UNIVERSITÀ DI PISA
SCUOLA DI INGEGNERIA
CORSO DI LAUREA MAGISTRALE IN INGEGNERIA ENERGETICA
3D Design and Optimization of Heat Exchanger Network for Solid Oxide Fuel Cell in
Hybrid Electric Vehicles
Tesi di laurea
Relatore/i Candidato
Prof. Umberto Desideri (Università di Pisa) Federico Tanozzi
Prof. Francois Maréchal (EPFL)
Dr. Shivom Sharma (EPFL)
Un ringraziamento sincero va al Prof. Desideri per avermi dato l’opportunità di vivere una magnifica esperienza nel mio soggiorno presso l’EPFL. I want to thank also Prof. Francois Maréchal for his hospitality and for the interesting work that he proposed me.
A special thank to Shivom, for his help and support in this work. He always gave me a strong feeling of confidence and I really appreciated working and talking with him. I would also like to thank Alberto and Stephane for their help.
I want to thank the IPESE group because I learnt lot of things in these five months. Meeting people with so many different cultures and experiences has been amazing for me and this helped me also to understand better my culture. A special hug goes to Gauthier and Navid for the nice conversations and the time we spent together.
Grazie all’ Università di Pisa per gli insegnamenti, per la fatica e per le persone che mi ha fatto incontrare. Un grazie particolare a Davide per le ore passate insieme tra Clara, balene, capesante e i progetti più disparati.
Grazie a tutti gli amici che ho sentito vicini in questi anni. Un ringraziamento speciale ai miei amici "sciemi", sappiate che per questa dedica chiederò un ringraziamento anche da parte vostra, perchè l’importante come sapete è "ringraziare" sempre.
Grazie a tutti i familiari e in particolare a Nonna Maria che mi ricorda sempre che "il Signore ci ha dato di vivere in un bel posto".
Grazie a "Siamo in Diversi" per essere una seconda famiglia, perchè "un sogno fatto da soli rimane un sogno, un sogno fatto in tanti diventa realtà".
Grazie a Mamma, Babbo e Cristina, quello che sono lo devo a voi e da voi ho imparato tutto. Grazie a Bene, per tutto l’amore e la poesia che mi regali.
The development of electric vehicles is considered as the most sustainable way in the auto-motive industry to reduce greenhouse gases emissions and to allow people transportation respecting the environmental targets required in present and future years. Due to the limited range of autonomy of the electric vehicles and the induced cost and environmental impacts of large capacity batteries, Hybrid electric vehicles have been deeply investigated and developed over the last years. A Solid Oxide Fuel Cell combined with Gas Turbines (SOFC-GT) operating in inverted Brayton cycles is used in this work as a Range Extender in Hybrid electric vehi-cle. The SOFC-GT system allow to increase the autonomy of the car and has high electric efficiency of 77 %. In this thesis, the Heat Exchanger Network (HEN) to recover thermal energy in the SOFC-GT, is studied. The HEN has to meet the targets of limited volume and weight to be compatible with the installation on the hybrid vehicle. The work is basically divided in three steps. In the first step the HEN Synthesis is performed with a mathematical program developed in AMPL, stating the optimal matches between hot and cold streams. In the second step, a model is developed in MSExcel to size the heat exchangers with the LMTD method, by performing iterative calculations. In the third step, an optimization problem is solved to minimize the volume of the HEN, sizing the heat exchangers with a global view of the overall system, considering their assembly in a limited space and defining the paths of the streams. Finally some heat exchangers have been printed using plastic with a SLA 3D printer, with presentation purpose.
Key words: Hybrid vehicles, electric vehicles, energy integration, optimization, SOFC, HEN, heat exchanger design
Acknowledgements/Ringraziamenti 1
Abstract 3
List of figures 7
List of tables 9
1 Introduction 1
2 Heat Exchanger Design method 5
2.1 The LMTD Method . . . 5
2.2 Forced Convection in Ducts . . . 7
2.2.1 Mean velocity and mean temperature . . . 7
2.2.2 The Laminar and Turbulent Flow . . . 8
2.2.3 The hydrodynamic and thermal Entrance length . . . 8
2.2.4 Effect of the entrance region on heat transfer coefficient in laminar regime 9 3 Heat Exchanger Network Design 11 3.1 Introduction . . . 11
3.2 The Energy-Capital Trade-off . . . 12
3.3 The Pinch Point and the Minimum Energy Requirement . . . 13
3.4 The Heat Exchanger Network Design . . . 16
3.4.1 Introduction . . . 16
3.4.2 The Pinch design method . . . 17
3.4.3 The mathematical programming approach . . . 20
4 The SOFC-GT System 25 4.1 The SOFC-GT Range Extender . . . 25
4.2 AMPL Model and Results for the Heat Exchanger Network . . . 26
5 Properties of Fluids and Materials Selection 33 5.1 Streams Properties . . . 33
5.2 Fouling Coefficients . . . 34
6 Double Pipe Heat Exchangers 37
6.1 Introduction . . . 37
6.2 Design of Double Pipe Heat Exchangers . . . 38
6.2.1 Introduction . . . 38
6.2.2 First trial sizing . . . 39
6.2.3 Heat transfer coefficient calculation . . . 43
6.2.4 Pressure drop calculation . . . 47
6.2.5 Double pipe heat exchangers results . . . 49
6.3 Conclusions . . . 54
7 Rectangular Mini-channel Heat Exchanger 55 7.1 Introduction . . . 55
7.2 Design of Rectangular Ducts Heat Exchanger . . . 56
7.2.1 Sizing of the rectangular duct heat exchanger . . . 57
7.2.2 The fin efficiency . . . 61
7.2.3 Heat transfer coefficient in rectangular ducts . . . 63
7.2.4 Pressure Drops in rectangular ducts . . . 65
7.2.5 Approximations made in design of condenser, evaporator and reformer 66 7.2.6 Cold utility heat exchangers . . . 69
7.3 Results of rectangular ducts heat exchangers Design . . . 70
8 Space Optimization of the SOFC-GT Heat Exchanger Network 75 8.1 Introduction . . . 75
8.2 Automatization of the Iterative Calculation . . . 76
8.3 Optimization Tool based on Genetic Algorithm . . . 76
8.3.1 The genetic algorithm . . . 77
8.3.2 The decision variables . . . 79
8.3.3 Constraints imposed to the problem . . . 81
8.4 The Number of Layers in Rectangular Duct Heat Exchangers . . . 82
8.5 Results of the optimization problem and design of the 3D-boxes . . . 83
8.6 Insulation of heat exchangers and 3D boxes . . . 93
8.7 3D Printing . . . 94
8.8 Distributors in Countercurrent Heat Exchangers . . . 96
9 Conclusion and Future Works 99
1.1 Key components of hybrid car. Picture retrieved from the website
www.circuitstoday.com/working-of-hybrid-cars . . . 2
1.2 SOFC- GT integrated hybrid system superstructure [1] . . . 3
1.3 Schematic diagram of series hybrid vehicle with ICE. Picture retrieved from www.slideshare.net/KaliNuska/hybrid-electric-vehicles-hev . . . 4
2.1 Development of the velocity profile in the hydrodynamic entry region of a pipe [10] . . . 9
2.2 Fully developed temperature profiles for constant heat rate and constant surface temperature [10] . . . 10
3.1 Energy-Capital trade-off . . . 12
3.2 Hot composite curve construction [11] . . . 14
3.3 Hot and Cold Composite Curves . . . 15
3.4 HEN grid representation . . . 17
3.5 Number of stream rules above the pinch point . . . 17
3.6 The Cp rule . . . 18
3.7 The synthesis pinch design method . . . 19
3.8 Mathematical programming techniques . . . 20
3.9 Example of objective function [13] . . . 21
3.10 Sequential approach scheme [13] . . . 22
3.11 HEN modeled with Simoultaneous approach [13] . . . 23
4.1 SOFC-GT system . . . 29
4.2 SOFC-GT system, connections calculated with AMPL-CPLEX . . . 30
4.3 SOFC-GT composite curves . . . 31
5.1 A flowsheet of part of the SOFC-GT system in Belsim Vali . . . 33
5.2 Aspen Plus user interface . . . 34
6.1 Double Pipe Heat Exchanger [19] . . . 37
6.2 U-shape Double Pipe Heat Exchanger [8] . . . 38
6.3 Multi-tube Double Pipe Heat Exchanger [8] . . . 38
6.5 Excel file input . . . 40
6.6 Friction factor for fully developed flow inside a circular duct [8] . . . 48
6.7 Double pipe heat exchangers Results . . . 49
6.8 Overall heat transfer coefficient trend increasing velocity . . . 50
6.9 Volume trend increasing velocity . . . 50
6.10 Pressure drop trend increasing velocity in tube . . . 51
6.11 Pressure drop trend increasing velocity in annulus . . . 51
6.12 Overall heat transfer coefficient trend splitting the streams FC2 and CT2 in more pipes . . . 52
6.13 Volume trend splitting the streams FC2 and CT2 in more pipes . . . 53
6.14 Pressure drop trend splitting the streams FC2 and CT2 in more pipes . . . 53
7.1 Plate-fin heat exchanger [3] . . . 55
7.2 Sketch of rectangular duct heat exchanger cross surface . . . 56
7.3 Design procedure of rectangular ducts heat exchanger . . . 60
7.4 Fin efficiencies of straight and circular fins of uniform thickness [5] . . . 62
7.5 NuH 1, for fully developed laminar flow, when one or more walls are transferring the heat . . . 64
7.6 Fraction of water to be injected at each step . . . 69
7.7 Results of rectangular ducts heat exchangers . . . 72
7.8 SOFC-GT HEN, 2 layers rectangular ducts results, manual calculation . . . 73
8.1 EMOO tool interface . . . 78
8.2 Flow Regimes Based on the Knudsen Number . . . 80
8.3 Heat exchanger stacking procedure . . . 82
8.4 Heat Exchangers design with optimization tool . . . 84
8.5 Hot temperature region; View from above . . . 85
8.6 Hot temperature region; Cross section view . . . 86
8.7 Pinch Point region; View from above . . . 87
8.8 Pinch Point region; Cross section view . . . 88
8.9 Cold temperature region; View from above . . . 89
8.10 Cold temperature region; Cross section view . . . 90
8.11 CO2 region; View from above . . . 91
8.12 CO2 region; Cross section view . . . 92
8.13 AT5-FP4 heat exchanger 3D model . . . 94
8.14 AT4-CT1 heat exchanger, 3D model . . . 95
8.15 SLA 3D printer interface . . . 95
8.16 Counterflow heat exchanger with partial crossflow inlet/outlet [6] . . . 96
8.17 Distributors for plate and fin heat exchangers [6] . . . 96
8.18 Inlet of streams in 3D printing;1 . . . 97
4.1 AMPL results; first calculation . . . 27
4.2 AMPL results; water contact evaporation injecting in stream FP-4 . . . 28
4.3 AMPL results; water contact evaporation in stream FP-1, separated CO2 com-pression system . . . 28
5.1 Fouling Coefficients; typical values . . . 35
5.2 Shortlist of the best potential metals to be used for the heat exchangers . . . 36
6.1 Typical overall heat transfer coefficients [3] . . . 41
6.2 Velocities of various media in tubes [m/s] [20] . . . 42
6.3 Nusselt number for the circular tube; constant heat rate; thermal entry length [10] 44 6.4 Circular-tube annulus solutions for constant heat rate and fully developed veloc-ity and temperature profiles [10] . . . 45
6.5 Nusselt numbers and influence coefficient for the circular-tube annulus family; constant heat rate;thermal entry length [10] . . . 46
7.1 NuH 1for fully developed laminar flow when one or more walls are transferring the heat . . . 63
7.2 Nusselt numbers for fully developed flow in rectangular ducts for different aspect ratio and different dimensionless lengths x*; boundary condition H1 . . . 65
8.1 Optimization problem definition . . . 82
8.2 Volume of Heat Exchangers and 3D boxes with and without insulation;values in cm3 . . . 94
To meet the targets of sustainable development and greenhouse emission reduction of the fu-ture commercial personal vehicles, the automotive industry needs to deploy cost-competitive and efficient advanced energy conversion systems. Electric vehicles are seen as a way to globally reduce the CO2emissions produced in the automotive field. The electric vehicle has high voltage batteries which work as electrochemical on-board energy storage devices. The batteries have lower energy density in comparison with hydrocarbon fuels, but the electric conversion systems to mechanical power have very high conversion efficiency. Thermal con-verters instead have low conversion efficiency and use fuels with a higher energy density [1]. Due to the limited range of autonomy of the electric vehicles and the induced cost and envi-ronmental impacts from the high voltage battery capacity increase, Hybrid electric vehicles have been deeply investigated and developed over the last years. Hybrid electric vehicles have two or more prime movers (Internal Combustion Engine or Fuel Cell and electric machine) and power sources (fuel tank and electrochemical battery) on their board. This arrangement allow to reach an efficiency increase in comparison to the thermal vehichles and longer ranges of autonomy in comparison to the electric vehicles. Hybrid electric vehicles proliferate under current technical developments and on the markets, because they are considered as a powerful technology to promote the change from conventional mobility to electric mobility.
The use of Fuel Cells for the application on hybrid electric vehicles has been deeply studied over the last years. The Polymer Electrolyte Membrane Fuel Cell (PEMFC) has been investi-gated for most of the automotive applications. The advantages of the PEM are that they offer high safety, support well transients and operate at low temperature (80°C). The shortcomings of the PEM is that they operate with hydrogen stored on the vehicle board [1]. With the limited hydrogen distribution infrastructure, the use of PEMFC is also limited. The hydrogen has to be stored at 700 bars and this introduces some safety constraints. However the PEMFC can be considered as the most mature fuel cell technology for vehicles propulsion. In this study a Solide Oxide Fuel Cell technology is considered to be applied on a hybrid car. The SOFC is a high temperature operating fuel cell – 800°C to 1000°C. This fuel cell can use a variety of fuels instead of hydrogen such as CH4 or others fossil fuels derived from biomass. The
Figure 1.1 – Key components of hybrid car. Picture retrieved from the website www.circuitstoday.com/working-of-hybrid-cars
SOFC installation has an integrated fuel reformer. In this case the SOFC is coupled with gas turbines which operate in inverted Brayton cycles, as shown in Figure 1.2. This is an innovative concept of vehicle propulsion which could increase the overall efficiency of the system from fuel reforming to electricity output up to 72% [2] . The main problem of the SOFC is that is not convenient for transient due to the high temperature operation. This issue can be overcome for the SOFC if it is considered as a range extender unit for the vehicle working on permanent regime and supplying electricity to the high voltage battery (series hybrid). Thus, the concept presents the advantage to extend the vehicle basic electric range thanks to this highly efficient converter. According to the study of Dimitrova [1] a 3.5 kW SOFC-GT module could increase the autonomy of the electric car from a mean value of 150/200 km up to 600 km. A second advantage is the reforming of a liquid fuel on board which avoids the hydrogen storage. The liquid fuel is methane produced from biomass and liquefied at 200 bars pressure in the vehicle tank.
The present work concerns the study of a Heat Exchanger Network (HEN) for the SOFC-GT system. The system in this case has an electric output of 5 kW. A scheme of the plant is shown in Figure 4.1. The SOFC is fed with methane, a burner for the combustion of unreacted gases is used and a CO2compression and liquefaction plant is included in the system, allowing the potential use of CO2in a Power-to-Gas plant for the production of methane. The Heat Exchanger Network design aims to create a feasible system, optimizing the heat recovery from hot streams to cold streams. Considering the necessity to install the exchangers on the hybrid car, the heat exchangers should have limited volume and weight in order to be compatible with the system.
1. The Heat Exchanger Network Synthesis indicates the best potential connections be-tween hot and cold streams.
2. The Heat Exchanger Design phase performs the actual sizing of heat exchangers using a model based on the Logarithmic Mean Temperature Method.
3. The 3D Space Optimization works on the final design of the system. The exchangers are supposed to be assembled one next to each other in a limited region on the car. The HE Design model is used to size the exchangers with an holistic view.
The Heat Exchanger Network Sinthesys aims to indicate the best connections between hot and cold streams. An optimization problem is solved, the objective function to minimize being the number of heat exchangers in the system. A mathematical tool written in AMPL language is used with the solver CPLEX. Many issues are considered simoultaneously in this model: number of connections between the streams, use of cold utility, total heat exchange area. Constraints can be imposed to avoid connections between specific streams.
The Heat Exchanger Design phase aims to size the heat exchangers prescribed by the AMPL code. Two solutions have been mainly investigated: Double Pipe Heat Exchangers and an arrangement with rectangular minichannels, similar to Plate and Fins Heat Exchangers. A model realized on an Excel file has been developed to perform the calculation. Several issues have been taken into account: interpolations of fluid properties, heat exchange in parallel with more than one stream, entrance region effects on the heat transfer coefficient, fin efficiencies and many others.
The 3D Space Optimization finalizes the global aspect of the HEN. Thanks to the aid of an op-timization tool named EMOO based on the genetic algorithm the exchangers are sized in order to be easily assembled together in a limited portion of space in the car. The placement of heat
exchangers, the feasibility of the stream paths between the exchangers and the minimization of total Volume and Weight are considered.
The state of the art concerning Heat Exchanger Design and HEN synthesis is treated in Chap-ter 2 and 3. The SOFC-GT system and the HEN synthesis performed with AMPL CPLEX is presented in Chapter 4. Chapter 5 concerns the setting up of a database of fluid properties to be used in the Heat Exchanger Design and the material selection for the exchangers. Chapters 6 and 7 present the realization of the Heat Exchanger Design model for Double Pipe and Rectangular Duct Heat Exchangers. Chapter 8 treats the final optimization to define the global aspect of the Heat Exchanger Network and presents the final results.
Figure 1.3 – Schematic diagram of series hybrid vehicle with ICE. Picture retrieved from www.slideshare.net/KaliNuska/hybrid-electric-vehicles-hev
2.1 The LMTD Method
The method utilised in the design of the exchangers has been the logarithmic mean temper-ature difference method (LMTD). The general equation for heat transfer across a surface is
˙
Q = U A∆Tm (2.1)
where Q[W ] is the heat transferred, U [W /m2K ] is the overall heat transfer coefficient,∆Tm[K ]
is the mean temperature difference. In the LMTD method, the inlet and outlet temperatures must be known or at least they should be obtainable by a simple first principle balance. When this condition is not satisfied other methods like the² − NTU are preferable. The main steps of the LMTD method are indicated by Towler [3] :
1. Define the heat transfer rate, fluid flow rates, temperatures.
2. Collect the fluid physical properties required: density, viscosity, thermal conductivity. 3. Decide on the type of exchanger to be used (e.g. double pipe, shell and tube, etc). 4. Select a trial value for the overall heat transfer coefficient, U.
5. Calculate the mean temperature difference,∆Tm.
6. Calculate the heat exchange area required from equation (2.1).
7. Decide the exchanger layout (lenght, number of tubes and diameter of tubes etc). 8. Calculate the individual heat transfer coefficients.
9. Calculate the overall heat transfer coefficient and compare with the trial value. If the calculated value differs significantly from the estimated value, substitute the calculated for the estimated value and return to step 6.
10. Calculate the exchanger pressure drop; if unsatisfactory, return to steps 7 or 4 or 3, in that order of preference.
11. Optimize the design: repeat steps 4 to 10, as necessary, to determine the cheapest exchanger that will satisfy the duty. Usually, this will be the one with the smallest area.
All these steps applied to the heat exchangers of the SOFC-GT system will be described more in detail in next chapters. The driving force in heat exchange is the temperature difference ∆Tm. We can estimate the∆Tmlooking at the difference of temperature beetween the streams
at the inlet and outlet sections. For sensible heat exchange and true counter-current flow the mean temperature difference can be imposed as the logarithmic mean temperature difference:
∆Tm= ∆Tl m=
(T1− t2) − (T2− t1)
l n(T1− t2)/(T2− t1)
(2.2)
where
∆Tl m= log mean temperature difference;
T1=hot fluid temperature, inlet; T2=hot fluid temperature, outlet; t1=cold fluid temperature, inlet; t2=cold fluid temperature, outlet;
In many heat exchangers usually the flow is not purely counter-current but is a mixture of co-current, counter-current and cross-flow. In this cases the mean temperature difference must be estimated using a correction factor Ft:
∆Tm= Ft∆Tl m (2.3)
Ftcan be determined using some emphirical correlation, functions of inlet and outlet
temper-atures and of the flow arrangement. Ftis always lower than one and it indicates the departure
from the arrangement utilized and the true counter-current flow. Diagrams for the deter-mination of Ft are available in Reference [4]. The counter-current flow arrangement infact
is the one which is thermodynamically superior to any other arrangement. It produces the highest temperature change in each fluid compared to any other two-fluid flow arrangements for a given overall thermal conductance (U A), fluid flow rates, and fluid inlet temperatures. Sometimes other kind of arrangements like the crossflow are preferred, because they greatly simplify the header design at the entrance and exit of each fluid. If the desired heat exchanger effectiveness is high (such as greater than 80 % ), the size penalty for crossflow may become excessive. In such a case, a counterflow unit is preferred [5] . Some technical solutions to solve
the problem of headers design in countercurrent flow are illustrated by Hesselgreaves[6]. Other design methods like the Effectiveness-Number of Transfer units (² − NTU) could be used: the approach can be shown to be mathematically equivalent to the LMTD method, the working equations of one being derivable from those of the other [6]. The main advantage of this method is that it does not require the evaluation of the mean temperature difference. It permits to obtain an unknown stream outlet temperature directly, without the need of iterative calculations. The² − NTU is usually more useful for rating than for design [3]and can be used to estimate the effectiveness ep si l on of the heat exchangers, once the heat transfer area will be known. The effectiveness ep si l on is defined as the ratio beetween the actual rate of heat transfer to the maximum possible rate:
² =Qr eal
Qmax
(2.4)
2.2 Forced Convection in Ducts
2.2.1 Mean velocity and mean temperature
When a fluid flows in a duct, the velocity profile and the temperature profile will not be uniform over the cross section. In our calculation, a mean velocity and a Mean temperature are used to describe the fluid behaviour. The mean velocity umis defined as the velocity that, multiplied
by the fluid densityρ and the cross-sectional area S, will provide the mass flowrate through the duct [7]. Hence
˙
m = ρumS (2.5)
The mean temperature (or "bulk" temperature) Tmof a fluid at a given cross section is defined
in terms of the thermal energy transported by the fluid as it moves through the cross section.
Tm is the temperature that, when multiplied by the mass flowrate and the specific heat,
provides the rate at which thermal energy is transported with the fluid as it moves along the duct [7].
˙
Et= ˙mcvTm (2.6)
The rate at which this transport occurs, ˙Et, may be obtained by integrating the product of the
mass flux (ρu) and the internal energy per unit mass (cvT ) over the cross section.
˙
Et=
Z
Sρucv
Hence from equation (2.6) and (2.7) we obtain Tm= R SρucvT d S ˙ mcv (2.8)
2.2.2 The Laminar and Turbulent Flow
When the fluid flow at low velocities or through small cross sections, the fluid particles move in definite paths called streamlines. This type of flow is called laminar flow. There is no component of fluid velocity normal to the duct axis in the fully developed region. The Reynolds number allow us to determine the flow regime of the fluid. It is defined as
Re =ρuDh
µ (2.9)
whereρ[mkg3] is the density, u[
m
s ] is the velocity,µ[Pas] is the dynamic viscosity and Dh[m] is
the hydraulic diameter defined as
Dh=
4S
P (2.10)
where S is the cross section area and P is the wetted perimeter of the duct.
Depending on the roughness of the duct and the inside surface, fully developed laminar flow will usually be obtained up to Re < 2300. If the velocity of the fluid is gradually increased, there will be a point where the laminar flow becomes unstable in the presence of small disturbances and the fluid no longer flows along smooth lines (streamlines) but along a series of eddies, which results in a complete mixing of the entire flow field. This type of flow is called turbulent flow. The Reynolds number at which the transition from laminar to turbulent flow starts, is called "critical" Reynolds number. The fully turbulent conditions will be reached at Re > 104. Between the lower and upper limits lies the transition zone from laminar to turbulent flow [8].
2.2.3 The hydrodynamic and thermal Entrance length
In most of the heat exchangers designed in this work, single phase forced convection correla-tions are used. Laminar and turbulent forced convection correlacorrela-tions represent an important class of heat transfer solution for heat exchanger applications. When a viscous fluid enters a duct, a boundary layer will form along the wall. The boundary layer gradually fills the entire duct cross section and the flow is then said to have a "fully developed velocity profile". The distance at which the velocity becomes fully developed is called the hydrodynamic or velocity entrance length (Lhe). Theoretically, the approach to the fully developed velocity profile is
asymptotic, and it is therefore impossible to describe a definite location where the boundary layer completely fills the duct. But for all practical purpose, the hydrodynamic entrance length is finite. [8]
Figure 2.1 – Development of the velocity profile in the hydrodynamic entry region of a pipe [10]
If the walls of the ducts are heated or cooled, also a thermal boundary layer will develop along the duct wall. At a certain downstream point, one can talk about "fully developed temperature profile" when the thickness of thermal boundary layer is approximately equal to half the distance across the cross section [8]. The distance at which the temperature profile becomes fully developed is called the thermal entrance length (Lt e). If the heat transfer starts from the
inlet of the duct, then both the velocity and the temperature profiles develop simoultaneously. The associated heat transfer problem is referred to as the simoultaneously developing region problem. The rates of development of the velocity and temperature profile depend on the fluid Prandtl number, defined as
P r =µCp
K (2.11)
whereµ[Pas] is the dynamic viscosity, Cp[kg KJ ] is the heat capacity at constant pressure and
K [mKW ] is the thermal conductivity of the fluid. For high Prandtl number (oils) the velocity profile is established more rapidly than the temperature profile; for low Prandtl number (liquid metals) the temperature profile is established more rapidly than the velocity profile; for Prandtl numbers around 1 (gases) the velocity and temperature profiles develop at similar rate, starting from uniform velocity and temperature at the duct entrance. In this work, we will assume that the hydrodynamic entrance length will already be reached before the entrance in the heat exchangers, so only the thermal entrance length will be considered. The thermal entrance length will take a relevant importance just in the case of Laminar flow.
2.2.4 Effect of the entrance region on heat transfer coefficient in laminar regime
The effect of the entrance region on the heat transfer coefficients and on pressure drops can be neglected for design purpose when turbulent flow occurs, as stated by Shah [5] and Incropera [7]. Nevertheless the entrance region effect can not be neglected for the laminar flow, which occurs in most cases analyzed in this work. The heat transfer coefficient is given by
h =NuK
Dh
where Nu is the adimensional Nusselt number, K [mKW ] is the thermal conductivity of the fluid and Dh[m] is the hydraulic diameter of the duct. In our cases, we will make the assumption of
fully developed velocity profile, therefore we will study just the thermal entry length problem. Because of the entrance region effect, the Nusselt number value decreases along the heat exchanger: in principle the Nusselt number is infinite at the entrance of the heat exchanger and decay to his asymptotic (fully developed) value flowing towards the outlet [7]. Local Nusselt values and mean Nusselt values at given cross section, (identified by the ratio x/Lhe
) are available in literature. Also the boundary condition applied on the duct area are very important to estimate the Nusselt number. Usually the most common cases analyzed are those with boundary conditions identified by the symbol "T" and "H-1" [9].
Figure 2.2 – Fully developed temperature profiles for constant heat rate and constant surface temperature [10]
The "T" boundary condition identifies the problem where the wall temperature is constant along the fluid flow direction.
The "H-1" boundary condition identifies the condition where the heat flux is constant along the fluid flow direction and the temperature of the duct is constant along the periphery of the cross section. The "H-1" boundary condition will be used for our purpose. Useful data concerning these cases for many different shapes of duct are available in the report "Laminar Flow Forced Convection Heat Transfer and Flow Friction in Straight and Curved Ducts-A summary of Analytical Solutions" by R.K. Shah and A.L. London [9].
3.1 Introduction
Heat Exchanger Network Design is basically performed with the aid of a method called Pinch analysis. The Pinch analysis is a method which aims to identify the heat recovery opportunities by heat exchange in complex thermal processes. It can be applied in various industrial sectors where heat recovery and energy saving can play an important role. The energy recovery is supposed to be obtained by counter-current heat exchanges between hot streams to be cooled down and cold streams to be heated up in a wide system.
Initially investigated by Umeda, it has mainly developed in the early 70’s by Linhoff and co-workers who worked on a graphical method to calculate the minimum energy requirement of a process and design the heat recovery exchanger network and by Grossmann and co-workers who developed a mathematical programming framework for the design of heat exchanger networks [10]. Nowadays different tools and methods have been developed to help in the identification of energy recovery by heat exchange and energy savings in complex systems. The pinch analysis is based on the definition of the minimum approach temperature (∆Tmi n)
that represents the energy-capital tradeoff between the energy savings obtained by heat exchange and the required heat exchangers investment. As explained in the book of Kemp "Pinch Analysis and Process Integration" [10], for a given system a pinch analysis is basically made by three steps :
1. the definition of hot and cold streams
2. the calculation of the minimum energy requirement (targeting step) 3. the design of the heat exchanger network (synthesis step)
The first step relies on the definition of the single process operations and their required thermodynamic operating conditions.
The second step of the analysis is made by computing the hot and cold composite curves of the process and identifying the Pinch Point location. The hot and cold composite curves represent respectively as a function of the temperature, the heat load available for heat exchange in the hot streams of the process and the heat required by the cold streams. The Pinch Point is identified by computing the heat cascade of the process that represents the maximum heat recovery between the hot and the cold streams, considering the minimum approach tempera-ture constraint. The identification of the Pinch Point allows one to compute the minimum energy requirement of the process prior to any heat exchangers network rearrangement. The third step, once that the location of the Pinch Point has been identified, relies on the design of the Heat Exchanger Network. This can be obtained using heuristic methods or more complex mathematical programming methods.
3.2 The Energy-Capital Trade-off
When heat exchange occurs between a hot and a cold stream, an important role is played by the∆Tmi n. This parameter represents the minimum difference of temperature beetween the
hot stream and the cold stream, and obviously it is supposed to be higher than zero, to not violate the second principle of thermodynamic.
In a heat exchanger design an Energy-Capital trade-off has to be made to consider the optimal ∆Tmi n: an high temperature approach beetween the streams will not require a high heat
trans-fer area, but the heat recovery would be penalised. To enhance the energy efficiency a lower temperature approach would be needed, but this implies also a higher heat transfer area and consequently an higher capital investment. An optimal∆Tmi ncan be calculated comparing
the annual operating cost (Energy curve in Figure 3.1) and the annualised investment (Capital curve).
3.3 The Pinch Point and the Minimum Energy Requirement
To identify the possible heat recovery in a process we will draw a Hot and a Cold composite Curve. The Composite Curves are represented on a Temperature-Enthalpy Diagram (called "Energy flow Diagram") and here their construction is briefly explained with the aid of Figure 3.2 from reference [10] : e.g. to make the Hot Composite Curve: we draw on the T-H diagram some segments which represent the trend of the hot streams from their inlet temperature and enthalpy to their outlet conditions.
Considering constant heat capacities, the Cp will be equal to the inversed slope of the segments represented. Highly non linear Cp is represented into successive segments with constant Cp. For each elementary temperature interval in the temperature range, the cumulated heat load is calculated as a sum of the contributions of each of the streams present in the interval, and an equivalent segment representing all the streams in that temperature interval can be represented as shown in Figure 3.2.
The total heat load required is computed as a sum of the heat loads in each temperature interval, eq.(3.1).
X ˙
MhC ph,k(Tk− Tk−1) (3.1)
The same procedure can be followed to build up the Cold Composite Curve.
For the whole system, the Composite Curves can be seen as two equivalent hot and cold streams that could exchange heat using counter-current heat exchangers. Heat recovery between hot and cold composite curves is feasible just when the hot composite is above the cold composite. Assuming a∆Tmi n value, the cold composite curve may be shifted
horizontally until the smallest vertical distance between the two curves reaches the∆Tmi n.
The point where this value of∆Tmi noccurs is called "Pinch Point". Consequently we can read
on the figure the minimum Hot and Cold Utilities Q+and Q−(fig.3.3). The minimum energy requirement (MER) is defined as the difference Q+−Q−.
The position of the Pinch Point indicates the temperature of the process where the heat transfer is most difficult and the temperature difference between the streams is lower. Away from this point the temperature approach increases and the heat exchange will be easier. To
Figure 3.2 – Hot composite curve construction [11]
locate the Pinch Point and to calculate the Minimum Energy Requirement we could use a graphical method like the one explained before or a mathematical approach which is proposed by Linhoff[11].
Comparing the MER obtained for one given∆Tmi nand the present energy consumption, we
are able to quantify the possible energy savings by heat recovery with a global vision of heat exchange in the system. In addition, considering that the heat load of the hot and cold streams is constant, each unit of energy supplied to the system by a hot utility in addition to the MER will, by energy balance, correspond to the same additional heat load to be evacuated by the cold utility. This is known as ”the more in - the more out” principle. This means also that any hot utility saving will result in the same energy saving for the cold utility. Therefore the following statement is valid:
Figure 3.3 – Hot and Cold Composite Curves
With respect to the MER, any additional unit of heat that is added to the system by a hot utility is in reality bought to heat up the cold utility, i.e. ”to heat up the environment” [10]
Another important statement deduced by the pinch analysis is:
Under a given∆Tmi nassumption, the Pinch Point divides the system in two independent
sub-systems: above the Pinch Point there is a heat sink, below the Pinch Point there is a heat source, between which there will be no heat exchange. This issue implies the following considerations
concerning the heat exchange between the streams:
• below the Pinch Point the heat available in the hot streams is greater than the heat re-quired by the cold streams. Therefore there is no need to supply energy with a hot utility below the pinch point . If a hot utility is used it will be added to the hot streams, therefore it will just heat up the environment and it will increase the cold utility requirement as explained by the "more in-more out" principle.
• above the Pinch Point the opposite situation occurs. There is a heat deficit so the heat content of the hot streams should be used to heat up the cold streams. If a cold utility is used less heat will be available for the cold streams so the hot utility requirement increases.
• the two sub-systems are independent and heat should not be cascaded across the Pinch Point. If a hot stream above the pinch point transfer heat to a cold stream below the pinch point, its heat will not be available for the cold streams above the pinch point, this will increase the hot utility required and consequently also the cold utility.
As in the case of a single heat exchanger, also when we consider the global system the∆Tmi n
assumption has to be tested against the energy-capital trade-off. The ∆Tmi n value is an
"experience value" chosen by an engineer. It is directly linked to the area of the heat exchanger through the∆Tl mand through the heat transfer coefficient. In order to confirm the validity of
the∆Tmi nit is necessary to make an estimation of the area required for the Heat Exchanger
Network that will realise the heat recovery. A first estimation of the total Area is needed before the design of the Heat Exchanger Network itself. This estimation can be obtained making some assumptions described in Reference [10], these are not indicated here for brevity.
3.4 The Heat Exchanger Network Design
3.4.1 Introduction
Starting from the definition of the complete list of streams to be considered, the Heat Ex-changer Network design task can be completed by answering three questions:
”Which hot and cold streams should exchange heat ?” ”What is the heat load corresponding to this exchange?”
”How are the heat exchangers interconnected?” (What are input and output temperatures? Is there a split? Etc...)
This is a combinatorial problem with many possible matches. Two types of approaches may be used to solve the heat exchanger network design problem.
1. The pinch design method which is a method mainly based on heuristic and feasibility rules
2. The mathematical programming methods state the HEN design problem as a Mixed Integer (Non)Linear programming problem, solving the combinatorial nature of the problem using specific optimisation algorithms.
Both approaches have advantages and disadvantages, it is usually advantageous to combine them to obtain the "optimal" HEN. For engineers, this optimality is not only the minimum total cost of the system. It has also to fulfil a set of criteria specific to the plant under study. These include the flexibility, reliability, safety, layout, starting, operability, retrofit (i.e. existing units) and technological constraint [10].
The HEN is usually represented graphically as a grid, as the one in Figure 3.4. The streams are represented by vertical lines, hot streams going top-down, cold streams going down-top. The horizontal lines represent the connections between the different streams, therefore the heat exchangers which are present in the system. The streams which have a lower temperature below the pinch point and the upper temperature over the pinch point are named "pinch
Figure 3.4 – HEN grid representation
streams", the exchangers that linked them are named "pinch heat exchanger". The HEN design starts from the pinch point where the approach temperature is known, and goes on getting farther from the Pinch Point.
3.4.2 The Pinch design method
The Pinch Design method is a heuristic method for the design of Heat Exchanger Network. It has been developed by Linhoff [11] and is summarised in Reference [10]. It follows some simple heuristic and feasibility rules. The feasibility rules concern the pinch heat exchangers, here they are explained focusing on the subsystem over the Pinch Point, but they are analogous for the lower subsystem. They are basically:
• The Number of stream rules:
Figure 3.5 – Number of stream rules above the pinch point
the hot pinch streams must be cooled down until the Pinch Point from the cold pinch streams. Therefore the number of cold pinch streams must be greater or equal to the number of hot pinch streams. When this condition is not verified the cold streams have
to be split as shown in Figure 3.5 and the heat exchange occurs in parallel.
• The Cp rule: as can be seen from Figure 3.6, the minimum temperature approach should
Figure 3.6 – The Cp rule
be respected. Above the pinch point the minimum temperature approach occurs on the cold side, therefore on the hot side the temperature approach should be higher. To allow this the ˙MCpof the cold streams must be higher than the one of the hot streams.
Furthermore, when the heat exchanger is placed, the remaining heat exchangers should still satisfy the Pinch Point, therefore the cumulated ˙MCpof the remaining cold streams
should be greater than the one of the hot streams. When the Cprule is not satisfied the
hot stream which has a too high ˙MCpshould be split and the number of stream rules
should be reexamined.
˙
MihotC pihot ≤ ˙Mjcol dC pjcol d (3.2)
nhot
X
i =1,i 6=ihot
˙ MiC pi≤ ncol d X j =1,j 6=jcol d ˙ MjC pj (3.3)
Many heuristic rules can also be followed:
• The tick off rule: once a heat exchanger is found the heat load must satisfy at least the heat requirement of one of the two streams involved
• Remaining problem analysis: once a heat exchanger is placed the two streams involved are no more available to exchange heat, therefore the streams list must be updated. A new heat cascade, a new MER and possibly a new Pinch Point should be calculated. If the heat exchanger was well placed, the new MER will be almost the same as the previous. Otherwise the heat exchanger is creating a penalty that we can decide to accept or not.
Figure 3.7 – The synthesis pinch design method
• Splitting factors: splitting some stream could be required for the heat exchanger place-ment, the splitting factor can be calculated in order to achieve isothermal mixing or the
˙
MCpratio between the streams can be considered to decide the splitting factor.
• Other heuristic rules
-When trying to identify the streams to be connected, a lot of possibilities remain. It is recommended to start the design procedure by considering first the cold and hot streams with the highest ˙MCp.
-The utility streams are usually at the end of the temperature range and have flowrates that can be manipulated, it is therefore recommended to place heat exchangers with the utility streams at the end of the heat exchange in order to control the target temperature of the associated process streams.
-For reason of flexibility, the utility streams are preferably split if they are matched with more than one process streams
Away from the Pinch Point the exchanges are usually easier, but the remaining problem analysis show that new Pinch Point can be created. A summary of the pinch design method that can be used (is just one method, not the optimal one) is summarised in Figure 3.7
3.4.3 The mathematical programming approach
The pinch design method is a sequential method, that does not guarantee that the sequence of decisions will lead to the best network or to a network that will have the expected minimum number of heat exchangers. Instead of applying heuristic rules in order to identify the streams
Figure 3.8 – Mathematical programming techniques
to be connected, a mathematical approach can be used. Mathemical programming is a powerful tool and can be used to solve an optimization problem. Basically a set of equations can be solved in order to minimize (or maximize) one or more objective functions, respecting some constraints imposed to the problem. The variables of the equations that make up the problem can be continuous or integer. Many techniques can be utilized to solve the mathematical problem as shown in Figure 3.8. In the case of the Heat Exchanger Network basically the problem statement is:
• Given a set of hot and cold process streams with given mass flow rates, inlet and outlet temperatures
• Given a set of available utility systems (e.g., cooling water, boiler, multiple-level steam cycle, refrigeration cycle, heat pump, etc) with given thermal streams snd given optional heat/energy storage systems
• Given cost data related to heat exchangers and utility systems
• Determine the optimum heat exchanger network configuration as well as design and the optimal selection, size and load of the utility systems such as Total Yearly Costs are minimized.
The Heat Exchanger Network is modeled considering a superstructure approach: binary variables (0-1) are used to assign matches of heat exchangers; continous variables are used to optimize mass-flows and temperatures on the superstructure.
Figure 3.9 – Example of objective function [13]
The objective function of the problem is not continuous and not derivable, vertical jumps are activated by integer variables, as shown in Figure 3.9 The optimization problem that arises is a hard NP problem, which is the most difficult class of optimization problems. This is due to many constraints that can not be avoided: the optimization problem must indeed identify the best matches between hot and cold streams taking into account the need for forbidden matches, the temperature dependence of physical and transport properties, the different type of streams (liquid, vapor, two-phase, condensing or evaporating streams), and other different issues.
The first times that the mathematical approach has been utilised for HEN was during 1980’s, thanks to the aid of the first computers an approach called "sequential approach" was devel-oped using MILP (Mixed Integer Linear Programming) and NLP(Non Linear Programming). During 1990’s the MINLP (Mixed Integer Non Linear Programming) solvers were developed and the first models with a "simoultaneous approach" were used. Nowaday also hybrid meth-ods between these has been developed as the one described in Reference [12]. The sequential and symultaneous approaches are here briefly described. The sequential approach was first proposed by Floudas and Grossmann [13]. It is based on the solution of three optimization models:
• Minimum operating cost optimization (LP): determines the minimum Utility costs • Minimum number of matches optimization (MILP): determines the pairs of streams
Figure 3.10 – Sequential approach scheme [13]
• Minimum area costs (NLP): determines the minimum heat exchanger area cost, mod-elling the superstructure, it determines if streams exchange in series, in parallel, splitters, mixers etc...
These three optimization problems are solved in sequence as shown in Figure 3.10. The main advantages of this kind of approach are: the capability to treat high size problems with many streams, thanks to the decomposition of the optimization problem in three steps and a superstructure which allow non-isothermal mixing. The problem does not require a high computational effort and is quite fast to solve. The main disadvantage is that this approach does not solve the problem with a global vision of the trade-offs to be taken into account, since it solves three problems in sequence, therefore it does not supply an optimal solution because the decisions taken at the first steps can affect the solution of the final step.
It is exactly for the lack of a global vision of the problem that the Simoultaneous approach has been developed. This was proposed by Yee and Grossmann [14]. It is based on one single optimization model which aims to minimize the total annual cost of the Heat Exchanger Network, taking into account the utilities, the number of connections and the cost of the exchangers at the same time. The model is a MINLP (Mixed Integer Non Linear Programming) and it is a NP-Hard Programming Problem, therefore it requires a high computational effort. The temperature interval is split in stages, the number of stages affect the computation time. The main advantage of this approach is that it properly estimates the trade-offs between the utility size, the number of exchangers and the cost of the heat exchanger areas. The main disadvantage is the computational effort required to solve the problem, this allow to solve just small scale problems. Additionally only isothermal mixing is possible and the hot and cold utility streams have to be placed on the top and on the bottom of the heat cascade, respectively. Hybrid approaches between the sequential and simoultaneous have been developed since
Figure 3.11 – HEN modeled with Simoultaneous approach [13]
2000’s, additionally the spread of derivative-free optimizers and parallel computing allowed to decompose simoultaneous MINLP algorithms [15].
In conclusion, the HEN design problem is by essence a multi-modal problem, i.e. an optimiza-tion for which several local optima exist [10]. Furthermore, several criteria are not explicitly considered in the optimization problem, it is therefore important to consider that several solutions exist and that a good HEN for one situation or location will not necessarily be an optimal system for another location or situation. One has also to keep in mind that the∆Tmi n
constraint is just an assumption that allows one to solve the problem and that the experience of engineers is fundamental to be used together with the aid of pinch analysis, in order to find a feasible and satisfying solution.
4.1 The SOFC-GT Range Extender
In this thesis a Heat Exchanger Network will be designed for a Solide Oxide Fuel Cell-Gas Turbine system integrated on a hybrid car.
Electric vehicles are a low pollution possibility for displacements but they are limited by the poor authonomy that they offer (about 200 km in average). The increase of battery capacity requires high cost and environmental impact.
The SOFC-GT system studied in the work of Dimitrova [1] and Facchinetti [2] proposes an innovative concept of vehicle propulsion. An electric vehicle with limited battery packs is coupled with a Solid Oxide Fuel Cell with gas turbines system, used as a range extender. This energy integrated converter is characterized by high energetic efficiency – around 70%, which includes also the integrated on board fuel reforming. Thus, the concept presents the advantage to extend the vehicle basic electric range thanks to this highly efficient converter. A second advantage is the reforming of a liquid fuel on board. Thus the H2 storage is avoided. The liquid fuel is methane produced from biomass and liquefied at 200 bars pressure in the vehicle tank. Many studies have been developed concerning the use of Fuel Cells in automotive applications, mostly on Polymer Electrolyte Membrane Fuel Cells (PEMFC). The advantages of the PEM are that they offer high safety, support well transients and operate on low temperature (80°C). The disadvantage of the PEM is that they operate with hydrogen stored on the vehicle board. With the limited hydrogen distribution infrastructure, the use of PEMFC is also limited. The use of SOFC avoids this problem. SOFC is a high temperature operating fuel cell – 800°C to 1000°C, which can use a variety of fuels instead of hydrogen such as CH4 or others fossil fuels. The studies of Facchinetti and Dimitrova investigated the SOFC to be applied on hybrid cars, with the main idea to use liquid fuel from renewable resources (for example methane from biomass). The installation has an integrated fuel reformer.
tur-bines for energy recovery in order to increase the overall system efficiency from fuel reforming to electricity output up to 72 % . The main inconvenient of the SOFC is that is not convenient for transient due to the high temperature operation. This issue can be overcome for the SOFC if it is considered as a range extender unit for the vehicle working on permanent regime and supplying electricity to the high voltage battery. The power required by the vehicle (for the powertrain and the comfort system) always comes from the battery and never directly from the SOFC-GT module. The SOFC should operate in on/off mode: when the battery charge is under a certain level the SOFC-GT will charge the battery and will be off when the maximum battery charge level is reached.
Professor Maréchal and his students developed an interesting concept of dual application of the SOFC-GT unit which consists to plug the SOFC unit to the house when the vehicle is not used. The SOFC-GT is supplied with renewable CH4 from the grid and produces electricity or can be a cogeneration unit if heat is also demanded.
The system proposed by Facchinetti has the particularity to work at atmospheric pressure overcoming the difficulty of maintaining the fuel cell pressurization and to have two gas turbines driven in an inverted Brayton-Joules cycle. This innovative concept is illustrated in the figure (4.1). The system proposes a separation of the cathodic and anodic flows. The anodic flow, which contains unconverted fuel due to the fuel utilization ratio inferior to 1 at the fuel cell, goes to the burner to combust the remaining fuel with pure oxygen used as oxidizer instead of air. The advantage to use O2 is that CO2 and water are the unique outputs. CO2 can be stored after removal of water by condensation. The cathodic flow which is basically impoverished in oxygen is expanded in the cathodic turbine for power generation. The electric power of the SOFC-GT system studied in our work is 5 kW.
4.2 AMPL Model and Results for the Heat Exchanger Network
From the scheme in fig. 4.1 we can see where heat exchanges are necessary to satisfy the required heat loads for the streams. In our system some hot streams have to be cooled down and some cold streams have to be heated up. These streams can be matched in order to satisfy their energy needs without using external hot or cold utilities.
A mathematical model written in AMPL language has been used in this work to optimize the heat recovery between hot and cold streams, minimizing the number of heat exchangers, in order to design a feasible Heat Exchanger Network. The code uses the symoultaneous technique described in chapter 3 to solve the optimization problem. Isothermal mixing of streams and heat exchange in parallel with more streams are allowed by the model. Constraints can be imposed in order to avoid heat exchange between specific streams, to avoid the splitting of streams or to limit the amount of Cold Utility that can be used. The first results obtained with the aid of the solver CPLEX are shown in table 4.1. The results of the model indicates 17 heat exchangers, among which 3 are with a Cold Utility. These results have been used in the design of the Double pipe heat exchangers. The "stages" of temperature are useful to understand
when a stream is exchanging heat in parallel with more streams. If a stream exchanges two or more times in the same stage of temperature, it means that it should exchange in parallel, so its mass flowrate has to be split in the design. The mass flowrate will be split in each heat exchanger proportionally to the corresponding heat load.
Table 4.1 – AMPL results; first calculation
Stream 1 Stream 2 Stage Heat load [W]
FC3 FP5 1 431 FC3 FC1 3 79 CT2 FC2 10 3280 CT3 FP1 1 69 AT4 FP5 2 426 AT4 CT1 1 231 AT5 FP2 11 919 AT5 FP3 9 487 AT5 FP4 9 269 AT5 FP5 4 659 AT5 FC2 2 256 AT6 FP1 3 12 CC1 FP1 1 47 CC2 FC2 11 47 CT3 ColdUtility 797 AT5 ColdUtility 1202 CC3 ColdUtility 94
Two other calculations were made with different inputs. In one, tab.4.2, we merged the streams FP-1,2,3,4 in one heat exchanger, the water being evaporated through straight injection in the fuel FP-4 (in the table this heat load is simply indicated as FP-1). 14 heat exchangers are prescribed, among which 3 are with the Cold Utility.
In the other one, tab.4.3 we imposed a constraint, the CO2 streams could not exchange with the other streams but should exchange with the Cold Utility. This allow potentially the separation of the CO2 compression plant from the rest of the system. 14 heat exchangers are prescribed, among which 5 are with a Cold utility. The first principle total efficiency is similar to the previous one, even with the separation of the CO2 streams. This results have been used in the design of minichannel heat exchangers and are proposed as final results of our work. In figure 4.2 we can see the connections between the streams.
Once that a list of matches between the streams is available we can start to design the single heat exchangers. To start with a simple layout, we will size the heat exchangers in a double pipe straight configuration, while more complex design will be analyzed farther. The LMTD method has been used to size the heat exchangers.
Table 4.2 – AMPL results; water contact evaporation injecting in stream FP-4
Stream 1 Stream 2 Stage Heat load [W]
FC3 FP5 5 431 FC3 FC1 1 79 CT2 FC2 1 3280 AT4 FP5 1 230 AT4 FC2 1 196 AT4 CT1 1 231 AT5 FP1 2 1807 AT5 FP5 1 855 AT6 FC2 9 12 CC1 FC2 9 47 CC2 FC2 11 47 CT3 Cold Utility 867
AT5 Cold Utility 1131
CC3 Cold Utility 94
Table 4.3 – AMPL results; water contact evaporation in stream FP-1, separated CO2 compres-sion system
Stream 1 Stream 2 Stage Heat load [W]
FC3 FP5 5 511 CT2 FC2 2 3280 AT4 FP5 2 346 AT4 FC1 2 79 AT4 CT1 1 231 AT5 FP1 2 1807 AT5 FP5 1 659 AT5 FC2 2 303 CT3 ColdUtility 867 AT5 ColdUtility 1024 AT6 ColdUtility 12 CC1 ColdUtility 48 CC2 ColdUtility 47 CC3 ColdUtility 95
Selection
5.1 Streams Properties
The properties of the streams have been listed on a sheet in an Excel file and will be recalled in the design of the heat exchangers. The temperatures, mass flowrate and volumetric flowrate were calculated with the software Belsim Vali, solving an optimization problem applied on the entire SOFC-GT system [16]. The termophysical properties have been identified using
Figure 5.1 – A flowsheet of part of the SOFC-GT system in Belsim Vali
the software Aspen Plus. The "REFPROP base method" has been used. This method pro-vides thermodynamic and transport properties of "industrially important fluids and their mixtures with an emphasis on hydrocarbons, especially Natural Gas systems", as mentioned in his description on Aspen Plus. Consequently this method has been considered suitable to correctly identify the properties of the main reference substances which are used in our system (Air, Water, CH4, CO2, H2...). Most of the streams are multi-component gaseous
Figure 5.2 – Aspen Plus user interface
mixtures, but also liquid, condensing and evaporating streams are present. In summary, the main properties which are required for heat exchanger design purpose are: mass and volumetric flowrate ˙m = [kg /s]; ˙Qv = [m3/s], Temperature T = [K ], Thermal Conductivity
K =£ W
mK¤, Densityρ = [kg/m3], heat capacity Cp=
h
J kg K
i
and dynamic viscosityµ = [Pas] . These properties have been collected at the inlet and outlet section of every component of the system (compressors, turbines, fuel cell, reformer...).
All of these thermodynamic data have been listed on an Excel file and will be used in the heat exchanger design, in order to calculate the sizing of heat exchangers. Sometimes mean values between the ones of the list were required in the HE design, in these cases linear interpolation has been used, approximating a linear trend of properties with temperature.
5.2 Fouling Coefficients
The Fouling Resistances have been taken from the Reference [3] and are indicated in Table 5.1. Mean values have been considered: 3000mW2K has been taken for water; 7500
W
m2K has been
taken for gaseous streams. These values have been used in the calculation of heat transfer coefficients. The cleaning of heat exchangers has not been investigated in this work. This issue should not cause too many problems because of the gaseous nature of the fuel, but should be taken into account in the final design of heat exchangers.
Table 5.1 – Fouling Coefficients; typical values
5.3 Materials Selection
The materials selection has been made following the indications of the reference [17]. A list of some materials that have been taken into account is presented in Table 5.2. The main parameters that have been considered are the Corrosion Resistance, the Thermal Conductivity, the Density, the Thermal Dilatation, the Melting temperature and the Price. In the final results of our work we will split our Heat Exchanger Network in four different regions: High temperature, Pinch Point Region, Low Temperature, CO2 compression. The Weight of the exchangers have been calculated using Tantalum for the Hot temperature region and Titanium for the others. Deeper studies should be developed in order to choose the optimal materials to be used, allowing a reasonable trade-off between the performances and the costs. The manufacturing technique should also be considered.
6.1 Introduction
A Double Pipe Heat Exchanger consists of one pipe placed concentrically inside another pipe of larger diameter called Annulus. The major use of the double-pipe heat exchanger is for sensible heating or cooling processes where small heat transfer areas (up to 50 m2) are required [8] .
Due to its simplicity and moderate heat loads of the heat exchangers in our system, this configuration has been chosen to be investigated at a first analysis. In our case a simple straight one-pass configuration will be analyzed, as the one shown in Figure 6.1.
Figure 6.1 – Double Pipe Heat Exchanger [19]
Double pipe HE can be arranged in various series and parallel arrangements to meet pres-sure drop and MTD (Mean Temperature Difference) requirements. The most conventional arrangement is the U-tube in Figure 6.2 , multiple tube layouts are also possible, Figure 6.3. In many common configurations the outer surface of the inner tube is finned, mostly when heat transfer coefficients are low: in these cases fin efficiency is higher. The fins increase the heat transfer surface per unit length, allowing to reduce the total length of the heat exchanger. One of the main advantages of double pipe heat exchangers is their ease of cleaning which allow them to be used also under severe fouling conditions. They usually operate in true
countercurrent flow, which yields the most efficient design for processes that have a close temperature approach [4].
Figure 6.2 – U-shape Double Pipe Heat Exchanger [8]
Figure 6.3 – Multi-tube Double Pipe Heat Exchanger [8]
6.2 Design of Double Pipe Heat Exchangers
6.2.1 Introduction
The design of Double Pipe Heat Exchangers has been developed using an Excel file. In the first worksheet of the Excel file all the properties of the streams of the SOFC-GT system are listed. To every stream is associated a number. In the second worksheet of the Excel file the design of heat exchanger is performed, using the iterative method described in Chapter 2. The file has been created to be as flexible as possible in order to have the possibility to change easily the matches beetween the streams.
The main concept is: for each heat exchanger prescribed by the AMPL code the numbers referring to each stream (as suggested in Figure 6.4), the inlet and outlet temperatures and the heat loads are typed. All of this data are supplied by the AMPL code.
Figure 6.4 – Streams list
The Excel file must be able to calculate the dimensions of pipes (and with them the heat transfer area), the heat transfer coefficients and the pressure drops of each heat exchanger. Some complications are occurring and must be taken into account:
• the calculation of heat transfer coefficient is not always straightforward, the turbulent and laminar case should be distinguished, the effect of the entrance region should be taken into account. In our calculations a constant heat transfer coefficient along the flow direction will always be used, using mean values of properties to assume it. • sometimes streams needs to be splitted in order to exchange heat in parallel with more
streams
• most of the times the properties of streams are required at temperatures which are different from the ones listed in worksheet n.1. Linear interpolation will be used to estimate them, considering linear trend with temperature.
• sometimes a change of phase occurs in the streams, in these cases the design becomes more complicated compared with the case of sensible heat transfer, some approxima-tions will be done to reduce the complexity of the model.
6.2.2 First trial sizing
As previously said, the AMPL results file show the optimal matches between the streams, the inlet and outlet temperatures of each exchange, the heat load, and whether heat exchange occurs in parallel with other streams.
In n er tu b e in p u t A n n u lu s in p u t H ea t ex ch an ge r in p u t an d r esu lts St rea m n . (1 ) St rea m n ame St rea m p h as e (l =1 ;v=2 ) Pres su re [b ar] T_i n [K ] (1 ) T_o u t [K ] (1 ) Sp lit V o l.f ra ct i o n ( 2) H E V o l.f ra ct io n ( 3) St rea m n . (1 ) St rea m n ame St rea m p h as e (l =1 ;v=2 ) Pres su re [b ar] T_i n [ K] (1 ) T_o u t[ K] (1 ) Sp lit V o l.f ra ct io n (2 ) H E V o l.f ra ct io n ( 3) To ta l h ea t lo ad [W ] 3 SR _W _1 ( FP -1 ) 1 1 305 374 0.5 94 82 8 0. 59 48 27 6 73 FC _C _7 ( C T-3) 2 1 488 473 1 1 69 3.1 SR _W _1 ( FP -1 ) 1 1 298 305 1 1 50 FC _A _8 ( A T-6) ** 2 1 393 353 1 1 12 3.2 SR _W _1 ( FP -1 ) 1 1 305 374 0.4 05 17 2 0. 40 51 72 4 59 C O 2_C O M P_1 ( C C -1 ) ** 2 1 505 360 1 1 47 4 SR _W _3 ( FP -2 ) * 1 1 374 375 1 1 46 FC _A _6 ( A T-5) 2 1 780 571 1 1 919 46 FC _A _6 ( A T-5) 2 0.2 00 07 4 952 780 0.6 4 0. 64 5 SR _W _4 ( FP -3 ) 2 1 375 950 1 1 487 46 FC _A _6 ( A T-5) 2 0.2 00 07 4 952 780 0.3 6 0. 36 8 SR _M _1 ( FP -4 ) 2 1 298 947 1 1 269 46 FC _A _6 ( A T-5) 2 0.2 00 07 4 1102 952 1 1 11 SR _IN (F P-5) 2 1 950 950 1 1 659 44 FC _A _5 ** (A T-4) 2 1 1634 1473 1 1 11 .1 SR _IN (F P-5) 2 1 950 950 1 1 426 26 FC _A _3 ( FC -3 ) 2 1 1356 1140 1 1 11 .2 SR _IN (F P-5) 2 1 950 950 1 1 431 26 FC _A _3 ( FC -3 ) 2 1 1140 1100 1 1 17 SR _O U T (F C -1 ) 2 1 950 1000 1 1 79 71 FC _C _5 ( C T-2) 2 0.2 00 00 2 1011 320 1 1 21 FC _C _1 ( FC -2 ) 2 1 307 950 1 1 3280 46 FC _A _6 ( A T-5) 2 0.2 00 07 4 1160 1102 1 1 21 .1 FC _C _1 ( FC -2 ) 2 1 950 1000 1 1 256 61 C O 2_C O M P_3 ( C C -2 ) ** 2 15 .0 37 6 505 360 1 1 21 .2 FC _C _1 ( FC -2 ) 2 1 298 307 1 1 47 44 FC _A _5 ** (A T-4) 2 1 1722 1634 1 1 69 FC _C O U T (C T-1) 2 1 1356 1400 1 1 231 40
