JIMEC Thermal modeling and Simulation of HX Conference Paper

The 8th Jordanian International Mechanical Engineering Conference (JIMEC’8) Amman – Jordan

THERMAL MODELING AND SIMULATION OF AN INDUSTRAIL SHELL AND

TUBE HEAT EXCHANGER

Fadi A. Ghaith, [email protected] School of Engineering and Physical Sciences, Heriot Watt

University, Dubai Campus, UAE.

Ahmed S. Izhar, [email protected] School of Engineering and Physical Sciences, Heriot Watt

University, Dubai Campus, UAE.

ABSTRACT

In this paper, an industrial shell-and-tube heat exchanger utilized for the purpose of cooling raw natural

gas by means of mixture of sale gases is considered. The main objective of this work is to provide an

optimum and reliable thermal design of a single-shelled finned tubes heat exchanger to replace the

existing two- shell and tube heat exchanger due to the space limitations in the plant. A comprehensive

thermal model was developed using the effectiveness-NTU method. The shell-side and tube-side overall

heat transfer coefficient were determined using Bell-Delaware method and Dittus-Boelter correlation,

respectively. The obtained results showed that the required area to provide a thermal duty of 1.4 MW is

about 1132 m2 with tube-side and shell-side heat transfer coefficients of 950 W/m2K and 495 W/m2K,

respectively. In order to verify the obtained results generated from the mathematical model, a numerical

study was carried out using HTRI software which showed a good match in terms of the heat transfer area

and the tube-side heat transfer coefficient.

Keywords: shell-and-tube heat exchanger, heat transfer coefficient, HTRI.

1. INTRODUCTION

Shell and tube heat exchangers are widely used in petrochemical and energy industries because of their

ability to adapt different process operating conditions. Their robustness and geometry make them very

suitable for high temperature and pressure applications. A compact formulation was developed by Serna

and Jiminez [1,2] based on Bell-Delaware method that integrates the pressure drop, the heat transfer area,

and the film heat transfer coefficient. Other widely accepted methods like Kern’s method [3,4] and

Donohue’s correlation may also be used but they are old and out-dated and lacking accuracy. On the other

hand, LMTD method and the ε-NTU approaches are considered powerful in determining the heat transfer


rate and the heat transfer area [5]. Shell and tube heat exchangers have many design considerations that

need to be taken into account while modeling and designing the heat exchanger to achieve better

performance. Hosseini et al. [6] performed an experiment comparing the heat transfer coefficient and

pressure drop for three different types of copper tubes (smooth, corrugated and micro-fins) and came out

with the result that at higher Reynolds number the performance of the heat exchanger with micro-finned

tubes greatly improved, if the geometry and all other configurations kept constant. Fabbri [7] goes as far

as comparing the heat transfer performance of a smooth wall channel with a corrugated one under laminar

flow conditions, with the aid of a finite element model. He found out that treated surfaces and rough

surfaces showed enhancement of up to 30% in heat transfer rate with respect to the heat dissipated by the

usual flat wall of same volume. This paper aims to develop a comprehensive thermal model which can

describe the thermal performance of shell-and-tube heat exchanger. The obtained model is implemented

to design a large-scale industrial shell and tube heat exchanger by determining the geometry and

estimating the heat transfer coefficients. Also a numerical study was established to validate the results

extracted from theory.

2. GENERAL DESCRIPTION

In this section, the system description and the associated industrial applications are discussed briefly.

2.1 Scope of Application

Raw natural gas (NG) from the gas wells consists of mainly methane along with other impurities like

heavier hydrocarbons, condensates, water content, traces of mercury, and other gaseous components like

CO2, N2, He, H2S and SO2 [8]. Methane (and ethane, in some cases) needs to be separated from the

impurities before it can be collected. The shell-and-tube heat exchanger modeled in this paper is basically

used to cool the raw natural gas to reduce the work input in processing of sales gases. The whole process

is shown schematically by Fig.1. During operation, hot raw NG is fed into the heat exchanger to be

cooled, which is then passes through a control valve to reduce pressure. Further reduction in pressure

reduces the temperature. At this stage, the raw NG is split into vapors (methane and ethane), condensate

(other impurities) and water. Finally, the vapors (sales gas) is fed back into the heat exchanger (from the

other side) to cool the incoming raw NG and bring the sales gas to an optimum temperature, ready for

transportation.


Fig. 1: Schematic of the heat exchanger unit.

2.2 Problem Statement

This work involves thermal design of a single shell-and-tube heat exchanger such to fulfill the operating

conditions and the space criteria of the plant. Table1 summarize the basic process conditions as well as

the main geometry requirements.

3. MODEL FORMULATION

In this section, the thermal model was formulated to predict the heat transfer coefficients and hence the

heat transfer surface area. The shell-side and tube-side overall heat transfer coefficient were determined

using Bell-Delaware method and Dittus-Boelter correlation, respectively. On the other hand, the

effectiveness-NTU method was used to calculate the heat transfer surface area. The main assumptions

underlay this formulation are [5]:

i. No external heat interaction takes place.

ii. Axial conduction is negligible.

iii. Kinetic and potential changes are assumed negligible.

iv. The overall heat transfer coefficient, U, remains constant throughout the heat exchanger.

v. The specific heat capacity, Cp, remains constant throughout the heat exchanger.

vi. The temperature of each fluid is constant over any cross-section of its path through the heat

exchanger.


vii. The flow rate of each fluid is constant throughout the heat exchanger and there is no bypassing of

sections.

viii. The temperature change of the shell-side fluid within one baffle space is small compared to its

overall temperature change.

Table 1: process conditions of the heat exchanger

Fluid Raw Natural Gas Sales Gas Flow Rate [kg/s] 19.05 18.86 Inlet Temperature [°C] 35.32 -2 Outlet Temperature [°C] 8.85 27.32 Length of Exchanger [m] < 8

3.1 Tube-side convective heat transfer coefficient

Based on the assigned internal mass flow rate of raw natural gas for this application, the internal flow can

be approximated as steady turbulent flow. Accordingly, the tube-side convective heat transfer coefficient

can be estimated using the Dittus-Boelter correlation

𝑁𝑢𝑡 = 0.023𝑅𝑒0.8𝑃𝑟𝑛

(1)

where Prt and Ret are Prandtl and Reynold’s numbers, respectively. For cooling process, n = 0.3.

The tube-side heat transfer coefficient, αt, is a function of the tube-side Nusselt Number, Nut, the thermal

conductivity k, and the internal diameter of the pipe at finned area, dti, and can be expressed as

(2)

3.2 Shell-side convective heat transfer coefficient

The shell-side convective heat transfer coefficient αs, can be evaluated using Bell-Delaware

method [9, 10]. This can be expressed as:

(3)

where αideal is the ideal heat transfer coefficient and JC, JL, JB, JS, JR and Jμ are the baffle cut,

baffle leakage, bundle bypass, unequal baffle spacing, laminar flow, and wall viscosity

correction factors, respectively. The relevant equations required to estimate the values of such

correction factors are summarized by Table 2.


Table 2: Set of equations used in evaluating the heat exchanger correction factors

Factor Relevant Equations

Baffle Cut

Correction Factor,

JC

, ,

The Baffle

Leakage

Correction factor,

JL

Bundle Bypass

Correction factor,

JB

, for layout angle of 30ᴼ



Cbh is the empirical factor and is equal to 1.35 for laminar flow and 1.25 for turbulent and

transitional flows.

Unequal baffle

spacing, JS

n= 0.6 for turbulent flow and 1/3 for laminar flow;

Wall viscosity

correction factor,

Jμ


The ideal tube bank convective heat transfer coefficient is calculated by

(4)

where Ji is the heat transfer factor and is evaluated using the equations (9a), (9b) and (9c):

where a1, a2, a3 and a4 are constants which depend on the Reynolds number and the tube layout

angle as listed in Table 2. Dreq is the equivalent projected diameter and is influenced by the fin

root diameter, Dfr, the fin height, Lfh, the fin density, Nf, and the fin thickness as expressed

below:

3.3 ε-NTU Method

The effectiveness, ε of the heat exchanger is defined as

Also it should be noted that the effectiveness for the counter flow configuration can be written

as:

where CR is the ratio between the highest and lowest thermal capacitances ratio and NTU is the

no. of transfer units which is defined as:

CRNTUCR

CRNTU

1exp1

1exp1


where Cmin is the minimum thermal capacitance of the fluids and U is the overall heat transfer

coefficient which can takes into account the effect of fouling and the influence of fins and may

be expressed mathematically as follow:

The effectiveness-NTU method is used to determine the required heat transfer area of the subject

heat exchanger.

Table 3: Empirical coefficients required to determine the heat transfer factor Ji

Layout Re a1 a2 a3 a4

30ᴼ

105-104 0.321 -0.388

1.450 0.519

104-103 0.321 -0.388

103-102 0.593 -0.477

102-10 1.360 -0.657

<10 1.400 -0.667

45ᴼ

105-104 0.370 -0.396

1.930 0.500

104-103 0.370 -0.396

103-102 0.730 -0.500

102-10 0.498 -0.656

<10 1.550 -0.667

90ᴼ

105-104 0.370 -0.395

1.187 0.370

104-103 0.107 -0.266

103-102 0.408 -0.460

102-10 0.900 -0.631

<10 0.970 -0.667

4. RESULTS AND DISCUSSION

This section describes the main findings obtained by solving the mathematical model provided in section

3 and the main results obtained form the HTRI numerical study.

4.1 HTRI Numerical Simulation

Heat Transfer Research Inc. (HTRI) is the most widely used tool for designing, rating and

simulating heat exchangers. The program Xist is a program that follows the industry standard to

design, rate and simulate a shell-and-tube type heat exchanger. Another program named Xvib

was used to perform the associated flow-induced vibration analysis including determination of

minC

UANTU


natural frequencies and amplitudes of vibration of individual tubes in a bundle. All the

simulations and ratings were performed using HTRI Xchanger Suite 5. Multiple iteration were

carried out before achieving the desired rating of the exchanger. The set of geometrical input

parameters are shown in Table 4. Also the material and process properties are listed in Table 5

and 6, respectively.

Table 4: Heat exchanger input geometry parameters

Type of Heat Exchanger NEN

Shell internal diameter 1000 mm

Shell orientation Horizontal

Hot fluid Tube-side

Tube diameter 15.875 mm

Tube thickness 1.753 mm

Tube pitch 23.812 mm

Pitch ratio 1.5

Tube layout angle 30o

Tubepasses 1

Length 6 m

Tube Material Carbon Steel

Fin type Low fin

Fins/unit length 1023.6 fin/m

Fin root diameter 12.7 mm

Fin height 1.448 mm

Fin thickness 0.305 mm

Wall thickness under fins 1.245

Baffle type NTIW Segmental

Cut orientation Parallel

Baffle cut 16.14 %

Fouling resistance Shell-side: 0.000176

Tube-side: 0.000176

Table 5: Heat exchanger materials of construction

Component Tubes Shell/Head

Material Carbon Steel Carbon Steel

Trade Name AISI 1018 AISI 1095 (A516)

εme , Elastic Modulus [MPa] 211,669.0 210,290.1

σys ,Yield Strength [MPa] 372.3 572.3

σts ,Tensile Strength [MPa] 441.3 965.3

ρ, Density [kg/m3] 7861.1 7861.1

Poisson’s Ratio 0.291 0.293


k, Thermal Conductivity [W/m2.K] 51.9 65.3

Table 6: Heat exchanger process parameters

Parameters Variables Tube-side values Shell-side values Units

Inlet Outlet Inlet Outlet -

Vapour Liquid Vapour Liquid

Flow Rate 19.05 18.86 kg/s

19.02 0.02735 18.968 0.082

Weight

Fraction

Vapour

wf

0.9986 0.0014 0.9957 0.0043 1 1 -

Density ρ 47.86 1080.35 55.1008 865.643 35.34 30.56 kg/m3

49.3055 58.5861

Viscosity μ 1.32e-5 3.0312e-3 1.26e-5 1.935e-3 1.44e-5 1.22e-5 Ns/m2

0.00001743 0.00002077

Specific Heat Cp 2665.8 3108 2774.6 2710 2547.2 2498.2 J/kgK

2666.4191 2774.3222

Thermal

Conductivity

k 0.0408 0.351 0.038 0.248 0.0338 0.0374 W/mK

0.04123 0.03890

Based on the conducted numerical analysis, It was noted that vibrations level can be reduced by

adjusting the baffle spacing in order to regulate the flow velocity. Also it was found that

installation of an impingement plate at the inlet to reduce the dynamic pressure which should not

exceed the value of 2232 kg/ms2 according to TEMA standard. Table 7 summarizes the main

results obtained from HTRI simulation. Detailed output summary reports are provided in

Appendix for both thermal rating and vibrations analysis. The obtained results showed that the

expected heat duty is about 1.4 MW. The overdesign percentage is considered to be 5.41 %

which takes into account any expected loss in the heat transfer coefficients due to extra fouling

or fluctuation about the design flow rates. Also it was found that such load can be achieved by

using a single shell-finned tube heat exchanger. This heat exchanger consists of single shell of

inner diameter of 1 m and length of 6 m. This design incorporates 1146 finned tubes. The tube

sheet is shown schematically in Fig.2. The obtained design was found successful to achieve

acceptable shell-side and tube-side pressure drops just not to exceed the allowed pressure heads

provided by the feed pumps


Table 7: Heat exchanger Output Summary generated from HTRI

Shell-side inlet pressure 4204.5 kPa

Tube-side inlet pressure 6501.5 kPa

Shell-side pressure drop, total/allowed 34.086 / 48.263 kPa

Tube-side pressure drop, total/allowed 15.321 / 48.263 kPa

Tube-side inlet velocity 4.22 m/s

Tube-side outlet velocity 3.72 m/s

Shell-side average film coefficient 902.77 W/m2K

Tube-side average film coefficient 1189.72 W/m2K

Overall Heat transfer coefficient, required/actual 140.12 / 147.70 W/m2K

Heat duty 1.3969 MW

Total area 1118.98 m2

Effective area 1105.58 m2/shell

Impingement diameter/nozzle 1.1

Crosspasses 13

Central baffle spacing 408.769 mm

Inlet baffle spacing 674.850 mm

Outlet baffle spacing 594.039 mm

Baffle thickness 6.350 mm

Effective length 5.765 m

Baffle-to-shell diametral clearance 6.3500 mm

Bundle-to-shell diametral clearance 14.1425 mm

Tube-to-baffle 0.7938 mm

Tube internal diameter 10.210 mm

Outer tube limit diameter 985.857 mm

Centre line tube diameter 969.982 mm

Equivalent projected diameter 13.604 mm

Diameter over fins 15.596 mm

Fin root diameter 12.700 mm

Wall thickness under fins 1.245 mm

Tubecount 1146

Overdesign 5.41 %


Fig. 2: Tubesheet layout

4.2 Thermal model results

In order to verify the accuracy of the thermal model derived in section 3, the thermal system equations

were solved numerically for the purpose of determining the heat transfer coefficients and the required heat

transfer area for the subject heat exchanger. In order to compare the mathematical model and HTRI

simulation results, the input parameters were used as common according to Table 4, 5 and 6. The solution

involved estimation of the correction factors listed in Table 2, followed by determining the shell-side and

tube-side heat transfer coefficients. Finally, the overall heat transfer coefficient was calculated to estimate

the required area of heat transfer using effectiveness-NTU method. An overall summary of the main

output results extracted from the mathematical model is shown in Table 8. A comparison study between

the main thermal model results and the corresponding ones resulted from HTRI simulation was

conducted. Fig.3 shows the estimated heat transfer area for the thermal model and HTRI rating. It was

found that the proposed mathematical thermal model was able to predict the required heat transfer area

accurately with percentage of error didn’t exceed 2.6 % in comparison with HTRI results. Moreover, the

relatively larger area predicted from the mathematical model can accommodate few fluctuations in the

operating conditions and fouling rates. Fig. 4 shows the effect of increasing the fouling factor on both

shell and tube sides in lowering the overall heat transfer coefficients.

Table 8: Thermal model results


Tube-Side Shell-Side

Prantdle No., Pr 0.952 Prantdle No., Pr 0.95

Reynolds No.,Re 108535.5 Reynolds No.,Re

34541

Nusselt No., Nu 242.01 Baffle Cut 1.133

Tube-side convective heat transfer

coefficient,αt (W/m2K) 949.75 Baffle Leakage 1.089

Fouling (m2 K/W) 0.000176 Baffle Bypass 1.043

Effectiveness,ε 0.785 Unequal Baffle Spacing 0.795

NTU 3.3 Wall Viscosity 0.997

Overall finned tubes area(m2) 1132 Shell-side convective heat transfer

coefficient,αt (W/m2K 495.16

Fig. 3: Heat transfer area generated by thermal model and HTRI Simulation


185

190

195

200

205

210

215

0 0.0002 0.0004 0.0006

Fouling/m2KW-1

Ove

rall

He

at T

ran

sfe

r C

oe

ffic

ien

t/W

m-2

K-1

Tube-side

Shell-lside

Fig. 4: Effects of tube-side and shell-side fouling on the overall heat transfer coefficients

Fig. 5 shows a comparison between mathematical and HTRI models in terms of the heat transfer

coefficients. It was found that the tube-side and shell-side heat transfer coefficients resulted from the

mathematical model are higher than the corresponding one generated by HTRI rating by 24 % and 40 %,

respectively. The obtained findings indicate that Dittus- Boelter correlation was able to predict the tube-

side heat coefficient efficiently. On the other hand, it was observed that Bell-Delaware method cannot

capture the shell-side heat transfer coefficient accurately. This is due to the complex flow regime on the

shell side which combines both cross and axial flow and subjected to fluctuations at the inlet and exit

nozzles and near the baffles. Furthermore, the mathematical model is still sufficient as it can predict the

heat transfer area with more conservative values of the heat transfer coefficients.


Fig. 5: Heat transfer coefficients generated by thermal model and HTRI Simulation

6. CONCLUSIONS

In the present work, the thermal performance of an industrial shell and tube heat exchanger was

considered. The thermal model describes the heat transfer coefficients as well as the required heat transfer

area were derived by means of Dittus-Boelter correlation and Bell-Delware method and by incorporating

the effectiveness-NTU method. Numerical simulation using HTRI software was conducted in order to

predict the heat transfer coefficients and the required area of heat transfer. The obtained results showed

that a single shell and tube heat exchanger of diameter of 1 m and length of 6 m is sufficient to provide

the thermal duty of 1.4 MW. This design incorporates 1146 finned tubes. An overdesign percentage of

5.41 % was selected to accommodate any variation in the design parameters. A comparison study was

established between the thermal model and HTRI simulation results, which showed that the heat transfer

area resulted from solving the mathematical model, is about 1132 m2 which is higher by 2.6 % only

compared to the HTRI simulation. Also this study showed that the mathematical model can predict more

conservative shell-side and tube-side heat transfer coefficient rather than HTRI simulation.


NOMENCLATURE

Ds Shell internal diameter Dof Diameter over fins

Di Tube internal diameter Dfr Fin root diameter

Dt Tube external diameter Dreq Equivalent projected diameter

Dti Internal diameter at fin area Lfh Fin height

Ltp Tube pitch Lfs Fin thickness

Lpp Tube pitch parallel to direction of flow Twf Wall thickness under fins

t Tube thickness Lbb Bypass channel diametral gap

L Tube length Lbch Baffle cut height

Le Effective length Lsb Baffle to shell diametric clearance

Nt Number of tubes Ltb Tube to baffle diametric clearance

Nf Fin density (no. of fins/meter) Lbc Central baffle spacing

Lbi Inlet baffle spacing Ntcw Number of tube rows crossed in

window area

Lbo Outlet baffle spacing T Bulk temperature

Dotl Outer tube limit diameter Twall Wall temperature

Dctl Centerline tube limit diameter JI Heat transfer factor

Bc Baffle cut Ao Heat transfer area

JC Baffle cut correction factor Aof Wetted surface area of finned tube

per unit length of tube

JL Baffle leakage correction factor th Head thickness

JB Bundle bypass correction factor ts Shell thickness

JS Unequal baffle spacing correction

factor

Rs Shell radius

JR Laminar flow correction factor Dh Head Diameter

Jμ Wall viscosity correction factor Flow rate

α Heat transfer coefficient wf Weight fraction

αi Ideal tube bank heat transfer

coefficient

ρ Density

FW Fraction of cross-sectional area

occupied by window

Cp Heat Capacity

ϴctl Baffle cut angle relative to center line k Thermal conductivity

Ssb Shell-to-baffle leakage area T Bulk temperature

Stb Tube-to-baffle leakage area Twall Wall temperature

Sm Cross-flow area at tube bundle

centerline

P Internal pressure

ϴds Baffle cut angle σts Tensile strength

Fsbp Bypass to cross-flow area ratio σys Yield stress

Sb Bypass area εme Elastic modulus

Nss Number of sealing strip pairs

Ntcc Number of tube rows passed between

baffle tips

Subscripts

rss Ratio of Nss to Ntcc i Inlet


Lpl Width of bypass lane between tubes o Outlet

Nb Number of baffle compartments t Tube-side

Nc Total number of tube rows crossed by

flow

s Shell-side

NTU No. of Transfer Units h Hot stream

ε effectiveness c Cold stream


ACKNOWLEDGEMENTS

The author is grateful for the support provided by Heriot-Watt University-Dubai Campus. Also Many

thanks to Exterran team for providing technical data used in the analysis of heat exchangers.

REFERENCES

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6. Hosseini R., Hosseini-Ghaffar A., Soltani M., (2007), “Experimental determination of shell

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8. Shale gas Wiki, (2010), Chemical Composition of Natural Gas, shalegaswiki.com, Retrieved

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http://www.shalegaswiki.com/index.php/Chemical_Composition_of_Natural_Gas

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JIMEC Thermal modeling and Simulation of HX Conference Paper

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