SimulationofanOxygenMembrane …projects.itn.pt/PTDC64357/SJ18.pdf(12) Campanari, S. Full load and...

590r 2009 American Chemical Society pubs.acs.org/EF

Energy Fuels 2010, 24, 590–608 : DOI:10.1021/ef9004253Published on Web 12/02/2009

Simulation of anOxygenMembrane-BasedGasTurbinePowerPlant:DynamicRegimes

with Operational and Material Constraints

Konrad Eichhorn Colombo,*,† Vladislav V. Kharton‡ and Olav Bolland†

†Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjoern Hejes vei 1B,NO-7491 Trondheim, Norway, and ‡Department of Ceramics and Glass Engineering, CICECO, University of Aveiro,

3810-193 Aveiro, Portugal

Received May 8, 2009. Revised Manuscript Received August 19, 2009

This paper investigates the transient behavior of a natural gas-fired power plant for CO2 capture thatincorporates mixed-conducting membranes for integrated air separation. The membranes are part of areactor system that replaces the combustor in a conventional gas turbine power plant. A highlyconcentrated CO2 stream can then be produced. The membrane modules and heat exchangers in themembrane reactor were based on spatially distributed parameter models. For the turbomachinerycomponents, performance maps were implemented. Operational and material constraints were empha-sized to avoid process conditions that could lead to instability and extensive stresses. Two load-controlstrategies were considered for the power plant with a gas turbine operating at constant rotational speed. Inthe first load-control strategy, variable guide vanes in the gas turbine compressor were used to manipulatethe mass flow of air entering the gas turbine compressor. This degree of freedom was used to control theturbine exit temperature. In the second load-control strategy, variable guide vanes were not used, and theturbine exit temperature was allowed to vary. For both load-control strategies, the mean solid-walltemperature of the membrane modules was maintained close to the design value. Simulation reveals thatthe membrane-based gas turbine power plant exhibits rather slow dynamics; fast load following was hencedifficult while maintaining stable operation. Comparing the two load-control strategies, load reductionwith variable air flow rate and controlled turbine exit temperature was found to be superior because of theconsiderably higher and faster load reduction capability, increased stability of the catalytic combustors inthe membrane reactor, and higher power plant efficiencies.

1. Introduction

The power and industry sectors combined contribute morethan 60% of all anthropogenic emissions of CO2.

1 Theincreasing demand for energy will lead to further emissionsincreases unless environmental issues are addressed. CO2

capture and storage (CCS) is one option in the portfolio ofactions for the stabilization of atmospheric greenhouse gases.2

In addition to system improvements to existing power plants,novel power plant configurations withCO2 capture have beendeveloped. Thesemay be largely classified into pre-, post-, andoxy-combustion power plants. One concept in the oxy-combus-tion family for natural gas is shown in layman terms inFigure 1.The combustor in a conventional gas turbine (GT) power plant

(Figure 2) is replaced by the membrane reactor, which iscomposed of ceramic high-temperature membrane modules,as well as heat exchangers (HXs), and catalytic combustors.3-6

Themembranemodules andHXs in themembrane reactorwereassumed to be fabricated as two-fluid monoliths7 (Figure 3).Themembrane-basedGTpowerplant shares certain similaritieswith solid oxide fuel cell GT hybrid cycles. For example, bothare operated at a similar temperature range.8 But whereas solidoxide fuel cell systems have been widely investigated in termsof operational and material constraints (e.g., refs 9-11 and

*To whom correspondence should be addressed. E-mail: (K.E.C.)[email protected]); (V.V.K.) [email protected]; (O.B.) [email protected].(1) Metz, B.; Davidson, O.; de Coninck, H.; Loos, M. Meyer, L.

Summary for Policymakers.Carbon Dioxide Capture and Storage; IPCCSpecial Report; Cambridge University Press: Cambridge, U.K., 2005.(2) Pacala, S.; Socolow, S. R. Stabilization Wedges: Solving the

Climate Problem for the Next 50 Years with Current Technologies.Science 2004, 305, 968–972.(3) Bruun, T. P., Grønstad, L., Kristiansen,K.,Werswick, B., Linder,

U. Device for combustion of a carbon containing fuel in a nitrogen freeatmosphere and a method for operating said device. WO 02/053969 A1,2002.(4) Bruun, T., Hamrin, S. Combustion installation. Int. Patent WO

2007/060209A1, 2007.(5) Linder, U.; Eriksen, E. H.; Asen, K. I. A method of operating a

combustion plant, and a combustion plant using separated oxygen toenrich combustion air. US 6,877,319 B2; 2005.

(6) Griffin, T.; Sundkvist, S. G.; Asen, K.; Bruun, T. Advanced zeroemissions gas turbine power plant. J. Eng. Gas Turbines Power 2005, 127(1), 81–85.

(7) Bruun, T., Werswick, B., Kristiansen, K., Grønstad, L. Methodand equipment for feeding two gases into and out of a multi-channelmonolithic structure. U.S. Patent 7285153, 2007.

(8) O’Hayre, R. P.; Colella, W.; Cha, S.-W.; Prinz, F. B. Fuel CellFundamentals, 2nd ed.; Wiley: Hoboken, NJ, 2009; pp XXV, 546.

(9) Bove, R., Ubertini, S., Modeling Solid Oxide Fuel Cells Methods,Procedures and Techniques; Springer: Netherlands, 2008.

(10) Vielstich, W.; Gasteiger, H. A.; Lamm, A. Handbook of FuelCells: Fundamentals, Technology and Applications; Wiley: Chichester,U.K., 2009; Vol. 6.

(11) Vielstich, W.; Gasteiger, H. A.; Lamm, A., Handbook of FuelCells: Fundamentals, Technology and Applications; Wiley: Chichester,U.K., 2009; Vol. 5.

(12) Campanari, S. Full load and part-load performance predictionfor integrated SOFC and microturbine systems. J. Eng. Gas TurbinesPower 2000, 122 (2), 239–246.

(13) Milewski, J.; Miller, A.; Saacinski, J. Off-design analysis ofSOFC hybrid system. Int. J. Hydrogen Energy 2007, 32 (6), 687–698.

(14) Stiller, C.; Thorud, B.; Bolland, O.; Kandepu, R.; Imsland, L.Control strategy for a solid oxide fuel cell and gas turbine hybrid system.J. Power Sources 2006, 158 (1), 303–315.

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Energy Fuels 2010, 24, 590–608 : DOI:10.1021/ef9004253 Eichhorn Colombo et al.

references therein), part-loadoperation (e.g., refs 12-15), andtransient behavior (e.g., refs 14-16), published literature on

the dynamic simulation of oxy-combustion and other CCSpower plants is not available to date,17 with one exception,18

to the best of the authors’ knowledge. A number of questionsarise when looking at the transient performance of themembrane-based GT power plant with regard to nearlystoichiometric combustion and large amounts of recycledgas. When operation conditions change in the membrane-based GT power plant (e.g., changes in load), the wholesystem responds because of the strong interaction of processcomponents. The GT power plant presented here was morecomplicated than the oxy-combustion process in ref 18 be-cause of the use of membrane modules as an integrated airseparation device. Hamrin19 stated (qualitatively) that fasttransient changes are not possible for this membrane-basedGT power plant. Load changes must be executed slowly,considering the operational and material constraints of themembrane reactor components.

This paper is divided into 8 sections. Section 2 describesthe GT power plant and its main components in moredetail. Section 3 outlines operational and material con-straints that must be considered to maintain a reasonablelifetime for process components. Section 4 summarizes thetime scales in the system. Section 5 explains the two load-control strategies for theGT power plant. Section 6 presents apossible start-up and shut-down procedure for the powerplant. Section 7 provides simulation results for a transientload decrease and transient load increase for both load-control strategies. Section 8 concludes with the key pointsof the paper. A detailed model description is given in theAppendix.

2. Gas Turbine Power Plant

In the membrane-based GT power plant (Figure 4), fuelis injected into the membrane reactor by means of subsonicejectors. Steam is extracted from the steam cycle and addedto the fuel for proper ejector performance. The fuel to thecatalytic combustors must be preheated to avoid two-phaseflow in the ejectors. The compressed air from the GT com-pressor is split, with the majority led through the low-temperatureHXs, membranemodules, and high-temperatureHXs. The remainder is fed to the bleed-gas HX branch.The air in these two branches is heated and mixed afterward.In the membrane modules, oxygen is transported from the airside to the sweep gas side. The temperature of the oxygen-depleted air is further increased in the afterburners beforebeing fed to the GT turbine. It should be noted that the CO2

produced in the afterburners is emitted to the atmosphere.Capturing these small amounts ofCO2 is not practical becauseof the low CO2 pressure. Geometric and operational con-ditions were adjusted to obtain required power plant perfor-mance in conjunction with satisfying all operational andmaterial constraints.

2.1. Gas Turbine. In this paper, a steady-state approxima-tion for the turbomachinery was assumed. The compressormaps are based on Mach number similarity, where second-order effects are neglected, such as changes caused by

Figure 1. Principle of the membrane-based combined cycle powerplant with CO2 capture. The temperature distribution is indicatedthroughout the process.

Figure 2. Conventional gas turbine power plant.

Figure 3. Oxygen mixed-conducting membrane module (top) andmodeling manifold (bottom) with design specifications.

(15) Magistri, L.; Traversa, A.; Cerutti, F.; Bozzolo, M.; Costamagna,P.; Massardo, A. F. Modelling of pressurised hybrid systems based onintegrated planar solid oxide fuel cell (IP-SOFC) technology. Fuel Cells2005, 5 (1), 80–96.(16) Roberts, R. A.; Brouwer, J. Dynamic simulation of a pressurized

220 kW solid oxide fuel-cell-gas-turbine hybrid system: Modeledperformance compared to measured results. J. Fuel Cell Sci. Technol.2006, 3 (1), 18–25.(17) Alie, C.; Douglas, P.; Croiset, E. Scoping Study on Operat-

ing Flexibility of Power Plants with CO2 Capture; www.ieagreen.org.uk;2008.(18) Imsland, L.; Snarheim, D.; Foss, B. A.; Ulfsnes, R.; Bolland, O.

Control issues in the design of a gas turbine cycle for CO2 capture. Int. J.Green Energy 2005, 2 (2), 303–315.

(19) Hamrin, S.Control of a gas turbinewith hot-air reactor.US2006/0230762A1; 2006.

(20) Riegler, C.; Bauer, M.; Kurzke, J. Some aspects of modellingcompressor behavior in gas turbine performance calculations. J. Turbo-machinery 2001, 123 (2), 372–378.

(21) Kurzke, J. Compressor and Turbine Maps for Gas TurbinePerformance Computer Programs;Component Map Collection; Gas-Turb: Dachau, Germany, 2004; http://www.gasturb.de.

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variations in fluid composition.20,21 The single-shaft GT isoperated at a constant rotational speed. The GT compressorwas based on performance maps,21 which are shown inFigure 5. Variable guide vanes (VGVs) were applied toreduce the mass flow of air into the GT compressor by asmuch as 30%.22,23 Variations of the turbine isentropicefficiency were based on a GT turbine chart.24 It is standardengineering practice to pass a fraction of compressed air overthe GT turbine disk and blades. This cooling air fraction wasalso determined by charts24 and represents a fixed parameterin off-design. In general, when matching GT components,individual process components should have the highestpossible efficiency. Furthermore, operation in regions ofinstability must be omitted, for instance where GT compres-sor surge is likely to occur. Maximum isentropic efficiencyfor the GT compressor could not be obtained because of thematching between individual process components. It shouldalso be noted that the high-temperature HXs were operatedat temperatures that are approximately 100 K less than thelimit reported in Sundkvist et al.25 Furthermore, state-of-the-artGTs allow formuch higher turbine inlet temperaturesthan was assumed here. Hence, the combination of opera-tional andmaterial constraints remains the same in principle.

2.2.Membrane Reactor Process Components. 2.2.1.Mem-brane Modules and Heat Exchangers. The dense membrane

layer in the membrane modules was assumed to be based onintergrowth La2NiO4þδ,

26,27 which shows a suitable combina-tion of substantially high oxygen permeability, low chemical

Figure 4. Membrane-based gas turbine power plant.

Figure 5. Off-design performance maps for the gas turbine com-pressor with respect to variations in mass flow and pressure ratio(bottom) and mass flow and isentropic efficiency (top).21

(22) Kim, T. S.; Hwang, S. H. Part load performance analysis ofrecuperated gas turbines considering engine configuration and opera-tion strategy. Energy 2006, 31 (2-3), 260–277.(23) Kim, J. H.; Kim, T. S.; Sohn, J. L.; Ro, S. T. Comparative

analysis of off-design performance characteristics of single and two-shaft industrial gas turbines. J. Eng. Gas Turbines Power 2003, 125 (4),954–960.(24) Walsh, P. P.; Fletcher, P. Gas Turbine Performance, 2nd ed.;

Blackwell Science: Maden, MA, 2004.(25) Sundkvist, S. G.; Julsrud, S.; Vigeland, B.; Naas, T.; Budd, M.;

Leistner, H.; Winkler, D. Development and testing of AZEP reactorcomponents. Int. J. Greenhouse Gas Control 2007, 1 (2), 180–187.(26) Smith, J. B.; Norby, T. On the steady-state oxygen permeation

throughLa2NiO4þδmembranes. J. Electrochem. Soc. 2006, 153 (2), 233–238.(27) Vigeland, B.; Glenne, R.; Breivik, T.; Julsrud, S. Membrane and

use thereof. U.S. 6,503,296B1, 2003.

(28) Paulsen, O. Rigid bonded glass ceramic seals for high temperaturemembrane reactors and solid oxide fuel cells. PhD thesis. NorwegianUniversity of Science and Technology, Trondheim, Norway, 2009.

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and thermal expansion, and relatively goodphase stability.27,28

The dense membrane layer was assumed to be coated on aporous support substratemade of the samematerial, to ensurethermomechanical and chemical integrity.29 The heat exchan-gers in the membrane reactor have the same geometric dimen-sions as the membrane modules, except for the length.

2.2.2. Staged-Catalytic Combustors.Themembrane-basedGT power plant contains two types of combustors. Theafterburners were assumed to be of a standard type. Themembrane reactor includes staged-catalytic combustorswhere catalytic partial oxidation of natural gas is followedby complete oxidation under lean conditions.30 Changes inoperation conditions in terms of temperature,mass flow, andpressure have a significant effect on the catalytic partialoxidation stage (e.g., H2 and CO yields) and therefore onthe overall combustor performance.31 Other hydrocarbonsmay also be found during partial oxidation of CH4, but thesesmall quantities were neglected. Carbon deposition was alsoneglected. To maintain stable and complete combustion,excess oxygen must be available.30,32 Both the staged cata-lytic combustor and afterburner model were based on com-plete oxidation. This assumption leads to improvednumerical stability. To substantiate this approach, an equi-librium-based combustorwas developed and implemented ingPROMS.33 In addition, these two gPROMS models werecompared to a HYSYS34 model. There was a very goodmatch between the three models.

2.2.3. Ejector. The one-dimensional ejector model wasdivided into five sections as shown in Figure 6: (i) nozzlecritical section, (ii) nozzle outlet, (iii) mixing section inlet, (iv)diffuser inlet/mixing section outlet, and (v) diffuser outlet.Studies have shown that in solid oxide fuel cell-GT hybridcycles, ejectors have a considerable effect on the overallpower plant performance.35,36 The ejectors were assumedto operate in the critical regime, which means at elevatedpressures of the actuating fluid (fuel and steam mixture).37

2.2.4. Recycle Loop inMembrane Reactor. The pressure inthe recycle loop depends on the total mass accumulated,which in turn depends on the volume of individual mem-brane reactor components. The outlet of the bleed-gas HXswas chosen as the pressure control location, but otherlocations can be used for this purpose as well.

2.2.5. Model Implementation. The GT power plant modelwas executed in gPROMS,33 an equation-oriented modelingtool. Physical gas properties were obtained from the prop-erty data package Multiflash33 using a Soave-Redlich-Kwong equation of state.

A total of 30 and 50 discretization elements in an axialdirection were used for the membrane module and mono-lithic HXs, respectively. Five discretization elements wereused in the radial direction. A higher number of discretiza-tion elements did not improve results in terms of accuracy,but significantly increased model complexity and requiredCPU time. Heat and mass balances for the cold-side fluidwere discretized by a forward finite difference method,whereas a backward finite difference scheme was applied tothe counter-current hot fluid. The solid-phase energy bal-ance was discretized by a central finite difference method1. Acentral finite difference method was used for the insulationlayer. Pipes were discretized using a backward finite differ-encemethodwith a total number of 15 distribution elements.The approximation of partial derivatives for all spatiallydistributed models was second order. The whole system wassolved by a variable order backward differentiation formulas(DASOLV solver).33 A general rule for the required calcula-tion time cannot be defined a priori. The solver variestime increments depending on discontinuities and currentchanges in process variables. The whole of the membrane-based GT power plant model consists of more than 12 000equations.

3. Operational and Material Constraints for Power Plant

Components

Table 1 shows themost important operational andmaterialconstraints that need to be considered for the membrane-based GT power plant. Some of these constraints are furtherdiscussed in this section. Additional information can be foundin Eichhorn Colombo et al.38

3.1.Mixed-ConductingMembraneModules.At isothermalconditions, the membrane expands with decreasing oxygenpressure. When decreasing the temperature at constant oxy-gen pressure, the membrane contracts due to geometricchanges caused by an increased equilibrium oxygen stoichi-ometry.39 These volume changes must be taken into accountduring operation to lower the risk ofmismatches between thedense membrane layer and the porous support materialand also between all connections of the membrane reactor

Figure 6. Sections of the constant-area ejector model.

(29) Kovalevsky, A. V.; Kharton, V. V.; Snijkers, F. M. M.;Cooymans, J. F. C.; Luyten, J. J.; Marques, F. M. B. Oxygen transportand stability of asymmetric SrFe(Al)O3-[δ]-SrAl2O4 composite mem-branes. J. Membr. Sci. 2007, 301 (1-2), 238–244.(30) Griffin, T.; Winkler, D.; Wolf, M.; Appel, C.; Mantzaras, J. In

Staged Catalytic Combustion Method for the Advanced Zero EmissionsGas Turbine Power Plant; Vienna, Austria, 2004; American Society ofMechanical Engineers: New York, 2004; pp 705-711.(31) Zhu, J.; Zhang, D.; King, K. D. Reforming of CH4 by partial

oxidation: Thermodynamic and kinetic analyses. Fuel 2001, 80 (7), 899–905.(32) Asen, K. I. Gas Processing and CO2, StatoilHydro ASA:

Porsgrunn, Norway, personal communication, 2008.(33) gPROMS (General ProcessModelling andSimulationTool), v 3.1.5,

Process Systems Enterprise Ltd.: London, www.psenterprise.com, 2008.(34) Aspen Technology Aspen HYSYS; Aspen Technology:

Cambridge, MA, 2006.(35) Marsano, F.; Magistri, L.; Massardo, A. F. Ejector performance

influence on a solid oxide fuel cell anodic recirculation system. J. PowerSources 2004, 129 (2), 216–228.(36) Zhu, Y.; Cai, W.; Li, Y.; Wen, C. Anode gas recirculation

behavior of a fuel ejector in hybrid solid oxide fuel cell systems:Performance evaluation in three operational modes. J. Power Sources2008, 185 (2), 1122–1130.(37) Yinhai, Z.; Wenjian, C.; Changyun, W.; Yanzhong, L. Fuel

ejector design and simulation model for anodic recirculation SOFCsystem. J. Power Sources 2007, 173 (1), 437–49.

1The application of mixed finite difference methods was necessary toobtain stable reduced-order models after linearization.

(38) Eichhorn Colombo, K.; ’Bolland, O.; Kharton, V. V.; Stiller, C.Simulation of an oxygen membrane-based combined cycle power plant:Part-load operation with operational and material constraints. EnergyEnviron. Sci. In press (DOI: 10.1039/b910124a).

(39) Carolan, M. F. A.; Watson, M. J.; Minford, E.; Motika, S. A.;Taylor, D. M. Controlled heating and cooling of mixed conductingmetal oxide materials. U. S. Patent7,122,072 B2, 2006.

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Table1.OperationandMaterialConstraintsoftheMem

brane-BasedGTPower

Plant(Figure

4)a

Process

component

constraint

effect

limit

catalyticcombustors

minim

um

oxygen

molefraction

perform

ance

loss

andfailure

dueto

unstableand

incomplete

combustion

0.5

mol%

32

catalystin

thecatalytic

combustors

maxim

um

sulfurconcentration

perform

ance

loss

andfailure

dueto

sulfurpoisoning

ppbrange5

7

ejectors

thermodynamicconditionswithrespectto

temperature,pressure,andcomposition

perform

ance

loss

dueto

form

ationofvapor-

liquid

phase

dependingonprocess

conditions

ejectors

minim

um

pressure

difference

inmixingsection

perform

ance

loss

dueto

operationoutsidethecriticalmode

035,95

ejectors

pressure

ofactuating(fuelandsteam

mixture)fluid

perform

ance

incriticalrange

dependingonprocess

conditions3

7

GTcompressor

maxim

um

variableguidevaneanglelimit

mass

flowreductionbyvariable

guidevanes

30%

22,23

GTcompressor

minim

um

surgemargin

perform

ance

loss

andfailure

due

toasudden

dropin

pressure

anddetrimentalaerodynamic

pulsation

5%

63,64

GTturbine

coolingairfractionto

GTturbine

perform

ance

loss

andfailure

due

tothermomechanicalstresses

dependingontechnology24

GTturbine

maxim

um

turbineinlettemperature

perform

ance

loss

andfailure

dueto

thermo-m

echanical

stresses

1530K

96

high-tem

perature

heatexchangers

maxim

um

temperature

perform

ance

loss

andfailure

dueto

thermomechanicalstresses

1573K

25

high-tem

perature

heatexchangers

maxim

um

sulfurconcentration

perform

ance

loss

andfailure

due

tosulfurpoisoning

dependingonprocess

conditions(poisoningis

favoredatlowtemperatures)

low-tem

perature

heatexchangers

minim

um

temperature

perform

ance

loss

andfailure

dueto


673K

25

low-tem

perature

heatexchangers

maxim

um

sulfurconcentration

perform

ance

loss

andfailure

dueto

sulfurpoisoning

50ppb25

dense

mem

branelayers

andporoussupport

maxim

um

sulfurconcentration

perform

ance

loss

andfailure

dueto

sulfurpoisoning

10ppb25

dense

mem

branelayers

andporoussupport

minim

um

temperature

perform

ance

loss

andfailure

dueto


1173K

25

dense

mem

branelayers

andporoussupport

maxim

um

temperature

perform

ance

loss

andfailure

dueto


andchem

ical

interaction

1323K

25

dense

mem

branelayers

andporoussupport

thermodynamicconditionswithrespect

tomem

branetemperature,CO

2andO

2

pressure

insw

eepgas

perform

ance

loss

andfailure

dueto

carbonate

form

ation

dependingonprocess

conditions2

5,43

dense

mem

branelayers

andporoussupport

thermodynamicconditionswithrespectto

mem

branetemperature,CO

2andO

2

pressure

insw

eepgas

perform

ance

loss

andfailure

dueto

oxidation

dependingonprocess

conditions2

5

dense

mem

branelayers

andporoussupport

thermodynamicconditionswithrespect

tomem

branetemperature,H

2O

andO

2

pressure

insw

eepgas

perform

ance

loss

andfailure

dueto

hydroxideform

ation

dependingonprocess

conditions(favored

atlowtemperatures)43

mem

branemodulesandmonolithic

heatexchangers

maxim

um

pressure

difference

perform

ance

loss

andfailure

dueto

mechanicalstresses

0.1

MPa

pipes

maxim

um

fluid

velocity

safety;perform

ance

loss

andfailure

dueto

noiseand

vibrationproblems

60m/s97

aConstraintsfortheconventionalgasturbinepower

plantare

indicatedbyitalicletters.

595


components. Essentially isothermal conditions and the high-est possible operating temperature should hence be em-ployed to minimize stresses.40,41 Decomposition of themembrane material can occur as a result of redox instability,interactionwith gaseous species or kinetic demixing.42,43 Thechemically induced expansion is among the most importantthermomechanical properties that relates to the volumechanges under the oxygen chemical potential gradients anddetermines the applicability of membrane materials. Similareffects can also result from thermal expansion. These volumechanges can ultimately lead to fracture.

When operating the membrane at a temperature range of973-1073 K at high CO2 and water vapor pressures, the useof any membrane material containing substantial amountsof alkaline-earth elements may be generally problematic, ifcarbonate formation or oxidation is thermodynamicallyfavorable under the corresponding equilibrium conditions.44

Sundkvist et al.25 provided a tentative stability diagram for amembrane that shows regions where carbonate formationand oxidation are likely to occur. This stability diagram wasextended by incorporating the oxygen pressure as an addi-tional parameter (Figure 7). Temperatures below 1173 K inconjunctionwith highCO2 pressures lead to the formation ofoxycarbonates, primarily La2O2CO3,

44 followed by com-plete decomposition. Increasing the oxygen pressure leadsto moderately higher CO2 stability (nonvertical dashed linein Figure 7). Reduced oxygen pressure has an opposite andstronger effect (nonvertical dotted line in Figure 7).

At moderate operation temperatures, the La2NiO4þδ

membrane may degrade because of oxidation.25,45 The sta-bility limit at low temperatures is shifted to the right (vertical

dashed line in Figure 7) and left (vertical dotted line inFigure 7) when the oxygen chemical potential increases ordecreases, respectively. However, both processes could pro-mote carbonate formation, thus leading to a more complexshape of the membrane stability boundary.

The dense membrane layer was assumed to be coated onthe feed side of the porous support because of the high risk ofcarbonate formation at the sweep gas inlet. The poroussupport acts as protection layer by limiting diffusion ofgaseous species such as CO2. Exposing the membrane tohigh oxygen pressures on the feed side increases the risk ofoxidation. But for the operation conditions studied in thiswork, the risk of carbonate formation was considered to bemore severe than oxidation risks. Stabilizing componentswere assumed to be incorporated into the pores of themembrane support layer that were at high risk of carbonateformation (at the sweep gas inlet) to provide sufficient long-term stability. These additives should be catalytically activeto increase oxygen permeation.

All knownmembranematerials contain chemical elementsthat may evaporate under operational conditions, for in-stance during start-up and shut-down of the power plant.43

For Ni-containing materials, this degradation mechanisminvolves primarily nickel hydroxide volatilization.46 Theresulting La-enrichment at the membrane surface may facil-itate other degradation processes such as lanthanum carbo-nate or hydroxide formation.

Pressure differences between the two fluids in the mono-lithic membrane modules and HXs larger than one barshould be avoided to maintain mechanical stability. Mini-mizing the wall thickness leads to increased oxygen and heattransport rates. On the other hand, using thinnerwalls comesat the expense of less operability and robustness as well as therequirement for a more advanced control strategy for thepower plant.

Industrial supplies of natural gas typically contain 1 ppmSO2,

47 which is still too high for the mixed-conductingmaterial assumed here. Deep desulfurization is needed.

The maximum difference in thermal expansion coeffi-cients of process components in the membrane reactorshould not exceed 10-17%.

3.2. Ceramic Heat Exchanger Monoliths and Seals. Themonolithic HXs in the membrane reactor are fabricated ofmaterials that are stable in atmospheres containing highoxygen pressure as well as gaseous species such as H2O,CO2, and CO.48 However, the HXs in the membrane reactorput some additional constraints on the power plant in termsof temperature limits (Table 1). Sulfur limitations and pres-sure differences between the two fluids are similar to thosespecified for the membrane modules.

The sealing of membrane reactor components poses addi-tional challenges. The sealant must be hermetic, as well aschemically and thermomechanically stable,28,49,50 for the

Figure 7. Stability diagram for the dense membrane layer andporous support based on ref.,25 showing stable and unstable opera-tion regions with respect to CO2 and oxygen pressure in the sweepgas as well as solid-wall temperature.

(40) Blond, E.; Richet, N. Thermomechanical modelling of ion-con-ducting membrane for oxygen separation. J. Eur. Ceram. Soc. 2008, 28(4), 793–801.(41) Hamrin, S.Control of a gas turbinewith hot-air reactor.US2006/

0230762A1; 2006.(42) Fontaine, M. L.; Larring, Y.; Norby, T.; Grande, T.; Bredesen,

R. Dense ceramic membranes based on ion conducting oxides. Ann.Chim. 2007, 32 (2), 197–212.(43) Drioli, E.; Giorno, L.Membrane Operations: Innovative Separa-

tions and Transformations; Wiley-VCH: Weinheim, 2009; p XXV, 551 s.(44) Foger, K. H., M.; Turney, T. W. Formation and thermal

decomposition of rare earth carbonates. J. Mater. Sci. 1992, 27 (1),77–82.(45) Bannikov, D. O.; Cherepanov, V. A. Thermodynamic properties

of complex oxides in the La-Ni-O system. J. Solid State Chem. 2006,179 (8), 2721–2727.

(46) Vigeland, B. E.; Bruun, T. Protection of process equipment withsignificant vapor pressure by adding an evaporating component to gas incontact with said equipment. WO 2008/007967 A1, 2008.

(47) Carroni, R.; Schmidt, V.; Griffin, T. Catalytic combustion forpower generation. Catal. Today 2002, 75 (1-4), 287–295.

(48) Julsrud, S. V.; Erlend, B. A ceramic heat exchanger. Int. PatentWO 03/033986 A1, 2003.

(49) Weil, K. S.; Koeppel, B. J. Comparative finite element analysis ofthe stress-strain states in three different bonded solid oxide fuel cell sealdesigns. J. Power Sources 2008, 180 (1), 343–53.

(50) Budd,M. Barium lanthanum silicate glass-ceramics. U. S. Patent7,189,668B2, 2007.

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entire operation range. The thermal expansion coefficients ofthe sealant and joined ceramic materials should be similar toavoid significant mismatches.25,28,50-52 The maximum leak-age rate should not be higher than 0.1%.

3.3. Catalytic Combustors. Standard combustion technol-ogy cannot be applied to the combustors in the membranereactor because of low excess oxygen concentrations inconjunction with high CO2 and water vapor dilution. Astaged catalytic combustor has therefore been proposed,where catalytic partial oxidation of methane is followed bycomplete oxidation under lean conditions. In the catalyticpartial oxidation, amixture ofCOandH2 is produced,whichprovides hydrogen-stabilized combustion for the secondcombustion stage.30,53,54 Supported Rh-based catalysts werefound to be suitable for the combustors because of their highactivity, selectivity, resistance to carbon deposition, andsulfur resistance.55,56 Nevertheless, deep desulfurization isrequired to prevent poisoning of the catalyst.57 The mechan-ical integrity of the catalyst and their supports should with-stand the possibility of thermal shocks that might occurduring rapid load changes as well as during start-up andshut-down of the power plant.47 Excess oxygen is required tomaintain stable and complete combustion.30,32 But highconcentrations of oxygen in the sweep gas are problematicsince higher energy and cooling water requirements areneeded for the purification system.58-60 As a result, powerplant efficiency drops.38 Moreover, degradation of processcomponents located downstream of the membrane reactorcan also occur.61

3.4. Turbomachinery and Further Fluid Components. TheGT should be operated with a sufficient surge margin, whichfor power applications is typically in the range of 15-20%.24

This margin was relaxed to approximately 10% to increasethe part-load capability of the membrane-based power plantfor the load-control strategy that uses VGVs. However,additional reduction below 5% should be avoided becausetheGTmay then be operating under a regimewhere subsonic

stall and blade flutter can occur.62-64 But it should be notedthat instability phenomena, apart from surging, were notincluded in the model because of a lack of available data.38

The GT compressor maps for off-design performance arepresented in Figure 5.

4. System Time Scales

The response of the oxygen transport in the membranelayer was assumed to be instantaneous for the sake ofsimplicity. This assumption is valid when all kinetic para-meters are constant, no microstructural changes in the mem-brane bulk and on the surface occur, and surface activation/passivation processes are negligible. While the latter assump-tions can be used for most mixed-conducting materials thatare stable under the membrane-based power plant condi-tions,25,65 the applicability of the former simplification isvery limited. For instance, the bulk oxygen diffusivity and theinterfacial exchange rate in La2NiO4þδ are both dependent onthe oxygen chemical potential.66 At the same time, the tran-sient times observed for dense single-layer nickelate mem-branes operating under oxidizing conditions at temperaturesabove 1200 K66 were indeed short, suggesting that theresponse of membrane modules should be primarily deter-mined by mass transfer phenomena in the membrane mod-ules. As an example, during isothermal cycling of thepermeate-side oxygen partial pressure in the range 102-103

Pa, steady-state oxygen fluxes through 0.6 mm thickLa2NiO4þδmembranes at 1223Kand feed side oxygen partialpressure of 21 kPa were reached after 30-400s; increasingtemperature to 1273 K makes the relaxation processes faster.Steady-state can then be reached within 100 s. The relativelyfast equilibration kinetics is in agreement with data in theliterature on La2NiO4-based materials (refs 67-69 and refer-ences therein). In fact, the rate of these transient processes atelevated temperatures becomes similar to that of the masspropagation in the gaseous phase, making the two virtuallyindistinguishable.

The time scales of the monolithic membrane modules andHXs were analyzed previously with respect to energy, mass,and species conservation, respectively. The temperature of themembrane modules reaches steady-state within minutes.70

(51) Sunarso, J.; Baumann, S.; Serra, J. M.; Meulenberg, W. A.; Liu,S.; Lin, Y. S.; Diniz da Costa, J. C. Mixed ionic-electronic conducting(MIEC) ceramic-based membranes for oxygen separation. J. Membr.Sci. 2008, 320 (1-2), 13–41.(52) Budd, M. Method of forming a glass ceramic material. U. S.

Patent 6,475,938B1, 2002.(53) Eriksson, S.; Boutonnet, M.; Jaras, S. Catalytic combustion of

methane in steam and carbon dioxide-diluted reaction mixtures. Appl.Catal., A 2006, 312 (1-2), 95–101.(54) Eriksson, S.; Wolf, M.; Schneider, A.; Mantzaras, J.; Raimondi,

F.; Boutonnet, M.; Jaras, S. Fuel-rich catalytic combustion of methanein zero emissions power generation processes. Catal. Today 2006, 117(4), 447–453.(55) Eriksson, S.; Nilsson, M.; Boutonnet, M.; Jaras, S. Partial

oxidation of methane over rhodium catalysts for power generationapplications. Catal. Today 2005, 100 (3-4), 447–451.(56) Shamsi, A. Partial oxidation of methane and the effect of sulfur

on catalytic activity and selectivity.Catal. Today 2009, 139 (4), 268–273.(57) Cimino, S.; Torbati, R.; Lisi, L.; Russo, G. Sulphur inhibition on

the catalytic partial oxidation of methane over Rh-based monolithcatalysts. Appl. Catal., A 2009, 360 (1), 43–49.(58) Pipitone, G.; Bolland, O., Power generation with CO2 capture:

Technology forCO2 purification. Int. J. GreenhouseGasControl In Press.(59) Li, H.; Yan, J.; Anheden, M. Impurity impacts on the purifica-

tion process in oxy-fuel combustion based CO2 capture and storagesystem. Appl. Energy 2009, 86 (2), 202–213.(60) Aspelund, A.; Jordal, K. Gas conditioning;The interface be-

tweenCO2 capture and transport. Int. J. Greenhouse Gas Control 2007, 1(3), 343–354.(61) Plasynski, S. I.; Litynski, J. T.; McIlvried, H. G.; Srivastava,

R. D. Progress and new developments in carbon capture and storage.Crit. Rev. Plant Sci. 2009, 123–138.(62) Saravanamuttoo, H. I. H., Rogers, G. F. C., Cohen, H., Straznicky,

P. V. Gas Turbine Theory; 6th ed.; Prentice Hall: 2009.

(63) Roumeliotis, I.; Mathioudakis, K., Evaluation of water injectioneffect on compressor and engine performance and operability. Appl.Energy (doi:10.1016/j.apenergy.2009.04.039).

(64) Brun,K.;Kurz,R.; Simmons,H.R.Aerodynamic instability andlife-limiting effects of inlet and interstage water injection into gasturbines. J. Eng. Gas Turbines Power 2006, 128 (3), 617–625.

(65) Vigeland, B., Glenne, R.; Breivik, T; Julsrud, S. Membrane anduse thereof. U.S. 6,503,296B1, 2003.

(66) Shaula, A. L.; Naumovich, E. N.; Viskup, A. P.; Pankov, V. V.;Kovalevsky, A. V.; Kharton, V. V., Oxygen transport in La2NiO4 þ δ:Assessment of surface limitations and multilayer membrane architec-tures. Solid State Ionics 2009, 180 (11-13), 812-816.

(67) Vashook,V.V.;Yushkevich, I. I.;Kokhanovsky,L.V.;Makhnach,L. V.; Tolochko, S. P.; Kononyuk, I. F.; Ullmann, H.; Altenburg, H.Composition and conductivity of some nickelates. Solid State Ionics 1999,119 (1), 23–30.

(68) Mauvy, F.; Bassat, J. M.; Boehm, E.; Dordor, P.; Grenier, J. C.;Loup, J. P. Chemical oxygen diffusion coefficient measurement byconductivity relaxation-correlation between tracer diffusion coefficientand chemical diffusion coefficient. J. Eur. Ceram. Soc. 2004, 24 (6),1265–1269.

(69) Kim, G.;Wang, S.; Jacobson, A. J.; Chen, C. L.Measurement ofoxygen transport kinetics in epitaxial La2NiO4þ thin films by electricalconductivity relaxation. Solid State Ionics 2006, 177 (17-18), 1461–1467.

(70) Eichhorn Colombo, K.; Imsland, L.; Bolland, O.; Hovland, S.Dynamic modelling of an oxygen mixed conducting membrane andmodel reduction for control. J. Mem. Sci. 2009, 336 (1-2), 50–60.

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The membrane reactor and pipes were assumed to be coatedwith a high-performance insulation material that preventslarge heat losses. Consequently, steady-state is reached afterseveral hours. Shorter start-up times, for example, after ashort stop, are also possible because the membrane reactorcan be maintained at a fairly high temperature.

Griffin et al.30 state that the required time for completemethane combustion in a highly diluted atmosphere is inthe range of milliseconds. A time range that is smallerthan one second was not considered in the power plantmodel to reduce numerical stiffness. Pressure and masspropagation in fluid machinery (GT, ejector) are assumedto occur instantaneously.9 The range of time scalesof individual GT power plant components is shown inTable 2.

5. Load-Control Strategies

Two load-control strategies were analyzed in this paper fortheGToperating at constant rotational speed: (i) load-controlusing VGVs in the GT compressor, while the turbine exittemperature was controlled2, and (ii) load-control, whereVGVs are not used and the turbine exit temperature remaineduncontrolled. For both load-control strategies, process con-ditions were adjusted such that the membrane modules werekept close to their design temperature when power output waschanged continuously.

The steady-state part-load analyses of themembrane-basedcombined cycle power plant operated with these two load-control strategies can be found elsewhere.38 Steady-state part-load operation maps for the membrane-based GT powerplant are shown in Figures 8 and 9, respectively. The steady-state operating line on the GT compressor map for the load-control strategy usingVGVs is shown inFigure 5. It should beemphasized that these operating lines represent the case ofperfect control, that is, where the output of the controller isidentical to the reference value. In reality, measured vari-ables may vary due to measurement errors. Furthermore,the turbomachinery and the membrane reactor componentsare exposed to degradation, and changes in ambient condi-tions also have a strong effect on the power plant per-formance.72

After a degree-of-freedom analysis of the power plantmodel, a set of controlled and manipulated variables wasfound, shown in Table 3. Pairs of corresponding controlledand manipulated variables were obtained by relative gainarray analyses at different load points and frequencies.73

Table 2. Range of Time Scales of Individual Process Components of

the Membrane-Based GT Power Plant

response in process components time scale [s]

oxygen permeation inmembrane layer

essentially instantaneous71

pressure and mass propagation influid machinery (GT, ejector)

essentially instantaneous9

thermal in combustion milliseconds30

mass propagation in membranemodules and HXs

seconds

thermal in membrane modulesand HXs

minutes

thermal in insulation material(membrane reactor, pipes)

hours

Figure 8. Steady-state part-load performance maps for the load-control strategy with variable guide vanes and controlled turbineexit temperature.

Figure 9. Part-load operation maps for the load-control strategywithout variable guide vanes and uncontrolled turbine exit tem-perature.

Table 3. Set of Controlled and Manipulated Variables of the Mem-

brane-Based GT Power Plant

controlled variable set manipulated variable set

power output fuel flow rate tothe afterburners

pressure in recycle loop recycle loop valve openingmean solid-wall temperature ofmembrane modules

fuel flow rate to themembrane reactor

ejector operational mode (critical) steam valve openingturbine exit temperature air mass flow to GT compressor

by VGVs

2 In modern GTs, however, the turbine exit temperature may still varywhen basically applying VGVs as a result of an optimization of efficiency forthe combined cycle power plant.(71) Zhang, W.; Smit, J.; van Sint Annaland, M.; Kuipers, J. A. M.

Feasibility study of a novel membrane reactor for syngas production.Part 1: Experimental study of O2 permeation through perovskitemembranes under reducing and non-reducing atmospheres. J. Membr.Sci. 2007, 291 (1-2), 19–32.

(72) Eichhorn Colombo, K.; Kharton, V. V.; Viskup, A. P.; Kova-levsky, A. V.; Shaula, A. L.; Bolland, O. Simulation of an OxygenMembrane-based Gas Turbine Power Plant: System Level Analysis ofOperation Stability and Individual Process Unit Degradation. In pre-paration.

(73) Skogestad, I. S. P.Multivariable Feedback Control: Analysis andDesign. 2nd ed.; Wiley: Chichester, U. K., 2005.

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Manipulated variables were varied such that all operationaland material constraints were satisfied (Table 1). In themembrane module model, the mean solid-wall temperaturerepresents a spatially distributed variable and cannotdirectly be measured. However, related gas properties of theair and sweep gases, at somewhat lower temperatures, can beused to calculate this value. Manipulated variables were repre-sented by nonlinear regression functions with respect to gen-erator power output. For the purposes of simplification, thetemperature of steam and preheated fuel that is supplied to themembrane reactor was assumed to be constant and also highenough to avoid the formation of a two-phase fluid.

6. Start-Up and Shut-Down Procedures

A special class of transients for (power) processes arethe start-up and shut-down procedures. In what follows,one possible strategy is presented on a qualitative basisfor the membrane-based power plant. Simulations werenot performed because several other material-specificproperties as well as operational effects need to be con-sidered that were not included in the GT power plantmodel.

Changes in operation conditions during start up and shutdown must be performed at a rate that is slow enough toprevent excessive stresses. But the required time should also beas short as possible to operate the power plant economically.At any rate, unfavorable operational conditions must beavoided. The number of auxiliary systems should also beminimal. This includes hot valves as well as valves in mainstreams, additional combustors, and the need for technicalgases.74 The extended flowsheet for the membrane-based GTpower plant with its proposed auxiliary components for start-up and shut-down is shown in Figure 10 (see Figure 4 forcomparison). Auxiliary process equipment, which is notnecessary for normal operation, is indicated by red boldcapital letters.

6.1. Start-Up Procedure. Initially, all valves in the GTpower plant as well as the VGVs in the GT compressor mustbe fully closed. Before any fuel or oxygen is fed to themembrane reactor, it must be purged to avoid ignition of

remaining combustible gases from previous operation orfailed start attempts.

The GT is started and operated at low rotational speed3 topurge themembrane reactor and to build up resistance to thefluid that is introduced into the membrane reactor. Simulta-neous with the GT starting procedure, the “split valve” and“N2 valve” are opened to allow nitrogen into the membranereactor, which is heated by an auxiliary combustion system.At the same time, the “air blow-off valve” is controlled tokeep the macroscopic stoichiometric composition in themembranes constant4. This method is known as iso-compo-sitional heating.39,75,76 In the chemical equilibrium betweengas and solid phase, oxygen will not pass into or out of themembranes. That means there is no gradient in the anionconcentration and variable-valence cations oxidation state,so that the strains caused by differential chemical expansionare therefore reduced. During the start-up process, themembrane modules are not homogeneously heated but therewill be a temperature gradient resulting in internal oxygen-stoichiometry differences.76 The maximum allowable differ-ential strain must be determined experimentally or by nu-merical methods.40,77 Carolan75 reported typical heating andcooling rates in the range of 0.25-10 K/min, but these mayalso be as low as 1K/h at low temperatures. Sundkvist et al.25

reported heating rates of approximately 3K/min and coolingrates of approximately 5 K/min25 for the ceramic HXmonoliths, which may also apply to the membrane modules.

Figure 10. Membrane-based gas turbine power plant with auxiliary process components for safe start-up and shutdown.

3 It is engineering practice to use the generator as starting motor.624Gases other than nitrogen may also be used, but CO2 and H2O should be

avoided to prevent degradation of the membranes.(74) Ferrari,M. L.; Traverso,A.; Pascenti,M.;Massardo, A. F. Early

start-up of solid oxide fuel cell hybrid systems with ejector cathodicrecirculation: Experimental results and model verification. Proc. Inst.Mechanical Eng., Part A: J. Power Energy 2007, 221 (5), 627–635.

(75) Carolan, M. F. Control of differential strain during heatingand cooling of mixed conducting metal oxide membranes. U. S. 2006/0060080, A1, 2006.

(76) Carolan, M. F. Operation of mixed conducting metal oxidemembrane systems under transient conditions. U. S. Patent 7,468,092B2, 2008.

(77) Hendriksen, P. V.; Larsen, P. H.;Mogensen,M.; Poulsen, F.W.;Wiik, K. Prospects and problems of dense oxygen permeable mem-branes. Catal. Today 2000, 56 (1-3), 283–295.

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The use of the heating rates provided by Sundkvist et al.25

would lead to start-up times of five hours or longer. Incomparison, amidmerit gas turbine as assumed in this work,requires approximately 10-15 min for start-up.24 Blond andRichet40 suggested an oxygen pressure rate not exceeding0.14 per hour. The oxygen pressure may be changed slowlyenough to allow (partial) creep relaxation of the membrane.The “N2 valve”, “air blow-off valve”, and theGT speedmusthence be carefully controlled. After the membrane reactorcomponents have adapted to the new conditions, “fuel valve1” opens, and fuel is introduced. Steammay also be requiredfor the start-up of the membrane reactor, controlled by the“steam valve”, to allow for a smooth transition of themembrane to high water vapor concentrations and properejector performance. But this is considered to be very criticalbecause of the formation of hydroxides at low tempera-tures.43 The amount of fuel must be carefully controlled by“fuel valve 1” to keep the pressure of the combustionproducts H2O and CO2 low enough to avoid hydroxideand carbonate formation. Next, the “anti-evaporationvalve” opens, and small amounts of the evaporating compo-nents of themembrane and porous support layer are injectedinto the recycle loop. However, after passing the membranemodules, the added components need to be recollected toavoid clogging membrane reactor components downstreamof the membrane modules.46

The catalyst used in the catalytic combustors (e.g., Rh78-80)must be able to withstand large thermal shocks during tran-sient operation.47 Propagating hot spots may occur78,81 thatcan lead to high surface temperatures and ultimately to sinter-ing and volatilization of the catalyst. Tavazzi et al.78 showedthat the catalyst aging phenomenon was enhanced when usinghigh preheating temperatures which could be useful in remov-ing carbon traces. On the other hand, loss of catalyst activitycould be avoided when applying moderate preheating tem-peratures. Hence, careful control of process conditions is alsoessential for the catalytic combustors.

During start-up, all gases are vented to the atmosphere.When the membrane reactor components have equalized tothe new process conditions, the rotational speed of the GT isincreased. The “air blow-off valve” is further controlled tomaintain optimal conditions for both the membrane reactorand the turbomachinery. The switch from auxiliary opera-tion to self-sustaining operation of the process must becarefully scheduled. In conventional GTs, this switch corre-sponds to a rotational speed of the GT of about 15-20% ofnormal.62 The ignition system (not shown in Figure 10) isturned off when the engine has reached self-sustaining con-ditions.62 The GT is then accelerated to idle by a steadyopening of “fuel valve 2” while continuing starter assistance.The starter is cut off when the speed reaches around 60% ofthe rated speed. The starter continues to assist the GT inreaching a higher rotational speed even after the torque of

the starter and GT are equalized.82 The time to bring the GTto a speed of either 2% lower than that for idle or of full-power is 10-15 min for aero-derivatives whereas it is 30 minto 4 h for heavy-duty engines.24 The fuel scheduling forengine acceleration during start-up must be such that un-desired performance phenomena are avoided.24,82 Further,the use of “fuel valve 2” and the starter cutoff time need tobe carefully scheduled to prevent extensive temperaturegradients. VGVs can assist in controlling instabilities,82 butcan also be the cause of instabilities in addition to reducedefficiency.83 After the GT power plant has reached self-sustaining conditions, the auxiliary system is cut off andthe fuel mass flow to the membrane reactor and afterburnersis increased. The GT power plant is then synchronized withthe electrical grid. The auxiliary valves are closed.

During start-up, steam is produced by an auxiliary steamgenerator until the steam cycle can generate steam with therequired properties by the GT exhaust or sweep gas. Allauxiliary components are in operation until the GT andmembrane reactor have reached self-sustaining conditions.The load is then further increased by opening the angle of theVGVs until the desired operation point is reached.

Purging of the heat recovery steam generator (HRSG)(Figure 1) is needed before the exhaust gas from the gasturbine can be introduced.82 Appropriate steam propertiesfor a steam turbine start-up in conventional combined cyclepower plants are reached at approximately 50-60%GT load.Before starting the steam turbine, the gland steam system5

must be in operation and the condenser evacuated. Until thesteam turbine takes over the available steam flow, the excesssteam flows across the steam turbine bypass.84 Modern com-bined cycle power plants in the range of 50-400MW can bestarted within 40-50 min after 8 h of standstill (hot start),within 75-110 min after 60 h standstill (warm start), andwithin 75-150 min after 120 h standstill (cold start).84,85

The CO2 purification and compression stage (Figure 1)can be considered as rather decoupled from the combinedcycle because of the low operation temperature with a timescale lower than that of the GT power plant and steam cycleandHRSG.86,87 The gas flow to theCO2 compression systemis gradually increased by closing the “sweep gas blow-offvalve”. During the start-up procedure, CO2 capture is re-garded as not feasible.

6.2. Shut-Down Procedure.Hamrin41 claimed that a rapidshut-downof theGTpowerplant canbeachievedbyusingaGTblow-off valve which bypasses the membrane reactor (notshown in Figure 10). Even faster cool-down of the GT turbinecan be achieved by fully opening the “air blow-off valve”.

(78) Tavazzi, I.; Beretta, A.; Groppi, G.; Maestri, M.; Tronconi, E.;Forzatti, P. Experimental and modeling analysis of the effect of catalystaging on the performance of a short contact time adiabatic CH4-CPOreactor. Catal. Today 2007, 129 (3-4), 372–379.(79) Williams, K. A.; Leclerc, C. A.; Schmidt, L. D. Rapid lightoff of

syngas production from methane: A transient product analysis. AIChEJ. 2005, 51 (1), 247–260.(80) Pena, M. A.; Fierro, J. L. G. Chemical structures and perfor-

mance of perovskite oxides. Chem. Rev. 2001, 101 (7), 1981–2017.(81) Maestri, M.; Beretta, A.; Groppi, G.; Tronconi, E.; Forzatti, P.

Comparison among structured and packed-bed reactors for the catalyticpartial oxidation of CH4 at short contact times. Catal. Today 2005, 105(3-4), 709–717.

5The gland steam system prevents both out-leakage of high-pressuresteam and in-leakage of air into the turbine, which would degrade theefficiency of the turbine by raising the condenser pressure.

(82) Kim, J. H.; Song, T. W.; Kim, T. S.; Ro, S. T. Dynamicsimulation of full startup procedure of heavy-duty gas turbines. J.Eng. Gas Turbines Power 2002, 124 (3), 510–16.

(83) Tsalavoutas, A.; Mathioudakis, K.; Stamatis, A.; Smith, M.Identifying faults in the variable geometry system of a gas turbinecompressor. J. Turbomachinery 2001, 123 (1), 33–39.

(84) Kehlhofer, R. H., Warner, J., Nielsen, H., Bachmann, R. Com-bined-Cycle Gas & Steam Turbine Power Plants, 2nd ed.; 1999.

(85) Sanaye, S.; Rezazadeh, M. Transient thermal modelling of heatrecovery steamgenerators in combined cycle power plants. Int. J. EnergyRes. 2007, 31 (11), 1047–1063.

(86) Soerensen, E.; Skogestad, S. Optimal startup procedures for batchdistillation. Comput. Chem. Eng. 1996, 20 (Suppl 2), S1257–S1262.

(87) Han, M.; Park, S. Startup of distillation columns using profileposition control based on a nonlinear wave model. Ind. Eng. Chem. Res.1999, 38 (4), 1565–1574.

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But these two shut-down strategies are not regarded to be safeshut-down methods if target lifetime of critical power plantcomponents is to be maintained. Instead, the reverse start-upprocedure should be applied to the shut-down of theGT powerplant. At zero load the GT and generator are disconnected.

In the event of an emergency, the breakers as well as thefuel flow rate will be tripped immediately without contin-uous reduction of the load to aminimum.88 In such incidents,the “air blow-off valve” will be opened.

The CO2 compression stage is not strongly affected bytransient phenomena in the power plant during shut-down.The load in the HRSG and steam cycle can be shut down byreducing themass flow of the exhaust and sweep gas from theGT by opening the “sweep gas blow-off valve”. When theexhaust gas temperature from the GT has reached a definedminimum level, the steam turbine is shut down. TheHRSG isthen further unloaded and also shut down.84

7. Results and Discussion

7.1. Design Case. Table 4 shows results for selected flowstreams of theGTpower plant. The outlet temperature of thecatalytic combustors was approximately 1470 K. The excessoxygenmole fraction was approximately 1%.A turbine inlettemperature of approximately 1530 Kwas assumed. Furthermodel assumptions can be found in Table 5. At design pointoperation, the GT power plant reaches an efficiency of33.4% with a power output of 19.9 MW.

7.2. Transient Load Reduction with Variable Inlet Guide

Vanes in the Gas Turbine Compressor and Controlled Turbine

Exit Temperature. Figure 11 shows the continuous loadreduction profiles for the membrane-based GT power plantusing VGVs in the GT compressor for mass flowmodulation.Fast load reduction rates (4.2% load/min) led to a smallerpart-load operation window due to limitations of the ejectors(see Figure 12). There was a rapid decrease in the pressuredifferencebetween theactuating fluid (fuel and steammixture)and the induced fluid (sweep gas in recycle loop).Values belowzero must be avoided to maintain physically correct per-formance of the ejector model. Also shown in Figure 11 isthe load profile (1.2% load/min) with the maximum loadreduction rate at which part-load can be fully obtained (58%),that is, until the limit of VGVs was reached (see Figure 8).Note that the pressure difference in the ejectors is also close tothe limit. Approximately 36 min is required to reach thisminimum. A combination of alternating high load reduc-tion rates of 3% load/min for the first reduction and 1.2%load/min for the second with periods of relaxation (500 s)

Table 4. Design Case Results for the Membrane-Based GT Power Plant (Figure 4)

stream number T [K] P [MPa] _m [kg/s] xN2[mol %] xO2

[mol %] xCH4[mol %] xH2O

[mol %] xCO2[mol %]

1 288 0.1 63.5 79 21 0 0 02 707 1.79 7.3 79 21 0 0 03 489 4 1.6 0 0 55.8 44.2 04 802 1.78 37.1 0 8.1 3.5 65.8 22.65 1473 1.76 37.1 0 1.1 0 72.8 26.16 1330 1.76 32.1 0 1.1 0 72.8 26.17 1258 1.76 35.5 0 8.7 0 67.2 24.18 1189 1.77 47.7 79 21 0 0 09 1258 1.76 44.7 83.7 16.3 0 0 010 278 1.75 0.3 0 0 100 0 011 1531 1.7 60.8 81.7 15.3 0 2 112 875 0.1 60.8 81.7 15.3 0 2 113 710 1.75 5 0 1.1 0 72.8 26.1

Table 5. Modelling Assumptions for theMembrane-Based GT Power

Plant (Figure 4)

fuel preparation, handling of power consumption, and ambientconditions

• fuel is assumed to be pure methane, available at 4 MPa• fuel temperature in the membrane-reactor after preheat = 398 K

(fuel heating, e.g., by the CO2-rich exhaust gas prior to the CO2

compression system, but the additional heat integration was notincluded in the analysis.)

• fuel temperature at the afterburners 278 K• lower heating value = 0.8 MJ/mol• ambient air: temperature = 288 K; pressure = 0.1 MPa;

composition: 79% nitrogen, 21% oxygen

membrane reactor• number of manifolds of type 1 is 12• number of manifolds of type 2 is 48• membrane modules length is 0.1625 m; high-temperature heat

exchanger length is 0.355 m; low-temperature heat exchangerlength is 0.9825 m; bleed-gas heat exchanger length is 1.5 m; theheight and width of all monoliths is 0.15 m

• gas channel width of membrane module and monolithic heatexchangers is 1.5 mm

• thickness of the membrane layer is 30 μm• length of porous support with protective additives is 0.01625 m• area-to-volume ratio of the monoliths is 895 m2/m3

• number of gas channels of the monoliths is 6690• split fraction of air to the bleed-gas heat exchanger is 15%• radiative interaction between reactor components is neglected

gas turbine• variations in the isentropic efficiency for compressors are calculated

by performance maps21 (84.5% in design)• variations in the isentropic efficiency for the turbine and the

amount of cooling air that is extracted from the com-pressor discharge are calculated by performance maps24 (86.8%in design)

• shaft mechanical efficiency is 99%98

• generator mechanical efficiency is 98.5%98

• cooling air fraction of compressed air is 11.6%24

pipes• diameter of pipe 1 is 0.39 m; diameter of pipe 2 is 0.53 m; length of

pipe 1 and pipe 2 is 5 m• diameter of pipe 3 is 0.2 m and length is 10 m• average velocity of pipe1 is 53.7m/s; average velocity of pipe 2 is 56.1

m/s; average velocity of pipe 3 is 21.1 m/s

ejector• heat loss = 1%• isentropic efficiency for the section-wise ejector model is based on

data from refs 99 and 100• operation in the critical mode36,37,101 (the mass flow of steam is

therefore set)• diffuser area = 0.058 m2; diffuser throat area = 9.86 cm2; nozzle

area = 0.064 cm2

• velocities in the mixing section and diffuser outlet are 121 and 2m/s,respectively.

catalytic combustors and afterburners• heat loss = 1%98

(88) Boyce, M. P. Gas Turbine Engineering Handbook, 3rd ed.; GulfProfessional Pub.: Boston, MA, 2006.

601


can be applied to reduce the required time to reachmaximumpart-load in conjunction with the VGV limit. One possiblescenario for stepped load reduction is shown in Figure 11,under which the required time could be reduced by 5 min.Further reduction could be achieved by using even higherload reduction rates in conjunction with more frequent andshorter relaxation periods. The mean solid-wall temperatureof the membrane modules for all three rates remains close tothe design value (Figure 13). The outlet temperature of the

catalytic combustors decreased during load reduction(Figure 13) while the excess oxygen mole fraction in thecatalytic combustors increased (Figure 14). The surge marginof the GT compressor was reduced at part-load but remainedwithin the specified limit (Figure 15). The pressure differencebetween the two fluids in the membrane modules increasedduring load reduction as a result of matching between theturbomachinery andmembrane reactor (Figure 16). At maxi-mum part-load operation, a pressure gradient of 77 kPa wasobtained, which was still below the assumed limit of 0.1MPa.Figure 17 shows the thermal efficiency of the GT power plantand specific emissions of CO2 produced by the afterburners.Less fuel was required during load reduction to keep theturbine exit temperature at its design value, which resulted inreduced emissions of CO2 in the GT exhaust gas. Figure 18shows the variations in turbine inlet temperature. Additionallimiting variables, given in Table 1, were not exceeded.

7.3. Transient LoadReduction without Variable Inlet Guide

Vanes in the Gas Turbine Compressor and Uncontrolled

Turbine Exit Temperature. The power plant behavior forthree continuous load reduction rates was analyzed duringwhich VGVs in the GT compressor were not used(Figure 19). Compared to the former load-control strategy,part-load capability was considerably reduced, that is, ap-proximately to 81% (Figure 9). But faster load-reductionrates can be applied without large penalties in load-reduc-tion capability. Since the mass flow of air was basically

Figure 11. Load reduction profiles of the membrane-based gasturbine power plant for the load-control strategy with variableguide vanes and controlled turbine exit temperature.

Figure 12. Pressure difference in ejector mixing section for loadreduction rates shown in Figure 11.

Figure 14. Excess oxygen fraction in the catalytic combustors forload reduction rates shown in Figure 11.

Figure 13.Outlet temperature of the catalytic combustors andmeansolid-wall temperature of themembranemodules for load reductionrates shown in Figure 11.

Figure 15.Gas turbine compressor surge margin for load reductionrates shown in Figure 11.

602


unchanged, there was a strong cooling effect on the mem-brane reactor. More fuel needed to be fed to the catalyticcombustors (Figure 9) to keep the mean solid-wall tempera-ture of the membrane modules close to their design value.Load reduction leads to a rapid decrease in excess oxygen inthe catalytic combustors (Figure 20). Itwas assumed that stableoperation of the catalytic combustors can be maintained

with excess oxygen fractions of 0.5 mol% (Table 1). Fast loadreduction rates (6% load/min) result in an overshoot (oxygenmole fraction >0.5%), followed by an undershoot (oxygenmole fraction <0.5%) around the limit. A new steady-statewas found at oxygen mole fractions above the limit. Negative

Figure 16. Mean pressure gradient of the membrane modules forload reduction rates shown in Figure 11.

Figure 17. Efficiency of the GT power plant and specific emissionsof CO2 for load reduction rates shown in Figure 11.

Figure 18.Turbine inlet temperature for load reduction rates shownin Figure 11.

Figure 19. Load reduction profiles of the membrane-based gasturbine power plant for the load-control strategy without variableguide vanes and uncontrolled turbine exit temperature.

Figure 20.Excess oxygen in the catalytic combustors for continuousload reduction rates shown in Figure 19.

Figure 21. Outlet temperature of the catalytic combustors andmean solid-wall temperature of the membrane modules for contin-uous load reduction rates shown in Figure 19.

603


as well as positive fluctuations around the limit are expected toresult in unstable operation of the catalytic combustors andshouldbe avoided.The transient load reductionprofile (0.47%load/min), where the limit was set to 0.51mol%of the oxygenmole fraction, allowing for a small undershoot down to thelimit of 0.5 mol %, is also shown in Figure 19. The minimumpart-load was reached after approximately 38 min. In the

extreme case without any undershoot of excess oxygen(0.006% load/min), maximum part-load was reached afterapproximately 52 h. These transient load reduction times aremuch longer than those for conventional GT power plants.The outlet temperature of the catalytic combustors increased,but themean solid-wall temperature of themembranemodulesremained nearly constant (Figure 21). The turbine inlet andturbine exit temperatures were reduced because of lower fuelflow rates to the afterburners (Figure 22). This has implica-tions when applying a steam cycle for further power produc-tion. Lower turbine exit temperatures result in a rapid dropof combined cycle efficiency. The pressure difference in themixing section of the ejectors was reduced (Figure 23). Thesurgemargin of theGT compressor increased as the result of anew matching point between turbomachinery and membranereactor (Figure 24). Low pressure differences across the wallsof the membrane modules (Figure 25) and monolithic HXswere obtained. The drop in thermal efficiency of theGTpowerplant is shown in Figure 26. Lower specific emissions of CO2

were obtained when the load was reduced because of thereduction in fuel fed to the afterburners. Further operationaland material constraint limitations from Table 1 were notexceeded.

7.4. Transient Load Increase. Figures 27 and 28 show loadincrease profiles for the two load-control strategies withrespect to power plant efficiency, excess oxygen mole frac-tion and outlet temperature of the catalytic combustors,

Figure 22.Turbine inlet and outlet temperature for continuous loadreduction rates shown in Figure 19.

Figure 23. Pressure difference in ejector mixing sections for contin-uous load reduction rates shown in Figure 19.

Figure 24.GT compressor surge margin for continuous load reduc-tion for continuous load reduction rates shown in Figure 19.

Figure 25. Mean pressure difference in membrane modules forcontinuous load reduction rates shown in Figure 19.

Figure 26. Efficiency of the GT power plant and specific CO2

emissions for continuous load reduction rates shown in Figure 19.

604


turbine inlet temperature, and, for the load-control strat-egy without VGVs, the turbine exit temperature. Theseload increase rates (0.09% load/min for the load-controlstrategy with VGVs and 0.28% load/min for the load-control strategy without VGVs) were the highest thatcould be achieved for a continuous load increase frommaximum part-load to design operation. For higher loadincrease rates, discontinuities appeared in approximatelyin 3-4% of load change differences, which led to numer-ical instability. The defined operating lines (Figures 8 and9) are presumably close to some thermodynamic stabilitylimits. To verify this hypothesis, operating lines at higheras well as lower average membrane module temperatureswere included in the power plant model. For the operatingline, where the average temperature of the membranemodules was higher, faster load increase rates could beobtained for both load-control strategies. However, thehigher temperature limit (Table 1) of the membrane mod-ules was exceeded. In contrast, under process conditionswhere the membrane modules were kept at a lower averagetemperature, numerical stability limits were reached even

faster, i.e. even lower load-reduction rates must be ap-plied. In this respect, high average temperatures of themembrane modules are more suitable in terms of transientoperation. But these could also exceed the temperaturelimits of membrane reactor components. Moreover, loaddecrease appeared tohave a stabilizing effect, that is, regions ofinstability were not passed. This phenomenon is the subject ofan ongoing investigation. For all further critical variables,listed in Table 1, specified limits were not exceeded.

Conclusion

On the basis of detailed modelling of process components,the transient behaviour during load reduction and loadincrease of the membrane-based GT power plant was ana-lysed. Operational and material constraints were emphasized.The GT was assumed to operate at constant rotational speed.Load reduction can then be accomplished by two strategies orby a mixture of the two: (i) load control with air mass flowmodulation by means of variable guide vanes (VGVs) andcontrolled turbine exit temperature and (ii) load control

Figure 27. Power output, efficiency of the GT power plant, excess oxygen in the catalytic combustors, turbine inlet temperature, and outlettemperature of the catalytic combustors for continuous load increase for the load-control strategy with variable guide vanes and controlledturbine exit temperature.

Figure 28.Power output, efficiency of the gas turbine power plant, excess oxygen in the catalytic combustors, turbine inlet temperature, turbineexit temperature, and outlet temperature of the catalytic combustors for continuous load increase for the load-control strategywithout variableguide vanes and uncontrolled turbine exit temperature.

605


without VGVs while the turbine exit temperature wasallowed to float. For both load reduction strategies, the meansolid-wall temperatures of the membrane modules were keptclose to the design value. For the first load-control strategy,load can be reduced to approximately 58%with the VGVs asthe limiting factor, while for the second load-control strategy,the maximum part-load was reached at approximately 81%.In that case, the amount of excess oxygen in the catalyticcombustors represented the limiting factor. Compared to aconventional GT power plant, three substantial differencescan be obtained for the membrane-based GT power plant.First, load reduction capability was considerably reduced.Second, transition times were longer. Third, membrane tech-nology for integrated air separation added several operationaland material constraints which need to be considered for safeoperation. For the load-control strategy where VGVs wereused, transition times could be shortened when using steppedload reduction, that is, relatively fast load reduction ratesalternated with sufficiently long relaxation periods. Simula-tions revealed that rather low load increase rates must be usedfor both load-control strategies to obtain numerical stability.The defined operation lines seemed to be close to somestability limits, which were passed if load increase rates exceeda certain limit. Shorter load increase rates would be possiblewhen allowing for higher mean solid-wall temperatures ofthe membrane modules, but temperature limits could beexceeded. A comparison of the two load-control strategiesreveals that the use of VGVs in the GT compressor, inconjunction with a controlled turbine exit temperature, wassuperior because of improved performance of the catalyticcombustors, increased part-load capability, and higherpower plant efficiency. A possible start-up and shut-downprocedure was presented on a qualitative basis, where thelong-term stability of critical process components could bemaintained. However, these procedures are complex andrequire several highly critical auxiliary process components.Compared to conventional GT power plants, the times re-quired for start-up and shut-down for the membrane-basedpower plant were much longer.

Acknowledgment. This publication forms a part of the BIG-CO2 project, which has been funded under the strategic ResearchCouncil of Norway programme called Climit. The authorsacknowledge the partners for their support: StatoilHydro, GEGlobal Research, Statkraft, Aker Clean Carbon, Shell, TOTAL,ConocoPhillips, ALSTOM, the Research Council of Norway(178004/I30 and 176059/I30), Gassnova (182070) and FCT,Portugal (PTDC/CTM/64357/2006).

Appendix

A.1.MembraneModule.The oxygen fluxwasmodelled usingan approximate of Wagner’s equation.89 Despite its simpli-fications, this equation describes situations where oxygentransport is limited by both surface-exchange kinetics andbulk ionic conduction, as is typical for La2NiO4-basedmaterials.65 Any influence of the porous membrane supporton the oxygen flux was neglected.

JO2¼ c0D0

4thmln

hpnO2, air -pnO2, sweepgas

ið1Þ

where JO2is the oxygen flux, c0 oxygen concentration,D0 the

self-diffusion coefficient, thml the membrane layer thickness,n a fitting parameter, and pO2

the oxygen partial pressure.The gas phase energy balance for air and sweep gas is

Fgcp, gDTg

Dtþ vg

DTg

Dz

� �¼ D

Dzλg

DTg

Dz

� �þ

Rhf ðTs -TgÞ ( 4JO2

DhO2, g

Dzð2Þ

using the following boundary conditions at inlet and outlet,respectively

Tgjinlet ¼ T0g ð3Þ

DTg

Dz

��outlet

¼ 0 ð4Þ

where Fg denotes the gas density, cp is the heat capacity,Tg is the temperature, t is the time, vg is the fluid velocity,z is the variable of spatial distribution, λg is the ther-mal conductivity, R specifies the area-to-volume ratio, hf isthe heat transfer coefficient, and hO2

is the enthalpy ofoxygen.

The energy balance for the solid wall (dense membranelayer and porous support) is given by

pscp, sDTs

DT¼ λs

D2Ts

DZ2þ R

X2k¼1

hf , k Tg, k -Ts

� � þ J02DΔho2DZ

ð5Þ

Applying the following boundary conditions

DTs

Dz

��inlet

¼ 0 ð6Þ

DTs

Dz

��outlet

¼ 0 ð7Þ

Heat transfer coefficients were calculated using the follow-ing Nusselt number90

Nu ¼ 3:091 ð8ÞFor the insulation, the energy balance is formulated in two

dimensions

Finscp, insDTins

Dt¼ λins

D2Tins

Dx2þ D2Tins

Dz2

!ð9Þ

using the following boundary conditions in the spatiallydistributed x-direction

Tsjz ¼ Tinsjx¼0, z ð10Þ

-λinsDTins

Dz

��x¼thins, z

¼ hconvðTins -TambÞþ

εinsσðT4ins - T4

ambÞ��x ¼ thins, z

ð11Þ

with hconv as the convective heat transfer coefficient, εins asthe emissivity, and σ as the Stefan-Boltzmann constant. Theindex amb denotes ambient conditions.

(89) Bouwmeester, H. J. M. Gellings, P. J. The CRC Handbook ofSolid State Electrochemistry; CRC Press: Boca Raton, FL, 1997.

(90) Kreith, F.; Bohn, M. S. Principles of Heat Transfer; 6th ed.;Brooks/Cole: Pacific Grove, CA, 2001.

606


For the y-direction, the following boundary conditions areused

DTins

Dz

��x, z¼0

¼ 0 ð12Þ

DTins

Dz

��x, z¼Lm

¼ 0 ð13Þ

The mean solid-wall temperature is obtained by

T s ¼ 1

Lm

Z Lm

0

Tsdl ð14Þ

with Lm as the length of the monolith.The species conservation balances areDCi

Dtþ vg

DCi

Dz¼ ( kJO2

with k 6¼ 0 for O2 and k

¼ 0 for N2,H2, CH4,H2O,CO,CO2 ð15Þwhere Ci is the concentration of gas phase species. Thecorresponding boundary condition is

Cijinlet ¼ C0i ð16Þ

The fluid velocity is based on

vg ¼ _nvnch

2w2ch

ð17Þ

where n·specifies the mole flow rate at the monolith inlet, vh is

the specific volume, nch the number of gas channels, and wch

is the channel width.The pressure drop ΔP in gas channels is calculated by91

f ¼ 1

2

wch

Lm

� �ΔP

Fv2

� �ð18Þ

Where the friction factor f and Reynolds number Re arecorrelated according to90

fRe ¼ 56:91 ð19Þ

A.2. Heat Exchanger. The heat exchanger models, mainlyemployed the same set of equations as for the membranemodule, but the source terms were omitted. Furthermore, atotal mass balance was used instead of individual speciesbalances to moderate model size

Dmg

Dtþ vg

Dmg

Dz¼ 0 ð20Þ

with mg as the mass flow.

A.3. Pipe. The energy balance for the gas phase reads92

Fgcp, gDTg

Dtþ vg

DTg

Dz

� �¼ D

Dzλg

DTg

Dz

� �-

4

Dinnerhf ðTg -TsÞ

ð21ÞThe corresponding boundary conditions are given in eqs 3

and4.For the solidphase, the following energybalance applies92

Fscp, sDTs

Dt¼ λs

D2Ts

Dz2þ 2D2

outer

D2outer -D2

inner

hf ðTg -TsÞ ð22Þ

where Dinner and Douter specify the inner and outer tubediameter, respectively. The corresponding boundary condi-tions are given in eqs 6 and 7.

The Dittus-Boelter correlation was used for the Nusseltnumber Nu90

Nu ¼ 0:023Re0:8Pr0:3 ð23Þwith Pr as the Prandtl number.

The pressure drop is calculated by eq 18 using the follow-ing friction factor90

fRe ¼ 64 ð24ÞThe fluid velocity is represented by

vg ¼ _nv

Dinner

2

� �2

π

ð25Þ

A.4. Gas Turbine. The GT compressor and turbine modelswere based on isentropic efficiency calculations62

ηc, is ¼ ΔHc, is

ΔHc, realð26Þ

ηt, is ¼ ΔHt, real

ΔHt, isð27Þ

with ηis as the isentropic efficiency and ΔH the enthalpydrop. The indexes c and t denote compressor and turbine,respectively.

Off-design behaviour of the GT compressor was repre-sented by performancemaps,21 shown inFigure 5.Nonlinearregression functions were applied to generate continuousexpressions for mass flow rate ( _m), pressure ratio (

Q), surge

margin, and isentropic efficiency. Employing auxiliary beta-lines (β), equi-spaced and parallel to the surge line, avoids theproblem of vertical portions of constant speed lines24

ξmap ¼ f ðN, βÞ with ξ ¼ Π, _m, ηis ð28ÞThe surge margin was calculated by24

SMc ¼ 100Πsurge -Πworking line

Πworking line

!ð29Þ

Changes in isentropic efficiency of the GT turbine werebased on a chart (page 140, ref 24), using the pressure ratio asa parameter in the nonlinear regression function

ηt, is ¼ f ðΠÞ ð30ÞA chart (page 282, ref 24) was also used for the cooling

flow requirement of the GT turbine and implemented byusing regression function with the turbine inlet temperatureas parameter6

_mcooling ¼ f ðTITÞ ð31Þ

(91) Bird, R. B., Stewart, W. E., Lightfoot, E. N. Transport Phenom-ena, 2nd ed.; Wiley: New York, 2002.

6Note that this function was only used for the design case. For part-load(off-design) operation, the mass flow fraction was fixed.

(92) Thomas, P. Simulation of Industrial Processes for Control En-gineers; Butterworth Heinemann: Oxford, U. K., 1999; p XXIV, 390 s.

607


Off-design performance of the GT turbine was modelledusing the Stodola equation93

_m

_mDP

¼ Pinlet

Pinlet,DP

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiMW

MWDP

r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiγinlet

γinlet,DP

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTinlet,DP

Tinlet

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1- Poutlet

Pinlet

� 21- Poutlet,DP

Pinlet,DP

� 2vuuuut

ð32Þwhere MW is the molecular weight and γ the heat capacityratio. The index DP indicates the design point.

Power outputPof theGTcompressor and turbine is givenby

P ¼ j _nΔhj ð33Þwith Δh as the specific enthalpy drop.

The power balance seen by the GT shaft is

0 ¼ Pt -Pc -Pgen -Pmech ð34Þgen and mech denote generator and mechanical loss, respec-tively.

A.5. Ejector. The section-wise defined ejector model is basedon an energy balance91

_minlet1 hinlet1 þ1

2vinlet12

� �þ _minlet2 hinlet2 þ

1

2vinlet22

� �¼

_moutlet houtlet þ 1

2voutlet2

� �þHloss ð35Þ

with Hloss as the heat loss, a mass balance91

_m1 þ _m2 ¼ F3v3A3 ð36ÞwhereA is the area, and a momentum balance for the mixingsection91

P3A3 - P2A2 - P1A1 ¼ _m1v1 þ m2v2 - _m3v3 ð37ÞFluid velocity is calculated by91

v ¼ MaffiffiffiffiffiffiffiffiffiffiγRT

pð38Þ

where Ma is the Mach number.With an ejector operating in the critical range, the follow-

ing condition holds37

Pejector, outlet ¼ 1:015Pind, inlet ð39Þ

A.6. Combustor. The combustor model (catalytic combus-tors and afterburners) was based on total conversion,

applying the following set of global reactions94

CH4 þ 2O2 w 2H2O þ CO2 ð40Þ

H2 þ 1

2O2 wH2O ð41Þ

COþ 1

2O2 wCO2 ð42Þ

The pressure drop was calculated by eq 18. Replacing thefluid velocity by

v ¼ _m

FAð43Þ

leads to

ΔP ¼ k_m2

Fð44Þ

The outlet temperature was calculated by the energybalance

_nhinlet ¼ _nhoutlet þHloss ð45Þwith a fixed percentage of the inlet energy for the heat loss.

A.7. Valve. The mole flow rate of the valve was calculatedby91

_n ¼ A

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2PinletFinlet

γ

γ-1

� �Poutlet

Pinlet

� �2=γ

-Poutlet

Pinlet

� �γþ 1=γs

ð46Þand the outlet temperature was obtained by

_nhinlet ¼ _nhoutlet ð47Þ

A.8. Mixer and Splitter. The mixer and splitter models wereconsidered to be ideal in the sense that there is no pressuredrop. Themixermodel applies an energy balance of inlet andoutlet streams

_noutlethoutlet ¼Xi

_ninlet, ihinlet, i ð48Þ

A.9. Power Plant. Power plant efficiency was determinedby62

ηpower plant ¼ Pgen -Pcons

_nfuelLHVfuelð49Þ

with the lower heating value of fuel calculated by

LHVfuel ¼ xH2ð-h0f ,H2O

ÞþxCH4ðh0f , CH4

-h0f ,CO2-2h0f ,H2O

ÞþxCOðh0f , CO - h0f , CO2

Þ ð50ÞPhysical properties were obtained from Multiflash in the

following form33

ξ ¼ f ðT ,P, xÞ with ξ ¼ F, cp, λ, h, xf , v ð51Þxf specifies the vapour fraction.

The ideal gas law was used to calculate the pressure in therecycle loop91

PV ¼ mRT

MWð52Þ

(93) Traupel, W., Thermische Turbomaschinen; 3rd ed.; Springer:Berlin, 1977.(94) Chan, S. H.; Ho, H. K.; Tian, Y. Modelling for part-load

operation of solid oxide fuel cell-gas turbine hybrid0f power plant. J.Power Sources 2003, 114 (2), 213–27.(95) Stiller, C. Design, Operation and Control Modelling of Sofc/Gt

Hybrid Systems. Doctoral Thesis, Norwegian University of Science andTechnology, Faculty of Engineering Science and Technology: Trondheim,Norway, 2006.(96) Rodrigues, M.; Walter, A.; Faaij, A. Performance evaluation of

atmospheric biomass integrated gasifier combined cycle systems underdifferent strategies for the use of low calorific gases. Energy Convers.Manage. 2007, 48 (4), 1289–1301.(97) Standards Norway, www.standard.no, 2009.(98) Cai, R.; Gou, C. A proposed scheme for coal fired combined

cycle and its concise performance. Appl. Thermal Eng. 2007, 27 (8-9),1338–1344.(99) Eames, I. W.; Aphornratana, S.; Haider, H. Theoretical and

experimental study of a small-scale steam jet refrigerator. Int. J. Refrig.1995, 18 (6), 378–386.(100) Huang, B. J.; Chang, J. M.; Wang, C. P.; Petrenko, V. A. 1-D

analysis of ejector performance. Int. J. Refrig. 1999, 22 (5), 354–364.

(101) Zhu, Y.; Li, Y., New theoretical model for convergent nozzleejector in the proton exchange membrane fuel cell system. J. PowerSources 2009, 191 (2), 510-519.

608


Nomenclature

A = area (m2)c0 = oxygen concentration (mol m-3)cp = heat capacity at constant pressure (J mol-1 K-1 or

J km-1 K-1)D0 = self-diffusion coefficient for oxygen (m2 s-1)f= friction factorh= specific enthalpy (J mol-1)h0f = enthalpy of formation (J mol-1)H = enthalpy (J)hf = heat transfer coefficient (J s-1 m-2 K-1)Hloss = heat loss (J s-1)JO2

= oxygen flux (mol m-2 s-1)k= constantL = monolith length (m)LHVfuel = lower heating value (J mol-1)m= mass flow (kg)_m = mass flow rate (kg s-1)Ma =Mach numberMW = molecular weight (kg mol-1)n= fitting parameter_n =mole flow rate (mol s-1)Nu= Nusselt numberP = pressure, power (Pa, J s-1)pO2

= oxygen pressurePr= Prandtl numberR = universal gas constant (J mol-1 K-1)Re= Reynolds numbert= time (s)T = temperature (K)T = mean temperature (K)th = membrane layer thickness (m)TIT = turbine inlet temperature (K)v = fluid velocity (m s-1)v = specific volume (mol m-3)wch = gas channel width of monolith (m)

x = mole fractionz = spatially distributed variable in axial direction (m)

Greek Letters

R = area-to-volume ratio of the monolith (m2/m3)γ = heat capacity ratioε = emissivityλ = thermal conductivity (J s-1 m-1 K-1)η = efficiencyΠsurge = compressor surge pressure ratioΠworking line = actual pressure ratioF = density (kg m-3)σ = Stefan-Boltzmann constant (J s-1 m-2 K-4)

Subscripts

amb = ambientc = compressorcons = consumerDP = design pointg = gas phasegen = generatori = chemical speciesind = induced fluid in ejectorins = insulationis = isentropick = sweep gas, airm = monolithmech = mechanicalml = membrane layers = solid phaset = turbine

Abbreviations

CCS = CO2 capture and storageGT= gas turbineHRSG = heat recovery steam generatorVGV = variable guide vane

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