditions for optimisation are

Table 5. The process data for the urea synthesis reactor

Sample no., k A (kT ) P f (kT ), bar P (kT ), bar

1 2.45 10.36 130.522 2.53 10.41 130.473 2.49 10.34 130.544 2.56 10.44 130.45...

......

...60 2.57 10.38 130.51



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as below:

∂F [ P ( t )]∂F [ A(t )]

= 0 at F ∗[ A( t )] , F ∗[ P f ( t )] (37)

∂F [ P ( t )]∂F [ P f ( t )]

= 0 at F ∗[ A(t )] , F ∗[ P f ( t )] (38)

The optimum outputs are as follows:

F ∗

[ A(t )] = 2 .54 F ∗[ Pf ( t )] = 10.37bar

F ∗[ P ( t )] = 130 .49bar

Also, optimal conditions using the mathematical model weredetermined through a trial and error procedure where the CO 2conversion to urea is maximised without economical considera-tions. According to this phase of study, NH 3 /CO 2 molar ratio of 2.7, the condenser feed pressure of 10.5bar and system pressure( P ) of 132bar are the optimal values for the process parameters.Using the equations for thermodynamic equilibrium (Equation15) and energy balance (Equation 23 or 24), the temperature cor-responding to this optimum pressure was determined equal to191 ◦ C which is the temperature of the output stream of the reac-tor. The amount of biuret produced at the optimum conditionsis predicted to be about 75 kmol/day which is much lower thanthe biuret ow rate (e.g. 170 kmol/day) in the urea reactor of Shi-raz petrochemical company at current operational conditions. Asthe optimum temperature of exit ow for real cases is usually inthe range of 184–195 ◦ C, the optimum temperature found in thisstudy would be within the tolerable upper limit of the temper-ature range and the amount of urea produced in the plant. Theacceptable closeness between optimisation data from mathemati-cal modelling and ANN systems shows clearly the validity of theoptimisation part of this study. It seems reasonable that the meanvalues of NH 3 /CO 2 , P f and P obtained from these two different

independent methods can be considered as operating conditionsto determine maximum amount of urea produced in the reactor.The optimum pressure is neither the lowest nor highest pres-

sure. As the reactor pressure increases, its temperature goes up. Toinvestigate the effect of pressure (or temperature) on the amountof urea produced, both reactions including carbamate formationand urea formation should be considered. As production of ammo-nium carbamate is exothermic, increasing the temperature lowersthe amount of ammonium carbamate formed in the process.Endothermic reaction of urea formation will gives higher amountof the product when the temperature is increased. Therefore, thereis an optimum value for the pressure (temperature) because of the opposite inuences of pressure on these two reactions tak-ing place in the reactor. On the other hand, further increasingtemperature or pressure causes production of biuret which is anundesired product in the urea production process. Such a physi-cal justication conrms the correctness of the optimum pressureobtained in this study, again.

It is clear that if the ratio of NH 3 /CO 2 and the amount of ureaproduced in the reactor are kept constant, it would be easier interms of process control to operate the reactor at the lowest pres-sure that provides more suitable environment for production of ammonium carbamate. It also saves more energy during the plantoperation.

It is worth noting that the carbamate condenser in the Stami-carbon technology is actually a heat exchanger in which the heat

generated during condensation of ammonia and carbon dioxide toform ammonium carbamate in thetubeside is used to produce lowpressure (e.g. 10–20bar) steam in the shell side being employedin other parts like stripper. Generating the steam with low pres-sure is based on a systematic engineering design planned by theStamicarbon Company through Pinch technique for minimisingenergy consumption in the urea plant.

From the optimisation study and also the parametric sensitiv-ity analysis conducted using the numerical modelling program,it was found that increasing pressure of the condenser causes an

increase in the temperature, leading to more formation of ammo-nium carbamate in the stream exiting from the condenser (theplant unit prior to urea reactor) that provides a better conditionfor urea production. Therefore, higher conversion percentages canbe achieved at any specic elevations of the urea reactor if the con-denser works at higher pressure. Also, the same amount of ureacan be produced in a reactor with smaller volume under higheroperating pressure condition.

ANN and Mathematical Models Versus Real CasePredictions obtained from neural network model and mathemati-cal systems were compared against the real data of urea reactor inShiraz Petrochemical Company. Table 6 gives the correlation coef-

cient ( R2

), MSE, maximum absolute percentage error (MAPE)and minimum absolute percentage error (MIPE) for the ANN andmathematical models to predict the amount of urea production.The statistical information clearly demonstrates that both ANNand mathematical models work properly to predict thermody-namic and synthesis behaviours with high precision. The highervalue of R2 for ANN compared with the mathematical modelling inthis study indicates a very satisfactory performance for the devel-oped neural network model. The proposed ANN model enhancedthe results from the thermodynamic and synthesis frameworksand the MSE and MAPE were decreased to ∼64.3% and ∼53.1%,respectively. Improvement in estimation of CO 2 conversion withrespect to R2 was approximately 5.4%. The obtained results alsoindicatethat theANN model proposed here is a proper tool for fast,

inexpensive and reliable prediction of amount of urea producedin synthesis reactor in the absence of sufcient experimental andcommercial plant data.

As Table 6 and Figure 13 show, there is a reasonable agreementbetween the computer simulations and ANN model results withthe commercial plant data.

The Relative Effects of Input VariablesA sensitivity analysis was conducted for the developed ANNmodel using the analysis of variance (ANOVA) technique. [38 ,39]

Dependence of the output variables (CO 2 conversion) on eachof the independent variables was also examined. The resultsobtained from the sensitivity analysis are presented in Figure 16.

A higher correlation between any input variable and the out-put variable indicates greater signicance of the variable on

Table 6. Performance of the proposed ANN and mathematicalmodels to predict the behaviour of urea reactor

Parameter Mathematical model ANN model

R2 0.9366 0.9874MSE 0.724 0.258MAPE, % 12.88 6.04MIPE, % 5.17 1.92



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Figure 16. Relative effects of important variables on CO 2 conversion.

the magnitude of the dependent parameter. Clearly, the feedtemperature, as shown by ‘ T ’, is the most important parameteraffecting the amount of urea produced as an increase in the feedtemperature leads to an increase in the CO 2 conversion. In addi-

tion, the impacts of NH 3 /CO 2 and H 2O/CO 2 on the CO 2 conversionare in agreement with the published studies. [1,7,10,12] Increase inNH3 /CO 2 results in an increase in the value of amount of pro-duced urea. As the H 2O/CO 2 increases, the magnitude of the CO 2conversion decreases.

CONCLUSIONS

A mathematical model and an ANN system were developed to sim-ulate the urea synthesis reactor of Shiraz Petrochemical Company.Combination of thermodynamics and reaction frameworks wereemployed in the present numerical simulation. Then, an optimi-sation study was conducted. The following conclusions can bedrawn based on the results of this study:

(1) An arrangement of CSTRs in series was used during this simu-lation study to predict the non-ideal hydrodynamic behaviourof the reactor. It was found that 12 CSTRs can suitably modelthe synthesis reactor.

(2) The reaction of the urea synthesis is generally exothermicand the temperature increases along the reactor from the feedstage to the product stage. As a result, the ow rates of ureaand H 2O increase with consumption of the key reactants thatcontain NH 3 and CO 2 .

(3) Simulation results and ANN predictions compared againstactual operation data show a reasonable agreement betweenthe calculated and measured values of the components owrates, urea conversion and temperature.

(4) The preferred temperature of 191 ◦ C, and a pressure of 132barwere determined as the optimum values of T and P to attaina maximum conversion of CO 2 to produce urea.

(5) A parametric sensitivity analysis using the ANOVA techniqueindicated that the feed temperature is the most importantfactor affecting the CO 2 conversion for urea formation.

(6) The ANN model is more precise and faster than the math-ematical method in use for predicting the thermodynamicand synthesis behaviour of urea reactor, especially when theexperimental information is limited. The average absolute rel-ative error with ANN for the test data was obtained to be2.35, while this value is ∼9.47 for the mathematical model.

In addition, the developed ANN model has lower calibrationerrors.

(7) The developed procedure for this numerical modelling andANN system can be applied in other industrial process whenthe mixture of CO 2–H 2O–NH 3–urea includes chemical andvapour–liquid equilibrium under wide ranges of thermody-namics conditions.

NOMENCLATURE

AcronymsANN Articial Neural NetworkBP back propagationCSTR continuous stirred tank reactorEOS equation of stateMAPE maximum absolute percentage errorMIPE minimum absolute percentage errorMLP multiple layer perceptronMSE mean squared error

Variables Ai constants of fugacity equation for ammoniaa ij UNIQUAC binary interaction parameters between com-

ponents i and j B3,1 interaction effect between components 1 and 3b closest distance between the ions (cm)C A concentration of component A in a mixture (mol/m 3)C T total concentration of components in a reaction mixture

(mol/m 3)C i,r coefcients of Equation (25)C Pmean ,i mean heat capacity of the component i at a constant

pressure E activation energy of reaction (J/mol) F i molar feed ow of the component i in the feed stream

(mol/s)

f 0i standard fugacity of component i as pure liquid at zeropressure (atm)

G Gibbs free energy g acceleration due to gravity (m/s 2 )¯ H i partial molar enthalpy of component i (J/mol)

H Ji total enthalpy of component i in the element J (J/mol) K r chemical equilibrium constant of reaction r K Hi,j Henry’s constant of component i in solvent j k reaction constant M i molecular weight of component i (g/mol)m i molality of component i in liquid solution (g solute/

1000g solvent) N i number of moles of component in number of CSTRs P absolute pressure (atm) P sati vapour pressure of component i (atm)Qf volumetric ow rate of feed (m 3 /s)Q̇ J rate of heat transfer to/from element J (J/s)qi area parameter of component i in UNIQUAC modelR gases constants (atm m 3 /molK)R2 coefcient of determination in statistical analysisRi reaction rate of component i (mol/s)r i volumetric parameter of component i in UNIQUAC modelT absolute temperature (K)V volume of reactor/condenser/stripper (m 3)vi molar volume of component i in liquid phase (m 3 /mol)



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v∞i molar volume of component i in dilute liquid solutionphase (m 3 /mol)

u ji a parameter in UNIQUAC model which resembles theinteraction parameter of components i and j

X matrix of mole fractions in liquid phasexi molar fraction of component i in liquid phaseyi molar fraction of component i in gas phase Z compressibility factor for gas phase z coordination number of the UNIQUAC model

Greek Symbols˛ r i stoichiometric coefcient of component i in reaction r ˛ ij constant for intermolecular forces between the molecules

i and j ˇ ij intermolecular forces between the molecules i and j

difference operator i activity coefcient of component i in liquid phase ∞i activity coefcient of component i in liquid phase in case

of innite dilution i surface area fraction of component iϕi volume fraction of component i

i fugacity coefcient of component i in gas phase

ij interaction term of components i and j in UNIQUACmodel, exp( − a ij /T )εr progress degree of reaction r

SuperscriptsC combinatorialDH Debye–HuckelE energyg gas phasel liquid phaseM modelP predictedR residualr reaction

Subscripts A component Acond condensere exit streamf feed streamg gas phasei component i J volumetric element J l liquid phasem mixturestrip stripper

ACKNOWLEDGEMENTS

The authors would like to acknowledge the Shiraz Petrochem-ical Company (SPC), Petrochemical Research and TechnologyCompany (NPC-RT) and Chemical and Petroleum EngineeringDepartment of the Shiraz University for providing the requireddata and support throughout this study. The nancial supportof the Mitacs Elevate and the Natural Sciences and Engineer-ing Research Council of Canada (NSERC) for this research is alsoappreciated.

APPENDIX A: MOLAR ENTHALPIES OF COMPONENTS

Partial molar enthalpies for H 2O (i = 1) and NH 3 (i = 2) areobtained through the relationship [21,22 ,30] :

¯ H i (T, x ) = H 0i (T ) − RT 2 ∂ ln i

∂T (A.1)

Also, H 0i (T ) in the above equation is computed using the fol-lowing equation [21,22 ,30] :

H 0i (T ) = H ∗

i (T ) − RT 2 ∂ ln f

0i

∂T (A.2)

H 0i (T ) in Equations (A.1) and (A.2) is the molar enthalpy of ahypothetical liquid and H ∗i (T ) isthe molar enthalpy ofa purecom-ponent at ideal gas condition, but zero pressure and the systemtemperature.

For CO 2 (i = 3), the reference state is assumed to be a very dilutesolution in water and its partial molar enthalpy is calculated bythe following expression [21,22 ,30 ,40] :

¯ H 3 (T, x ) = H 03 (T ) − RT 2 ∂ ln 3

∂T (A.3)

¯ H 03 (T ) as a reference enthalpy is expressed as follows[21,22 ,30] :

¯ H 03 (T ) = ¯ H ∗

3 (T ) − RT 2 ∂ ln K H 3,1

∂T (A.4)

In the above equation, K H 3,1 is the Henry’s constant of CO 2 inwater which is obtained as follows [21,22 ,30] :

ln K H 3,1 = ln ∞3 (T ) + ln f 03 (T ) (A.5)

where ∞3 is the activity coefcient of CO 2 when its concentration

approaches to zero. This parameter is calculated by[21,22,30]

:

ln ∞3 =a 31T

− q3 31 + C 3 (A.6)

All parameters except C 3 in Equation (A.6) are known. C 3 isa constant for each component and assumed to be zero for CO 2component.

To estimate the partial molar enthalpies of the other compo-nents, the following general formula is used [21,22 ,41] :

¯ H 0i (T, x ) = ¯ H 0i (T ) − RT

2 ∂ ln i∂T

(A.7)

¯ H 0i (T ) is the molar enthalpy of component i at standard condi-tions.

Anions and cations formed in the solution are not in neutralcharge conditions. Therefore, it is not possible to predict theirconcentrations, independently. To tackle this issue, anions andcations are considered as dual combinations in order to deter-mine their molar enthalpies. Thus, the ionic molar enthalpies of ammonium ( i = 4), bicarbonate ( i = 5) and carbamate ( i = 6) arecomputed using the following formulas [22 ,30 ,40] :

¯ H 4,5(T, x ) = ¯ H 04,5(T ) − RT 2 ∂ ln

04

∂T +

∂ ln 05∂T

(A.8)



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¯ H 4,6(T, x ) = ¯ H 04,6(T ) − RT 2 ∂ ln

04

∂T +

∂ ln 06∂T

(A.9)

¯ H 04,5(T ) = ¯ H 04 (T ) + ¯ H

05 (T ) (A.10)

¯ H 04,6(T ) = ¯ H 04 (T ) + ¯ H

06 (T ) (A.11)

Following the Van’t Hoff approach, molar enthalpies of compo-nents at reference states are as follows [21,22,30] :

¯ H 04,6(T ) = 2 H 02 (T ) + ¯ H

03 (T ) + RT

2 ∂ ln K 1(T )∂T

(A.12)

¯ H 04,5(T ) = H 01 (T ) + H

02 (T ) + ¯ H

03 (T ) + RT

2 ∂ ln K 2(T )∂T

(A.13)

Consequently, molar enthalpy of urea can be presentedas [21,22 ,41] :

¯ H 07 (T ) = H 01 (T ) + 2 H

02 (T ) + ¯ H

03 (T ) + RT

2 ∂ ln K 3(T )∂T

(A.14)

The enthalpy of the liquid mixture is obtained as follows:

H (T, x ) =n

i= 1

xi ¯ H i (T, x ) (A.15)

xi is the molar fraction of component i in the liquid mixture andn is the number of components.

The enthalpies of gas phase components are determinedby [21,22 ,41] :

H i(T ) = H ig0 + C P mean ,i (T − T 0) + H

Ri (A.16)

H ig0 is the enthalpy of component i at ideal gas state condition attemperature T 0 and pressure P 0 as reference conditions. C Pmean ,iis the mean heat capacity of component i at a constant pressurein the temperature range of T and T 0 . H Ri is the residual (excess)enthalpy of the component i which shows the difference betweenenthalpies of component i at ideal and non-real states.

APPENDIX B: ACTIVITY COEFFICIENT OF LIQUIDCOMPONENTS

Based on the UNIQUAC model, the ln Ci (x) and ln Ri (T, x ) values

are determined by the following expressions [21,22,29] :

ln Ri (T, x ) = − qi ln n

j = 1

i ij − 1 +n

j = 1

j ij n

k = 1 k kj

(B.1)

ln Ci (x) = lnϕi

xi+

z2

qi ln iϕi

+ li −ϕi

xi

n

j = 1

xi li (B.2)

z is the coordination number of the UNIQUAC model.

APPENDIX C: MODEL EQUATIONS FOR CONDENSER ANDSTRIPPER

The main equations to simulate the condenser are as follows:

- Two equations for the phase equilibrium of NH 3 (2), CO 2 (3):f gi = f

li ( i = 2, 3). It is acceptable to assume that no water exists

in the tube part of the condenser.- Four equations for the material balance of NH 3 (2), CO 2 (3),

NH+4 (4) and H 2NCOO− (6) are written as the following:

F i, in − F i, out = V cond ˛ r = 4i Rr = 4 i = 2, 3, 4, 6 (C.1)

where V cond is the volume of the condenser. F i,in and F i,out arethe molar ow rates of component i entering and exiting thecondenser, respectively.

It should be noted here that just NH 3 (2), CO 2 (3), NH +4 (4) andH2NCOO− (6) areavailable in the condenser. Also, the only reac-tion occurred in the condenser is the formation of ammoniumcarbamate ( r = 4).

- One equation for the energy conservation in the condenser isexpressed as:

F li, in

H li, in

+ F gi, in

¯ H gi, in

− F li,out

¯ H li,out

− F gi,out ¯ H gi,out =

Q̇w (C.2)

Here, Q̇w represents the enthalpy change of the water phase inthe shell.

According to the process design of the stripper, the chemicalsin the stripper include NH 3 (2), CO 2 (3), NH +4 (4), and H 2NCOO

−

(6), H 2NCONH 2 (7), and H 2NCONHCOH 2 N (8). Thus, the samethermodynamic equilibrium equations are written for ammoniaand carbon dioxide. Also, the material balance for the above com-ponents is as follows:

F i, in − F i,out = V strip ˛ ri Rr i = 2, 3, 5, 6, 7, 8 (C.3)

where V strip stands for the volume of the stripper.Similar energy conservation equation should be written for this

process element as below:

F li, in H li, in + F

gi, in

¯ H gi, in − F li,out

¯ H Ei, out

− F gi, out ¯ H gi, out =

Q̇s (C.4)

In the above equation, Q̇s shows the enthalpy change of thesteam phase.

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Manuscript received October 17, 2012; revised manuscript received December 26, 2012; accepted for publication January 5,2013 .

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