Étude techno-économique de la récupération de
chaleur dans les effluents gazeux des cuves
d’électrolyse d’une aluminerie
Mémoire
François Jordana
Maîtrise en Génie Mécanique
Maître ès sciences (M.Sc.)
Québec, Canada
Résumé
L’objectif de cette étude est de proposer des stratégies de récupération de chaleur au sein d’une aluminerie en se basant sur des considérations techniques et économiques. Après analyse des principaux postes de pertes de chaleur de l’aluminerie, l’étude foca-lise sur une source particulière : les effluents gazeux issus des cuves d’électrolyse. Deux applications sont envisagées et analysées dans deux articles scientifiques : le chauf-fage de bâtiments dans l’aluminerie, et le chaufchauf-fage d’une serre. Dans les deux cas, une modélisation dynamique de la demande de chauffage est proposée, accompagnée d’un dimensionnement détaillé des échangeurs de chaleur et des équipements. Puis, une optimisation est réalisée pour minimiser les coûts de capital et d’opération de l’implan-tation. Enfin, des cas d’étude sont proposés afin d’analyser la variabilité des solutions retenues.
Abstract
The objective of this study is to propose heat recovery strategies in a primary aluminum smelter by considering technical and economic aspects. After analyzing the various heat sources and sinks, it was decided to focus the study on the flue gases exiting the electrolysis cells. Two applications are envisioned and presented in two scientific articles: heating buildings within the aluminum smelter, and heating a greenhouse. In both cases, a dynamic model of heating requirement is proposed, associated to the detailed design of heat exchangers and equipment. Then, an optimization is performed to minimize the implementation capital and operation costs. Last, several case studies are presented in order to analyze the variability of the retained solutions.
Table des matières
Résumé iii
Abstract v
Table des matières vii
Liste des tableaux xi
Liste des figures xiii
Nomenclature xv Remerciements xix Avant-propos xxi Chapitre 1 : Introduction 1 1.1 Problématique . . . 1 1.1.1 Mise en contexte . . . 1 1.1.2 Présentation du procédé . . . 2
1.1.3 Présentation de l’aluminerie Alcoa Deschambault . . . 4
1.1.4 Cartographie des sources/puits de chaleur . . . 6
1.2 Objectifs . . . 7
1.2.1 Objectif principal . . . 7
1.2.2 Objectifs secondaires . . . 8
1.3 Méthode et présentation du document . . . 8
1.3.1 Chapitre 2 - Étude techno-économique de la récupération de cha-leur des effluents gazeux d’une aluminerie pour le chauffage de bâtiments . . . 9
1.3.2 Chapitre 3 - Étude techno-économique de la récupération de cha-leur des effluents gazeux d’une aluminerie pour le chauffage d’une serre . . . 10
Chapitre 2 : Article #1 11 Résumé . . . 12
2.1 Introduction . . . 12
2.2 Problem formulation and proposed design methodology . . . 14
2.3 Modeling and cost estimation . . . 16
2.3.1 Heat transfer and pressure drop calculations . . . 17
2.3.2 Capital cost . . . 18
2.3.3 Operational cost . . . 19
2.3.4 Total cost . . . 20
2.4 Calculation procedure . . . 21
2.4.1 Strategy for accommodating transient conditions (off-design ope-ration) . . . 21
2.4.2 Main steps of the design strategy . . . 22
2.4.3 Constraints . . . 24
2.4.4 Genetic algorithm optimization . . . 25
2.5 Case study : Waste heat recovery from aluminum electrolytic cells for heating buildings . . . 26
2.5.1 Waste heat recovery from aluminum electrolytic cells . . . 26
2.5.2 Technology selection and localization . . . 27
2.5.3 Materials selection and corrosion prevention . . . 28
2.5.4 Heat recovery system integration . . . 30
2.6 Optimal design under current conditions . . . 31
2.7 Effects of the main problem parameters . . . 33
2.7.1 Fouling resistance . . . 33
2.7.2 Impact of pot ventilation reduction . . . 34
2.7.3 Impact of energy price . . . 36
2.7.4 Configuration with gases in the shell . . . 36
2.8 Conclusion . . . 37
Chapitre 3 : Article #2 39 3.1 Introduction . . . 40
3.2 Heat recovery system from the aluminum smelter perspective . . . 42
3.3 Heat recovery system from the greenhouse perspective. . . 46
3.3.1 Greenhouse heat transfer model . . . 46
3.3.2 Internal gains . . . 48
3.3.3 Climate regulation . . . 49
3.4 Synergetic cost estimation . . . 51
3.4.1 Global costs estimation . . . 51
3.4.2 Synergistic cost distribution . . . 53
3.5 Optimization procedure . . . 54
3.5.1 Step-by-step calculation procedure . . . 54
3.5.2 Genetic algorithms . . . 56
3.5.3 Constrains . . . 56
3.6 Optimal solution for the reference scenario . . . 57
3.7 Effect of the energy cost . . . 59
3.8 Effect of the localization . . . 60
3.10 Conclusion . . . 62
Chapitre 4 : Conclusion 63
Liste des tableaux
1.1 Composition des effluents gazeux issus des cuves . . . 5
2.1 Capital cost factors expressed as a percentage of the equipment purchase . 19
2.2 Constraints according to the formulation of Eq. 2.14 for the optimization problem . . . 24
2.3 Resulting optimal designs . . . 33
3.1 Characteristics of the reference case greenhouse . . . 48
3.2 Optimal design characteristics for the reference case and for the localization in Iceland . . . 59
Liste des figures
1.1 Schéma d’une cuve d’électrolyse . . . 2
1.2 Schéma du procédé de production . . . 3
1.3 Alcoa Deschambault Québec (ADQ) . . . 4
1.4 Température extérieure au cours de l’année 2012 mesurée à l’Université La-val, Québec . . . 5
1.5 Puissances extractibles pour les différentes sources de rejets thermiques et besoins en chaleur . . . 6
2.1 Schematic representation of the heat recovery system with parallel heat ex-changers . . . 14
2.2 Overall heat recovery system design procedure . . . 23
2.3 Main components of a typical aluminum electrolytic cell . . . 26
2.4 Space heating requirement qn as a function of the outdoor temperature,
along with the recovered and backup heat transfer rates qr and qbackup for
the optimized design . . . 30
2.5 Chart of annualized costs and savings for the optimal designs . . . 32
2.6 Fluids temperature as a function of the outdoor temperature for the optimal design . . . 34
2.7 Impact of tube-side fouling resistance on minimized annualized costs and savings . . . 35
2.8 Impact of cell ventilation airflow rate on minimized annualized costs and savings . . . 36
2.9 Impact of energy price on minimized annualized costs and savings . . . 37
3.1 Schematic representation of a typical Hall-Héroult electrolysis cell. . . 43
3.2 Layout of the collaborative heat integration system with both partners. . . 46
3.3 TRNSYS model used to calculate the greenhouse heating requirements. . . 47
3.4 Heat balance in the greenhouse model . . . 49
3.5 Step-by-step cost calculation and optimization procedure.. . . 55
3.6 Savings for the greenhouse as a function of those for the smelter in the optimized collaborative heat integration (Pareto front). . . 57
3.7 Optimal cost distribution for the reference case, and for another localization. 58
3.8 Impact of the energy price on the profitability. . . 60
Nomenclature
A heat exchanger area (m2)
ADQ Alcoa Deschambault Québec
C cost (CA$)
CC capital cost (CA$)
Cp heat capacity (J kg–1 K–1)
dpipe pipe diameter (m)
es saturation vapour pressure for a given time period (kPa)
ea actual vapour pressure (kPa)
ETo water volume evapotranspirated (m s–1)
F correction factor f capital cost factor
G ground heat flux (W m–2)
GTC Gas Treatment Center HE heat exchanger
h convection coefficient (W m–2 K–1)
i interest rate (%)
k thermal conductivity (W m–1 K–1)
M penalty cost (CA $) ˙
m fluid mass flow rate (kg s–1)
OC operation cost (CA $)
PSAT saturated liquid-vapor pressure (Pa)
p partial pressure (Pa) q heat transfer rate (W) Q transferred heat (Wh)
R” surface fouling resistance (m2 K W–1)
r resistivity (s m–1)
T temperature (°C)
TCC total capital cost ($ y–1)
U overall heat transfer coefficient (W m–2 K–1)
V flow velocity (m s–1)
Greek symbols
∆ rate of change of saturation specific humidity with air temperature (Pa K–1)
∆Tlm log-mean temperature difference (°C) γ psychrometric constant (Pa K–1)
effectiveness
λ latent heat of vaporization (J kg–1) χ energy price (CA $)
η efficiency
Subscripts
Al relative to aluminum smelter a relative to the dry air
c cold-fluid side
ext outdoor
Gr relative to greenhouse
g gas-side
h hot-fluid side
i inlet of the exchanger
j jth element
o outlet of the exchanger
op operation
r recovered
s shell-side or stoma sat saturation vapor
t tube-side
w water-side or wall Superscripts
A annual cash flow ($ y–1)
Remerciements
De prime abord, je souhaite remercier mon directeur de recherche, Louis Gosselin, qui a su me guider dans mes recherches, m’encourager et me donner tout l’appui nécessaire pour mener à bien cette maîtrise. Son soutien aura été admirable et indéfectible, je l’en remercie.
Je tiens ensuite à remercier chaleureusement tous les étudiants du Laboratoire de Trans-fert Thermiques et d’Energétique (LTTE). Ce fut un plaisir de travailler aux côtés de Jean-Michel Dussault, Maxime Tye Gingras, Raphaël Croteau, Jean Rouleau, Ruijie Zhao, Nicolas Blanchette, Michael Cain Skaff, Félix Robert, Christian Chabot, Jona-than Dallaire, François Mathieu Potvin, et Olivier Lassagne. Leur appui au quotidien a été remarquable, je les en remercie. Une mention spéciale à Jean-Michel qui m’a beaucoup aidé dans l’élaboration du modèle de serre sur Trnsys.
Je souhaite également remercier Damien De Halleux et Nicolas Pelletier de la Faculté des sciences de l’agriculture de l’alimentation pour toute l’information et les conseils qu’ils m’ont apportés lors de l’élaboration du modèle thermique de la serre.
De plus, je tiens à remercier le Fonds Québécois de la Recherche sur la Nature et les Technologies pour le soutien financier qui m’a été accordé et sans lequel tout ceci n’aurait pas été possible.
Enfin, je souhaite remercier ma famille et mes amis qui ont su me soutenir aux cours de ces deux années. Vous avez contribué vous aussi à la réussite de cette belle aventure.
Avant-propos
Les deux articles formant le corps de ce mémoire ont été coécrits par l’auteur du mé-moire, François Jordana, et son directeur de recherche, Louis Gosselin. Les recherches, la programmation numérique des modèles, les simulations numériques, le traitement des résultats et l’essentiel des textes d’articles ont été effectués par François Jordana, qui en est l’auteur principal. La collaboration du co-auteur Louis Gosselin s’est avé-rée indispensable dans la supervision des travaux de recherche, l’appui à l’analyse des résultats ainsi que dans l’aide à la rédaction et à la correction des articles. Les deux articles sont présentement soumis pour publication. De leur version originale, seulement des modifications de forme ont étés apportées aux articles afin d’en faciliter la lecture dans le mémoire : les numéros des tableaux et figures ont été modifiés en suivant la numérotation des sections du mémoire, la numérotation des références bibliographiques est adaptée à l’ordre de présentation du mémoire et la mise en page des articles a été ajustée dans le but d’être conforme aux exigences de la Faculté des études supérieures et postdoctorales.
Chapitre 1 : Introduction
1.1
Problématique
1.1.1
Mise en contexte
Au cours de la dernière décennie, l’exploitation de ressources d’hydrocarbures non-conventionnels tels que les gaz de schistes a considérablement modifié le paysage éner-gétique mondial. Dans son rapport annuel [1], l’Agence Internationale de l’Énergie (AIE) estime que les États-Unis deviendront le premier producteur de pétrole d’ici 2015, devant l’Arabie Saoudite et la Russie. À cela, viennent s’ajouter les besoins éner-gétiques croissants des grandes puissances émergentes (BRICS : Brésil, Russie, Inde, Chine, Afrique du Sud). Le marché mondial de l’énergie est ainsi amené à se transformer profondément au cours des prochaines années.
Dans un marché de plus en plus mondialisé et inter-connecté, ce premier constat im-plique de lourdes conséquences sur la compétitivité des industries qui consomment de grandes quantités d’énergie. La rentabilité de ces entreprises n’est pas uniquement liée aux prix locaux de l’énergie, mais aussi aux prix de l’énergie dans d’autres régions du monde. Cette problématique est notamment visible pour les producteurs d’aluminium primaire dans la province du Québec (Canada).
L’industrie québécoise de l’aluminium représente près de 10,000 emplois directs, 20,000 emplois indirects et 10% des exportations de la province [2]. Source de revenus im-portants pour le Québec, cette industrie est à la pointe en terme de productivité, de rémunérations, d’efficacité énergétique et de réduction de gaz à effet de serre. Cepen-dant, la nouvelle donne énergétique mondiale place le Québec dans la fourchette haute des prix de l’énergie comme le révèle le mémoire publié par l’Association de l’Alumi-nium du Canada (AAC) [2]. Or, près de 13 MWh sont nécessaires pour produire une tonne d’aluminium, et il est estimé que le coût de l’énergie représente près de 35% du
coût de production de l’aluminium primaire. La compétitivité de ces industries est donc directement liée au prix d’achat de l’énergie.
Au moment de déposer ce mémoire, les alumineries sont en négociation avec le gouver-nement provincial afin de déterminer les conditions d’achat de l’énergie hydro-électrique produite par Hydro-Québec [3]. Une hausse de 60% des tarifs d’électricité réservés aux alumineries était prévue, mais ces dernières souhaitent continuer à profiter d’un tarif modulé en fonction du prix de l’aluminium sur les marchés internationaux.
Dans une perspective de réduction des coûts de production, deux solutions peuvent alors être envisagées : l’amélioration de la productivité, et/ou le changement de lieu de production. Ce projet de maîtrise se situe dans la première solution, et focalise sur la production d’aluminium primaire.
1.1.2
Présentation du procédé
L’aluminium est un métal très abondant sur Terre. Il représente en moyenne 8 % de la masse des matériaux de la surface solide de notre planète. Cependant, il ne se présente pas sous sa forme pure, mais sous sa forme oxydée : l’alumine. Cet oxyde se trouve en grandes quantités dans un minerai rouge, la bauxite. L’alumine est extraite de la bauxite par un procédé d’affinage dit de Bayer.
Figure 1.1 – Schéma d’une cuve d’électrolyse
Il s’agit ensuite d’effectuer la réduction de l’alumine par le procédé électrolytique de Hall-Héroult, pour obtenir de l’aluminium. Deux tonnes d’alumine sont nécessaires pour produire une tonne d’aluminium. Au cours du procédé de Hall-Héroult, l’alumine est
réduite selon la réaction suivante :
2Al2O3(solution)+ 3C(solide) →4Al(liquide)+ 3CO2(gaz) (1.1)
L’électrolyse est effectuée dans des cuves semblables à celle présentée à la Figure 1.1. L’alumine est tout d’abord dissoute dans un bain fluoré à près de 960°C [4]. Puis, un fort courant électrique continu (entre 100,000 à 400,000 ampères) circule entre les anodes et la cathode, entraînant la formation d’aluminium au niveau de la cathode et de dioxyde de carbone à l’anode. Toutes les cuves d’électrolyse (souvent plusieurs centaines) sont connectées en série afin de bénéficier d’un courant maximal. Les anodes sont issues de la cuisson d’un mélange de coke et de brai.
Une fois l’aluminium obtenu, il est siphonné au fond de la cuve, puis envoyé dans des fours de maintien. Il est ensuite coulé sous la forme de lingots, en gros blocs, en barres en T, ou en longs cylindres à des températures d’un peu plus de 700°C (voir Fig. 1.2). Au cours de processus de production, il est généralement estimé que près de la moitié de l’énergie consommée par l’aluminerie est perdue sous forme de chaleur[5]. Il apparaît donc intéressant de chercher à récupérer et valoriser ces rejets. Dans la suite de ce mémoire, nous allons nous intéresser à l’aluminerie Alcoa Deschambault Québec.
Salle des cuves
Coke Pitch Anodes Alumine Four de maintien Centre de coulée Lingots Réseau électrique Effluents gazeux
1.1.3
Présentation de l’aluminerie Alcoa Deschambault
Située à une centaine de kilomètres de Québec, l’aluminerie Alcoa Deschambault Qué-bec (ADQ) (voir Fig.1.3, Réf. [6]) produit chaque année près de 260 000 tonnes d’alu-minium sous forme de lingots. L’usine compte 264 cuves d’électrolyse de type AP30, chacune composée de 40 anodes. Chaque cuve est ventilée par un débit d’air d’environ 2.4 Nm3/s/cuve (Nm3 étant le voulme normalisé aux conditions de pression et
tempé-rature normales, i.e. 1.013×102 Pa et 15°C) permettant de diluer le dioxyde de carbone
à des concentrations entre 1 et 2%. Dans toute la suite du mémoire, lorsque l’on parlera d’« effluents gazeux », il sera fait référence aux gaz issus des cuves d’électrolyse.
Figure 1.3 – Alcoa Deschambault Québec (ADQ)
Les effluents gazeux contiennent des substances chimiques toxiques et corrosives telles que le fluorure d’hydrogène HF, et le dioxyde de souffre SO2. Le tableau 1.1 répertorie
les espèces présentes et leurs concentrations [7]. Afin de retirer le fluorure d’hydrogène, les effluents gazeux sont collectés dans de larges conduites et amenés jusqu’au Centre de Traitement des Gaz (GTC). La quasi-totalité (plus de 99.5 %) des HF est retirée, permettant ainsi de relâcher les effluent gazeux dans l’atmosphère.
Table 1.1 – Composition des effluents gazeux issus des cuves Espèces Masse moléculaire (g/mol) Fraction Molaire (%)
Air (g) 28.966 97.8600 CO2 (g) 44.01 1.6300 CO (g) 28.011 0.3900 HF (g) 20.01 0.0280 SO2 (g) 64.06 0.0270 AL2O3 (s) 101.96 0.0360 AlF3 (g) 83.98 0.0175 Suies (s) 12.01 0.0017
Par ailleurs, cette aluminerie doit faire face à des conditions climatiques très variables comme le montre la Fig. 1.4, issue des données météorologies fournies par le Dépar-tement des sols et de génie agroalimentaire de l’Université Laval. La température ex-térieure moyenne est de 4.5°C, avec environ 4 300 degrés-jour de chauffage annuels (référence : 18°C). Les températures sur une année varient entre –33°C et 31°C, ce qui impose des règles de conception assurant une robustesse suffisante des systèmes.
-30 -20 -10 0 10 20 30 40 janvi er févri er
mars avril mai juin juillet août septe mbre octobre nove mbre déce mbre T emp ér atu re e xté ri eu re (° C )
Figure 1.4 – Température extérieure au cours de l’année 2012 mesurée à l’Université Laval, Québec
1.1.4
Cartographie des sources/puits de chaleur
Un inventaire des « sources » et des « puits » d’énergie présents dans l’aluminerie a été mené au cours d’un précédent projet de maîtrise par Cassandre Nowicki. Deux articles publiés ([5] et [8]) présentent et analysent les possibilités de couplage en se basant sur la théorie de l’exergie. L’exergie constitue le travail utile que l’on peut obtenir à partir d’une source d’énergie. Une étude éxergétique est proposée afin de déterminer la qualité de la chaleur disponible dans l’aluminerie de Deschambault. La figure 1.5 présente les différentes sources d’énergies exploitables ainsi que les systèmes qui en requièrent [5].
3 5 4 6 2 1 1 2 3 4 5 6 7 8 9 1E-2 1E-1 1E+0 1E+1 1E+2 0 100 200 300 400 500 600 Heat transfer rate (MW) Temperature (°C)
1. Air compressor cooling loop 2. Casting water
3. Potline exhaust gas
4. Baking furnace exhaust (w/ exfiltrations) 5. Pot sidewalls
6. Holding furnace chimneys !
1. Gate house
2. Administration building
+ Mobile equipment storage and repair + Potline annexes and crudible cleaning + Warehouse and central maintenance shop 3. Potline to baking sector corridor 4. Cast house
5. PTM crane repair, pot lining and re-lining 6. Paste plant coke pre-heaters
7. Cast house pre-heaters
8. Hypothetical alumina pre-heating 9. Hypothetical anode pre-heating
102! 101! 100! 10%1! 10%2! ! Extractable!heat! ! Space!hea2ng!sinks! ! Other!heat!Sinks!
Figure 1.5 – Puissances extractibles pour les différentes sources de rejets thermiques et besoins en chaleur
On peut constater que les puissances disponibles sont très importantes mais que les températures sont relativement faibles pour la récupération de chaleur. De plus, les systèmes qui requièrent un apport en énergie thermique sont à la fois peu nombreux et peu énergivores. Cette conclusion constitue le principal obstacle à la récupération de chaleur. Des cycles organiques de Rankine seraient capables de récupérer une partie de cette chaleur [8], mais en raison de leurs coûts, il serait préférable de chercher à la réutiliser directement.
De plus, les alumineries souhaitent augmenter l’ampérage utilisé pour l’électrolyse afin d’augmenter la productivité des cuves. Ceci s’accompagne d’un augmentation de la température des effluents gazeux qu’il faut alors davantage refroidir. En effet, la tem-pérature de gaz doit demeurer inférieure à 120°C à l’entrée du GTC pour des raisons d’efficacité de la capture des HF [9]. Actuellement à ADQ, les gaz sont refroidis si requis par augmentation du débit d’air entrant - c’est ce que l’on appelle la dilution. Cepen-dant, cela augmente par la même occasion les coûts de pompage. Par conséquent, la récupération de chaleur apparaît comme une solution prometteuse permettant à la fois de refroidir les gaz et de réutiliser la chaleur.
Le présent projet de maîtrise focalise sur un couplage : les effluents gazeux à la sortie des cuves d’électrolyse afin de chauffer des bâtiments. C’est un couplage encore peu utilisé dans l’industrie. Quelques prototypes d’échangeurs de chaleur ont déjà été pré-sentés dans la littérature (voir [10] et [9]), mais leur utilisation est très peu répandue. Les bâtiments pourront être soit internes à l’aluminerie (bâtiments administratifs et industriels), ou bien externes. Dans ce cas, une collaboration devra être imaginée entre l’aluminerie et une entité externe. Typiquement, du chauffage résidentiel peut être envi-sagé ; cependant, dans le cas de ADQ, il n’existe pas de réseau de chauffage urbain dans les environs, ni de zones résidentielles à proximité pouvant utiliser la chaleur récupérée. Une autre solution potentielle serait de vendre cette chaleur à une autre industrie. Le choix s’est rapidement orienté vers une industrie qui nécessite de très grandes quantités d’énergie à faibles températures : les serres de tomates [11].
Au Québec, il est estimé que près de 300 W/m2 sont requis pour chauffer une serre.
Les serres locales de production de tomates faisant plusieurs hectares [11], l’attrait d’une source de chauffage au tarif moins élevé que celui du marché pourrait inciter des producteurs à collaborer avec des alumineries. Un partenariat semblable a d’ailleurs été mis en place entre le producteur de tomates Savoura et un site d’enfouissement à proximité de Saint-Etienne-des-Grès, afin de chauffer la serre de 52 000 m2 avec du
biogaz.
1.2
Objectifs
1.2.1
Objectif principal
L’objectif principal de ce projet de maîtrise est de proposer une solution technique et économiquement viable, afin de récupérer et réutiliser la chaleur contenue dans les
effluents gazeux à la sortie des cuves d’électrolyse. Il s’agira de développer des outils de dimensionnement capables de tenir compte des variations temporelles de l’offre et de la demande, ainsi que des contraintes du problème. En effet, les valeurs proposées dans la Figure 1.5 sont calculées pour le site de Deschambault au mois de janvier. Or comme le montre la Fig. 1.4, les conditions varient sensiblement au cours d’une année. Par conséquent, le design et l’intégration d’un système de récupération de chaleur devront tenir compte de l’aspect transitoire de la source de chaleur et du chauffage des bâtiments.
1.2.2
Objectifs secondaires
Cet objectif principal peut être subdivisé en plusieurs sous-objectifs :
? Développer une méthode de dimensionnement et de régulation d’un réseau d’échangeurs de chaleur. Le dimensionnement des systèmes devra tenir compte des contraintes inhérentes au procédé telles que le caractère corrosif des effluents gazeux et les contraintes de température au niveau du GTC.
? Développer une méthode d’estimation des coûts de capital et d’opérations de l’implantation. Dans le cas d’une serre, il s’agira de développer une méthode de répartition des coûts entre les deux partenaires.
? Modéliser les besoins en chauffage des bâtiments et de la serre en fonction du temps. En particulier, il conviendra de développer un système de contrôle des conditions climatiques de la serre, et de calculer les besoins en chauffage pour chaque heure de l’année.
? Minimiser le coût total de l’implantation au moyen d’un algorithme génétique à un objectif dans le cas du chauffage des bâtiments de l’aluminerie, et à deux objectifs dans le cas du partenariat avec la serre.
? Effectuer une étude de sensibilité des principaux paramètres. En effet, étant donné que toutes les considérations proposées dans ce mémoire ne sont we théoriques et non expérimentales, il s’agira de veiller à la validité des données utilisées.
1.3
Méthode et présentation du document
La démarche suivie au cours de ce projet de maîtrise s’est divisée en deux phases successives, correspondant respectivement au chauffage des bâtiments de l’aluminerie et d’une serre. Les approches utilisées pour atteindre les différents sous-objectifs présentés précédemment sont développées pour chacun de ces deux axes.
L’originalité de cette étude est à la fois de développer des outils de conception et d’op-timisation, mais aussi d’appliquer cette méthodologie au cas particulier de l’aluminerie de Deschambault. Cette démarche peut aisément être reproduite pour d’autres sys-tèmes, climats et applications. De plus, cette étude vise à répondre aux interrogations exprimées par l’industrie concernant la viabilité économique de tels projets.
Le mémoire est présenté sous forme de deux articles scientifiques rédigés par l’auteur. Les articles sont présentement soumis auprès de journaux spécialisés. Les deux articles sont présentés aux Chapitres 2 et 3. Ils traitent respectivement du chauffage des bâti-ments de l’aluminerie et du chauffage d’une serre.
1.3.1
Chapitre 2 - Étude techno-économique de la
récupération de chaleur des effluents gazeux d’une
aluminerie pour le chauffage de bâtiments
Cette section est regroupée dans le premier article rédigé par l’auteur du mémoire. Il constitue le premier axe du projet de maîtrise : le chauffage des bâtiments de l’alumi-nerie. Ce premier article a été écrit dans le but de développer une méthode de dimen-sionnement généralisable à d’autres applications. Les premières sections présentent les équations régissant les échanges thermiques, la modélisation des besoins en chauffage ainsi que les méthodes d’estimations de coûts utilisées. Une stratégie de régulation au cours du temps du réseau d’échangeurs est proposée pour ajuster la récupération de chaleur aux besoins des bâtiments. L’aspect transitoire est traité grâce à la méthode des degrés-jours, ce qui limite considérablement le temps de calcul. Par ailleurs, un système d’appoint est considéré afin de se laisser la possibilité de sous-dimensionner le réseau d’échangeurs. En effet, dimensionner pour le pire scenario n’est pas nécessaire-ment le plus rentable. Ensuite, un algorithme génétique génère des designs à partir des variables et des contraintes du problème. Pour chaque design, la procédure de calcul estime les coûts annualisés de capital et d’opérations. Cette procédure est alors réitérée pour minimiser le coût total annualisé de l’implantation.
Dans un second temps, la méthodologie et la procédure de calcul sont appliquées au cas de l’aluminerie ADQ dans le but de chauffer ses bâtiments. Les résultats obtenus sont alors présentés pour déterminer la viabilité du projet. Une étude de sensibilité est finalement proposée pour quatre paramètres cruciaux : la résistance thermique d’en-crassage, la ventilation dans les cuves, le coût de l’énergie et le changement des fluides dans les échangeurs.
1.3.2
Chapitre 3 - Étude techno-économique de la
récupération de chaleur des effluents gazeux d’une
aluminerie pour le chauffage d’une serre
Cette section est regroupée dans le second article rédigé par l’auteur du mémoire. Il constitue le second axe du projet de maîtrise : le chauffage d’une serre.
Dans ce second article, la méthodologie développée est sensiblement la même que celle du première article, à la différence près que l’échelle de temps utilisée est d’une heure. Un modèle de serre est développé afin de déterminer les besoins en chauffage d’une serre de 200 × 200 m2 en tenant comptes des données climatiques propres à Deschambault.
Ce modèle de serre est développé sur TRNSYS, un logiciel de calculs transitoires pour les bâtiments. Une stratégie de contrôle qui régule les systèmes de ventilation externe, d’humidification / déshumidification, et de rideaux est implantée afin de maintenir les conditions de température et d’humidité favorables au développement des cultures. Fi-nalement, ce modèle donne accès aux besoins en chauffage pour chaque heure de l’année. Cette information est alors utilisée par la procédure d’optimisation pour dimensionner le réseau d’échangeurs de chaleur le plus économique. Là encore, un système d’appoint est associé à la récupération de chaleur.
Dans le cas de la synergie, deux optimisations par algorithme génétique sont effectuées et comparées : une optimisation à un objectif minimisant le coût total, et une optimi-sation à deux objectifs minimisant à la fois les coûts pour l’aluminerie et pour la serre. La première option ne tient pas compte de la vente de l’énergie par l’aluminerie à la serre, alors que la deuxième s’intéresse au prix de la vente. Les résultats obtenus sont présentés sous la forme d’un front de Pareto. Finalement, une étude de sensibilité est proposée afin de déterminer la taille de serre optimale ainsi que l’impact du coût de l’énergie et du climat.
Chapitre 2 : Article #1
Techno-economic design optimization of
waste heat recovery systems with
time-varying supply and demand, with
application to primary aluminum
production
Co-auteurs :
François Jordana, Louis Gosselin
Article soumis le 14 juin 2014 au journal Energy Conversion and Management
Résumé
Grandes consommatrices d’énergie, les industries rejettent de grandes quantités de cha-leur. De fait, la récupération de chaleur représente un potentiel de réduction de leur consommation énergétique et de leur empreinte environnementale. Cet article présente une méthode pour le dimensionnement, l’optimisation et l’intégration d’échangeurs de chaleur de type tubes et calandre afin de récupérer de la chaleur. Basée sur une évalua-tion des coûts, cette approche a pour objectif de déterminer les condiévalua-tions de dimension-nement optimales et de dimensionner un réseau d’échangeurs de chaleur en associant à la fois les données climatiques, les aspects transitoires, les besoins énergétiques, les pertes de charge, l’encrassage et la corrosion. Cette méthodologie est appliquée à une usine de production d’aluminium primaire, Alcoa Deschambault Québec (ADQ). Des investigations sont menées pour déterminer la viabilité économique d’utiliser la cha-leur contenue dans les effluents gazeux issus des cuves d’électrolyse afin de chauffer les bâtiments de l’aluminerie.
Abstract
Energy intensive industries often reject a significant amount of waste heat. Conse-quently, heat recovery is a potential solution to reduce their overall energy consump-tion and environmental footprint. This paper presents a method to design, optimize and integrate shell-and-tube heat exchangers to recover waste heat, considering transient off-design aspects. Based on cost evaluation, the approach determines the best design conditions, and sizes heat exchangers accordingly considering climate data, power re-quirement, pressure drop, fouling, and corrosion. As a case study, this methodology is applied to a primary aluminum smelter. Investigations are led to determine the econo-mic viability of recovering waste heat from pots exhaust gases and reusing it for space heating within the plant.
2.1
Introduction
In industrialized countries, the industrial sector accounts for a wide part of the total energy consumption. In Canada, it constitutes roughly half of the total annual energy consumption [12], and in the U.S., it represents nearly one-third [13]. Since the cost of energy in manufacturing industries has a crucial impact on the production cost, the volatility of energy prices has led energy intensive industries to constantly improve the
efficiency of their processes. Actually, it is estimated that nearly 75% of all Canadian industrial energy consumption is dedicated to process heat [12]. However, it is worth mentioning that between 20 and 50% of this heat is lost as waste heat contained in flue streams [13]. These facts reveal an economical and environmental opportunity to take advantage of this residual heat in industries.
Heat integration is a common strategy adopted to improve energy efficiency. According to the International Energy Agency (IEA), the combination of heat recovery and process improvement represents a potential benefit in terms of global energy efficiency between 18 and 26% [14]. Reference [15] presents an overview of the economic and environmental potential of heat recovery.
Depending on the quality of available waste heat, different strategies can be imple-mented for heat recovery. For example, high-enthalpy waste heat can be harvested by thermoelectric heat exchangers [16] [17]. Organic Rankine Cycles (ORC) may also pro-vide interesting solutions to generate electricity out of the waste heat as presented in references [18] and [19]. However, in industrial processes, waste heat often exhibits large fluxes but low temperatures, thus limiting heat recovery possibilities. Therefore, when it is possible, a direct integration within the process itself (for example in Ref. [20] ) or with another system requiring low-enthalpy energy could be preferable ; the latter being the strategy retained in the current paper. Most of the time, this requires transferring heat to another fluid via heat exchangers (HE), the design of which can be optimized in order to maximize the overall energy, economic and environmental benefits. In [21], a methodology is developed to determine the best type of HEs according to the ap-plication envisioned. Furthermore, since several HEs may be required, it is worth to pay attention to the conception and optimization of the network, as presented, among others, in [22], [23] and [24].
Heat recovery projects have to conciliate both technical feasibility and economic viabi-lity. As described below, this article is meant to provide a methodology to design heat recovery systems in order to minimize the overall cost of such a project, by including several considerations that are often disregarded. In particular, the transient features associated to the waste heat source and to the heat sink are taken into account. In the second part of the paper, the procedure is applied to the recovery of waste heat from the exhaust gases of an aluminum smelter to heat buildings.
2.2
Problem formulation and proposed design
methodology
Most methods to design waste heat recovery equipment and thermal integration layouts are based on a steady-state analysis. In other words, these methods suppose that the availability and the demand of waste heat are not changing with time. Although this proves correct in several contexts, there is a wide range of industrial applications for which either the temperature or the flow rate of streams from which heat is to be recovered from, or delivered to, is not constant. This section formulates mathematically a methodology to size and design waste heat recovery equipment in such conditions.
To GTC From pots From buildings To buildings h,o T , c i T c m! c,o T h,i T h m! q HE
Figure 2.1 – Schematic representation of the heat recovery system with parallel heat exchangers
Consider a hot stream with a mass flow rate ˙mh and temperature Th. Both quantities
can change in time. In this paper, we assume that in the absence of a thermal integration initiative, the hot stream would simply be dissipated in the environment. Heat is to be recovered from this stream in order to satisfy a given need, which can be formulated in different ways. Here, we assumed that the recovered energy will be used to heat a cold stream ˙mc from a temperature Tc,i to a temperature Tc,o. Again, these quantities
can be functions of time. The problem is schematized in Fig.2.1, with the hot stream in red, and the cold one, in blue. As shown, several heat exchangers in parallel could
be used to facilitate the adaptation of the heat recovery system to transient changes of the operating conditions. Additionally, for convenience we indicated in Fig. 2.1 to which particular component the hot and cold streams are linked in the test case that will be described later : in the test case, the hot stream is constituted by the exhaust gases of electrolytic pots and is transported to the gas treatment center (GTC), while the cold stream is used to provide heat to buildings (see Section 2.5 for more details). Our objective is to minimize the total cost of the waste heat recovery project, which includes the capital cost (i.e., purchase of heat exchangers, piping, installation, etc.) as well as the operating cost (i.e., pumping, backup heating/cooling, maintenance, etc.). Sizing such a system is not trivial. If the equipment is sized for the “worst case scenario”, it could be able to recover enough heat from the hot stream at all time to satisfy entirely the heating need of the cold stream. However, most of the time, the system will be “under-used”, and the important invested capital required to achieve a design satisfying all heating needs leads to a long payback period. On the other hand, too small a heat recovery system will only benefit from a marginal portion of the available waste heat, and minor energy savings will be realized.
Another difficulty related to the heat exchanger system is the choice of a robust design that will work properly under various heat transfer and flow conditions. In order to constantly adapt the operation to current conditions, it makes sense to consider a system consisting of several heat exchangers in parallel so that when the mass flow rate is going down, fewer exchangers can be used with a flow rate per exchanger that stays more constant in time. Again, choosing the right number of exchangers is not trivial : too many exchangers will increase the capital cost, whereas not enough exchangers will reduce the adaptability of the system and deteriorate its overall performance under time-changing conditions.
Again, the objective of the present method is to find conveniently the number of heat exchangers, their features, and their operating conditions in order to minimize the total cost of the project. The main inputs required by the design methodology are the mass flow and temperature of the hot stream ˙mh(t) and Th,i(t), and the heat needed for the
application considered qn(t). The design variables that are considered are :
? 11 variables related to the heat exchangers geometry (i.e. shell diameter, tube outer diameter, tube pitch, tube layout pattern, number of tube passes, baffle spacing at the center, baffle spacing at the inlet and outlet, baffle cut, tube–to-baffle diametrical clearance, shell-to-tube–to-baffle diametrical clearance, tube bundle
ou-ter diameou-ter). The length of the heat exchangers is not an independent variable : it is calculated based on the above-mentioned geometrical parameters and on the desired heat transfer rate between the two fluids ;
? The number of heat exchangers Ndesign;
? Pieces of equipment such as heat exchangers are normally sized based on speci-fied “design conditions” that often correspond to the worst-case scenario. In heat recovery systems with time-varying conditions, the design conditions for which the exchangers are sized could literally be optimized. The variables characteri-zing the design conditions are the design inlet fluids temperature and the design heat transfer rate to be recovered from the waste heat source. For the specific test case considered in the present study, a relation between these design conditions variables was found in such a way that the total number of variables required to specify the design conditions could be reduced to a single one, namely a design out-door temperature (see Section 2.5). However, the method introduced here could easily be used with more design variables to characterize the operating conditions. ? The design hot fluid mass flow rate ˙mh,design going through the heat recovery system is considered as a design variable since it can be chosen to be inferior to the total available mass flow rate when that is more beneficial in terms of cost ; ? The shell-side fluid velocity Vs,design is considered as a design variable for the
case study, and corresponds in the test case to the cold fluid velocity. This design variable is meant to insure that shell-side velocity remains in an adequate range. For liquids, shell-side velocities assume values between 0.5 and 2 m/s [25]. The shell-side mass flow rate is then calculated based on this velocity and on the HE geometry.
? The cold stream temperature at the inlet, Tc,i.
A set of these parameters represents completely the design of the heat recovery system, the overall cost of which can be evaluated as presented in the next section. Additionally, different case-dependent constraints can be invoked in the optimization process.
2.3
Modeling and cost estimation
In this section, we present the heat transfer and fluid flow model required to evaluate the total cost of the project, as well as the details regarding cost estimations.
2.3.1
Heat transfer and pressure drop calculations
The heat transfer rate between the hot and cold fluids in the heat exchanger can be calculated by the log-mean temperature difference method qr = FUA∆Tlm [26]. The
index r stands for “recovered” in order to differentiate the actual heat transfer rate recovered by the heat recovery system and the heat transfer rate that is needed by the system to which the cold stream is connected (the difference between the two being provided by a backup system). The recovered heat transfer rate can also be determined from an energy balance in the cold and hot fluids :
q = ˙mhCp,h(Th,i– Th,o) = ˙mcCp,c(Tc,o– Tc,i) (2.1)
The factor F is defined as the ratio between the real heat transfer rate and the theoretical counter-flow configuration having the same UA, and fluid inlet and outlet temperatures. The exact formulation of this factor can be found in [26].
The overall heat transfer coefficient U depends on the design adopted. In the case of shell-and-tubes heat exchangers which are considered in this paper, U can be written as (based on the shell-side surface area) :
1 U = 1 hs + R 00 s + dolog(d2k o/di) w + R 00 tddo i + 1 ht do di (2.2)
The tube-side heat transfer coefficient ht is calculated thanks to the Dittus-Boelter correlation, and the shell-side heat transfer coefficient hs is determined from the Bell-Delaware method [26]. The latter consists in correcting an ideal heat transfer coefficient with several empirical factors taking into account the shell geometry as well as various leakages and bypass streams. Details are available elsewhere [27], and due to space limitations, they are not repeated here. In the end, when the heat exchanger geometry is given, along with the operating (design) conditions, the overall heat transfer coefficient can be calculated, and then, the required heat exchanger length can be determined in order to fulfill the specified heat transfer duty. Eventually, the effectiveness can be determined for the design conditions :
= qdesign
Ndesign( ˙mCp)min(Th,i– Tc,i) (2.3)
Pressure drop calculations are also based on the Bell-Delaware method, and again, more information on this well-established approach is presented elsewhere [26].
2.3.2
Capital cost
The evaluation of the cost for the purchase of heat exchangers is based on the heat transfer surface area A :
CHEX = 3.28 × 104 80A !0.68
(2.4) This formulation can be adjusted to take into account different materials or constraints (such as operating pressure) [25]. When the purchase of several heat exchangers is considered, Eq.2.4 has to be multiplied by the number Ndesignof heat exchangers, and
A1HE in Eq. 2.5 will be the surface area of one of these exchangers, i.e. :
CNHX= 3.28 × 104Ndesign A1HE80 !0.68
(2.5) The calculation of the required surface area is based on the detailed procedure presented above and detailed in [27]. As explained above, for a given set of the design variables listed above, the required length of the heat exchanger (and thus its surface area) is determined, which allows calculating its cost.
As mentioned previously, the sizing of the heat exchangers is based on specific “design operating conditions” (i.e., inlet temperatures, mass flow rates of both streams, heat transfer rate). However, it is important to note that these design conditions are repre-sented by design variables in the present method, and as such, they will be optimized in order to minimize global cost. Furthermore, the actual operating conditions of the sys-tem will likely be different from these design conditions since they change in time. Once the geometry of the heat exchanger is specified, it is possible to evaluate its performance under conditions that are not the design conditions (i.e. off-design conditions).
The capital cost also has to take into account direct and indirect costs, such as en-gineering and construction costs. In the present paper, a factorial method is used to estimate these costs [25], i.e. that they are expressed as a percentage of the equipment purchase cost of Eq.2.5 :
TCC =X j
fj×CNHX (2.6)
Table 2.1 lists the numerical values fj retained in the present study [25].
In order to facilitate the comparison between capital and operational costs, the capital cost has been annualized, assuming an interest rate i and a number of years n during
Table 2.1 – Capital cost factors expressed as a percentage of the equipment purchase
Direct costs Factors fj
Equipment delivered cost 1.0
Equipment erection 0.4
Instrumentation & controls (installed) 0.2
Off-sites 0.2
Site preparation 0.1
Total capital cost of installed equipment 1.9 Indirect costs
Design, engineering and construction 1.0 Contingency (about 10% of fixed capital costs) 0.4 Total fixed capital cost 3.3
which the system will operate : CA
TCC = TCC
i(i – 1)n
(i + 1)n– 1 (2.7)
The superscript A is to remind that this cost is an annualized cost. The interest rate i considered in this paper is 8% and the number of year n is 20 years.
2.3.3
Operational cost
The total operational cost includes four main elements, namely the hot stream pumping, cold stream pumping, backup heating and cooling, and maintenance :
CA
op= CApump,h+ CApump,c+ CAbackup+ CAmaint (2.8)
In order to evaluate the operational costs, it is necessary to look at how the system will perform at all times, i.e. under all possible conditions and not just the design conditions. For example, the annual cost for pumping either the hot or cold stream can be written as : CA pump = 1 η X j χj∀j∆Pj∆t (2.9) where χjis the value of energy at time tjin $/kWh, ∀jand ∆Pjare the volume flow rate
and resulting pressure drop at time tj, and ∆t is the time step (e.g., 1 hour). The price
of energy considered in this study amounts to 50$/MWh, which is typical of current rates in Québec, Canada. The heat exchanger model introduced above [27] allows to
calculate the pressure drop on each side of the exchanger for a given geometry and for a given flow rate.
The cost of the heating and cooling supplied by the backup system depends on the application of interest. As mentioned previously, in the present paper, we assumed that there is no cooling requirement for the hot stream. This assumption could easily be released in future work, but for the application envisioned (See Section 2.5), this assumption was correct. On the other hand, it is possible in the method proposed not to fulfill with the recovery system all the heating requirement of the cold stream. Therefore, a backup system will potentially need to provide additional heating. The cost of the additional heating is thus :
CA backup= X j χj qn,j– ˙mc,jCp,c Tc,o– Tc,i j | {z } qr,j ∆t (2.10)
The first term in the parentheses (qn,j) is the actual heating need at time j, and the
second term is the heat recovered from the hot stream at the same time. At a given time, when all the required heating is provided by heat recovery, then no backup cost is included.
Finally, duties such as cleaning of heat exchangers correspond to a maintenance cost. They imply working time, and potentially, costs related to the fact that the heat ex-changers might be out of service during maintenance in such a way that the expected savings will not materialize during a certain period of time. These costs are highly in-fluenced by the application considered. In the test case presented in the present paper (i.e. building heating), the heat exchangers are not used during a significant portion of summer, and as a consequence, it was assumed that maintenance could be performed during that period and that its cost was negligible in front of the other costs involved in the project.
2.3.4
Total cost
The total cost function that will be minimized is the summation of the capital and operational costs :
CA
tot = CATCC+ CAop (2.11)
Based on the annualized total cost, a payback period can also be defined by comparing the total cost of Eq. 2.11 to that achieved when no waste heat recovery system is
installed since the difference between the two represents the total annualized savings SavA.
2.4
Calculation procedure
As mentioned above, our objective is to determine the best waste heat recovery system design. In order to do that, the objective function to be minimized is the total cost of the project, i.e. Eq. 2.11. A set of design variables has been presented at the end of Section 2.2. These design variables can be varied in order to minimize total cost. The present section describes the optimization procedure which is schematized in Fig. 2.2, with the main constraints and assumptions.
2.4.1
Strategy for accommodating transient conditions
(off-design operation)
The inputs to the problem ˙mh(t), ˙mc(t), Th,i(t), Tc,i(t) and qn(t) are assumed to be
time-dependent. To deal with this transient evolution of the operating conditions, we varied the number of heat exchangers that are in use at a given time among the Ndesign
available. The power which can be recovered by each exchanger is : qr,1HE(t) = ˙ mCp min Th,i(t) – Tc,i (2.12) The strategy retained in this paper consists in adjusting the number of heat exchangers in operation proportionally to the instantaneous load :
N(t) = min Ndesign,floor "
qn(t)
qr,1HE(t) #!
(2.13) where qn is the actual need, and qr,1HE the heat transfer rate that one exchanger
can recover in the current conditions. This means that the available heat exchangers are arranged in parallel as shown in Fig. 2.1. It is further assumed that the hot fluid stream is thus split into two streams : one that goes in the heat exchangers, and one that bypasses them. The first interest of this strategy is to maintain flow rate conditions that are close to the design values in each individual heat exchanger that is in operation at a given time. This is beneficial since maintaining the operation in a specific velocity range for both streams has shown to be critical to maintain adequate heat transfer as well as to prevent excessive fouling, erosion, and pumping requirement [28].
2.4.2
Main steps of the design strategy
Considering the different elements presented previously, the design procedure shown in Fig. 2.2 will be described step-by-step. Given a set of design variables (geometrical features of the HE, their number and the design conditions), one calculates the required length L of the heat exchangers in order to achieve the required heat transfer rate for the design conditions. This fixes entirely the geometry of the HEs. The heat transfer surface can thus be calculated, and thanks to Eq. 2.5, the annualized capital cost of the project CA
TCC can be determined.
Then, the performance of the HE design as a function of time (i.e. for off-design condi-tions) has to be determined to evaluate operating costs. For each time step, the reco-verable power qr(t) is evaluated with Eq.2.12, and the number of HEs in operation at
that time step is determined in Eq. 2.13. With this procedure, the hot and cold fluid mass flow rates in each HE in operation do not vary over the time. As a consequence, the time evolution of the overall heat transfer coefficient U(t) is small and only comes from fluids viscosity variations due to changes of temperature. This also means that to accommodate heat load variations, only incremental changes of mass flow rates are feasible : the total hot fluid flow rate can only change by multiples of the mass flow rate in an individual HE under design conditions.
Furthermore, in the case of hot corrosive gases such as those considered in the test case presented below, the dew point temperature of the hot stream mixture imposes a limit on the cold fluid temperature at the inlet, in order to avoid damageable condensa-tion (see Seccondensa-tion 2.5.3). This value was simply considered via the design variable Tc,i,
which was imposed constant over time, i.e. equal to the design variable. The outlet temperatures, Th,o(t) and Tc,o(t), can be determined from inlet temperatures by using
Eq.2.1.
Then, pressure drops ∆Pc and ∆Ph are calculated at each time step. They must be
recalculated when the effect of temperature on viscosity is accounted for. These two pressure drops directly lead to the pumping cost via Eq.2.9. Finally, the total annualized project cost, Eq.2.11, is calculated.
C ol d st re am in le t te m pe ra tu re D es ig n va ri ab le s H E G eo m et ry N um be r of H E s Nde si gn D es ig n co nd it io ns D et er m in e L C al cu la te C al cu la te C al cu la te C al cu la te W ea th er d at a G en et ic a lg or it hm A tot C r (t ) U( t q ) P( t) Δ A TC C C A op C S he ll -s id e ve lo ci ty Vs H ea ti ng lo ad
q
n In pu t p ar am et er s c, i T2.4.3
Constraints
Ten constraints have to be invoked in the optimization procedure in order to insure the feasibility of the solution. All the constraints can be formulated in the following way :
x1≤j≤10 ≤x1≤j≤10,ref (2.14)
where xj is the value of the jth parameter, and xj,ref, its maximal allowable value.
These constraints are included in the formulation in such a way that when they are not respected by a design, an extra cost (proportional to the violation of the constraint) is added to the total annualized cost previously calculated. The total penalty cost C∗
takes the following form :
C∗ =X10 j=1 Mjmax h xj– xj,ref,0 i (2.15) where Mj is the weight associated with the violation of the jth parameter. As can be
seen, when the constraints are respected, C∗ becomes zero, and no penalty applies.
Values of Mj were chosen in such a way that all terms in the summation of Eq. 2.15
were of a similar order of magnitude. The identified constrains are presented in Table
2.2, according to the formulation of Eq. 2.14, and they are briefly justified below.
Table 2.2 – Constraints according to the formulation of Eq. 2.14 for the optimization problem j ≤ Justification 1 –L/Ds ≤ –3 Mechanical 2 L/Ds ≤ 12 Mechanical 3 –Is ≤ –15% Fouling 4 Is ≤ 25% Fouling 5 ∆Pt ≤ 7 × 104 Pa Mechanical 6 ∆Ps ≤ 104 Pa Mechanical 7 –Vt ≤ –5 m/s Fouling 8 Vt ≤ 40 m/s Erosion
First, typical shell & tubes heat exchangers have a ratio of length over shell diameter between 3 and 12. This rule of thumb is commonly used in the industry to insure the mechanical integrity of HEs.
Second, constraints on the tube-side velocity are invoked. A minimal velocity is required to limit fouling, and an upper velocity, to limit the rate of erosion as well as vibrations.
For liquids, tube-side velocities must be maintained between 1 and 3 m/s [25]. For gases at atmospheric pressure, velocities are usually between 5 and 70 m/s, but the maximum value may be reduced to avoid erosion : here, a maximum value of 40 m/s is used. Pressure drops on tube side and shell side have to be kept under allowable values in order to respect hydraulic requirements [29]. Typical values for carbon steel and stainless steel are respectively of the order of 104 Pa and 7 × 104 Pa.
Last, a constraint related to fouling can be considered. As fouling occurs, an additional thermal resistance develops on the heat transfer surfaces, and the overall performance of the heat exchanger can decline. The fouling thermal resistances were included in the heat transfer model described previously, and thus, a specified fouling resistance value is included in the design procedure. However, the heat exchangers should be designed in such a way that the performance does not drop too much when fouling occurs, or said differently, in such a way that the performance of clean versus fouled heat exchangers are not too dissimilar. This is usually taken into account by considering the surface coefficient Is [27], defined as :
Is= Afoul– Aclean
Aclean (2.16)
where Afoul and Aclean are respectively the required surface area when fouling is
consi-dered, and when it is not present. Commonly, good design practices require that Is be
between 15% and 25%.
2.4.4
Genetic algorithm optimization
In order to find the best values of the design variables in a given situation, an opti-mization strategy needs to be implemented. The one that was chosen in this paper is based on a genetic algorithm such as the one introduced in [27]. This type of heuristic can converge to a global extremum, by evaluating a small portion of the design space. Details regarding how genetic algorithms work are available elsewhere, and therefore, they will not be repeated here, see [30]. Only the main features of the genetic algorithm used here are presented. First, the algorithm randomly generates an initial population of 50 designs. Each design is expressed as a phenotype composed of the different design variables presented in Section 2.2. Design variables were considered to be discrete, and a certain number of possibilities was associated with each one, as in [27]. Then, the objective function of all designs, i.e. its total cost, is calculated as described above. Constraints are verified for each design, and if applicable, the objective function is pe-nalized to take into account constraints that are not respected. Based on how well each
design performs, crossovers between pairs of designs are performed, and new off-spring designs are created and inserted in the next generation. Mutations are randomly ap-plied. The procedure goes on, until no improvement of the objective function is observed for 300 consecutive generations.
In the next section, we apply the procedure presented in Sections2.3 and 2.4 to design a heat recovery system for a primary aluminum production facility.
2.5
Case study : Waste heat recovery from
aluminum electrolytic cells for heating buildings
2.5.1
Waste heat recovery from aluminum electrolytic cells
Primary production of aluminum requires extensive amounts of energy, between 13 and 15 MWh per ton of aluminum produced [5]. Roughly half of this energy input is eventually lost to the environment as waste heat. In particular, exhaust gases from the electrolytic cells (see Fig. 2.3, based on Ref. [8]), in which the Hall-Héroult process is conducted, contain significant amounts of thermal energy. These exhaust gases are a mixture of CO2 (released as a result of alumina reduction in the cells) and of potroomair, which is driven in the upper part of pots due to a negative pressure that is main-tained in the pot to avoid contaminants release in the workplace. In other words, the CO2 is diluted with air in such a way that the concentration of CO2 in the effluents is
typically around 1 or 2%.
Despite of the important amount of energy in the exhaust gases, few heat recovery strategies have been implemented in practice in primary aluminum production plants [5]. Among the main technical difficulties associated with waste heat recovery in this industry are : (i) the low quality of the waste heat, i.e. low temperature, (ii) the presence of contaminants and fouling agents in the flue ; (iii) the long distances over which heat should be transported, since typical potrooms could extend over 1 km ; (iv) the absence of processes in the plant requiring large amounts of low temperature heat. In the present paper, we considered the possibility to use the heat contained in the pot exhaust gases for space heating considering a smelter located in a cold climate. As a matter of fact, heat recovery opportunities vary according to the geographical situation of the plant. For smelters situated in cold regions, exhaust gases temperature will be low and space heating important, whereas in hot regions, exhaust gases will be warm and space cooling will be required.
In this paper, the primary aluminum production plant of Alcoa in Deschambault (ADQ), in Canada (46.65°, –71.93°W), will be considered as a test case for the me-thodology outlined in Sections 2.3and 2.4. ADQ produces ∼ 260, 000 ton of aluminum per year with 264 AP30 pot. Pot exhaust gas flow rate is of the order of 2.4 Nm3s/pot
with a temperature of approximately 100°C above ambient. The average outside tem-perature at Deschambault is 4.5°C, with 4,300 heating degree day, and with outdoor air temperature varying over the year between –33°C and 31°C. At ADQ, the peak demand for space heating was estimated to be around 16 MW [5]. This demand is due mainly to 5 spaces, namely the gate house, administration buildings, potline-to-baking corridor, cast house, and crane repair, pot lining and re-lining.
2.5.2
Technology selection and localization
For the purpose of this study, it was decided to position the heat recovery system upstream of the gas treatment center (GTC) for two main reasons. First, it takes advantage of the fact that the potline exhaust gases are warmer there than at the outlet of the GTC. The exhaust gases temperature, Th,i, varies from 70 to 125°C,
depending on the outside temperature [31]. The second reason is to cool down flue gases before the GTC to maintain an incoming temperature below 120°C because of two limitations. First, filter bags used in the GTC are made of organic media which cannot sustain temperatures higher than 140°C [32]. Second, when gases temperature is higher than 120°C, the gas treatment efficiency dramatically drops, causing an increase in fluoride emissions [33]. In practice, gases are further diluted with additional ambient
air to cool them down at the inlet of the GTC when their temperature is too high. This solution requires more fan capacity and more filter compartments in the GTC in order to treat more important gas flow rates. Thus, implementing HEs at the inlet of the GTC may provide a ‘side-effect’ benefit.
Several technologies can be considered to recover heat from the exhaust gases of elec-trolytic cells, among which hairpin coolers, water spray and heat exchangers [32]. For instance, Alstom tested full scale fire tube heat exchangers in Alcoa Mosjøen, Norway [34], with flue gases in the tubes. After 14 months of test, they observed a thin layer of fouling (less than 1 mm thickness), but no cleaning of the tubes was required. Another example is provided by [9] which consists of finned oval tubes HEs, with a water/glycol mixture inside tubes, and flue gases outside. In this second design, only a limited fou-ling was experimentally observed. Finally, in [35], a comparison is presented between finned tubes and circular tubes, with flue gases outside, and several fouling factors were measured for different mass flow rates. Based on this data, and considering that veloci-ties in the tubes are large (20 m/s), a value of R00
fouling = 0.003 Km2/W appears to be
representative. More details on the impact of this value are presented in Section 2.7.1. Because of their capacity to recover large amounts of heat over a wide range of tem-peratures, heat exchangers, and more precisely shell & tubes heat exchangers, were selected in the present study. They present strong advantages : proven design methods and standards, versatility for handling a wide range of operating conditions, and a good fouling cleanability. Since cleaning tubes is far easier than cleaning shell baffles, it was decided to have the exhaust gases to flow in the tubes and the water, in the shell, similarly to the design in [10]. The TEMA E design was considered.
2.5.3
Materials selection and corrosion prevention
The selection of the material of the HEs is dictated in part by the corrosive nature of the gases from which heat is to be recovered in the present test case. Furthermore, it has a heavy impact on the capital cost. In the current case, flue gases contain heavy dusts (0.26-0.38 g/kg of gas), mainly composed of carbon, oxygen, fluorine and alumina [36]. The detailed composition of the gases can be found in [37]. In particular, in presence of liquid water, small amounts of SO2 and HF may form sulfurous and hydrofluoric acids :
SO2+ H2O *)HSO–3+ H+ (2.17)
In order to prevent the formation of acids, the HE design and operation were selected in order prevent condensation. First, it is necessary to determine the dew point tem-perature of flue gases. This has to be repeated at different moments of the year since the water contents in the gases change in time. The acid dew point of a flue gas is the temperature at which any gaseous species in the flue gas starts to condense into liquid acid. To prevent it, the easiest solution is to maintain the transfer surface temperature above the dew point.
Dew point calculation for a gas mixture is calculated by solving numerically the follo-wing equation [25] where T is the unknown parameter :
X j yj Psat j (T) = 1 P (2.19)
where yjis the molar fraction of each component and P the total pressure of the mixture
(in this case, the atmospheric pressure). The species considered are HF, SO2, CO2, CO
and H2O. The saturation pressure of component j can be calculated with the following
extended Antoine’s equation whose constants are available in [38] :
log Psat
j (T) = Aj+
Bj
T + Cjlog T + DjT + EjT2 (2.20)
with T in Kelvin, P in mm Hg.
The dew point temperature is calculated for different relative humidity ratios of the mixture. Thus, it is possible to know the maximum allowable temperature. For the case of Deschambault, a value of 30.05°C is computed, which is very close to the water dew point (30°C). By comparison, a value of 42°C was measured in [35] for off-gases temperature in the range of 100-200°C. The difference might be due to the difference of gases temperature. Thus, in the present case, it was decided to use lower bound of 50°C for the inlet temperature in order to prevent condensation and corrosion with an adequate factor of safety.
As mentioned above, the choice of HE construction material is crucial since it signifi-cantly affects the cost. Because the formation of acids is limited thanks to the imposed minimal water temperature, stainless steel alloys can be expected to resist to corrosion [37]. Nickel alloys, such as inconel and monel, present better resistance to corrosion [39], but they are much more expensive [40]. The convenient tradeoff retained in the present study is to use stainless steel for the tubes, and carbon steel for the shell, leading to a material cost factor in Eq. 2.7 of fm = 1.7 [25].
