In industrial refinery furnaces, the efficiency of thermal transfer to heat crude oil before distillation is often altered by coke deposition inside the fuel pipes. This leads to increased production and maintenance costs, and requires better understanding and control. Crude oil fouling is a chemical reaction that is, at first order, thermally controlled. In such large furnaces, the predominant heat transfer process is thermal radiation by the hot combustion products, which directly heats the pipes. As radiation fluxes depend on temperature differences, the pipe surface temperature also plays an important role and needs to be predicted with sufficient accuracy. This pipe surface temperature results from the energy balance between thermal radiation, convective heat transfer, and conduction in the solid material of the pipe, meaning that the thermal behavior of the whole system is a coupled radiation–convection–conduction problem. In this work, this coupled problem is solved in a cylindrical furnace, in which the crude oil flowing in vertical pipes is heated. The thermal radiation of combustion gases is modeled using the discrete ordinate method (DOM) with accurate spectral models and is coupled to heat conduction in the pipe to predict its wall temperature. The flame is described with a complex chemistry combustion model. An energy balance confirms that heat transfers are effectively dominated by thermal radiation. Good agreement with available measurements of the radiative heat flux on a real furnace shows that the proposed approach predicts the correct heat transfers to the pipe. This allows an accurate prediction of the temperature field on the pipe surface, which is a key parameter for liquid fouling inside the pipe. This shows that the thermal problem in furnaces can be handled with relatively simple models with good accuracy.

References

References
1.
Thackery
,
P.
,
1979
, “
The Cost of Fouling in Heat Exchange Plant
,”
Effluent Water Treat. J.
,
20
(
3
), pp.
111
115
.
2.
Garrett-Price
,
B.
,
1985
,
Fouling of Heat Exchangers: Characteristics, Costs, Prevention, Control and Removal
,
Noyes Publications
, Saddle River, NJ.
3.
Pilavachi
,
P.
, and
Isdale
,
J.
,
1993
, “
European Community R&D Strategy in the Field of Heat Exchanger Fouling: Projects
,”
Heat Recovery Syst. CHP
,
13
(
2
), pp.
133
138
.
4.
Zhi-Ming
,
X.
, and
Zhong-Bin
,
Z.
,
2008
, “
Costs Due to Utility Fouling in China
,”
Heat Exchanger Fouling and Cleaning VII
, Stuttgart, Germany, July 1–7.
5.
Sheikh
,
A.
,
Zubair
,
S.
,
Younas
,
M.
, and
Budair
,
M.
,
2000
, “
A Risk Based Heat Exchanger Analysis Subject to Fouling: Part II: Economics of Heat Exchangers Cleaning
,”
Energy
,
25
(
5
), pp.
445
461
.
6.
Ishiyama
,
E.
,
Paterson
,
W.
, and
Wilson
,
D.
,
2008
, “
The Effect of Fouling on Heat Transfer, Pressure Drop and Throughput in Refinery Preheat Trains: Optimisation of Cleaning Schedules
,”
Heat Transfer Eng.
,
30
(
10–11
), p.
805814
.
7.
Epstein
,
N.
,
1983
, “
Thinking About Heat Transfer Fouling: A 5 × 5 Matrix
,”
Heat Transfer Eng.
,
4
(
1
), pp.
43
56
.
8.
Asomaning
,
S.
,
1997
, “
Heat Exchanger Fouling by Petroleum Asphaltenes
,” Ph.D. dissertation,
University of British Columbia
,
Vancouver, BC, Canada
.
9.
Saleh
,
Z.
, and
Sheikholeslami
,
R.
,
2004
, “
Fouling Characteristics of a Light Australian Crude Oil
,”
Heat Transfer Eng.
,
26
(
1
), p.
1522
.
10.
Srinivasan
,
M.
, and
Watkinson
,
A.
,
2005
, “
Fouling of Some Canadian Crude Oils
,”
Heat Transfer Eng.
,
26
(
1
), pp.
7
14
.
11.
Crittenden
,
B.
,
Kolaczkowski
,
S.
, and
Downey
,
I.
,
1992
, “
Fouling of Crude Oil Preheat Exchangers
,”
Chem. Eng. Res. Des.
,
70
(
6
), pp.
547
557
.
12.
Zubair
,
S.
,
Sheikh
,
A.
,
Younas
,
M.
, and
Budair
,
M.
,
2000
, “
A Risk Based Heat Exchanger Analysis Subject to Fouling: Part I: Performance Evaluation
,”
Energy
,
25
(
5
), pp.
427
443
.
13.
Niaei
,
A.
,
Towfighi
,
J.
,
Sadrameli
,
S.
, and
Karimzadeh
,
R.
,
2004
, “
The Combined Simulation of Heat Transfer and Pyrolysis Reactions in Industrial Cracking Furnaces
,”
Appl. Therm. Eng.
,
24
(
14–15
), pp.
2251
2265
.
14.
Bahadori
,
A.
, and
Vuthaluru
,
H. B.
,
2010
, “
Novel Predictive Tools for Design of Radiant and Convective Sections of Direct Fired Heaters
,”
Appl. Energy
,
87
(
7
), pp.
2194
2202
.
15.
Stefanidis
,
G.
,
Merci
,
B.
,
Heynderickx
,
G.
, and
Marin
,
G.
,
2006
, “
CFD Simulations of Steam Cracking Furnaces Using Detailed Combustion Mechanisms
,”
Comput. Chem. Eng.
,
30
(
4
), pp.
635
649
.
16.
Oprins
,
A.
, and
Heynderickx
,
G.
,
2003
, “
Calculation of Three-Dimensional Flow and Pressure Fields in Cracking Furnaces
,”
Chem. Eng. Sci.
,
58
(
21
), pp.
4883
4893
.
17.
Heynderickx
,
G.
,
Oprins
,
A.
,
Marin
,
G. B.
, and
Dick
,
E.
,
2001
, “
Three-Dimensional Flow Patterns in Cracking Furnaces With Long-Flame Burners
,”
AIChE J.
,
47
(
2
), pp.
388
400
.
18.
Habibi
,
A.
,
Merci
,
B.
, and
Heynderickx
,
G.
,
2007
, “
Impact of Radiation Models in CFD Simulations of Steam Cracking Furnaces
,”
Comput. Chem. Eng.
,
31
(
11
), pp.
1389
1406
.
19.
Lan
,
X.
,
Gao
,
J.
,
Xu
,
C.
, and
Zhang
,
H.
,
2007
, “
Numerical Simulation of Transfer and Reaction Processes in Ethylene Furnaces
,”
Chem. Eng. Res. Des.
,
85
(
12
), pp.
1565
1579
.
20.
Hu
,
G.
,
Wang
,
H.
,
Qian
,
F.
,
Geem
,
K. V.
,
Schietekat
,
C.
, and
Marin
,
G.
,
2012
, “
Coupled Simulation of an Industrial Naphtha Cracking Furnace Equipped With Long-Flame and Radiation Burners
,”
Comput. Chem. Eng.
,
38
, pp.
24
34
.
21.
Morales-Fuentes
,
A.
,
Picón-Núñez
,
M.
,
Polley
,
G.
, and
Méndez-Díaz
,
S.
,
2014
, “
Analysis of the Influence of Operating Conditions on Fouling Rates in Fired Heaters
,”
Appl. Therm. Eng.
,
62
(
2
), pp.
777
784
.
22.
Jegla
,
Z.
,
Vondál
,
J.
, and
Hájek.
,
J.
,
2015
, “
Standards for Fired Heater Design: An Assessment Based on Computational Modelling
,”
Appl. Therm. Eng.
,
89
, pp.
1068
1078
.
23.
Wang
,
L.
, and
Pitsch
,
H.
,
2007
, “
Large-Eddy Simulation of an Industrial Furnace With a Cross-Flow-Jet Combustion System
,”
Center for Turbulence Research, Annual Research Briefs
, pp.
231
240
.
24.
Coelho
,
P.
, and
Carvalho
,
M.
,
1997
, “
A Conservative Formulation of the Discrete Transfer Method
,”
ASME J. Heat Transfer
,
119
(
1
), pp.
118
128
.
25.
Koch
,
R.
,
Krebs
,
W.
,
Wittig
,
S.
, and
Viskanta
,
R.
,
1995
, “
Discrete Ordinates Quadrature Schemes for Multidimensional Radiative Transfer
,”
J. Quant. Spectrosc. Radiat. Transfer
,
53
(
4
), pp.
353
372
.
26.
Fiveland
,
W.
,
1984
, “
Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures
,”
ASME J. Heat Transfer
,
106
(
4
), p.
699706
.
27.
Raithby
,
G.
,
1990
, “
A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures With Participating Media
,”
ASME J. Heat Transfer
,
112
(
2
), p.
415423
.
28.
Amaya
,
J.
,
Cabrit
,
O.
,
Poitou
,
D.
,
Cuenot
,
B.
, and
Hafi
,
M. E.
,
2010
, “
Unsteady Coupling of Navier–Stokes and Radiative Heat Transfer Solvers Applied to an Anisothermal Multicomponent Turbulent Channel Flow
,”
J. Quant. Spectrosc. Radiat. Transfer
,
111
(
2
), pp.
295
301
.
29.
Joseph
,
D.
,
Perez
,
P.
,
Hafi
,
M. E.
, and
Cuenot
,
B.
,
2009
, “
Discrete Ordinates and Monte Carlo Methods for Radiative Transfer Simulation Applied to Computational Fluid Dynamics Combustion Modeling
,”
ASME J. Heat Transfer
,
131
(
5
), p.
052701
.
30.
Liu
,
F.
,
Becker
,
H.
, and
Bindar
,
Y.
,
1998
, “
A Comparative Study of Radiative Heat Transfer Modelling in Gas-Fired Furnaces Using the Simple Grey Gas and the Weighted-Sum-of-Grey-Gases Models
,”
Int. J. Heat Mass Transfer
,
41
(
22
), pp.
3357
3371
.
31.
Claramunt
,
K.
,
Consul
,
R.
,
Carbonell
,
D.
, and
Perez-Segarra
,
C.
,
2006
, “
Analysis of the Laminar Flamelet Concept for Nonpremixed Laminar Flames
,”
Combust. Flame
,
145
(
4
), pp.
845
862
.
32.
Fiorina
,
B.
,
Gicquel
,
O.
,
Vervisch
,
L.
,
Carpentier
,
S.
, and
Darabiha
,
N.
,
2005
, “
Approximating the Chemical Structure of Partially Premixed and Diffusion Counterflow Flames Using FPI Flamelet Tabulation
,”
Combust. Flame
,
140
(
3
), pp.
147
160
.
33.
Liu
,
F.
,
Guo
,
H.
, and
Smallwood
,
G.
,
2006
, “
Evaluation of the Laminar Diffusion Flamelet Model in the Calculation of an Axisymmetric Coflow Laminar Ethylene-Air Diffusion Flame
,”
Combust. Flame
,
144
(
3
), pp.
605
618
.
34.
Bilger
,
R.
,
Starner
,
S.
, and
Kee
,
R.
,
1990
, “
On Reduced Mechanisms for Methane—Air Combustion in Nonpremixed Flames
,”
Combust. Flame
,
80
(
2
), pp.
135
149
.
35.
Bilger
,
R.
,
2010
, “
A Mixture Fraction Framework for the Theory and Modeling of Droplets and Sprays
,”
Combust. Flame
,
158
(
6
), p.
191202
.
36.
Poinsot
,
T.
, and
Veynante
,
D.
,
2005
,
Theoretical and Numerical Combustion
,
RT Edwards
,
Philadelphia, PA
, p.
522
.
37.
Bilger
,
R. W.
,
Yip
,
B.
,
Long
,
M. B.
, and
Masri
,
A. R.
,
1990
, “
An Atlas of QEDR Flame Structures
,”
Combust. Sci. Technol.
,
72
(
4–6
), pp.
137
155
.
38.
Abramowitz
,
M.
, and
Stegun
,
I.
,
1972
, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (National Bureau of Standards Applied Mathematics Series 55),
10th printing
,
Dover, New York
.
39.
Barlow
,
R. S.
,
Franck
,
J.
,
Karpetis
,
A.
, and
Chen
,
J.-Y.
,
2005
, “
Piloted Methane/Air Jet Flames: Transport Effects and Aspects of Scalar Structure
,”
Combust. Flame
,
143
(
4
), pp.
433
449
.
40.
Bilger
,
R. W.
,
1988
, “
The Structure of Turbulent Non Premixed Flames
,”
Symp. (Int.) Combust.
, pp.
475
488
.
41.
Goodwin
,
D. G.
,
2009
, Cantera code site.
42.
Poitou
,
D.
,
2009
, “
Modélisation du rayonnement dans la simulation aux grandes échelles de la combustion turbulente
,” Ph.D. thesis, INPT, Toulouse, France.
43.
Joseph
,
D.
,
Hafi
,
M. E.
,
Fournier
,
R.
, and
Cuenot
,
B.
,
2005
, “
Comparison of Three Spatial Differencing Schemes in Discrete Ordinates Method Using Three-Dimensional Unstructured Meshes
,”
Int. J. Therm. Sci.
,
44
(
9
), pp.
851
864
.
44.
Truelove
,
J.
,
1987
, “
Discrete-Ordinate Solutions of the Radiation Transport Equation
,”
ASME J. Heat Transfer
,
109
(
4
), pp.
1048
1051
.
45.
Lebedev
,
V.
,
1975
, “
Values of the Nodes and Weights of Ninth to Seventeenth Order Gauss–Markov Quadrature Formulae Invariant Under the Octahedron Group With Inversion
,”
USSR Comput. Math. Math. Phys.
,
15
(
1
), pp.
44
51
.
46.
Carlson
,
B.
, and
Lathrop
,
K.
,
1968
, “
Transport Theory—The Method of Discrete Ordinates
,”
Computing Methods in Reactors Physics
,
Gordon and Breach
,
New York
.
47.
Amaya
,
J.
,
2010
, “
Unsteady Coupled Convection, Conduction and Radiation Simulations on Parallel Architectures for Combustion Applications
,”
Ph.D. thesis
, INPT, Toulouse, France.
48.
Koch
,
R.
, and
Becker
,
R.
,
2004
, “
Evaluation of Quadrature Schemes for the Discrete Ordinates Method
,”
J. Quant. Spectrosc. Radiat. Transfer
,
84
(
4
), pp.
423
435
.
49.
Duchaine
,
F.
,
Corpron
,
A.
,
Pons
,
L.
,
Moureau
,
V.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2009
, “
Development and Assessment of a Coupled Strategy for Conjugate Heat Transfer With Large Eddy Simulation. Application to a Cooled Turbine Blade
,”
Int. J. Heat Fluid Flow
,
30
(
6
), pp.
1129
1141
.
50.
Kays
,
W.
,
Crawford
,
M.
, and
Weigand
,
B.
,
1993
,
Convective Heat and Mass Transfer
,
McGraw-Hill
,
New York
.
51.
Bejan
,
A.
, and
Kraus
,
A.
,
2003
,
Heat Transfer Handbook
,
Wiley
,
Hoboken NJ
.
52.
Lienhard
,
J.
,
Eichhorn
,
R.
, and
Lienhard
,
J.
,
1987
,
A Heat Transfer Textbook
,
Phlogiston Press
,
Cambridge MA
.
53.
Oosthuizen
,
P.
, and
Naylor
,
D.
,
1999
,
An Introduction to Convective Heat Transfer Analysis
,
William C. Brown Pub.
,
Dubuque, IA
.
54.
Viskanta
,
R.
, and
Mengüç
,
M. P.
,
1987
, “
Radiation Heat Transfer in Combustion Systems
,”
Prog. Energy Combust. Sci.
,
13
(
2
), pp.
97
160
.
55.
Pedot
,
T.
,
2012
, “
Modelisation du couplage thermique entre la combustion et l'encrassement des tubes dans un four de raffinerie
,” Ph.D. thesis, INPT, Toulouse, France.
56.
Enomoto
,
H.
,
Tsai
,
Y.
, and
Essenhigh
,
R.
,
1975
, “
Heat Transfer in a Continuous Model Furnace: A Comparison of Theory and Experiment
,”
ASME
Paper No. 75-HT-5.
57.
Hottel
,
H.
, and
Sarofim
,
A. F.
,
1967
,
Hottel and Sarofim Radiative Transfer
,
McGraw-Hill Book Company
, New York.
58.
Wauters
,
S.
, and
Marin
,
G. B.
,
2002
, “
Kinetic Modeling of Coke Formation During Steam Cracking
,”
Ind. Eng. Chem. Res.
,
41
(
10
), pp.
2379
2391
.
You do not currently have access to this content.