bradscholars

Modelling of an industrial naphtha

isomerization reactor and development and
assessment of a new isomerization process

Item Type Article

Authors Ahmed, A.M.;Jarullah, A.T.;Abed, F.M.;Mujtaba, Iqbal

Citation Ahmed AM, Jarullah AT, Abed FM et al (2018) Modelling of an

industrial naphtha isomerization reactor and development
and assessment of a new isomerization process. Chemical
Engineering Research and Design. 137: 33-46.

DOI https://doi.org/10.1016/j.cherd.2018.06.033

Rights © 2018 Institution of Chemical Engineers. Published by Elsevier

B.V. All rights reserved. Reproduced in accordance with the
publisher's self-archiving policy. This manuscript version is made
available under the CC-BY-NC-ND 4.0 license.

Download date 2025-04-14 12:23:26

Link to Item http://hdl.handle.net/10454/16401

Modelling of an Industrial Naphtha Isomerization Reactor and

Development and Assessment of a New Isomerization Process

Ahmed M. Ahmed1, Aysar T. Jarullah1,a , Fayadh M. Abed 2, Iqbal M. Mujtaba3,a

1
Tikrit University, College of Engineering, Chemical Engineering Department
2
Tikrit University, College of Engineering, Mechanical Engineering Department
3
Chemical Engineering Division, School of Engineering, University of Bradford,
Bradford BD7 1DP UK
a
Corresponding Author. Email: A.T.Jarullah@tu.edu.iq ; I.M.Mujtaba@bradford.ac.uk

Abstract
Naphtha isomerization is an important issue in petroleum industries and it has to be a

simple and cost effective technology for producing clean fuel with high gasoline octane

number. In this work, based on real industrial data, a detailed process model is developed

for an existing naphtha isomerization reactor of Baiji North Refinery (BNR) of Iraq

which involves estimation of the kinetic parameters of the reactor. The optimal values of

the kinetic parameters are estimated via minimizing the sum of squared errors between

the predicted and the experimental data of BNR. Finally, a new isomerization process

(named as AJAM process) is proposed and using the reactor model developed earlier, the

reactor condition is optimized which maximizes the yield and research octane number

(RON) of the reactor.

Key words: Isomerization, Kinetic Parameters, Optimization, Mathematical Modeling

1. Introduction

Isomerization reactor is the heart of isomerization process (Figure 1) in petroleum

refineries to enhance Research Octane Number (RON) of gasoline products.

Isomerization is the rearrangement of straight-chain hydrocarbons components

converting to branched hydrocarbons components with higher octane number [1].

Contents of aromatics and olefins in the gasoline should be reduced for environmental

protection and the loss of octane number caused by the reduction of aromatics and olefins

should be compensated by addition of some compounds that have higher octane numbers.

One possible alternative of aromatics and olefins is the branched alkanes with high octane

numbers. Therefore, skeletal isomerization of alkanes is regarded a key reaction for

producing environmentally benign gasoline in industries [2].

Reforming process is employed to produce high octane compounds, but this process is

exclusively used for treating heavy naphtha (C7-C8). The isomerization process is

regarded to be a simple, economic and very attractive solution to produce clean gasoline

with a high octane number. Light naphtha is desirable to be included in gasoline

formulation to meet the front-end distillation cut and octane number specs. The normal

paraffins (C5/C6) is difficult to be included in the gasoline pool as it is because they have

low octane number. Converting them to branched compounds with high octane number

via isomerization process makes them more favorable for inclusion in gasoline [3,4].

Catalytic isomerization of pentanes and hexanes mixtures is usually conducted over a

fixed bed of catalyst using hydrogen at operating conditions which minimizes the

hydrocracking reactions but enhances the isomerization reactions. One or two reactors in

series are used in such process, each one has an equal catalyst volume, and the reaction is

acquired in the liquid or gas phase according to the catalyst used in the system [3,5].

The octane number of produced isomerizate is mainly dependent on the operation

temperature of the reactor. Hydrocarbons isomerization reactions are reversible reactions

and equilibrium conversion of n-paraffins increases with decreasing temperature (Figure

2). However, it is achieved after an infinite contact time of the feed in the reaction zone

or at an equivalent very small value for liquid hourly space velocity. Such behavior is
represented in Figure 2 by theoretical conversion line (that neglects the effect of catalyst

activity). In other words, for the actual behavior (represented in Figure 2 by actual

conversion line), a decrease in temperature always corresponds to a decrease in reaction

velocity due to decrease the effectiveness of the catalyst. Hence at low temperature, the

actual conversion will be lower than the equilibrium conversion. On the other hand, as

the isomerization reactions are exothermic, at high temperature (higher than the optimal

temperature) the yield of iso-paraffins decreases with increasing temperature due to

thermodynamic limitation [1,6].

In the traditional once through isomerization process (Figure 1), feedstock containing

both iso-paraffins and normal paraffins are fed into the reactor where normal paraffins are

converted to iso-paraffins to enhance the RON. The reaction products then pass through

the stabilization unit and isomerizate is produced. Mathematical modeling of an industrial

catalytic refining process is an important direction for technical improvement. Many

studies in the past have greatly contributed to the improvement of the method of

mathematical modeling for catalytic isomerization of light naphtha which is one of the

most common high-tech industrial process [7,8].

This study aims to develop the process model of an industrial (BNR) isomerization

reactor which requires development of kinetic models for the process. For this purpose, a

full process model (taken from the literature) is used and the kinetic parameters (order of

hydrocarbon concentration(n), order of hydrogen concentration in cracking reaction (m),

order of hydrogen concentration in hydrogenation reaction (o), kinetic coefficient of

intermolecular interactions intensity (α, γ), activation energies (Ej), pre-exponential factor

(Aj)) of the model are estimated via minimizing sum of the squared error between the real

industrial data (of BNR) and the model predictions to find the best kinetic parameters.

Using the model, the reactor is then simulated by varying a number of operational
parameters. Finally, we have proposed a new isomerization process (named as AJAM

process) configuration which is different from the existing BNR isomerization process.

We have evaluated this proposed process by comparing its performance (in terms of yield

and RON) with the existing BNR process. The validated isomerization reactor model

developed earlier is employed in the new process.

2. Industrial Reactor Operation

All the industrial data including the reactor dimensions, catalyst specifications, reactor’s

feedstock, product’s composition and operating conditions, which are presented in Tables

1, 2, and 3 are taken from the actual isomerization unit at Baiji North Refinery (BNR),

Iraq. Isomerization unit of BNR operates in once through mode using zeolitic catalyst

system. As illustrated in Figure 1, the fresh feedstock (light naphtha) obtained from

hydrotreating process is fed to the unit feed storage drum and then mixed with

compressed hydrogen before being heated in heat exchangers and furnace system, which

raises the temperature of the feed to the optimal reactor inlet temperature. Thereafter, the

light naphtha passes through the isomerization reactor only once where the n-paraffins

are converted to iso-paraffins.

The isomerization reactions take place in the reactor (cylindrical with a height of 13.840

m and diameter of 2.9 m) loaded with a bed of zeolite catalyst. Unstabilized isomerizate

is sent to stabilization unit in order to separate light hydrocarbons (mainly CH4, C2H6 and

C3H8 which used to produce LPG). The stabilized isomerizate is taken out from the

bottom of the column as a final product.

3. Mathematical model of BNR isomerization reactor

The model equations of isomerization reactor are represented by a system of equations of

material balance and heat balance for each component as shown below:

3.1 Mass balance equation

Eq. (1) is an ordinary differential equation used to describe the concentration of every

component through the catalyst bed. However, solution of this differential equation gives

the concentration profile of components with unit volume of catalyst bed [9].

𝑑𝐶𝑖
𝐺 = ∑𝑚
𝑗=1 𝑎𝑗 . 𝑟𝑗 (1)
𝑑𝑉

The initial conditions of this equation are:

At V=0, Ci = Ci,in

3.2. Heat Balance Equation

Solution of the following ordinary differential Eq. (2) gives the temperature profile over

the unit volume of the catalyst bed [9].

𝑑𝑇 1
𝐺 𝑑𝑉 = 𝜌 ∑𝑚
𝑗=1 𝑄𝑗 . 𝑎𝑗 . 𝑟𝑗 (2)
∁𝑚
𝑝

The initial conditions can be written as:

At V=0, T=Tin

3.3. Reaction Rate Equations

According to the chemical reaction, power rate law non-elementary reaction rate at the

set temperature is proportional to the concentration of reacting substances based on the

order of n, m and o as shown below [9]:

𝑟𝑗 = Ƞ𝑗 𝑘𝑗 𝐶𝑖𝑛 (3)
𝑟𝑗 = Ƞ𝑗 𝑘𝑗 𝐶𝑖𝑛 𝐶𝐻2
𝑜
(4)

𝑟𝑗 = Ƞ𝑗 𝑘𝑗 𝐶𝑖𝑛 𝐶𝐻2
𝑚
(5)

Eq. (3, 4 and 5) represents the isomerization, hydrogenation and hydrocracking reactions

rate respectively.

Reaction rate constant (𝑘𝑗 ) can be described by Arrhenius equation as follow:

−𝐸
𝑘𝑗 = 𝐴𝑗 exp ( 𝑅 𝑇𝑗) (6)

The concentration of each component can be described by the ideal gas law with taken

into account the compressibility factor:

𝐶𝑖 = (𝑦𝑖 𝑝 )/(𝑍𝑖 𝑅 𝑇) (7)

The compressibility factor for every species is given by the following equation [10]:

(𝑇 ⁄𝑇𝑐𝑖 )
𝑍𝑖 = 1 − 0.04188423(𝑇⁄𝑇𝑐𝑖 )
(8)
(𝑃⁄𝑃𝑐𝑖 )(0.36748758− )
(𝑃⁄𝑃𝑐𝑖 )

Based on the operating data of different isomerization process, Chekantsev et al. [9]

have proposed a scheme of the isomerization reactions process presented in Figure 3,

which is employed in the modeling of naphtha isomerization process according to the

chemical reaction equations presented in Table 1.

3.4. Catalyst Activity

The dependence of catalyst activity on time has been taken in to account that can be

represented by the following equation [9]:

 𝑘𝑗,𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑎= (9)
𝑘𝑗,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

3.5. Effectiveness Factor

The effectiveness factor of reactions represents the ratio of the reaction rate into the

particle to the rate of reaction at the surface of the particle as submit by Bischoff [11] and

Mohammed et al. [12] and can be estimated as a function of Thiele Modulus valid for

cylindrical particle as follow:

tanhφj
Ƞ𝑗 = (10)
φj

For 𝑛𝑡ℎ -order reaction, the general Thiele Modulus (𝜑) can be evaluated using the

following relationship [12,13]:

𝑉𝑃 𝑛+1 𝑟𝑗 𝐶𝑖−1 𝜌𝑝
𝜑= √( )( ) (11)
𝑆𝑃 2 𝐷𝑒,𝑖

The Particle density (𝜌𝑝 ), is estimated using the following relation [14]:

𝜌
𝑐𝑎𝑡
𝜌𝑝 = 1−𝜖 (12)
𝐵

The Bed porosity (𝜖𝐵 ) of the catalyst can be estimated for undiluted sphere packed

catalyst from the following equation [12]:

𝑑
( 𝑡 −2 )2
𝑑𝑝𝑒
𝜖𝐵 = 0.38 + 0.073 (1 + 𝑑 ) (13)
( 𝑡 )2
𝑑𝑝𝑒

Equivalent diameter of particle (dpe) can be defined as the diameter of the sphere having

the same external volume as the real catalyst particle [15,16].

 6(𝑉𝑝 ⁄𝑆𝑝 )
𝑑𝑝𝑒 = (14)
∅𝑠

surface area of a sphere of equal volume

∅𝑠 = (15)
𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

For cylindrical shape, the external volume (Vp) and the surface area (Sp) of particle is

calculated as shown below:

𝜋
𝑉𝑝 = 4 𝑑𝑝2 𝐿 (16)

𝑆𝑃 = 𝜋 𝑑𝑝 𝐿 (17)

The effective diffusivity of every component (𝐷𝑒,𝑖 ) can be estimated utilizing the next

relation [12] taking into account the tortuosity of the pore network inside the catalyst

particle considering the porosity in the modeling.

𝜖𝑆 1
𝐷𝑒,𝑖 = 1 1 (18)
Ԏ 𝑔 +
𝐷 𝐷𝑘𝑖
𝑚𝑖

Catalyst particle porosity (ϵS ) is calculated by using the equation below, which depends

on the particle density and pore volume:

𝜖𝑆 = 𝜌𝑝 𝑉𝑔 (19)

The tortuosity factor (Ԏ ) can be estimated by the following equation [13].

1−0.5𝑙𝑜𝑔𝜀𝑠
Ԏ= (20)
𝜖𝑠

Knudsen diffusivity represents the diffusivity of components into pores of the catalyst for

each component, which can be calculated utilizing the following equation [12]:
 𝑇
𝐷𝑘𝑖 = 349200 𝑟𝑔 √𝑀𝑊 (21)
𝑖

The mean pore radius can be calculated by the following equation [12].

2𝑉𝑔
𝑟𝑔 = (22)
𝑆𝑔

The molecular diffusivity coefficient of species i in the gas phase can be calculated from

equation (23) depending on the binary diffusion coefficient of component i through the

other components [17]

𝑔 𝑦
𝐷𝑚𝑖 = (1 − 𝑦𝑖)1/ ∑𝑁𝐶𝐺
𝑘≠𝑖 𝐷
𝑘
(23)
𝑖,𝑘

The binary diffusion coefficient can be calculated from the following equation [18].

1 1 1
𝐷𝑖,𝑘 =188.2458*10−20 √𝑇 3 (𝑀𝑊 + 𝑀𝑊 ) 𝑃 𝜎2 (24)
𝑖 𝑘 𝑖,𝑘 ∩𝐷

The average collision diameter and the collision diameter of each component is

calculated by the equation bellow [19]:

𝜎𝑖 +𝜎𝑘
𝜎𝑖,𝑘 = (25)
2

1
𝜎𝑖 = 1.18 ∗ 10−9 (𝑉𝑏𝑖 )3 (26)

The diffusion collision integral for gases molecules can be calculated using the equation

below [20].

1.06036 0.193 1.03587 1.76474

∩𝐷 = (𝑇 ∗)0.1561 + exp(0.47635𝑇 ∗) + exp(0.01529𝑇 ∗) + exp(3.89411𝑇 ∗) (27)
The dimensionless temperature is calculated as a function of Boltzmann constant (CB) and

Characteristic (minimum) energy (𝜀𝑖𝑘 ) [19].

𝑇
𝑇∗ = 𝜀 (28)
𝑖𝑘 ⁄𝐶𝐵

𝜀𝑖𝑘 ⁄𝐶𝐵 = 0.75𝑇𝑐,𝑖𝑘 (29)

𝑇𝑐,𝑖𝑘 = √𝑇𝑐𝑖 𝑇𝑐𝑘 (30)

3.6 Density of Mixture

The density of mixture (𝜌) represents the light naphtha vapor density (𝜌𝑙𝑛 ) and hydrogen

gas density (𝜌𝐻2 ) as follow:

𝜌 = 𝜌𝑙𝑛 𝑊𝑡𝑙𝑛 + 𝜌𝐻2 𝑊𝑡𝐻2 (31)

The density of light naphtha is estimated as a function of pure components density and

their weight fractions as follow:

𝜌𝑙𝑛 = ∑𝑖 𝜌𝑖 𝑊𝑡𝑖 (32)

Where, 𝜌𝑖 : Density of i hydrocarbon component vapor, kg/m3, Wti: Weight fraction of i

hydrocarbon component, (-).

The density of hydrogen and of each hydrocarbon component in the gas phase can be

estimated as a function of temperature and pressure based on ideal gas equation with

taking into account the gas compressibility factor where the gas at these conditions has

trend toward the reality state. The equation can be written as shows:

𝑃𝑀𝑊𝑖
𝜌𝑖 = (33)
𝑍𝑖 𝑅𝑇
Where:

P: Pressure, pa

T: Temperature, K

Zi: The gas compressibility factor, (-)

𝑅: Gas constant, J/mol. K

MWi: Molecular weight of ith component, kg/kmol

The density of the components at normal boiling point can be calculated from the

following equation [18]:

𝑀𝑊𝑖 𝑃𝑐𝑖
𝜌𝑏𝑖 =𝑅 𝑇 (34)
𝐶𝑖 𝑍𝐶𝑖 (1+(1−𝑇𝑟𝑖 )2⁄7 )

Where:

𝜌𝑏 : The density at boiling point, kg/m3

Zc: Critical compressibility factor, (-)

Tr: Reduced temperature, (-)

Pc: Critical pressure, pa

Tc: Critical temperature, K

𝑇
𝑇𝑟 = (35)
𝑇𝑐

3.7 Heat of Reaction Calculation

The heat of reaction as a function of temperature is calculated from the following

equations:

° 𝑇
𝑄𝑗 = ∆𝐻𝑟𝑥𝑛,𝑗 + ∫298 ∆ 𝐶𝑝𝑗 𝑑𝑇 (36)

° ° °
∆𝐻𝑟𝑥𝑛,𝑗 = ∑ 𝑦𝑖 ∆ 𝐻𝑓𝑖,𝑝 − ∑ 𝑦𝑖 ∆ 𝐻𝑓𝑖,𝑟 (37)
∆𝐶𝑝𝑗 = ∑ 𝑦𝑖 𝐶𝑝𝑖,𝑝 − ∑ 𝑦𝑖 𝐶𝑝𝑖,𝑟 (38)

𝐶𝑝𝑖 = 𝐴 + 𝐵𝑇 + 𝐶𝑇 2 + 𝐷𝑇 3 (39)

The heat capacity of mixture (𝐶𝑝𝑚 ) can be calculated from following equation:

𝐶𝑝𝑚 =∑ 𝑦𝑖 𝐶𝑝𝑖 (40)

3.8 Flow Rate of Raw Material

The feed stock to the reactor contains hydrogen gas and light naphtha vapor that can be

calculated as a function to the mass flow rate of light naphtha (𝑊𝑙𝑛 ) and hydrogen (𝑊𝐻2 )

as follow:

𝐺 = 𝑊𝑙𝑛 ⁄𝜌𝑙𝑛 + 𝑊𝐻2 ⁄𝜌𝐻2 (41)

The mass flow rate of light naphtha is calculated as a function to LHSV and the volume

of the bed (V):

𝑊𝑙𝑛 = 𝑄𝑙𝑛 ∗ 𝑠𝑝. 𝑔𝑟 ∗ 𝜌𝑤 (42)

𝑄𝑙𝑛 = 𝐿𝐻𝑆𝑉 ∗ 𝑉 (43)

𝑊𝐻2 = 𝑚𝑟 ∗ 𝑀𝑙𝑛 ∗ 𝑀𝑊𝐻2 (44)

𝑊
𝑀𝑙𝑛 = 𝑀𝑊𝑙𝑛 (45)
𝑙𝑛

𝑀𝑊𝑙𝑛 = ∑𝑖 𝑦𝑖 𝑀𝑊𝑖 (46)

3.9 Research Octane Number (RON) and yield

The model has taken into account the physicochemical nature of mixing process and non-

additive properties of gasoline. Thus, the model of mixing octane number can be written

as [21]:
𝑅𝑂𝑁 = ∑𝑚
𝑖=1(𝑅𝑂𝑁𝑖 . 𝑦𝑖 ) + 𝛽 (47)

1
𝛽 = 100 ∑𝑚−1 𝑚
𝑖=1 ∑𝑗=2 𝛽𝑖 𝛽𝑗 𝑦𝑖 𝑦𝑗 (48)

𝐷𝑖𝑖 𝛾
𝛽𝑖 = 𝛼 (𝐷𝑖 ) (49)
𝑚𝑎𝑥

𝑌𝑖𝑒𝑙𝑑 = 𝑀𝑖𝑠𝑜 /𝑀𝑙𝑛 (50)

4. Estimation of kinetic parameters of the reactor model

Accurate estimations for kinetic parameters are required to describe the actual behavior

of process. However, parameter estimation is a difficult step in the development of

process models and requires experimental data. Thus, the best evaluation of such

parameters is based on minimum errors between the experimental (industrial) data and

the predicted data from the mathematical model [16].

The optimal kinetic parameters of an industrial light naphtha isomerization reactor model

are estimated using gPROMS software. The optimal values of activation energy (𝐸𝑗 ) and

pre-exponential factor (𝐴𝑗 ), components concentration orders (o, m & n) and kinetic

coefficient of intermolecular interactions intensity (γ & α) for every reaction in the

process were directly calculated by using non-lineal approach. Also, such parameters

were simultaneously calculated in this approach based on minimization of the sum of the

squared error (SSE) between experimental and predicted weight fraction, yield and RON.

𝑒𝑥𝑝.
SSE= ∑(∑𝑚
𝑖=1((𝑊𝑖 – 𝑊𝑖𝑝𝑟𝑒𝑑. )2 + (𝑦𝑖𝑒𝑙𝑑 𝑒𝑥𝑝. − 𝑦𝑖𝑒𝑙𝑑 𝑝𝑟𝑒𝑑. )2 + (𝑅𝑂𝑁 𝑒𝑥𝑝. −
𝑅𝑂𝑁 𝑝𝑟𝑒𝑑. )2 ) (51)

4.1 Optimization problem formulation for parameter estimation

The optimization problem formulation of naphtha isomerization process can be described

as follows:
Give: The reactor configuration, the initial hydrocarbons and hydrogen

concentration, the catalyst, reaction temperature and pressure,

liquid hourly space velocity and flow rate.

Obtain: The reaction orders of hydrocarbon (n), hydrogen (m, o), pre-

exponential constant (𝐴𝑗 ), activation energy (𝐸𝑗 ) of each reaction

and also kinetic coefficients (𝛼&𝛾).

So as to minimize: The sum of square errors (SSE).

Subjected to: Constraints of process and linear bounds upon all optimization

variables in this process.

Mathematically, the optimization problem can be represents as shown below:

Min SSE

s.t. f (v, (v),x ˜ (v), u (v), z) = 0, [v0 , vf ] (model, equality constraint)

nL ≤ n ≤ nU (Inequality constraints)

mL ≤ m ≤ mU (Inequality constraints)

oL ≤ o ≤ oU (Inequality constraints)

EjL ≤ Ej ≤ 𝐸𝑗𝑈 (Inequality constraints)

ALj ≤ Aj ≤ AUj (Inequality constraints)

αLj ≤ αj ≤ αU
j (Inequality constraints)

YjL ≤ Yj ≤ YjU (Inequality constraints)

Where: f (v, x(v), x ˜ (v) , u(v), v) = 0 : represents the model of process which presented

in the previous sections. V: the reactor bed volume. U (v): the decision variables (n,

m,𝐸𝑗 ,𝐴𝑗 , α, Y). X (v): gives the set of all algebraic and differential variables (𝐶𝑖 , T, 𝑅, ….).
x ˜ (v): represents the differential variables derivative with respect to volume of the

𝑑𝐶 𝑑𝑇
reactor bed such as ( 𝑑𝑉𝑖 , , …). V: volume (independent constants parameters) or
𝑑𝑉

variables of design such as (R …). [v0 ,vf ],: the volume interval of interest. The function f

is supposed to be continuously differentiable with regard to whole its arguments.

The optimization solution method used by gPROMS is a two-step method known as

feasible path approach. The first step performs the simulation to converge all the equality

constraints (described by f) and to satisfy the inequality constraints. The second step

performs the optimization (updates the values of the decision variables such as the kinetic

parameters). The optimization problem is posed as a Non-Linear Programming (NLP)

problem and is solved using a Successive Quadratic Programming (SQP) method within

gPROMS software.

4.2 The kinetic model of the industrial reactor

All the catalyst specifications, inlet and outlet composition of the industrial isomerization

reactor, operating condition of the industrial isomerization reactor and the physical

properties of light naphtha components are given in Tables (2 - 5). The critical properties

and molecular weight of each component were taken from Perry and Green [22], pure

components RON were taken from Chekantsev et al. [9] and dipole moment values were

taken from Vogel and Mobius [23]. The lower and upper bounds for all listed inequality

constraints in addition to the initial values of the applied model are presented in appendix

A (Table A1).

The optimal values of activation energy (𝐸𝑗 ) and pre-exponential factor (𝐴𝑗 ) for every

reaction in the process have been calculated using Arrhenius equation. Also, the optimal

values of components concentration orders (o, m & n) and kinetic coefficient of

intermolecular interactions intensity (γ & α) were simultaneously estimated. Such

parameters are presented in Tables 6 and 7.

The optimal kinetic parameters have been estimated based on a maximum error of 0.1%

among all results between the experimental and predicted results of average reactor

output data of three test runs. The composition of isomerizate components (𝑊𝑖 ), research

octane number of isomerizate (RON) and reactor outlet temperature (T) are obtained via

simulation process and presented in Table 8.

As can be seen from this Table, the error between the industrial data and predicted results

is very small giving a clear indication that the results obtained have an excellent match

among theoretical and practical results. Therefore, the model can now be applied

confidently for further applications for the purpose of improving the yield and RON of

such process. Many researchers have studied the kinetics of isomerization of light

naphtha, as reported in literatures [9,24,25]. They have assumed that the concentration

orders used in the simulation of isomerization process equal to the number of molecules,

which enter the reaction. Thus, huge errors (more than 5%) between the industrial and

theoretical results were reported in the past giving high deviation.

5. Simulation of Industrial Reactor

After getting the accurate kinetic model, the parameters are used to describe the influence

of operating conditions on the reactions occurring through the bed of catalyst. Increasing

the RON of the light naphtha and isomerizate yield are the main goal of the isomerization

process. Therefore, the variables are considered as an index for analyzing the

performance of the reactor.

5.1 Effect of Temperature and Pressure on the isomerizate RON and yield
Figures 4 and 5 show the influence of the feed stock temperature and pressure on the

RON and yield of isomerizate respectively. Feed stock no.1 was used to describe the

behavior of this process at constant LHSV equal to 1.489 hr −1 and hydrogen ratio equal

to 3.22.

It can be observed that temperature has the most impact on the performance of the

isomerization reactions. In Figure 4, at the beginning of the curve (region one 512-534K),

the RON decreases with increasing temperature, which can be related to the

thermodynamic properties of such reactions and accelerated the hydrocracking of

hydrocarbons containing six carbon atoms such as 2,2-DMB, 2,3-DMB, MCP, and CH.

Therefore, the high octane number species are converted to lighter ones such as methane,

propane and butanes. These light species are separated from the product in the form of

fuel gas and the reduction of octane number continues until hydrocarbon species

containing six carbons are hydrocracked. Finally, the upward trend of RON in the second

region is due to increase the percentage of pentane at higher temperatures [26].

Since hydrocracking reactions have a negative effect on the yield of the gasoline

production, it is concluded that the optimal isomerization temperature is located in the

first region in which RON and yield are both at the optimal values. This Figure also

indicates that 0.2 MPa increment in pressure leads to increase the optimal temperature

about 2oC. Figure 5 demonstrates the dependency of RON on pressure when hydrogen to

hydrocarbon molar ratio and LHSV are kept constant. The optimal reactor inlet

temperature depends on the pressure and the results showed that by decreasing the reactor

pressure. The reactor inlet temperature should be reduced until the desired temperature

inside the reactor is achieved for the purpose of reducing the hydrocracking reactions,

which absorbs some of isomerization reactions emitted heat [1, 27].

Figure 5 presents the effect of inlet feed stock temperature and pressure on the

isomerizate yield at constant LHSV and hydrogen to hydrocarbon mole ratio. The results

show that the yield of isomerizate decreases with increasing inlet temperature leading to

enhancement of hydrocracking reactions rate. Also, this Figure shows that the increase in

pressure can decrease the isomerizate yield due to increase in the partial pressure of

hydrogen [23,26].

5.2 Effect of Hydrogen to Hydrocarbon Mole Ratio on the isomerizate RON and yield

Hydrogen is desired to complete the reactions and to reduce the deposition of coke on the

surface of the catalyst. Figures 6 - 8 show the influence of the hydrogen to hydrocarbons

mole ratio on the RON and Figure 9 - 11 illustrate the impact of hydrogen to

hydrocarbons mole ratio on the yield of isomerizate at constant temperature, pressure and

liquid hourly space velocity. It is has been observed from Figure 6, 7 and 8 that the

product RON depends on the hydrogen over feed molar ratio. These results show that at

constant feed flow rate and by increasing hydrogen to feed molar ratio, the RON of

product decreases due to increase the rate of hydrocracking reactions (which considered

endothermic reactions) within the reactor [23, 26].

Figures 9 - 11 demonstrate the high negative impact of hydrogen to hydrocarbon mole

ratio on the isomerizate yield. Increasing of such ratio leads to decrease in the yield of

isomerizate owing to the increase of hydrogen partial pressure. This Figure also indicates

that 0.2 unit increments in hydrogen-to-hydrocarbon molar ratio decreases the yield of

isomerizate about 1.3% at constant temperature.

5.3 Effect of LHSV on the isomerizate RON and yield

Figures 12 - 14 present the effect of LHSV on the RON and Figures 15 - 17 illustrate the

influence of LHSV on the yield of isomerizate at constant H2/HC mole ratio, temperature

and pressure. According to Figure 8, the RON of the product depends on the LHSV.

Indeed, the residence time decreases by increasing the LHSV, so that the conversion of

normal paraffin's decrease [27].

The negative effect of increasing the LHSV on the RON can be overcome by increasing

the inlet temperature of reactor feed stock. This method can be recommended for

increasing the capacity of light naphtha isomerization reactor, accordingly, increasing the

reactor operating temperature increases the capacity of gasoline production while the

RON of product remains at the desired value. This procedure is highly appreciated when

there is limitation in increasing hydrogen to hydrocarbon molar ratio due to the process

limitations such as the loading capacity of hydrogen compressor [23].

6. A new isomerization process configuration

Figure 18 shows the new proposed configuration of the isomerization process. Compared

to the traditional process (BNR) shown in Figure 1, the new configuration separates the

normal paraffins from the izomerizate. Only normal paraffins are allowed to go into the

isomerization reactor. The process is expected to maximize the yield and RON of the

isomerizate. In all other traditional isomerization technologies, the adsorption equipment

are located after the reactor to separate the normal paraffins and recycling them to the

reactor. Such processes results in increase in the isomerization feed stock leading to

increase in the equipment capacity. In the new configuration, based on the specifications

of naphtha feed stock at BNR isomerization unit, the separation process can take place

first (adsorption equipment located before the reactor) to reduce the benzene percentage

less than 0.62%, so that it is not hydrogenated through isomerization process (benzene
components are left the adsorber with branched paraffins). Also, this procedure reduces

the reactor feed stock by 46% in comparison with once through process.

As can be seen in Figure 18, the naphtha feed stock enters to the adsorption column

where the normal paraffins are adsorbed by the molecular sieve then desorbed by

hydrogen stream and the stream of normal paraffins and the hydrogen are sent to the

reactor to produce the branched chain paraffins. The reactor outlet stream is a mixture of

normal and iso-paraffins, so it is combined with the naphtha feed stock stream to separate

the normal paraffins through adsorption process. The benefits expected of using such new

configuration is increased RON of the isomerizate unit and reduced isomerization reactor

feed stock, increased yield in comparison with the traditional once through process. Also

this procedure will reduce the isomerization reactor capacity compared to theonce

through process. Due to the separation and by-pass operation made for iso-paraffins, the

yield of isomerizate will increase owing to reduction of the hydrocracking reactions.

6.1 Modeling of the proposed isomerization process

The reactor model presented in section 3 with the optimal kinetic parameters (calculated

in section 4) is used to represent the isomerization reactor of the new configuration

(Figure 18) and is incorporated in an optimization framework to maximize (RON and

yield) of the reactor, taken into account the change of feed stock rate and inlet

composition of component due to separation of normal paraffins upfront. The

performance of the reactor is optimized according to Eq. (52) below:

𝑂𝐵𝐽 = ∑(𝑅𝑂𝑁 + 𝑌𝐼𝐸𝐿𝐷) (52)

Given Initial concentration, kinetic parameters, reactor configuration,

process specifications.
Determine Initial temperature, pressure, LHSV and hydrogen to

hydrocarbon mole ratio.

So as to maximize OBJ (RON & yield).

Subject to Process constraints and linear bounds on all decision variables.

The optimization problem is stated as:

Max 𝑂𝐵𝐽

P, T, LHSV, 𝑚𝑟 , WnC5 , WnC6

s.t f(x(z),u(z), v) = 0 (model equation, equality constraint)

𝑃𝐿 ≤ 𝑃 ≤ 𝑃𝑈 (inequality constraints)

𝑇𝐿 ≤ 𝑇 ≤ 𝑇𝑈 (inequality constraints)

𝐿𝐻𝑆𝑉 𝐿 ≤ 𝐿𝐻𝑆𝑉 ≤ 𝐿𝐻𝑆𝑉 𝑈 (inequality constraints)

𝑚𝑟𝐿 ≤ 𝑚𝑟 ≤ 𝑚𝑟𝑈 (inequality constraints)

𝑙 𝑈
𝑊nC 5
≤ 𝑊𝑛𝐶5 ≤ 𝑊nC5
(inequality constraints)

𝑙 𝑈
𝑊nC 6
≤ 𝑊𝑛𝐶6 ≤ 𝑊nC6
(inequality constraints)

6.2 Performance of the new isomerization process and comparison with the BNR
isomerization process
The optimal results obtained for the new process configuration (Figure 18) (that has not

previously been reported in the literature) and the comparison with the current once

through BNR process (Figure 2), are presented in Table 9. As clearly noted, the highest

RON and yield is obtained by using the new process compared with those obtained by

traditional method. Increase in RON from 79.45 to 90.81 is due to increase in the total

conversion of normal paraffins. While, increase in the yield from 97.68 to 99.2 is due to

decrease in the reactor feed stock rate by 48.34 wt% compared to once through process.
Also, the bed volume (V) of the proposed new process has been decreased by 46.5% in

comparison with once through process.

7. Conclusions
In this work, an isomerization reactor model of a traditional once through process (Figure

1) is developed using industrial data of Baiji North Refinery (BNR). The parameters of

the kinetic models have been determined by using model based parameter estimation

technique. The model is then used to simulate the industrial reactor and to study the

effect of different operating parameters such as temperature, pressure, H2/HC mole ratio

and LHSV on the performance of the reactor in terms of RON and the yield. Finally, a

new isomerization process configuration (Figure 18) is proposed and its performance is

evaluated and compared with the traditional process. For this purpose, the reactor model

developed earlier is used to optimize the reactor conditions giving the maximum RON

and isomerizate yield. The new process outperforms the traditional process in terms of

reactor feed rate and reactor bed volume has been decreased by 46% (at the same unit

feed rate for both) compared with once through process.

Often, in the literature a process model is developed based on lab scale experimental

process which is then used to evaluate large scale process by incorporating conditions for

scape-up. However, in this work the model is developed based on real large scale

industrial data which shows the novelty of this work and then the model is used to

develop and assess a new (which is again novel) isomerization process.

Finally note, if someone wants to use the model developed in this work for small scale

process, they have to change the flow rate and the size of the catalyst used to get the same

trends observed in this study.

Abbreviations

Symbols Definitions

2,2-DMB 2,2-Dimethyl butane

2,3-DMB 2,2-Dimethyl butane

2-MP 2-methyl pentane

3-MP 3-methyl pentane

ACP Advanced configuration process

B Benzene

C5 Pentane components

C6 Hexane components

CH Cyclo hexane

CP Cyclo pentane

H2 Hydrogen

HC Hydrocarbons

i-C4 Iso-butane

i-C7 Iso-heptane

i-P Iso-pentane

n-C4 Normal butane

n-C7 Normal heptane

n-P Normal pentane

n-H normal hexane

Pt platinum

Wt% weight fraction

Nomenclature
Symbol Description Unit

a Catalyst activity (-)

A Pre-exponential factor (mol/m3)1-nhr-1

Β is a total deviation of hydrocarbons octane number (-)

from additively

CB Boltzmann constant (-)

CH2 Hydrogen concentration mol/m3

Ci Concentration of ith component mol/m3

Ci,in Initial (inlet) concentration of ith component mol/m3

Cp The heat capacity of streams kJ/(kg.ºC)

Cpi,p Heat capacity of reaction product components J/mol.K

Cpi,r Heat capacity of reaction reactant components J/mol.K

Cpm Heat capacity of mixture J/(kg. k)

CpH2 The specific heat capacity at constant pressure J/(kg. k)

dpe Equivalent particle diameter m

De Effective diffusivity m2/hr

Di,k Binary diffusion coefficient of ith component m2/hr

through the other components

Dki Knudsen diffusivity coefficient of species i in the gas phase m2/hr

Dgmi Molecular diffusivity coefficient of species i in the gas m2/hr

phase

Dr Reactor diameter

Dii Dipole moment of molecule i Debye

Dimax Maximum possible dipole moment of the Debye

 hydrocarbons mixture

E Activation energy J/mol.K

G raw material flow rate m3/hr-1

i hydrocarbon components number (-)

j Reaction number (-)

k Apparent reaction rate constant (mol/m3)1-nhr-1

L Particle length m

LHSV Liquid hourly space velocity hr-1

m Order of hydrocarbons concentration in (-)

dehydrogenation reaction

mr Mole ratio of hydrogen to light naphtha (-)

M Total moles interred the reactor mol

Miso. Moles of isomerizate mol

MH2 Total moles interred the reactor mol

Mln Moles of naphtha feed mol

MWi Molecular weight of hydrocarbon i kg/kmol

MWH2 Molecular weight of hydrogen kg/kmol

MWln Molecular weight of light naphtha kg/kmol

n Order of hydrocarbons concentration (-)

o Order of hydrocarbons concentration in (-)

hydrogenation reaction

P Reactor pressure Pa

qj Heat of jth reaction kJ/mol

qp power of ith pump kJ/hr

 rg Mean pore radius, m

R Gas constant J/mol.K

RON Research octane number (-)

RONi ith pure component research octane number (-)

Sg Specific surface area of particle m2/kg

Sp Total geometric surface area m2

sp.gr Specific gravity (-)

T* Dimensionless temperature (-)

y Mole fraction (-)

Z Compressibility factor (-)

Greek Letter

ɳ Effectiveness factor (-)

ⱷ Thiel Modulus (-)

Ρln Liquid (naphtha) density kg/m3

ΡH2 Vapor (hydrogen) density kg/m3

ρp Particle density kg/m3

ρbi Liquid density of component i at normal boiling Point kg/m3

ЄB Bed porosity (-)

Φs Shape factor (-)

Єs Catalyst particle porosity (-)

σi,k Average collision diameter m

∩D Collision integral for diffusion (-)

σi Collision diameter of ith m

σk Collision diameter of kth components m

 𝜀 I,k Characteristic (minimum) energy K

∆H̊rxn,j Standard heat of jth reaction kJ/mol

∆Cpj Heat capacity of jth reaction kJ/mol.K

∆H̊fi,p Standard heat of formation of reaction product components kJ/mol

∆H̊fi,r Standard heat of formation of reaction reactant components kJ/mol.K

y Mole fraction (-)

ßi ,ßk Parameters showing the tendency of ith molecule to (-)

intermolecular interaction with kth molecule

γ, α Kinetic coefficients defining the intensity of intermolecular (-)

interactions from dipole moment

err Error function (-)

τ Tortuosity factor

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List of Tables

Table 1: Chemical reactions equations for isomerization processes

Table 2: Catalyst specifications

Table 3: Inlet and outlet composition of isomerization reactor through test run days
Table 4: Operating condition of isomerization reactor through test run days

Table 5: Values of physical properties of light naphtha components used in the model

Table 6: Optimal values of pre-exponential factor and activation energy of every reaction

Table 7: Optimal orders of components concentration and kinetic coefficient of

intermolecular interactions intensity

Table 8: The comparison between the experimental data and the mathematical model

results (predicted)

Table 9: Comparison between the performance and operating conditions of once through

(conventional method) and proposed process

Table A1: Lower and upper bounds for all listed inequality constraints of the applied
model
Table A2: Initial values for all listed inequality constraints of the applied model

List of Figures

Figure 1: Block diagram of once through process (BNR process)

Figure 2: Effect of temperature on the conversion of n-paraffins [1]

Figure 3: Scheme of formalized reaction for isomerization process

Figure 4: Effect of temperature on the RON of product at different pressure with

constant LHSV of 1.489 hr-1 and H2/HC at 3.22 mole ratio

Figure 5: Yield of isomerizate at different temperature and pressure and at constant

LHSV of 1.489 hr-1 and H2/HC at 3.22 mole ratio

Figure 6: Effect of H2/HC on the RON at constant temperature equal to 523K, LHSV at

1.489 hr-1 and pressure of 2.4MPa

Figure 7: Effect of H2/HC on the RON at constant temperature of 523K, LHSV of 1.489

hr-1 and pressure at 2.4MPa

Figure 8: Effect of H2/HC on the RON at constant temperature of 526K, LHSV of 1.489

hr-1and pressure at 2.4MPa

Figure 9: Yield of isomerizate at constant temperature of 520K, LHSV of 1.489 hr-1and

pressure of 2.4MPa

Figure 10: Yield of isomerizate at constant temperature of 523K, LHSV of 1.489 hr-1 and

pressure of 2.4MPa

Figure 11: Yield of isomerizate at constant temperature of 526K, LHSV of 1.489 hr-1and

pressure of 2.4MPa

Figure 12: Effect of LHSV on RON at constant temperature of 520K, H2/HC at 3.22 and

pressure of 2.4 MPa

Figure 13: Effect of LHSV on RON at constant temperature of 523K, H2/HC at 3.22 and

pressure of 2.4 MPa

Figure 14: Effect of LHSV on RON at constant temperature of 526K, H2/HC at 3.22 and

pressure of 2.4 MPa

Figure 15: Effect of LHSV on yield at constant temperature of 520K, H2/HC of 3.236

and pressure of 2.4MPa

Figure 16: Effect of LHSV on yield at constant temperature of 523K, H2/HC of 3.236

and pressure of 2.4MPa

Figure 17: Effect of LHSV on yield at constant temperature of 526K, H2/HC of 3.236

and pressure of 2.4MPa

Figure 18: Block diagram of the proposed new isomerization process (named as AJAM

process) in this study

 Table 1: Chemical reactions equations for isomerization processes

Reaction Chemical reaction Reaction Chemical reaction

NO. (j) equations NO. (j) equations
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑛­𝐶5 𝐻12 → 𝑖­𝐶5 𝐻12 𝑛­𝐶4 𝐻10 + 𝐻2 → 𝐺𝑎𝑠
1 19
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑖­𝐶5 𝐻12 → 𝑛­𝐶5 𝐻12 𝑖­𝐶4 𝐻10 + 𝐻2 → 𝐺𝑎𝑠
2 20
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑛­𝐶6 𝐻14 → 2­𝑀𝑃 𝑛­𝐶5 𝐻12 + 𝐻2 → 𝐺𝑎𝑠
3 21
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
2­𝑀𝑃 → 𝑛­𝐶6 𝐻14 𝑖­𝐶5 𝐻12 + 𝐻2 → 𝐺𝑎𝑠
4 22
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑛­𝐶6 𝐻14 → 3­𝑀𝑃 𝑛­𝐶6 𝐻14 + 𝐻2 → 𝐺𝑎𝑠
5 23
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
3­𝑀𝑃 → 𝑛­𝐶6 𝐻14 2­𝑀𝑃 + 𝐻2 → 𝐺𝑎𝑠
6 24
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
2,3 − 𝐷𝑀𝐵 → 2­𝑀𝑃 3­𝑀𝑃 + 𝐻2 → 𝐺𝑎𝑠
7 25
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
2­𝑀𝑃 → 2,3 − 𝐷𝑀𝐵 2,3­𝐷𝑀𝐵 → 𝐺𝑎𝑠
8 26
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
2,3𝐷𝑀𝐵 → 2,2 − 𝐷𝑀𝐵 2,2­𝐷𝑀𝐵 → 𝐺𝑎𝑠
9 27
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
2,2𝐷𝑀𝐵 → 2,3 − 𝐷𝑀𝐵 𝑛­𝐶7 𝐻16 + 𝐻2 → 𝐺𝑎𝑠
10 28
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑛­𝐶7 𝐻16 → 𝑖­𝐶7 𝐻16 𝑖­𝐶7 𝐻16 + 𝐻2 → 𝐺𝑎𝑠
11 29
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑖­𝐶7 𝐻16 → 𝑛­𝐶7 𝐻16 𝐶𝐻 + 𝐻2 → 𝑛­𝐶6 𝐻14
12 30
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑀𝐶𝑃 → 𝐶𝐻 𝑀𝐶𝑃 + 𝐻2 → 2­𝑀𝑃
13 31
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝐶𝐻 → 𝑀𝐶𝑃 𝑀𝐶𝑃 + 𝐻2 → 3­𝑀𝑃
14 32
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
3 − 𝑀𝑃 → 2­𝑀𝑃 𝑀𝐶𝑃 + 𝐻2 → 2,2­𝐷𝑀𝐵
15 33
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
2 − 𝑀𝑃 → 3­𝑀𝑃 𝑀𝐶𝑃 + 𝐻2 → 2,3­𝐷𝑀𝐵
16 34
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑐­𝐶5 𝐻12 + 𝐻2 → 𝑛­𝐶5 𝐻12 𝐵 + 3𝐻2 → 𝐶𝐻
17 35
𝑦𝑖𝑒𝑙𝑑𝑠 𝑦𝑖𝑒𝑙𝑑𝑠
𝑐­𝐶5 𝐻12 + 𝐻2 → 𝑖­𝐶5 𝐻12 𝐵 + 3𝐻2 → 𝑀𝐶𝑃
18 36
 Table 2: Catalyst specifications

Parameter Symbol Unit Value

Catalyst bed length L m 11.24

Catalyst bed diameter 𝐷𝑟 m 2.9

Catalyst bulk density 𝜌𝑐𝑎𝑡 𝑘𝑔⁄𝑚3 741

length of catalyst particle 𝑙𝑝 m 3. 5 × 10−3

Diameter of catalyst particle 𝑑𝑝 m 1.8 × 10−3

Specific volume of particle Vg 𝑚3 ⁄𝑘𝑔 0.4

Specific surface area of particle Sg 𝑚2 ⁄𝑘𝑔 450

 Table 3: Inlet and outlet composition of isomerization reactor through test run days

Test run 1 Test run 2 Test run 3 Average

Hydrocarbon components inlet outlet inlet outlet inlet outlet input outlet

n-Butane (nC4) 2.821 1.222 4.253 1.970 3.549 1.963 3.479 1.855

n-Pentane( nC5) 23.954 18.267 25.977 18.362 26.59 17.423 25.81 18.39

n-Hexane(nC6) 17.338 7.540 14.320 7.597 15.09 8.169 15.95 7.343

n-Heptane (nC7) 1.221 0.040 2.816 0.059 1.401 0.032 1.314 0.051

i-Butane (iC4) 0.216 0.517 0.353 0.963 0.259 0.735 0.287 0.950

i-pentane (iC5) 17.775 35.013 20.652 35.689 22.00 35.982 20.11 36.07

2,2 Di Methyl Butane

0.622 7.766 0.451 7.356 0.581 7.170 0.548 7.293
(2,2DMB)

2,3 Di Methyl Butane

2.180 3.567 1.472 3.092 1.748 3.029 1.911 3.390
(2,3DMB)

2 Methyl Pentane (2MP) 12.314 12.493 9.311 12.597 9.736 12.978 10.26 12.561

3 Methyl Pentane (3MP) 9.996 9.296 7.294 8.599 7.946 8.243 8.401 8.404

i-heptane (iC7) 3.764 0.412 5.084 0.250 3.483 0.298 3.556 0.273

Cyclo Pentane (CP) 1.529 1.138 1.312 1.369 1.175 1.054 1.174 1.054

Methyl Cyclo Pentane

2.973 1.450 2.574 1.072 3.078 1.144 2.873 1.144
(MCP)

Cyclo Hexane (CH) 1.137 0.436 1.270 0.316 1.101 0.353 1.240 0.353

Benzene (C6) 0.496 0.000 0.433 0.000 0.498 0.004 0.470 0.000
 Table 4: Operating condition of isomerization reactor through test run days

Liquid hourly space Temperature Pressure Hydrogen make-up

velocity (𝐡𝐫 −𝟏 ) (K) (MP) (𝐤𝐠 𝐇𝟐 /𝐤𝐠 𝐇𝐂 )

First day 1.489 523.12 2.340 3.324

Second day 1.561 525.72 2.472 3.227

Third day 1.622 526.2 2.430 3.381

average 1.557 524.14 2.414 3.310

Table 5: Values of physical properties of light naphtha components used in the model

Molecular Critical Critical Critical Dipole Research

Components Weight temperature Pressure compressibility Moment octane

(kmol/kg) (K ) (Mpa) Factor, (-) (depy) number

Normal butane 58.123 425.16 3.7963 0.2791 0.127 95

Iso-butane 58.123 407.85 3.6397 0.2780 0.132 100.2

Normal pentane 72.125 471.10 3.3550 0.2747 0.114 62

Iso-pentane 72.125 469.70 3.3812 0.2611 0.121 92

Cyclo-pentane 70.135 511.60 4.5057 0.2871 0.241 102.3

Normal hexane 86.177 488.71 3.0068 0.2642 0.080 24

2-methyl pentane 86.177 497.50 3.0096 0.2669 0.097 74.4

3-methyl pentane 86.177 504.50 3.1240 0.2732 0.099 75.5

2,3-dimethyl butane 86.177 500.21 3.8163 0.3284 0.121 105

2,2-dimethl butane 86.177 488.71 3.0816 0.2704 0.124 95

Cyclo-hexane 84.162 553.40 4.0710 0.2791 0.320 84

Normal heptane 100.25 540.206 2.7358 0.2624 0.0 0

Iso-heptane 100.25 530.30 2.7397 0.2597 0.0 84

Methyl cyclopentane 84.162 531.70 3.7845 0.2724 0.0 96

Benzene 78.114 562.16 4.8953 0.2713 0.0 120

Hydrogen 2.0160 33.200 1.3000 0.3050 (-) (-)

 Table 6: Optimal values of pre-exponential factor and activation energy of every reaction

Reaction Activation energy Pre-exponential Reaction Activation energy Pre-exponential

number (j) (𝐄𝐣 ), J/mol factor (Aj) number (j) (𝐄𝐣 ), J/mol factor (Aj)

1 10359.1 30328.2 19 410171 1.20053E+37

2 10359.1 11973.8 20 382917 1.11887E+37

3 1779.64 8101.04 21 329776 6.71002E+31

4 1779.64 12237.8 22 342906 2.04715E+31

5 3098.58 34360 23 266712 6.27716E+26

6 3098.58 6149 24 264004 3.04961E+26

7 12499.3 36715.9 25 294374 6.36194E+26

8 12499.3 7720 26 277806 1.70425E+27

9 8551.55 8549.55 27 273965 6.77152E+26

10 8551.55 2516.07 28 220534 3.17332E+23

11 12410.4 246504 29 216658 3.51283E+23

12 12410.4 11903 30 128748 1.74229E+15

13 5888 4326.49 31 91332.9 283811864

14 5888 4610.34 32 98599.4 15238268830

15 7703 102328 33 97396.6 9654847240

16 7703 2806.19 34 91034.3 1400727929

17 185323 1.20775E+16 35 259025 2.92353E+29

18 180018 3.98326E+16 36 255393 2.90342E+26

 Table 7: Optimal orders of components concentration and kinetic coefficient

of intermolecular interactions intensity

Parameter Symbol Unit Value

Order of hydrocarbon concentration n (-) 0.9412

Order of hydrogen concentration in cracking reaction m (-) 0.9350

Order of hydrogen concentration in hydrogenation reaction o (-) 3.279

α (-) 1.463
Kinetic coefficient of intermolecular interactions intensity
γ (-) 0.8154
 Table 8: The comparison between the experimental data and the mathematical

model results (predicted)

Test run 1 Test run 2 Test run 3

Hydrocarbon
Absolute Absolute Absolute
components Exp. Theo. Exp. Theo. Exp. Theo.
Error (%) Error (%) Error (%)

n-Butane(nC4) 1.222 1.2208 0.0982 1.970 1.9681 0.0964 1.963 1.9611 0.0968

n-Pentane(nC5) 18.267 18.248 0.101 18.362 18.179 0.101 17.423 17.250 0.101

n-Hexane(nC6) 7.540 7.5329 0.094 7.597 7.5893 0.094 8.169 8.1606 0.094

n-Heptane(nC7) 0.040 0.4004 0.100 0.059 0.0591 0.1094 0.032 0.3203 0.0938

i-Butane(iC4) 0.517 0.5165 0.0967 0.963 0.9621 0.0934 0.735 0.7343 0.0953

i-pentane(iC5) 35.013 34.977 0.1028 35.689 35.653 0.1008 35.982 35.946 0.1005

2,2 Di Methyl Butane

7.766 7.7589 0.0914 7.356 7.3487 0.0992 7.170 7.1629 0.0990
(2,2-DMB)
2,3 Di Methyl Butane
3.567 3.5635 0.0981 3.092 3.0889 0.1002 3.029 3.0259 0.1023
(2,3-DMB)
2Methyl Pentane
12.493 12.469 0.1001 12.597 12.472 0.1001 12.978 12.965 0.1001
(2MP)
3Methyl Pentane
9.296 9.2867 0.1002 8.599 8.5903 0.1015 8.243 8.2345 0.1009
(3MP)

i-heptane (iC7) 0.412 0.4116 0.0990 0.250 0.2498 0.0992 0.298 0.2977 0.0979

Cyclo Pentane (CP) 1.138 1.1391 0.1007 1.369 1.3703 0.0981 1.054 1.0551 0.0998

Methyl Cyclo Pentane

1.450 1.4488 0.0832 1.072 1.0712 0.0786 1.144 1.1431 0.0720
(MCP)

Cyclo Hexane (CH) 0.436 0.4356 0.0910 0.316 0.3157 0.0879 0.353 0.3527 0.0728

Benzene (C6) 2.87E-6 2.89E-6 0.6969 2.76E-6 2.78E-6 0.7246 2.83E-6 2.84E-6 0.3536

Temperature (T) 552.12 551.34 0.1012 550.72 551.67 0.097 554.2 553.4 0.1006

RON 79.33 79.374 0.0554 79.41 79.452 0.0528 79.26 79.317 0.0719
Table 9: Comparison between the performance and operating conditions of once through

(conventional method) and proposed process

Value

Proposed
Variables Unit
Once Through
Process
Process (Figure 1)
(Figure 18)

(-) 79.452 90.81

RON

(%) 97.6831 99.20

Yield

Unit feed rate Ton/hr 75.841 75.841

Reactor feed rate Ton/hr 75.841 40.96

Isomerizate rate Ton/hr 74.083 75.234

Bed volume (V) 74.20 39.74

m3

K 524.314 521.09
T

MPa 2.406 2.104

P

LHSV ℎ𝑟 −1 1.507 1.503

(-) 3.31 3.46

𝒎𝒓
 Light Off gas
Naphtha Storage
system

Izomerizate
Stabilization

H2 Izomerization
Reactor

Figure 1: Block diagram of once through process (BNR process)

The
o
Iso-P concentration

retic
al c
onv
ersi
on (
equ
on ilibr
e rsi ium
nv )
l co
tua
Ac Kinetik Thermodynamic
limitation limitation
Toptimal

Figure 2: Effect of temperature on the conversion of n-paraffins [1]

 MCP B

3-MP

2,2-DMB 2,3-DMB 2-MP n-C6 CH

n-C4 Gas i-C7

i-C4 i-C5 n-C5 n-C7

c-C5
Figure 3: Scheme of formalized reaction for isomerization process

88
86
84
82
RON

80 2.1 MP

78 2.3 MP
2.5 MP
76
74
72
500 510 520 530 540 550 560
Temperature, K

Figure 4: Effect of temperature on the RON of product at different pressure

with constant LHSV of 1.489 hr-1 and H2/HC at 3.22 mole ratio
 100
98
96
94
yield (%)

92
2.1 MPa
90
2.3 MPa
88
2.5 MPa
86
84
82
523 K 528K 533K
Temperature, K

Figure 5: Yield of isomerizate at different temperature and pressure and at

constant LHSV of 1.489 hr-1 and H2/HC at 3.22 mole ratio

79.6
79.4
79.2
79
78.8
78.6
RON

78.4
78.2
78
77.8
77.6
3.1 3.2 3.3 3.4 3.5 3.6 3.7
H2/HC mole ratio

Figure 6: Effect of H2/HC on the RON at constant temperature equal to 523K,

LHSV at 1.489 hr-1 and pressure of 2.4MPa

 80
79.8
79.6
79.4
79.2
79
RON

78.8
78.6
78.4
78.2
78
77.8
3.1 3.2 3.3 3.4 3.5 3.6 3.7
H2/HC mole ratio

Figure 7: Effect of H2/HC on the RON at constant temperature of 523K, LHSV

of 1.489 hr-1 and pressure at 2.4MPa

80.5

80

79.5
RON

79

78.5

78
3.1 3.2 3.3 3.4 3.5 3.6 3.7

H2/HC mole ratio

Figure 8: Effect of H2/HC on the RON at constant temperature of 526K, LHSV

of 1.489 hr-1and pressure at 2.4MPa

 98.4
98.2
98
97.8
97.6
97.4
yield (%)
97.2
97
96.8
96.6
96.4
96.2
3.1 3.2 3.3 3.4 3.5 3.6 3.7
H2/HC mole ratio

Figure 9: Yield of isomerizate at constant temperature of 520K, LHSV of

1.489 hr-1and pressure of 2.4MPa

98

97.5

97
yield (%)

96.5

96

95.5

95
3.1 3.2 3.3 3.4 3.5 3.6 3.7
H2/HC mole ratio

Figure 10: Yield of isomerizate at constant temperature of 523K, LHSV of

1.489 hr-1 and pressure of 2.4MPa

 96.5

96

95.5
yield (%)

95

94.5

94

93.5
3.1 3.2 3.3 3.4 3.5 3.6 3.7
H2/HC mole ratio

Figure 11: Yield of isomerizate at constant temperature of 526K, LHSV of

1.489 hr-1and pressure of 2.4MPa

79.5

79

78.5
RON

78

77.5

77

76.5
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
LHSV, hr-1

Figure 12: Effect of LHSV on RON at constant temperature of 520K,

H2/HC at 3.22 and pressure of 2.4 MPa

 80.5
80
79.5
79
78.5
RON

78
77.5
77
76.5
76
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
LHSV, hr-1

Figure 13: Effect of LHSV on RON at constant temperature of 523K,

H2/HC at 3.22 and pressure of 2.4 MPa

81.5
81
80.5
80
79.5
RON

79
78.5
78
77.5
77
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

LHSV, hr-1

Figure 14: Effect of LHSV on RON at constant temperature of 526K,

H2/HC at 3.22 and pressure of 2.4 MPa

 98.5

98

97.5
yield (%)

97

96.5

96
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

LHSV, hr-1

Figure 15: Effect of LHSV on yield at constant temperature of 520K, H2/HC

of 3.236 and pressure of 2.4MPa

98

97.5

97

96.5
yield (%)

96

95.5

95
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

LHSV, hr-1

Figure 16: Effect of LHSV on yield at constant temperature of 523K, H2/HC

of 3.236 and pressure of 2.4MPa

 97
96.5
96
95.5
95
yield (%)

94.5
94
93.5
93
92.5
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
LHSV, hr-1

Figure 17: Effect of LHSV on yield at constant temperature of 526K, H2/HC

of 3.236 and pressure of 2.4MPa

Off gas

Izomerizate
Stabilization
H2

Light
Naphtha
Molecular Sieves
Izomerization
Reactor

H2, n-C6 & n-C5

Izomerizate, n-C6 & n-C5

Figure 18: Block diagram of the proposed new isomerization process (named as AJAM

process) in this study

Appendix A: Supporting information

Table A1: Lower and upper bounds for all listed inequality constraints of the applied
model
Variable Upper bounds Lower bounds

E1 – E36 1E50 10

A1 – A36 1E50 10

n 3 0

m 2.5 0

o 10 0

𝛂 10 0

𝛄 10 0
Table A2: Initial values for all listed inequality constraints of the applied model
Variable Initial value

Temperature (T) 524.14 (K)

Concentration of normal hexane (C nC4) 0.009157242 (mol/m3)

Concentration of normal pentane (CnC5) 0.058854476 (mol/m3)

Concentration of normal hexane (C nC6) 0.029798934 (mol/m3)

Concentration of normal heptane (CnC7) 0.002546383 (mol/m3)

Concentration of iso-butane (CiC4) 6.68367E-4 (mol/m3)

Concentration of iso pentane (CiC5) 0.04853589 (mol/m3)

Concentration of di-methyl butane (C2,2DMB) 0.0011211892 (mol/m3)

Concentration of di-methyl butane (C2,3DMB) 0.003171765 (mol/m3)

Concentration of methyl pentane (C2MP) 0.01907564 (mol/m3)

Concentration of methyl pentane (C3MP) 0.015434657 (mol/m3)

Concentration of iso –heptane (CiC7) 0.0062734256 (mol/m3)

Concentration of methyl cyclo pentane (CMCP) 0.005840283 (mol/m3)

Concentration cyclo hexane (CCH) 0.003946619 (mol/m3)

Concentration of benzene (CB) 9.6205925E-4 (mol/m3)

Concentration of cyclo pentane (Ccp) 0.0025210315 (mol/m3)

Concentration of hydrogen (CH2) 0.50420004 (mol/m3)

Concentration of gases (CG) 0.0 (mol/m3)