International Journal of Refrigeration 104 (2019) 189–200

Contents lists available at ScienceDirect

International Journal of Refrigeration

journal homepage: www.elsevier.com/locate/ijrefrig

Optimization of mixed fluid cascade LNG process using a multivariate

Coggins step-up approach: Overall compression power reduction and

exergy loss analysis

Alam Nawaz

a , Muhammad Abdul Qyyum

a , Kinza Qadeer a , Mohd Shariq Khan

b , Ashfaq Ahmad

c , Sanggyu Lee

d , Moonyong Lee

a , ∗

a School of Chemical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea b Department of Chemical Engineering, Dhofar University, Salalah 211, Oman c Department of Computer Science, COMSATS University Islamabad (CUI), Lahore Campus, Defense Road, Off Raiwind Road, Lahore, Pakistan d Gas Plant R&D Center, Korea Gas Corporation, Incheon 406-130, Republic of Korea

a r t i c l e i n f o

Article history:

Received 19 December 2018

Revised 4 March 2019

Accepted 1 April 2019

Available online 9 April 2019

Keywords:

Exergy analysis

Energy efficiency

LNG

Mixed fluid cascade process

Multivariate Coggins

Natural gas liquefaction

a b s t r a c t

The mixed fluid cascade (MFC) process is considered one of the most promising candidates for producing

liquefied natural gas (LNG) at onshore sites, mainly owing to its high capacity and relatively high po-

tential energy efficiency. The MFC process involves three refrigeration cycles for natural gas precooling,

liquefaction, and subcooling, making its operation more complex and sensitive. Each refrigeration cycle

consists of a different mixed refrigerant, which must be optimized to change feed and ambient condi-

tions to operate efficiently. Any sub-optimal solution can lead to high exergy losses, ultimately reducing

the process energy efficiency. Operating optimally is a challenging task, mainly owing to the non-linear

interactions between the constrained decision (design) variables and complex thermodynamics involved

in MFC refrigeration cycles. In this context, we employ a multivariate Coggins step-up approach to reduce

the exergy losses associated with the MFC process. This study reveals that the overall exergy losses can be

minimized to 35.91%; resulting in 25.4% overall energy savings compared to sub-optimal MFC processes.

© 2019 Elsevier Ltd and IIR. All rights reserved.

Optimisation du processus de liquéfaction de gaz naturel en cascade avec un

mélange de fluides à l’aide d’une approche multivariée progressive de Coggins:

réduction globale de la puissance de compression et analyse de la perte d’exergie

Mots-clés: Analyse exergétique; Efficacité énergétique; GNL; Processus en cascade à mélange de fluides; Algorithme multivariables de Coggins; Liquéfaction de gaz naturel

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. Introduction

The energy demand has a direct impact on a country’s eco-

omic success, and is in turn a direct function of the population

ensity and living standards ( Qyyum et al., 2018c ). An increase in

opulation density and living comfort of approximately 30% has

een projected by the International Energy Agency (IEA) ( SHELL,

017 ) between 2016 and 2040. Thus, a steady increase in global

∗ Corresponding author.

E-mail address: mynlee@yu.ac.kr (M. Lee).

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ttps://doi.org/10.1016/j.ijrefrig.2019.04.002

140-7007/© 2019 Elsevier Ltd and IIR. All rights reserved.

nergy demand of 48% is expected between 2012 and 2040 ac-

ording to the U.S. Energy Information Administration ( EIA, 2017b ).

s a comparatively clean energy source ( He et al., 2018b; Kähm

nd Vassiliadis, 2018 ), natural gas (NG) has attracted attention for

ulfilling this global energy demand ( He et al., 2019a ). Electrical

ower can be produced from NG with 50% less greenhouse gas

missions than generated using coal ( SHELL, 2017 ). Therefore, there

as been rapid growth in the NG trade ( Markana et al., 2018 ) com-

ared with oil and coal, ( BP, 2017; EIA, 2017a ) and NG is often re-

erred to as the bridge fuel to renewable future, mainly owing to

ts lower air-pollutant emissions, as illustrated in Fig. 1 , which is

190 A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200

Fig. 1. Air pollutant emissions analysis for natural gas compared with coal and oil.

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Nomenclature

f objective function

GA genetic algorithm

S i step size

NG natural gas

T temperature ( °C)

P pressure (bar)

P a penalty function

MR mixed refrigerant

Subscripts

i i th compressor

−ve negative

+ ve positive

Abbreviations

N 2 nitrogen

C 1 methane

C 2 ethane

C 3 propane

iC 5 iso-pentane

m mass flow rate ((kg h ̂ ( −1)))

CHX cryogenic heat exchanger

MFC mixed fluid cascade

C 3 MR propane precooled mixed refrigerant

TDCC temperature difference between composite curves

THCC temperature-heat flow composite curves

DMR dual mixed refrigerant

JTV Joule Thomson valve

KBO knowledge-based optimization

MCD modified coordinate descent

HMCD hybrid modified coordinate descent

LNG liquefied natural gas

W i i th compressor work

MAT minimum approach temperature

X i key design variables

SMR single mixed refrigerant

MVS ®16 Microsoft Visual Studio 2016

MITA minimum internal temperature approach

drawn using the data reported in Energy Information Administra-

tion and Gas (1999 ) and Qyyum et al. (2019a , 2019b ).

The transportation of NG from its remote location to the world

market is completely dependent on the means of transportation,

such as pipelines (gaseous form) or cargo ships (in liquid form

i.e., liquefied natural gas (LNG)). To date, natural gas transporta-

tion in the form of LNG (which has 600 times less volume than

the gaseous state) has matured to become the most promising and

economical approach ( Abdul Qyyum et al., 2018; Wu et al., 2018 ).

Nevertheless, NG liquefaction consumes an enormous amount of

energy in terms of the compressor shaft work requirements, mak-

ing liquefaction a cost/energy intensive operation. As reported by

Qadeer et al. (2018 ), liquefaction consumes approximately 42% of

the total LNG project cost. However, this percentage can vary be-

tween 40% and 60% with plant site conditions and the involved

liquefaction processes ( Qyyum et al., 2018c ). Several NG liquefac-

tion processes have evolved over time for onshore and offshore

LNG production, differing in capacity, efficiency, and complexity

( Khan et al., 2013 ). Nevertheless, cascaded refrigeration cycles ( Li

et al., 2018; Lim et al., 2013; Venkatarathnam, 2011 ), such as the

mixed fluid cascade (MFC) and ConocoPhillips cascade processes,

are considered among the most suitable for onshore LNG produc-

ion ( He et al., 2018a; Khan et al., 2017; Lim et al., 2013; Qyyum

t al., 2018c ).

The MFC process involves three different refrigeration cycles

o separately perform precooling, liquefaction, and subcooling of

G. These three refrigeration cycles operate at different pressure

nd temperature levels, ultimately increasing the overall exergy

oss and reducing the energy efficiency of the liquefaction process.

owever, the different compositions of mixed refrigerants (MR)

or precooling, liquefaction, and subcooling cycles make the MFC

rocess a promising candidate for energy minimization through

ptimization. Nevertheless, optimizing the MFC liquefaction pro-

ess is a challenging exercise, owing to the high dimensionality

ith multiple constraints and non-linear thermodynamic interac-

ions between the design variables, constraints, and the objective

unction, i.e., the overall shaft power requirements. The high dis-

repancy between the upper and lower bounds of each MR com-

onent of the precooling, liquefaction, and subcooling refrigeration

ycles also leads to convergence issues during the MFC process op-

imization. Solving these issues associated with the optimization of

he MFC-LNG process manually or by applying intuition is virtually

mpossible. Thus, an effective and rigorous optimization technique

s required to solve the highly complex MFC process optimization

roblem to minimize the exergy loss.

Several studies have addressed MFC optimization through dif-

erent strategies. For instance, self-optimizing control strategies to

ptimize the operation of an MFC process were reviewed by Jórgen

auck Jensen (2006 ). Mahmoodabadi (2017 ) performed optimiza-

ion of the MFC process by implementing a genetic algorithm

GA), and reduced the overall compressor power. Yoon et al. (2013 )

odeled and optimized the cascaded (C 3 H 8 –N 2 O

–N 2 ) LNG process

hrough a built-in Aspen Hysys optimizer, considering the overall

ompression power as an objective function. Xiong et al. (2016 )

dopted a cascaded process to produce pressurized liquefied nat-

ral gas (PLNG) and developed a connection between Hysys and

ATLAB for optimization using GA. Another study also employed

A to optimize single-stage single compressor- and two-stage sin-

le compressor-based cascaded LNG processes, and minimized the

otal energy consumption ( Jackson et al., 2017 ). In a similar study,

t was also applied the Hysys optimizer using an original mode to

educe the energy consumption for the MFC process ( Jackson et al.,

017 ).

A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200 191

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From the above literature, it can be observed that stochastic

earch methods such as GA have been applied successfully to cas-

ade process optimization. However, the termination of stochastic

ptimization can occur mainly owing to the impracticable region

i.e., negative approach temperature inside the main cryogenic

xchanger) before reaching the best global optimal solution ( Ali

t al., 2018b; Qyyum et al., 2018b ). This comprises one of the

ajor issues associated with stochastic methods. Considering

his, it is challenging to obtain the global optimal solution for

igh-dimensional and non-linear systems, such as MFC processes.

high computational cost and difficulty in constraint handling

re additional drawbacks of stochastic optimization approaches

Khan et al., 2017; Qyyum et al., 2018c ). To solve these issues, the

ultivariate Coggins algorithm will be considered to minimize

he exergy losses for the MFC process to improve the energy

fficiency. To improve the search using the Coggins algorithm,

knowledge-based optimization (KBO) method is integrated to

enerate the initial point. The optimal values of the decision

ariables obtained through the Coggins approach will be com-

ared with MFC process optimized through a modified coordinate

escent (MCD) that have been used by Abdul Qyyum et al. (2018 ),

ark et al. (2015 ) and Qyyum et al. (2018a ) for optimization of

NG processes. The coggins-optimized MFC process will also be

ompared with the latest published ( Ding et al., 2017 ) optimal

FC liquefaction process. The major contribution of this study

s to minimize the exergy loss associated with each equipment

f the MFC liquefaction process in order to reduce the overall

ompression power through sole optimization.

. Multivariate Coggin’s step-up approach

A number of univariate techniques for optimization have

volved over time. The Coggins method, proposed by Davies and

owell, is a univariate optimization method that decreases the

umber of function assessments. The Coggins approach has been

xtended to multivariate (multivariable) optimization. Some stud-

es have considered univariate search techniques ( Kuester, 1973 ).

hese are outdated, owing to the slower computational speed for

igher-dimensional problems. Furthermore, high-dimensional op-

rational problems for which multivariable optimization fails, as

eported by Subramaniam (2002 ). The multivariate Coggins algo-

ithm for resolving unconstrained n-dimensional optimization was

roposed by Bamigbola and Agusto (2004 ) and tested on a differ-

nt set of problems. The study presented by Bunday (1984 ) and

ao (1991 ) can also be concerned for further details about the cog-

ins algorithm.

A random selection of initial points can affect the success of

methodology. Typically, a random search algorithm converges

uickly to find a good solution, but sacrifices a guarantee of opti-

ality to a certain extent ( Zabinsky, 2010 ). Therefore, this study is

ocused on a version of the univariate coordinate descent method-

logy called the Coggins algorithm, extended to multivariate op-

imization ( Kuester, 1973 ). However, in the proposed optimization

tudy, the first set of process variable values (which was obtained

hrough knowledge-based approach in base case 1 and Ding et al.,

017 in base case 2) was taken as initial set and then based on

his first set, the optimizer randomly search the new set for pro-

ess variable values, as shown in Fig. 2 and provided pseudo code

f Coggins approach. Fig. 2 presents the conceptual algorithm uti-

ized to optimize the MFC-LNG process.

A brief description of the working patterns of the Coggins ap-

roach is given as follows.

Let us consider the unconstrained problem

min ︷︷︸ z

f ( z ) ( z ∈ Z

n ) , (1)

here f ( z ) is the objective function, and its minimizer w.r.t. z is

∗. With the help of the search parameter and search direction, ψ

∗

nd s , respectively, the optimum is obtained as z(ψ) = z ∗ + ψ

∗s .

Then, ψ

∗ is the optimum of all one-dimensional directions with

he least positive value of ψ , for which the function

f ( ψ ) = f (z + ψs ) (2)

ttains a local minimum.

Hence, if the original function f ( z ) is given in terms of an ex-

licit function of z i ( i = 1 , 2 , 3 , ..., n ) , then expression ( 2 ) can be

ritten as �z i for any specific vector s , to obtain ψ

∗ in terms of

and s by solving ( df ( ψ) / dψ ) = 0 . However, in many practical

roblems the interpolation method can be applied to find the value

f ψ

∗, because the function f ( ψ) cannot be expressed explicitly in

erms of ψ .

Three processes are involved in obtaining an optimum solution:

search space direction, an optimum location, and an interpolation

ormulation.

.1. Search space direction

For higher-dimensional problems, many different directions can

e searched giving different results ( Bunday, 1984 ). As mentioned

n Subramaniam (2002 ), it is clear that the non-inclusion of search

irections is a considerable factor in avoiding a poor convergence

ate. To ensure that the convergence rate is accelerated, a method

s employed that aims to optimize the region for exploring the

earch parameter. For the direction vectors, the applied Coggins

ethod starts with the base case of the current values of variables,

nd then moves in a forward direction in the search space to a lo-

al minimum to find an optimal solution.

The search direction s is given by s = −∇ f (z) , where s de-

otes the direction directly forward (or backward), and ∇f ( z ) is

he gradient of the objective function f ( z ). As the first move, each

ariable is boosted by a distance z j+1

, and the objective func-

ion f ( z ) is calculated using an optimizer coded in the visual ba-

ic language using the MVS ®16 integrated development environ-

ent (IDE). An updated point is obtained for the i th iteration by

etting Eq. (2) as z i j+1

= z i j + s j ( j = 1 , 2 , ..., n ) , where the updated

oint is z j+1

. A step size �z i is chosen where s i = s i ( z i ) , in accor-

ance with Coggins algorithm. If the objective function is improved

nder the constraints, then the search algorithm keeps moving in

he forward direction, and doubles the step interval for the next

ove. Otherwise, the direction is reversed, and the best-known

alue is adopted for the current variables for the next iteration.

his search process is repeated until a local optimum solution is

eached.

.2. Optimum location

For the unconstrained problem in Eq. (1) , the objective function

( z ) is optimized using the formalism of Coggins method, which

tilizes the approximation

f ( z ) ≈ z T αz + βz + γ (3)

here z T is the transpose of z, α is a positive-definite symmetric

atrix, β is a column vector, and γ is a constant matrix.

Eq. (3) shows that if z is an eigenvector of z T z , then it is also an

igenvector of z 2 . This means that the matrices z share the same

igenspace. The gradient of f ( z ) is 2 αz ∗ + β = 0 .

192 A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200

Fig. 2. Applied Coggins optimization algorithm.

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Thus, the solution of problem ( Eq. (1) ) is z ∗ = − 1 2 (

adj( α) / | β| ) ,where the adjugate α is the transpose of the cofactor matrix z of

α, i.e., adj(α) = z T .

2.3. Interpolation formulation

As an interpolation method (for predicting unknown values),

Coggins method can be employed to solve the problem in Eq. (1) .

This is an effective method, which utilizes distinct points to sup-

port the minimum based on evaluating few functions, followed by

the second-order proximal method (successive quadratic approx-

imations) to achieve a brisk convergence to the optimum. Hence,

the extension of the Coggins method can optimize a multivariable

objective function on Z

n where z ∈ Z

n .

To regulate the number of unknown parameters of the approxi-

mation, a number of points (an interpolation) are employed by the

addition of different entries of the matrices α, β , and γ . This is

nown as the interpolation method. Thus, Eq. (3) becomes

= A n x (4)

here F is the collection of the function’s interpolation points; x

enotes the collection of points in the matrices α, β , and γ ; and

n is non-singular.

After rearranging, Eq. (4) can be written in the form x = A

−1 n F ,

nd can also be expressed as f ( z ) ≈ Hx . After setting the value of x ,

he objective function can be calculated as

f ( z ) ≈ HA

−1 n F (5)

Furthermore, the pseudo code for the Coggins step-up approach

or the optimization of the MFC process is provided as follows:

A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200 193

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(1). start with initial set; V 0 = i 0 , starting the guess by random search method

(2). for generation = 1, 2, …

(3). do while

(4). for i = 1, 2, …, V 0 – 1

(5). do while

(6). optimum j = V 0 , j (7). V 0, j = optimum j – step j (8). Update the simulation variable

(9). if [ lb j 〈 (V 0, j + step j ) ] or [ ub j 〉 (V 0, j – step j ) ]

(10). compute the optimum value and upgraded under constraints

condition

(11). double the step size; step j = step j ∗ 2

(12). constraints are not satisfied

(13). reverse the direction; step j = - step j (14). else

(15). step j = step j / 2

(16). end if

(17). V 0 , j = optimum j (best known value updated)

(18). end loop

(19). for j = 1, 2, …, V 0 – 1

(20). opt j = optimum j (assign best-known value to optimal)

(21). end for

(22). end for

(23). for j = 1, 2, …, V 0 – 1

(24). lb j = V 0, j - step j (25). ub j = V 0 , j + step j (26). step j = step j / 10

(27). end for

(28). end loop

(29). end for

. Process simulation and description

.1. Simulation bases and assumptions

Aspen Hysys® v10.0 was adopted to simulate and model the

FC-LNG process. The Peng–Robinson equation of state was se-

ected as the thermodynamic property method, which is appro-

riate for petrochemical applications and gas processes, espe-

ially at high pressures. Table 1 lists the major parameters of the

teady-state MFC-LNG process simulation. The assumptions con-

idered for the optimization of the MFC process include the fol-

owing: the feed gas pressure P NG (stream 1) is 50 bar, the tempera-

ure for T NG (stream 1) is 30 °C, and the flowrate is approximately 1

kg h ̂ ( −1)).

.2. Process description

The MFC process employs 2–3 cascade of mixed refrigerants to

erform NG liquefaction. Many attributes of MFC make it a suitable

echnology for NG liquefaction satisfying following diverse needs:

� Smooth operation is different climate.

able 1

eed conditions and process simulation assumptions ( Ding et al., 2017 ).

Natural gas feed Value

Temperature ( °C) 30

Pressure (bar) 50

Flow rate ((kg h ̂ ( −1))) 1

Compositions Mole%

Methane 91.6

Ethane 4.5

Propane 1.1

i-butane 0.5

n-butane 0.3

Nitrogen 2.0

Adiabatic compressor efficiency 80%

MITA( X ) CHX-1 = MITA( X ) CHX-2 = MITA( X ) CHX-3 ( °C) 3

Water-cooler outlet temperature ( °C) 30

Water-cooler inside pressure drop (bar) 0.30

Pressure drop in each LNG heat exchangers (bar) 0

4

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� Offering a range of liquefaction capacities.

� Support variety of drive concepts.

� Support heavy hydrocarbon and NGL extraction schemes.

� Direct sea water cooling for all compressors and coolers.

� Suitable in using aero derivative gas turbines for power

generation.

� Generators feeding into a common power grid, provides a

greater flexibility if one of the drivers is down.

� High energy efficiency since each MR can be tuned to the vari-

ous cooling curves for each refrigerant system.

The MFC process flow diagram is presented in Fig. 3 . For sim-

licity, the different streams in the MFC process description are

entioned with their unique name “stream-x” ( x = 1a, 2a…, 1b,

b . . . . . ). Fig. 3 presents a schematic diagram of the MFC-LNG lique-

action cycle. This encompasses three cycles (refrigeration), and the

istinct MR compositions are arranged for each cycle to achieve

recooling, intermediate cooling (liquefaction), and subcooling, re-

pectively. As shown in Fig. 3 , the natural gas feed enters the LNG

eat exchanger (CHX-1), passes through remaining heat exchang-

rs (CHX-2 and CHX-3), and is liquefied when the temperature is

ecreased to −147.1 °C. The LNG (liquefied natural gas) pressure

s reduced to the LNG storage pressure when it passes through

he throttling valve (JTV-4). In the precooling MR cycle, the pre-

ooling refrigerants contain ethylene, propane, and n-butane. First,

tream-4c refrigerants pass through single-stage compression and

re cooled by a water cooler. The high-pressure refrigerants (pre-

ooling) are again cooled by a heat exchanger (CHX-1). Once the

efrigerants have been expended by the throttling valve (JTV-1), it

roduces vapor and removes the heat of vaporization to produce

old, which helps to precool the NG. The refrigerant is subcooled

o −27 °C, and then the precooling refrigerant (super-heated) is

ecirculated to the compressor to complete the cycle. In the in-

ermediate cooling (liquefaction) cycle, the refrigerant consists of

ethane, ethylene, and propane. The intermediate cooling refrig-

rant undergoes one-stage compression, and it is then treated by

water cooler, CHX-1, and CHX-2, respectively. The pressure and

emperature are reduced when it undergoes expansion through the

hrottling valve (JTV-2). In the liquefaction heat exchanger (CHX-2),

he low-pressure refrigerants cool the subcooling refrigerant and

atural gas (NG) to −88.9 °C. In the subcooling refrigerant cycle,

thylene, methane, and nitrogen with a lower boiling point com-

rise the subcooling refrigerants. Following single-stage compres-

ion, the refrigerants are cooled simultaneously by CHX-1, CHX-2,

nd CHX-3 respectively. After reducing the pressure and temper-

ture, the refrigerant enters the throttling valve (JTV-3). This ex-

ands the MR to leave it cold, which is then used to cool the NG

o −147.1 °C.

. Optimization framework for MFC process

The Microsoft Visual Studio ® (MVS) v16 environment was cho-

en to develop a user-friendly robust optimizer to optimize the

FC process operations. A component object model (COM) func-

ionality was adopted for building up an interface between Aspen

ysys and the optimizer. COM is referred to as a binary standard

hat applies after a program has been translated to binary machine

ode. This binary code consists of one or more sets of related func-

ions in terms of a dynamic linking library (DLL) files. This DLL was

ccessed as a referencing an object of Aspen Hysys into the opti-

izer (MVS).

.1. Optimization problem formulation

The performance of the MFC process is based on some impor-

ant key parameters, such as the mixed refrigerant flowrates, re-

rigerant condensation pressure, refrigerant evaporation pressure,

194 A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200

C1-1C2-1C3-1

N2-2C1-2C2-2

C2C3C4

1a

1b

1c

2a

2b

2c

3c

4c

3a

4a

5a

3b

4

5b

6b

7b-V

7b-L

8b-V

8b-L

6a-V

6a-L

7a-V

7a-L

8a

9a (Recycled MR)

5c-V

6c-V

5c-L6c-L

7c

8c

9c (Recycled MR)

NG (stream-1)

2 3

6 (LNG)

5

End flash gas

K-1

K-2

K-4

P-1

P-2

P-3

mix-1

mix-2

mix-3

mix-4

mix-5

mix-6

V-1

V-2

V-3

V-5

C-1

C-3

C-4

Q1

Q2

Q4

JTV-1 JTV-2 JTV-3

JTV-4

CHX-1

CHX-2

CHX-3

9b (Recycled MR)

4b

Fig. 3. Schematic representation of MFC-LNG process flow diagram.

Table 2

Key decision variables of the MFC process and their upper and lower bounds.

Decision variables Lower bound Upper bound

Subcooling MR

Suction pressure (stream-5b), P 5b (bar) 2 8

Discharge pressure (stream-9b), P 9b (bar) 15 40

Flowrate of methane, m C 1 (kg h ̂ ( −1)) 1.623 5.5

Flowrate of ethane, m C 2 (kg h ̂ ( −1)) 1.771 7.5

Flowrate of nitrogen, m N 2 (kg h ̂ ( −1)) 0.85 3.5

Subcooling temperature (stream-4b), T S ( °C) −110 −170

Intermediate cooling MR

Suction pressure (stream-4a), P 4a (bar) 2 8

Discharge pressure (stream-7a-V), P 7a-V (bar) 10 35

Flowrate of methane, m C 1 (kg h ̂ ( −1)) 2.2 7.5

Flowrate of ethane, m C 2 (kg h ̂ ( −1)) 10.0 35.0

Flowrate of propane, m C 3 (kg h ̂ ( −1)) 5.5 22.0

Liquefaction temperature (stream-3a), T L ( °C) −70 −130

Precooling MR

Suction pressure (stream-3c), P 3c (bar) 2 8

Discharge pressure (stream-6c-V), P 6c-V (bar) 10 25

Flowrate of ethane, m C 2 (kg h ̂ ( −1)) 6.8 24.8

Flowrate of propane, m C 3 (kg h ̂ ( −1)) 9.5 28.0

Flowrate of n-butane, m nC 4 (kg h ̂ ( −1)) 12.0 55.0

Precooling temperature (stream-2c), T P ( °C) −20 −60

c

M

�

X

V

V

V

and temperatures of the three cycles (subcooling, precooling, and

liquefaction). Thus, it is necessary to optimize the decision vari-

ables to achieve minimum energy for natural gas liquefaction. The

minimum energy requirement for liquefying a given load of NG

was chosen as the optimization objective. This problem is con-

strained by the minimum internal temperature approach (MITA)

inside the cryogenic heat exchangers. In the proposed study, the

objective function was constrained by the defined MITA value of

3 °C in all the exchangers. Although, the MITA value can be defined

between the range of 1–3 °C, as reported by Hasan et al. (2009 )

and Qadeer et al. (2018 ). However, NG liquefaction plant employs a

specially built cryogenic or compact heat exchanger to pack more

area in small volume. So that it achieves a high area to volume

ratio, giving it ability to operate close to 3 °C approach temper-

ature. The MITA value less than 3 °C leads to larger area, which

ultimately increases the capital investment. Therefore, several lat-

est studies ( Ali et al., 2018a , 2019; He et al., 2019b; Qyyum et al.,

2018d, 2018e ) relevant to development and optimization of LNG

processes adopted the most feasible MITA value of 3.0 °C.

4.2. Decision variables, objective function, and constraints

The energy consumption in the MFC process is affected by the

flowrate of each refrigerant, the MR system pressures, and the

temperatures. Thus, these are selected as key/decision variables

for optimizing the MFC-LNG process. For each LNG exchanger, the

condensation/evaporation pressures are directly related to the MR

system suction/discharge pressures. Finding the minimum differ-

ence between the suction and discharge limits the compression

ratio and saves energy. The key/decision variables are recorded in

Table 2 , with their respective lower and upper bounds.

It is important to satisfy the process design constraints to ob-

tain practically meaningful results. One important constraint in liq-

uefaction is the minimum internal approach temperature (MITA)

in the cryogenic exchanger. If the MITA is less than 3 °C inside a

heat exchanger (CHX-1, CHX-2, and CHX-3), then the exchanger be-

comes enormous in size, thus to practically restrict the exchanger

size the lowest MITA value should be 3 °C. An additional design

concern is to restrict the liquid entering the normal operation of

compressors. This can be achieved by prescribing the degree of su-

perheating for the refrigerant leaving an exchanger.

In this study, the optimization objective of minimizing the total

ompression energy is given by equation below.

in f ( X ) = Min.

(

n ∑

i =1

W i / m LNG

)

(6)

Subject to:

T min 1 ( X ) ≥ 3 ; �T min 2 ( X ) ≥ 3 ; �T min 3 ( X ) ≥ 3 ,

lb < X < X ub

S = ( P 5 b , P 9 b , m C1 , m C2 , m N2 , T S ) (7)

L = ( P 4 a , P 7 a −V , m C1 , m C2 , m C3 , T L ) (8)

P = ( P 3 c , P 6 c−V , m C2 , m C3 , m C4 , T P ) (9)

A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200 195

Table 3

Description and comparison of optimization results.

Decision Variables Base case-1 Base case-2 ( Ding et al., 2017 ) MCD Coggins

Subcooling MR

Suction pressure (stream-5b), P 5b (bar) 2.77 4.19 2.50 3.12

Discharge pressure (stream-9b), P 9b (bar) 35.00 41.19 20.00 34.00

Flowrate of methane, m C 1 (kg h ̂ ( −1)) 5.658 69.28 5.214 4.640

Flowrate of ethane, m C 2 (kg h ̂ ( −1)) 3.541 21.09 8.245 4.520

Flowrate of nitrogen, m N 2 (kg h ̂ ( −1)) 1.650 9.62 0.986 1.369

Subcooling temperature (stream-4b), T S ( °C) −155.8 −150.1 −149.7 −147.1

Intermediate cooling MR

Suction pressure (stream-4a), P 4a (bar) 2.00 3.72 2.31 2.878

Discharge pressure (stream-7a-V), P 7a-V (bar) 23.00 20.63 21.30 27.90

Flowrate of methane, m C 1 (kg h ̂ ( −1)) 3.450 10.55 4.156 2.60

Flowrate of ethane, m C 2 (kg h ̂ ( −1)) 22.31 78.29 22.15 26.40

Flowrate of propane, m C 3 (kg h ̂ ( −1)) 8.0 0 0 11.16 11.35 7.573

Liquefaction temperature (stream-3a), T L ( °C) −93.30 −92 −101.4 −88.90

Precooling MR

Suction pressure (stream-3c), P 3c (bar) 2.091 1.53 2.505 2.505

Discharge pressure (stream-6c-V), P 6c-V (bar) 20.00 13.16 20.00 9.851

Flowrate of ethane, m C 2 (kg h ̂ ( −1)) 11.12 7.26 10.55 10.79

Flowrate of propane, m C 3 (kg h ̂ ( −1)) 13.86 77.43 20.25 9.456

Flowrate of n-butane, m nC 4 (kg h ̂ ( −1)) 29.42 15.31 32.07 55.24

Precooling temperature (stream-2c), T P ( °C) −27.81 −40 −40.72 −27.76

Constraints

MITA( X ) CHX-1 ( °C) 3.394 > 3.00 3.006 3.0

MITA( X ) CHX-2 ( °C) 5.266 > 3.00 3.001 3.0

MITA( X ) CHX-3 ( °C) 4.869 > 3.00 3.001 3.0

Liquefaction rate (%) 95 95 95 95

Total compression power (kWh) a 5.571 4.655 b 4.844 4.156

Specific compression power (kWh/kg-NG) a 0.2946 0.2462 b 0.256 0.2197

Relative energy saving (%) a – 16.4 b 13.1 25.4

a Optimization objective. b From literature.

w

s

t

X

c

s

m

l

4

c

w

2

o

i

M

�

w

X

e

M

w

5

t

w

e

t

F

t

t

t

C

p

t

t

i

t

t

f

t

m

F

t

here X, V S , V L , and V P are the vectors of decision variables,

ubcooling, liquefaction, and precooling decision variables, respec-

ively. Thus,

= ( V S , V L , V P ) (10)

Nonlinear interactions between the decision variables and the

onstrained objective function make it difficult to optimize this

ystem using process simulation software that is available for com-

ercial use. Thus, an external platform was employed to achieve a

ower compression energy.

.3. Constraint handling

The proposed MFC-LNG process exhibits an inequality between

onstraints (MITA > 3 °C). The exterior penalty function method

as implemented during the optimization process ( Khan and Lee,

013; Venkataraman, 2009 ), to fold all three constraints into the

ne objective function and thus enable the handling of the inequal-

ty constraints.

The constraints and objective function in this study are

inimize f ( X ) = Min.

(

n ∑

i =1

W i / m LNG

)

(11)

Subject to

T min 1 ( X ) ≥ 3 ; �T min 2 ( X ) ≥ 3 ; �T min 3 ( X ) ≥ 3 ,

here X is a decision variable vector, bounded as

LB j ≤ X j ≤ X

UB j j = 1 , 2 , 3 , . . . , n (12)

After formulating and reconstructing the objective function, the

quivalent unconstrained objective function is given by

inimize f (X )

= Min.

(

n ∑

i =1

W i / m LNG + P a ( max { 0 , (3 . 0 − MIT A (X )) } ) )

(13)

here P a is a positive penalty parameter.

. Results and discussion

To access the performance of the Coggins step-up approach for

he MFC liquefaction process, two cases with different parameters

ere selected as base case 1 and base case 2, adopted from Ding

t al. (2017 ). The parameter details and a comparative analysis of

hese with the coggins-optimized case are presented in Table 3 .

urthermore, the temperature and pressure of each stream ob-

ained through coggins optimization are provided as Table S-1 in

he Supporting information.

Figs. 4–6 present composite curve analyses between the op-

imized and base-case MFC-LNG processes for heat exchangers

HX-1, CHX-2, and CHX-3, respectively. These illustrate the ap-

roach temperature (TDCC) and heat-flow (THCC) variation along

he length of each exchanger. As a rule of thumb, more space be-

ween composite curves (CC) represents more work lost through

rreversibility. Thus, the optimizer aims to reduce the space be-

ween hot and cold CCs, while satisfying the approach tempera-

ure criteria. As observed in Table 3 , for the optimization to per-

orm better than base case 1, the decision value must be lower

han 0.2462 kW/kg-NG.

Individual refrigerant components directly affect the perfor-

ance of the liquefaction process. The TDCC plot presented in

ig. 4 analyzes these effects while determining the efficiency of

he MFC process through the CCs. A gap of > 3 °C between the hot

196 A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8 9 10-50-40-30-20-10

0102030405060708090

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8 9 10-50-40-30-20-10

0102030405060708090

(erutarep

meThcaorpp

Ao C

)

Temperature (oC)

Cold composite curveHot composite curve

a b

Tem

pera

ture

(o C)

Heat Flow (kW)

Cold composite curveHot composite curve

c

(erutarep

meThcaorpp

Ao C

)

Temperature (oC)

Cold composite curveHot composite curve

d

Tem

pera

ture

(o C)

Heat Flow (kW)

Cold composite curveHot composite curve

Fig. 4. (a) TDCC and (b) THCC composite curves for the base case, and optimized (c) TDCC and (d) THCC composite curves for the Coggins-optimized MFC-LNG process for

the heat exchanger CHX-1.

T

s

t

c

a

2

r

g

5

p

t

g

p

l

r

a

g

s

and cold CCs implies an enhanced irreversibility, which directly in-

creases the NG liquefaction cost. Thus, reducing the gap between

the hot and cold CCs is equivalent to reducing the NG liquefaction

cost.

5.1. Precooling cycle

Fig. 4 presents the TDCC and THCC curves of the precooling

heat exchanger associated with MFC process. Fig. 4 (a) and (b) show

the cooling curves before optimization and there appear more gap

between cooling curves. The gap between cooling curves repre-

sents the opportunity for energy saving by tuning decision vari-

ables. This opportunity is exploited by coggins approach by finding

optimum values of decision variables that minimizes the cooling

curves gas (represented in Fig. 4 (c) and (d)). Reduction in cooling

curves gap near cold section of the exchanger is more rewarding.

This trend is closely followed in the cold section of the exchanger

from −40 °C to 10 °C. As illustrated in Fig. 4 (a), a greater gap be-

tween the TDCC plots and a minimum approach temperature of

> 15 °C is achieved between −50 °C and −10 °C. The gap between

the TDCC regions can be narrowed further by suitable tuning of

the flowrates of ethane, propane, and n-butane listed in Table 2 .

he region between −30 °C and 30 °C exhibits a phase change, and

o some irreversibility cannot be avoided in this region. Most of

he effort s are concentrated toward the low-temperature end, be-

ause generating low temperatures costs more energy.

An overall compression power saving of ≤ 25.4% and ≤ 11% was

chieved in comparison with the base cases 1 and 2 ( Ding et al.,

017 ), respectively. Fig. 4 (c) and (d) present the TDCC and THCC,

espectively, obtained in the Coggins-optimized case for the cryo-

enic exchanger CHX-1.

.2. Liquefaction cycle

The liquefaction regime CCs are illustrated in Fig. 5 (a). Tem-

eratures in this regime vary between −110 °C and −30 °C, with

he approach temperature constrained to be over 10 °C. This higher

ap between CCs presents an opportunity to further optimize the

rocess with a new constraint of 3 °C MITA, which leads to a

ower energy requirement. The heat-transfer performance in this

egime is significantly affected by low boiling components such

s methane, ethane, and propane. Optimizing these minimizes the

ap in the middle of the TDCC, as can be seen from the compari-

on in Fig. 5 (a) and (c).

A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200 197

-100 -80 -60 -40 -20 0 20 40 60 800

10

20

30

40

50

60

70

a

Cold composite curveHot composite curve

(erutarep

meThcaorpp

Ao C

)

Temperature (oC)0 1 2 3 4 5 6 7 8 9 10

-100

-80

-60

-40

-20

0

20

40

60

80

b

Cold composite curveHot composite curve

Tem

pera

ture

(o C)

Heat Flow (kW)

-100 -80 -60 -40 -20 0 20 40 60 800

10

20

30

40

50

60

70

c

Cold composite curveHot composite curve

(erutar ep

meThcaorpp

Ao C

)

Temperature (oC)0 1 2 3 4 5 6 7 8 9 10

-100

-80

-60

-40

-20

0

20

40

60

80

d

Cold composite curveHot composite curve

Tem

pera

ture

(o C)

Heat Flow (kW)

Fig. 5. (a) TDCC and (b) THCC composite curves for the base case, and optimized (c) TDCC and (d) THCC composite curves for the Coggins-optimized MFC-LNG process for

the heat exchanger CHX-2.

fl

C

l

a

h

5

a

T

e

c

F

b

t

(

c

b

i

o

s

p

f

s

1

g

u

6

t

c

�

p

y

e

a

Fig. 5 (b) and (d) illustrate the approach temperature and heat

ow along the length of the CHX-2 exchanger for the base case and

oggins-optimized case, respectively. According to Fig. 5 (d), in the

iquefaction regime, the temperature difference between the hot

nd cold CCs is significantly smaller than in the other two regimes,

elping to minimize irreversibility of the entire process.

.3. Subcooling cycle

The subcooling regime ranges from −90 to −160 °C, and the

pproach temperature is constrained to be 3 °C. A TDCC and

HCC curve comparison for the subcooling regime in the CHX-3

xchanger is presented in Fig. 6 (a,b: base case; c,d: optimized

ase). The peak of TDCC in Fig. 6 a is significant higher than that of

ig. 6 c, which shows the inefficient heat transfer. Similarly, the gap

etween THCC for base case (see Fig. 6 b) is larger as compared to

he optimized THCC (see Fig. 6 d). In fact, for an energy-efficient

i.e., low energy demand) liquefaction process, the hot and cold

omposite curves of the natural gas and mixed refrigerant should

e located as within the defined feasible approach temperature,

.e., 3 °C ( Qyyum and Lee, 2018 ).

Base case 1 in Table 3 is optimized using the MCD method-

logy, while base case 2 is adopted from Ding et al. (2017 ). The

ame objective of specific energy minimization is chosen to com-

are the results with the Coggins step-up approach implemented

or MFC. Compared with the Coggins approach, overall compres-

ion power savings of 25.4% (base case 1), 10.8% (base case 2), and

4.2% (MCD) are achieved. This proves the effectiveness of the Cog-

ins approach. Furthermore, not only MFC, but also any other liq-

efaction cycle can be optimized using this.

. Exergy loss analysis and coefficient of performance

The general equation for the exergy flow without considering

he kinetic and potential energy of the fluid ( Atmaca et al., 2019 )

an be written as ( Saeid Mokhatab, 2014 ):

E = (H − H O ) − T O (S − S O ) (14)

A breakdown of the useful energy loss for individual MFC

rocess components is best illustrated through an exergy anal-

sis ( Pourfayaz et al., 2019 ). This provides an opportunity for

xamining the individual process components, and helps to cre-

te an action plan for better efficiency. After performing the

198 A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200

-160 -150 -140 -130 -120 -110 -100 -902

4

6

8

10

12

14

16

18

a

Cold composite curveHot composite curve

(er ut are p

meTh caorppA

o)

C

Temperature (oC) 0.0 0.3 0.6 0.9 1.2 1.5

-160

-150

-140

-130

-120

-110

-100

-90

b

Cold composite curveHot composite curve

Tem

pera

ture

(o C)

Heat Flow (kW)

-160 -150 -140 -130 -120 -110 -100 -902

4

6

8

10

12

14

16

18

c

Cold composite curveHot composite curve

(eru ta r ep

m eThc aor pp A

o)

C

Temperature (oC)0.0 0.3 0.6 0.9 1.2 1.5

-160

-150

-140

-130

-120

-110

-100

-90

d

Cold composite curveHot composite curve

Tem

pera

ture

(o C)

Heat Flow (kW)

Fig. 6. (a) TDCC and (b) THCC composite curves for the base case, and optimized (c) TDCC and (d) THCC composite curves for the Coggins-optimized MFC-LNG process for

heat exchanger CHX-3.

Fig. 7. Exergy loss (%) disintegration for the MFC-LNG processes using Coggins optimization.

Table 4

Expression associated with equipment for exergy loss calculation ( Venkatarathnam,

2008 ).

Equipment Exergy loss (kJ/h)

Compressor E LOSS = (m )( E IN − E OUT ) − W

Pump E LOSS = (m )( E IN − E OUT ) − W

Air cooler exchanging

heat with ambient

E LOSS = (m )( E IN − E OUT )

Phase separator E LOSS = m IN (E IN ) − m LIQU ID (E LIQU ID ) − m VAPO UR (E VAPO UR )

JT (throttle) valve E LOSS = (m )( E IN − E OUT ) ∑ ∑

optimization, the exergy loss analysis for each component asso-

ciated with MFC-LNG processes were calculated. In this study,

the exergy loss calculations were performed based on expressions

adopted from Venkatarathnam (2008 ), as provided in Table 4 .

The exergy analysis for the base case and coggins-optimized

case of MFC-LNG process is summarized in Table 5 .

Furthermore, Fig. 7 illustrates a breakdown of the exergy loss

for the MFC-LNG process in terms of the percentage for each

component associated with coggins-optimized MFC liquefaction

process.

LNG heat exchanger E LOSS = (m ) E IN − (m ) E OUT

A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200 199

Table 5

Coggins exergy loss minimization/maximization in comparison with base case 1.

Equipments Exergy loss (kJ/h) Exergy loss (%)

Base case-1 Coggin’s

Compressors

C-1 (K-4) 1337.52 1008.53 –24.60

C-2 (K-2) 1319.77 1149.65 –12.89

C-3 (K-1) 519.40 471.71 –9.18

Net exergy loss 3167.70 2629.89 −17.21

Pumps

P-3 0.00 2.20 –

P-2 0.00 7.51 –

P-1 7.48 4.74 –

Net exergy loss 7.48 14.45 + 93.15

Cryogenic LNG exchangers

CHX-1 1552.41 773.30 −50.19

CHX-2 1886.01 1149.06 −39.07

CHX-3 1267.77 693.71 −45.28

Net exergy loss 4706.19 2616.07 −44.41

Air coolers

C-3 3577.72 1921.02 −46.31

C-4 3.08 16.53 + 437.30

C-1 840.75 345.98 −58.85

Net exergy loss 4421.55 2283.52 −48.35

Phase separators

V-3 0.00 48.41 –

V-2 140.65 197.65 + 40.53

V-1 128.26 64.78 −4 9.4 9

Net exergy loss 268.91 310.84 −15.59

Flash valves

JTV-1 299.28 106.31 −64.48

JTV-2 438.44 323.16 −26.29

JTV-3 193.68 193.62 –0.03

JTV-4 507.23 507.23 0.00

Net exergy loss 1438.64 1130.33 −21.43

Overall process exergy loss 14019.46 8985.10 −35.91

-ve shows exergy loss minimization, + ve shows exergy gain.

Table 6

Comparison of coefficient of performance (COP) of each refrigeration loop.

Decision variables Coefficient of performance (COP)

Base case-1 Base case-2

( Ding et al., 2017 )

MCD Coggins

Subcooling MR 1.83 2.07 2.53 2.04

Intermediate cooling MR 2.29 3.45 2.79 4.88

Precooling MR 3.05 3.57 3.76 5.88

L

w

I

n

t

M

e

t

a

t

r

c

b

o

A

o

c

s

1

Fig. 8. Overall exergy loss (kJ/h) analysis of Coggins optimized MFC-LNG in com-

parison with base case 1 and the MCD approach.

s

C

7

t

c

a

t

r

b

a

a

p

i

a

c

f

p

c

a

b

D

A

g

t

g

f

S

f

It can be seen that the exergy loss through compressors and

NG exchangers are highest, at 29.27% and 29.12% respectively,

hile the intercooler accounts for 25.42% of the total exergy loss.

n fact, the heat transfer and compression are always accompa-

ying with increase in the entropy, which is the main reason of

he highest exergy loss through LNG exchangers and compressors.

ore entropy generation more exergy losses. In heat exchanges

xergy losses occur due to the three reasons, heat transfer be-

ween the hot and cold fluids; heat transfer between the exchanger

nd its surroundings; and the movement of the fluids. Tempera-

ure drop between the fluids during the heat exchange is the main

eason for exergy losses and can be minimized but not eliminated

ompletely.

An exergy loss comparison between the Coggins optimized case,

ase case 1, and the MCD approach is presented in Fig. 8 .

Furthermore, Table 6 lists the coefficient of performance (COP)

f each refrigeration cycle involved in MFC liquefaction process.

ccording to Table 6 , it can be observed clearly that under the

ptimal conditions obtained by coggins approach, the COP of pre-

ooling and intermediate refridgeration loops are 5.88 and 4.88, re-

pectively, which are significant higher than that of MCD, base case

, and base case 2. These higher COP value for coggins-optimized

ubcooling refrigeration cycle contributes to improve the overall

OP of coggins-optimized MFC liquefaction process.

. Conclusions

The Coggins algorithm has successfully been implemented for

he optimization of the MFC-LNG liquefaction process. The key de-

ision variables were optimized while satisfying constraints on the

pproach temperature in all heat exchangers. Through optimiza-

ion with the Coggins approach, the specific compression power

equirement decreased by ≤ 25.4% and ≤ 11% in comparison with

ase cases 1 and 2 ( Ding et al., 2017 ). The result for the Coggins

pproach was also compared with the well-known MCD approach,

nd it outperformed MCD by 14.2% in terms of the specific com-

ression power requirement. Thus, the Coggins algorithm exhib-

ted a superior performance compared with a proven optimization

lgorithm, and can also be implemented for other liquefaction cy-

les. An exergy analysis of the Coggins-optimized MFC-LNG lique-

action process revealed that the liquefaction process can be im-

roved further through better compressor, intercooler, and LNG ex-

hanger designs. For the existing design, the Coggins algorithm can

ssist process engineers in overcoming energy efficiency challenges

y running MFC-LNG liquefaction processes in an optimized state.

eclaration

The authors declare no competing financial interests.

cknowledgments

This research was supported by the Basic Science Research Pro-

ram Foundation of Korea (NRF) funded by the Ministry of Educa-

ion ( 2018R1A2B6001566 ) and the Priority Research Centers Pro-

ram through the National Research Foundation of Korea (NRF)

unded by the Ministry of Education ( 2014R1A6A1031189 ).

upplementary materials

Supplementary material associated with this article can be

ound, in the online version, at doi: 10.1016/j.ijrefrig.2019.04.002 .

200 A. Nawaz, M.A. Qyyum and K. Qadeer et al. / International Journal of Refrigeration 104 (2019) 189–200

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M

M

Q

Q

Q

Q

Q

Q

R

S

S

V

V

V

W

X

Y

Z

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