Mohamed Kanniche
email: mohamed.kanniche@edf.fr

Chakib Bouallou
email: chakib.bouallou@ensmp.fr

CO 2 capture study in advanced Integrated Gasification Combined Cycle

Keywords: CO 2 capture, coal, slurry, methanol, MDEA, power plant, avoided CO 2

This paper presents the results of technical and economic studies in order to evaluate, in the French context, the future production cost of electricity from IGCC coal power plants with CO 2 capture and the resulting cost per tonne of CO 2 avoided. The economic evaluation shows that the total cost of base load electricity produced in France by coal IGCC power plants with CO 2 capture could be increased by 39% for 'classical' IGCC and 28% for 'advanced' IGCC.

The cost per tonne of avoided CO 2 is lower by 18% in 'advanced' IGCC relatively to 'classical' IGCC. The approach aimed to be as realistic as possible for the evaluation of the energy penalty due to the integration of CO 2 capture in IGCC power plants. Concerning the CO 2 capture, six physical and chemical absorption processes were modeled with the Aspen Plus™ software. After a selection based on energy performance three processes were selected and studied in detail: two physical processes based on methanol and Selexol™ solvents, and a chemical process using activated MDEA. For 'advanced' IGCC operating at high-pressure, only one physical process is assessed: methanol.

Syngas: synthetic gas produced by the gasification

Introduction

To meet the growing world demand for energy, which will be driven increasingly by the developing countries, recourse to fossil fuels will remain dominant at least for the first half of the 21 st century. The tendency for CO 2 emissions to increase will therefore be considerable, though the objective should be to stabilize the concentration of CO 2 in the atmosphere to an acceptable level: for example 550 ppm in 2100. This objective cannot be achieved by simply stabilizing the quantities of CO 2 discharged into the atmosphere, but by reducing them by at least a factor of 2 or 3 as a world average [START_REF] Philibert | Beyond Kyoto: energy dynamics and climate stabilisation[END_REF]. In addition to the use of nuclear power and renewable energy, the need to reduce CO 2 emissions substantially could therefore lead to the capture and storage of the CO 2 emitted by large combustion plants in underground geological formations (depleted hydrocarbon reservoirs or deep saline aquifers) as it does not seem possible to envisage storage of CO 2 in the ocean in the near future.

Integrated Gasification Combined Cycles (IGCC) is the type of power technology particularly favorable for carbon dioxide capture as this latter can be removed at a convenient stage of the process where its partial pressure is high [START_REF] Chiesa | Shift reactors and physical absorption for Low-CO 2 emission IGCCs[END_REF]. The various options analyzed in the literature concerning this integration are described in [START_REF] Pruschek | Combined cycle power plant with integrated coal gasification, CO shift and CO 2 washing[END_REF], [START_REF] Chiesa | CO 2 emission abatement in IGCC power plants by semi closed cycles: Part A-with oxygen-blown combustion[END_REF] and [START_REF] Chiesa | CO 2 emissions abatement in IGCC power plants : Part B with air blown combustion and CO 2 physical absorption[END_REF]: pre-combustion with a modification of the power station structure; post-combustion with a low pressure separation before the stack in an "end of pipe" separation process; decarbonization of the fuel by producing hydrogen, methanol or ammonia; modified cycle as oxy-combustion O 2 /CO 2 cycle.

The CO 2 removal requires the addition of two main units: a CO shift conversion unit downstream from the gas dedusting system and a CO 2 separation and compression unit meeting the transport conditions.

This paper presents a summary of the results of technical and economic studies conducted by EDF-R&D in collaboration with various organizations: Ecole des Mines de Paris, Technip and UOP for the CO 2 capture processes at the power plant, with the financial support of ADEME, the French agency for environment and energy management, and with Géostock and Tractebel for the CO 2 transport and storage. The aim was to evaluate, in the French context, the levelized cost of electricity from coal with and without CO 2 capture and storage and the cost per tonne of CO 2 avoided. The coal option was chosen on account of the large proven reserves of this fossil fuel (2 to 3 centuries at present consumption rate) and oxygen blown IGCC was selected as it seems to be the best alternative for electricity generation from coal in the medium/long term [START_REF] Ordorica-Garcia | Technoeconomic evaluation of IGCC power plants for CO 2 avoidance[END_REF], [START_REF] Sekar | Future carbon regulations and current investments in alternative coal-fired power plant technologies[END_REF] and [START_REF] Aineto | Thermal expansion of slag and fly ash from coal gasification in IGCC power plant[END_REF], showing some specific advantages:

-IGCC is a clean coal technology that today offers significant reduction in air-pollutant emissions, -In this process, coal reacts under pressure with oxygen and steam in the gasifier producing a syngas which can be shifted to CO 2 /H 2 mixture in a catalytic reactor leading to a high partial pressure of CO 2 which is favorable for its capture, -After CO 2 capture, the fuel gas is essentially hydrogen which can be used to generate electricity in a combined cycle or, in the future, in fuel cells in order to increase the overall efficiency, and -IGCC may offer opportunities to produce power as well as synthetic fuels and chemicals.

We focus in this paper on a CO 2 separation in order to integrate this option into the power plant cycle, upstream from the gas turbine.

Capturing CO 2 at the power plant

EDF-R&D has carried out an investigation, in close collaboration with the Ecole des Mines de Paris, in order to select the best processes for collecting CO 2 to be integrated into an IGCC power plant and to calculate its impact on efficiency. Moreover, with the assistance of the Technip Company and UOP, the investment costs associated with the new equipment have been estimated and the total cost per kWh (with and without CO 2 capture) has been evaluated.

Capture technology

Various processes may be envisaged for separating the CO 2 : chemical or physical absorption (or an association of both), adsorption onto solids, separation by membranes and cryogenic separation. Obviously these processes are not all equivalent, nor all at the same stage of development. Cryogenic separation needs too much energy and appears to be too expensive; separation by membranes is attractive (a principle similar to filtration) but today the 'right' membranes required are under development and do not yet exist for an industrial scale; adsorption onto a solid does not seem very suitable for processing huge volumes of gas.

In the end, only physical and chemical (or mixed) absorption methods seem suitable for large power plants, but the choice of the 'best' solvent is still a very open question. A typical absorption process is shown in Figure 1: the gas to be treated is injected at the bottom of the absorption column after it is cooled at a first step in a heat exchanger which heats the treated gas exiting the column and depending on the process type (e.g. for methanol, NMP and Selexol™ processes) in a second step using a refrigeration system. The solvent is injected at the top of the absorption column to absorb the CO 2 from the gas. The rich solvent is then heated by exchanging heat with the lean solvent coming from the desorption column. The solvent is regenerated in the desorption column using low-pressure steam condensation in the reboiler.

CO 2 separation processes with chemical solvents (alkanolamines) have been industrialized

since the seventies and licensors have been looking these last few years at specific solvent formulations: primary or secondary amines and anti-corrosion additives, tertiary amines with promoters or activators and with antifoaming additives. Mixing of chemical solvents, such as tertiary amines and a relatively small amount of the primary amine, aims to combine the advantages of the two solvents. The target of such mixed chemical solvents is to achieve a better absorption capacity, to avoid solvent degradation and to limit corrosion. Physical solvents (methanol, propylene carbonate, n-methyl-pyrrolidone (NMP), Dimethylether of polyethylene glycol (Selexol™)) are known for their chemical stability and for a non-induced corrosion effect. Moreover, their high absorption capacities make them interesting for bulk removal. However, methanol needs low operating temperatures because of its higher volatility.

The high volatility is a disadvantage with regard to the potential solvent losses. Even if the process streams are chilled to -30°C, it is necessary, before the transport and the storage of the CO 2 , to add to the CO 2 compression unit a wash water column to capture methanol with water from the CO 2 stream (Figure 2). For the CO 2 transportation, the water content should not exceed 20 ppmm to avoid corrosion problems. This threshold value was specified by gas transportation experts of Tractebel licensed by EDF for CO 2 transportation. For this purpose a dehydration system based on tri-ethylene-glycol (TEG) is added in the compression unit (Figure 2). For methanol recovery from water a distillation column is then added to the CO 2 capture unit (Figure 3). NMP also requires a refrigeration system to meet relatively low temperatures. The refrigeration system uses electricity for the compression of the refrigeration media, which means a higher energy penalty for the process than cooling water.

Mixing the chemical and physical solvents (hybrid solvent) allows an increased CO 2 absorption capacity compared to chemical solvent alone. The solubility of carbon dioxide in primary or secondary amines is improved by the addition of NMP, [START_REF] Murietta-Guevara | Solubility of carbon dioxide in binary mixtures of N-Methyl-Pyrrolidone with alkanolamines[END_REF]. The solubility of carbon dioxide is compared in a mixture of methyldiethanolamine, MDEA and methanol, and in methanol, [START_REF] Henni | Solubility of carbon dioxide in methyldiethanolamine methanol and water[END_REF]. The physical solvent polarity and permitivity are significant on the ionization of the species and on reaction kinetics. However, the kinetics of CO 2 absorption by physical solvents and amines, in aqueous solution form or not, are still unknown.

In this work, six processes are evaluated as stand alone units, fed with the same synthesis gas (50 kg/s and 24 bar): three physical processes, methanol, n-methyl-pyrrolidone (NMP), Selexol, and three chemical processes, a sterically hindered amine 2-amino-2-methyl-1propanol (AMP), activated methyldiethanolamine (A-MDEA) and a mixture of methyldiethanolamine and monoethanolamine in aqueous solution (MDEA 25 mol % /MEA 5 mol %). We considered the electrical and thermal consumption for the CO 2 capture. The electrical consumption is similar for the six processes, while thermal consumption is rather high for chemical processes as can be seen in Figure 4. Then three processes are selected for the integration in the global IGCC system. These processes are: methanol, Selexol and activated MDEA. The activated MDEA process was integrated into the IGCC and added to the comparison study in order to evaluate a chemical process relative to the two physical ones.

Particular attention was paid to thermodynamic models. A simple equation of state, Redlich Kwong Soave, is chosen for the synthesis gas and the flue gas, but the thermodynamic model Steamnbs [START_REF] Descamps | Etude de la captation du CO 2 par absorption physique dans les systèmes de production d'électricité basés sur la gazéification du charbon intégrée à un cycle combiné[END_REF] (based on the 1984 NBS/NRC steam table correlation for thermodynamic properties and International Association for Properties of Steam IAPS for the transport properties) is used for pure water and steam, and the Electrolyte Non Random Two Liquid model for the aqueous electrolyte system. The Redlich Kwong Soave equation of state, with the Holderbaum and Gmehling mixing rule [START_REF] Holderbaum | PSRK: A contribution equation of state based on unifac[END_REF] is chosen for the CO 2 capture process.

The calculation of the activity coefficient model is done by Uniquac for which the interaction parameters are fitted on measured data from the literature [START_REF] Hong | Vapor liquid equilibrium studies for the carbon dioxidemethanol system[END_REF]. The CO 2 methanol equilibrium, [START_REF] Hong | Vapor liquid equilibrium studies for the carbon dioxidemethanol system[END_REF] and [START_REF] Suzuki | Isothermal vaporliquid equilibrium data for binary systems at high pressures[END_REF], was studied and modeled to optimize the methanol loss calculation in the CO 2 stream leaving the desorption column. The simulation of the absorption and desorption is performed with a rigorous distillation model.

Moreover, an optimized case has been studied, which consists in the adjustment of the thermodynamic parameters and in improvement of the capture process. Hydrogen coabsorption in methanol has been studied in order to improve the calculation of the hydrogen losses by absorption in the solvent. The hydrogen/methanol binary interactions were measured and the interaction parameters of the thermodynamic model (Uniquac) were calculated. The methanol flow rate is slightly reduced when the H 2 -methanol binary interaction parameter is taken into account, leading to a reduced consumption of steam in the thermal regeneration.

The separation process flow diagram has been improved by the addition of two flash drums in order to reduce the CO 2 compression power.

Finally, the solvent flow rate is optimized to perform the CO 2 separation with a minimum of steam consumption in the thermal regeneration. The solvent regeneration column is calculated for each case, as a residual CO 2 concentration is determined in the lean solvent in order to be compatible with the required CO 2 purity in the top of the absorption column. A low operating temperature of -30 °C is chosen for the methanol in order to minimize the solvent losses and to maximize the carbon dioxide solubility.

Integration to IGCC systems

For a 'classical' IGCC power plant, the study was based on the Puertollano [START_REF] Font | Condensing species from flue gas in Puertollano gasification power plant[END_REF] scheme operating at 27 bars and where 100% of air feeding the air separation unit (ASU) producing oxygen and nitrogen is extracted from the gas turbine (full integration). As the coal is injected in dry form using pure nitrogen (given by the ASU) as the transportation medium from coal grinder to the gasifier, the necessary steam for the gasification is extracted from the combined cycle. The CO 2 separation unit was integrated downstream from the existing desulphuration unit, and after a CO shift conversion unit (Figure 5). The integration of the three selected processes was performed as realistically as possible: avoiding great modifications of the existing IGCC, conserving the existing sulphur removal unit, adding a shift conversion in the appropriate part of the system to conserve equilibrated H 2 S/CO 2 acid gas for the Claus plant (pure sulphur production), fully integrating the combined cycle and the shift conversion (this latter produces a smaller amount of Medium Pressure steam than it consumes), bleeding steam from the appropriate part of the combined cycle, thermal balancing of the feed water flash tank, using saturated steam instead of superheated steam for the solvent regeneration column, adjusting thermodynamic parameters of gas/solvent binary interactions (the hydrogen/methanol binary interactions are measured, others are taken from published experimental data), adding steam to the gas turbine in order to ensure low NOx emission as the synthetic gas now has hydrogen as its major component, conserving the design parameters of both gas turbine and steam turbine. The design parameters of the gas turbine (the turbine inlet temperature and the equivalent weight flow) and of the steam turbine (Stodola criteria) are taken into account, and the reduction of the NOx production in the combustion chamber is considered. Thus the choice is made to feed the gas turbine of the combined cycle with a diluted synthesis gas, having a low heating value similar to that produced without the CO 2 capture. As a consequence, a significant amount of steam is injected into the combustion chamber. We focus on the energy consumption of CO 2 capture and on the energy penalty of optimised retrofit IGCC.

Concerning the 'advanced' IGCC system (Figure 6) which is fed with a mixture of coal and water (slurry), the shift conversion is inserted immediately downstream from the gasification system as the synthetic gas contains enough water to convert CO into CO 2 . The coal feed in slurry form enables the gasifier to operate at high pressure, 64 bars which permits an economy in the process volume and this high pressure is also favorable to physical absorption (Henry law). After a gas treatment where heat is recovered to produce medium and low-pressure steams, the CO 2 and H 2 S are captured in the same unit. The acid gas containing more than 25% H 2 S is sent to a Claus unit for sulphur recovery and the CO 2 is sent to a compression unit. The clean gas is expanded in order to recover electrical power and heated before dilution with waste nitrogen coming from the air separation unit.

We could notice that here (see figure 6) only 50% of the air needed by the ASU is extracted from the gas turbine; the remaining 50% is taken from ambient air using an ASU dedicated compressor. In fact, the optimum of integration depends on the type of gas turbine and specific studies should be performed for each gas turbine considered. Moreover, as the gasification is fed with slurry, the synthetic gas contains a relatively high amount of CO 2 compared to dry gasification. Therefore there is no more need of gas saturation with water or steam injection in the combustion chamber to meet low level of NOx pollutant, the low heating value (LHV) of the diluted syngas being sufficiently low.

Performance in terms of energy of CO 2 capture

We have based our evaluation on the IGCC unit of Puertollano [START_REF] Aineto | Thermal expansion of slag and fly ash from coal gasification in IGCC power plant[END_REF], [START_REF] Font | Condensing species from flue gas in Puertollano gasification power plant[END_REF] revaluated under ISO conditions (1.013 bar, 15°C, 60% relative humidity) and using an international coal (16 % ash, 2 % moisture and 1 % sulfur) instead of the mixture of Puertollano local coal + petroleum coke. Under these 'standard' conditions, the net power of the plant is 326 MW and the LHV efficiency is 44 %. Several physical and chemical absorption processes have been modeled

with Aspen Plus™ software to compare their energy performance. However, to avoid too many power plant design modifications, the gasification pressure has been kept equal to 27 bars, although for physical solvents a higher pressure would have been more favorable. That is why after an initial selection, three processes were finally adopted and studied in detail: a physical absorption process by methanol, another physical absorption process, the Selexol process, in which the solvent is based on dimethylether polyethylene glycol (DMPEG), and a process using an activated amine-based chemical solvent, methyl-diethanolamine (MDEA).

In addition to the equipment required for CO 2 separation (absorption and desorption columns, pumps, heat exchangers, pressure reduction tanks, etc.), we also included in the process:

-a catalytic device for conversion of the CO into CO 2 ("shift conversion") upstream of the separation in order to increase the CO 2 content and thus improve the efficiency of the capture; -a refrigeration system for the methanol process to maintain an optimum temperature of -30°C in the absorption column and a downstream recovery system to limit losses of the absorbent;

-a device to reduce the water content in the CO 2 produced to less than 20 ppmm to prevent acid corrosion in the transport pipes;

-a 150 bar CO 2 compression station linked to a gas cooling system (final temperature < 40°C) in order to comply with the specifications of the CO 2 transport network.

The CO 2 absorption rate in the IGCC integrated methanol process has been varied from 77 to 88 mol %, with a CO conversion rate fixed at 90 mol %. Figure 7 shows that 85% CO 2 recovery seems to be a good compromise: above this recovery rate, the energy penalty grows quite steeply, while below 85% recovery rate the energy penalty decreases almost linearly. In fact, 85% was then chosen to compare the three processes integrated into the global IGCC system. This takes into account the efficiency of conversion of CO into CO 2 (90 %) and that of the separation of the CO 2 itself (approximately 95%). The efficiency loss shown in Figure 8 is calculated by the difference in efficiency of IGCC with and without capture divided by the efficiency of IGCC without capture.

The power output of the gas turbine was maintained nearly constant with the CO 2 capture operation by adding enough coal flow rate to the gasifier. The auxiliary electric consumption takes into account all the electric power needed by pumps and compressors, including the CO 2 inter-cooling compressor which delivers a CO 2 flux at 150 bar and 37°C, the solvent recycling pump, and the compressor for methanol refrigeration (see Figure 9). As can be seen in Figure 9, all the solvents have almost similar consumption for the CO 2 compression and for the standard auxiliaries (such as Air Separation Units and pumps and compressors of the units other than the CO 2 capture one). However, the chemical solvent shows a higher consumption due to the steam bleeding for solvent regeneration. This consumption was calculated by disconnecting the steam flux going from the combined cycle to the solvent regeneration column and calculating the difference in the power output when this flux is fully integrated.

Figure 8 shows the performance of the three solvents integrated into the IGCC, compared to the IGCC without capture. The comparison of the different energy balances is presented for 85% recovery of CO 2 . The best energy performance is obtained with the methanol process although the performance of the other two systems is close. The efficiency of 'classical' IGCC with CO 2 capture using methanol is 33.5% and is therefore 10.5 points lower than that of the reference IGCC power plant, which represents a relative reduction of 24 %. The fact that physical and chemical processes show similar energy performance was expected as the 'classical' IGCC operates at relatively low pressure (27 bars) which delivers CO 2 to the capture system at a partial pressure around 8 bars. This is the starting point of chemical absorption saturation and the lower limit of physical absorption efficiency. With 'advanced' IGCC operating at a higher pressure (64 bars instead of 27 bars for 'classical' IGCC), the CO 2 capture using a physical solvent like methanol seems to be more interesting than the same operation in 'classical' IGCC because of high partial pressure of CO 2 in the former case. The efficiency loss is only 9.3 points (see Table 1) in 'advanced' IGCC whereas in 'classical'

IGCC the efficiency drop is above 10 points. However, in the cases without CO 2 capture 'advanced' IGCC has lower efficiency than 'classical' IGCC. This is because 'advanced' IGCC uses feedstock in slurry form which should contain a maximum of 64% solids otherwise the compression operation to 64 bars could be risky because of increasing viscosity with solid contents. Therefore there is a high amount of water to evaporate in the slurry gasifier, which leads to higher production of oxygen by the ASU, leading to higher electrical consumption by this latter compared to the ASU of 'classical' IGCC. This consumption by the ASU in 'advanced' IGCC is greater than the lack of electricity production due to the steam consumption needed in 'classical' IGCC. However the benefit of high-pressure gasification remains in capital cost of equipment as can be seen in the next section.

The cost of CO 2 capture

The cost of construction of the 'classical' IGCC (without capture) was established on the basis of the economic data of Puertollano, eliminating the redundant equipment and redimensioning the devices on the basis of ISO conditions and the use of an international standard coal. The following are included: the costs of supply, erection and commissioning of the different devices and ancillary infrastructure (roads, offices, parking area, lighting, etc.) and a provision for contingencies and project management charges (owner's cost).

The construction costs of the devices associated with CO 2 capture were calculated on the basis of an investigation entrusted to Technip concerning the processes with methanol and activated MDEA, including the system for dehydration of the flow of CO 2 produced, the methanol recovery system and the 150 bars CO 2 compression station. The construction cost of the Selexol process was calculated from information supplied by UOP, the licensor for this type of process.

The cost of 'advanced' IGCC was taken from a detailed study published by the Green House Gas division of the International Energy Agency [START_REF]Potential improvement in gasification combined cycle power generation with CO 2 capture[END_REF].

The investment costs for all cases with and without capture were obtained by adding to the construction costs the interest during construction (calculated for a construction period of four years), the preproduction costs and a contingency fund. Table 1 shows the relative investment costs, taken 'classical' IGCC as reference, for an IGCC power plant with and without a CO 2 capture device. We note that the 'advanced' IGCC shows lower specific cost relatively to 'classical' IGCC thanks to higher pressure of the process and probably also thanks to bigger scale. The transport and storage costs are detailed in reference [START_REF]Potential improvement in gasification combined cycle power generation with CO 2 capture[END_REF].

In the end (see Table 1), the absolute investment cost of a 'classical' IGCC power plant would increase by 33% if a CO 2 capture device were to be included (methanol or MDEA), however the specific investment cost is increased by higher value, 53%, due to efficiency decrease induced by CO 2 capture option. For 'advanced' IGCC without capture the specific investment cost is lower by 14% than the one of 'classical' IGCC without capture, and for 'advanced' IGCC with capture one should add approximately 28% to 'classical' IGCC without capture and 49% to the case of 'advanced' IGCC without capture.

If we consider only the construction costs, Figure 10 shows that in the case of the process with methanol the CO 2 separation system represents 15% of the total cost of the equipment and that the shift conversion and the CO 2 compression each represent 4% of the total, which brings the proportion of the cost of capture to 23% of the construction cost of the power plant.

Recent work [START_REF] Klemeš | Techno-economic modelling and cost functions of CO 2 capture processes[END_REF] compared the estimate of the cost obtained by the authors with estimate available in the literature. The different cost estimates were updated and levelled to late 2004 US$ levels and the technologies studied are coal-fired power plant, IGCC, and GTCC using amine scrubbing technology for CO 2 capture. Their results show a good agreement of the newly developed model with the previous studies. Analysis of the data series provided three power plant capacity ranges (2000-1500, 1500-900 and 900-300 MWe) in which the patterns of CO 2 avoidance costs become steeper. Our results are in agreement with those provided in [START_REF] Klemeš | Techno-economic modelling and cost functions of CO 2 capture processes[END_REF] in particular with regard to the new IGCC.

Conclusion

The integration of CO 2 capture in a complete and detailed IGCC power station simulation model has been studied in order to calculate the final efficiency. We chose for this study a detailed representation of the process and the related thermodynamic parameters in order to represent the processes as realistically as possible. An important aspect of CO 2 capture is the auxiliary amount of energy required by using such systems. This energy consumption reduces the overall efficiency of power generation, typically by 24%, which is a substantial price to pay for capturing CO 2 . One attraction of the methanol process is that the required energy consumption is moderate for this operation compared to chemical absorption. There is continuous research to reduce energy consumption for the overall process. The use of the new technologies such as gasification under high pressure can lead to better performance for physical solvents even if the consumption induced by high water content of the slurry leads to a higher energy penalty even for the case without CO 2 capture. Also using gas turbines operating with high turbine inlet temperature and therefore presenting a higher efficiency (60% in a combined cycle instead of 53% used in 'classical' IGCC) will increase the power production and the electric net efficiency, which is a complimentary way to reduce fossil fuel consumption and therefore the CO 2 emission.

This investigation into the overall cost per kWh generated by a coal-fired IGCC power plant with CO 2 capture shows that the integration of the CO 2 capture system must be optimized carefully (choice of the absorbent, operating pressure, etc.) to limit the loss of efficiency, which has a severe impact on the generating cost per kWh.

Having stated these reservations, the results show that the basic generating cost from [START_REF] Mckee | Solutions for the 21 st century: Zero emissions technologies for fossil fuels[END_REF].

Absolute values of cost estimate are not given here and those given elsewhere [START_REF] Jaud | Technico-economic feasibility study of CO 2 capture, transport and geo-sequestration: a case study for France[END_REF] should be viewed with caution as they are made to an accuracy of ±30%. Moreover, metal market and contract prices have been rising for two years and this will probably lead to a much higher cost for the power plant if based on 2007euro values but will probably not lead to significant change in differential comparisons between the different options. In the other hand, these values could also fall in the medium / long term as a function of technical progress on process efficiency and capture technologies.

  ether of polyethylene glycol (DMPEG)

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 9 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 8 .Fig. 9 .

 123492345689 Fig. 1. : Typical absorption process

  'classical' IGCC with capture would increase by 39% relatively to 'classical' IGCC without capture. The incremental production cost induced by CO 2 capture for 'advanced' IGCC is only 28% which leads to a relatively lower cost per tonne of CO 2 avoided which is 82% lower in the case of 'advanced' IGCC than in 'classical' IGCC.Even though the incremental costs are substantial, they do not appear to constitute in themselves an obstacle to the development of the capture / storage of CO 2 if financial mechanisms are established to combat global warming. For example, in 1996 Statoil created a storage facility in the Sleipner field in order to avoid a Norwegian tax of about $ 50 / tonne on offshore releases of CO 2

Table 1 :

 1 Comparison between 'classical' and 'advanced' IGCC with and without capture (methanol process for 85% of CO 2 capture -8% interest rate for economic evaluation) all the costs are expressed relatively to 'classical' IGCC without capture which is taken as reference

	'Classical' IGCC	'Classical'	'Advanced'	'Advanced'
	without capture	IGCC with	IGCC without	IGCC with
		capture	capture	capture

*

Acknowledgments

The authors wish to thank the ADEME 'Agence de l'Environnement et de la Maîtrise de l'Energie' the French public environmental agency

Combined


Antonio Gómez

Norberto Fueyo
email: norberto.fueyo@unizar.es

Ignacio Luis

Díez

Modelling and simulation of uid-ow and heat transfer in the convective zone of a power-generation boiler

Keywords: Heat exchangers, power station boiler, convective zone, heat transfer, CFD, modelling

The convective zone of a power-station boiler is a complex piece of engineering equipment, which comprises a multiplicity of inter-connected heat-exchanging elements.

This paper presents a mathematical model of the convective zone, which allows for the calculation of the shell-side ow and the shell-side, tube-side and tube-wall, thermal elds, and of the shell-tube heat-exchange. The model is solved using conventional CFD techniques, in which the individual tubes are treated as sub-grid features. A geometrical model is used to describe the multiplicity of heat-exchanging structures, and the interconnections between them.

The CFD model is rst validated by comparison with simple heat-exchanger geometries which can be solved with analytical methods, and then applied to an actual 350 MW (e) power-station boiler.

Introduction

The shell-and-tube heat-exchanger is a ubiquitous piece of equipment in the power-generation and processes industries. In this type of heat exchanger, heat is transferred to (or from) a uid owing through a tube bundle from (or to) another uid which ows around the tubes through the shell. Both uids are everywhere separated by the tube wall (usually metal-made) and never become in direct contact.

The convective zone of a power-station boiler is a complex assembly of interconnected heat exchangers. Around 50% of the cycle heat generated in the boiler may be transferred in this zone, and hence the interest of the modelling of uid ow and heat transfer. An accurate computer model can provide convenient and economical assistance in the design and in the operation of the convective zone, and can contribute signicantly to the improvement of eciency and durability. For the modelling to be accurate enough, a desirable feature of the model should be the ability to calculate simultaneously the (spatially-varying) temperature of both the shell and the tube uids.

The modelling of shell-and-tube heat exchangers using Computational Fluid Dynamics techniques dates back to the early days of the discipline. It is dicult therefore to trace it to a seminal paper; however, the technique described in the one by Patankar and Spalding [START_REF] Patankar | A calculation procedure for the transient and steady-state behaviour of shell-and-tube heat exchangers[END_REF] was perhaps the rst one capable of calculating simultaneously the thermal elds in both uids and in the tube metal, and can be regarded as the framework from which successive contributions were developed.

A literature survey, however, shows that most of the published CFD-type simulations of large, shell-and-tube heat-exchangers pay much attention to the prediction of the aerodynamics (such as ow distribution or pressure losses), but fewer contributions can be found in which the thermal elds and heat transfer are also considered. This is the case in the early paper by Rhodes and Carlucci [START_REF] Rhodes | Predicted and measured velocity distributions in a model heat exchager[END_REF], which reports the rst aerodynamic calculation of a model heat exchanger, and a comparison with experimental measurements. Despite the crude geometrical representation and discretisation, due to the limitations imposed by the computers available at the time, the mathematical model had many of the features still used nowadays for calculating the tube-bundle aerodynamic performance, such as the use of porosities, friction factors and eective viscosities to represent the eect of the tube bundle on momentum transport. The problem was later revisited by Theodossiou et al [START_REF] Theodossiou | Flow eld predictions in a model heat exchanger[END_REF].

The simulation of power-plant condensers, which for the purpose of this paper can be regarded as a derivative of the heat exchanger, has attracted much attention in recent years. One of the most comprehensive three-dimensional models is that used by Zhang et al [START_REF] Zhang | The numerical and experimental study of a power plant condenser[END_REF], Zhang and Zhang [START_REF] Zhang | A quasi-three-dimensional approach to predict the performance of steam surface condensers[END_REF] and Zhang and Bokil [START_REF] Zhang | A quasi-three-dimensional approach to simulate the twophase uid ow and heat transfer in condensers[END_REF] for power-plant condensers, albeit the tube-side uid is treated in a less general manner than that employed in this paper. Ormiston et al [START_REF] Ormiston | Numerical modeling of power station steam condensers. part 1: Convergence behavior of a nite-volume model[END_REF] [START_REF] Ormiston | Numerical modeling of power station steam condensers. part 2: Improvement of solution behavior[END_REF] provide a literature survey of recent CFD models of power-plant condensers, as well as some modications to the solution algorithm which can lead to better convergence behaviour. Prithiviraj and Andrews [START_REF] Phrithiviraj | Three-dimensional numerical simulation of shelland-tube heat exchangers. Part I: Foundation and uid mechanics[END_REF] [10] reformulate the nite-volume equations for the tube bundle using control-volume integrals of the model equations. The treatment of the tube-side enthalpy is again rather simple, since the condensers considered in their paper are single-pass ones.

No previous multi-dimensional simulations of the uid ow and heat transfer in the convective zone of a power-station boiler, addressing both the shell-side and the tube-side elds have been traced in the open literature. The paper by Tu et al [START_REF] Tu | Numerical modelling of three-dimensional y-ash ow in power utility boilers[END_REF] addresses the CFD modelling of the y-ash ow (without heat transfer) in power-utility boilers (including both the furnace and convective section) using Eulerian-Eulerian models. However, the emphasis is placed on the multi-phase, gas-particle model, and the representation of the convective section appears to be a simplied one. Coelho [START_REF] Coelho | Mathematical modeling of the convection chamber of a utility boiler an application[END_REF] has reported results from a CFD model of a boiler similar to the present one, but, unlike this work, the modelling is restricted to the shell side, and either the tube-side temperature is assumed or the overall heat transfer in a tube bank is known and distributed along the bank. Diez et al [START_REF] Diez | Modelling of pulverized coal boilers: review and validation of on-line simulation techniques[END_REF] address the modelling of the same boiler as featured in this work, but using a zonal method for the gas ow and lumped-parameter heat-exchanger network for the tube-side, together with CFD calculations of the combustion chamber to provide inlet conditions for the zonal model. Such a simplied model, it is argued, has the attractive merit of being usable on line. A similar method is used by Niu and Wong [START_REF] Niu | Adaptive simulation of boiler unit performance[END_REF]. Huang et al [START_REF] Huang | Numerical predicion of high eciency boiler heat exchanger performance[END_REF] model the combustion chamber and heat exchanger of a domestic boiler; although few details of the mathematical model and numerical procedure are given, the method employed is probably similar to the one used in the present work. This paper presents a mathematical model that can be used for the CFD simulation of uid ow and heat transfer in the convective section of power-station boilers. The model, which builds on the method by Patankar and Spalding [START_REF] Patankar | A calculation procedure for the transient and steady-state behaviour of shell-and-tube heat exchangers[END_REF], represents the tubes as subgrid features; the meshing of individual tubes or periodically-repeating tube-arrays, while useful to improve the design of tube banks or to calculate their heat-exchanging or aerodynamic performance, such as pressure losses (see, eg, [START_REF] Horvat | Comparison of heat transfer conditions in tube bundle cross-ow for dierent tube shapes[END_REF]), is computationally impractical for complex arrays of interconnected banks. The present model, on the other hand, allows for the simultaneous calculation of the shell-side, tube-side and metal thermal elds even when several interconnected heat exchangers have to be considered, as it is the case in power-station boilers.

The present mathematical model can be best viewed as representing three superimposed spaces or worlds, which coexist in physical space: the shellside of the heat exchanger, the tube side and the metal. Conservation equations are solved for the relevant magnitudes in these three spaces, and include the appropriate exchange terms between them (eg, heat transfer).

Thus, for the shell-side, the relevant equations are continuity, momentum and enthalpy conservation. The continuity equation is:

∂ s ρ s ∂t + ∇ • ( s ρ s v s ) = 0 ( 1
)
where s is the void fraction, ie the fraction of local space available to the shell-side uid; ρ s is the shell-uid density; and v s is the shell-uid interstitialvelocity vector.

The shell-side-momentum equation is:

∂ ( s ρ s v s ) ∂t + ∇ • ( s ρ s v s v s ) -∇ • ( s µ s ∇ v s ) = -s ∇P -F (2)
where µ s is either the molecular viscosity (if the ow is laminar) or an eective (molecular plus turbulent) one if the ow is turbulent and an eddy-viscosity model is used; P is the pressure; and F is a friction term (specied below) that accounts for the pressure losses in the tube bank.

The shell-side-enthalpy (h s ) equation reads:

∂ ( s ρ s h s ) ∂t + ∇ • ( s ρ s v s h s ) -∇ • ( s Γ s ∇h s ) = α s→w (T w -T s ) (3)
where Γ s is a diusion coecient; α s→w is a volumetric heat transfer coecient from the shell uid to the tube wall, with units W/m 3 K; T s is the local shelluid temperature; and T w is the local tube-wall temperature. The use of a volumetric heat-transfer coecient in this equation is required for dimensional reasons; it is calculated from the usual, per-unit-surface one using the ratio of tube surface to shell volume as detailed below. Other heat sources, such viscous heating or radiative heat-exchange, have been neglected in this equation.

If the ow in the shell side is turbulent, as it is usually the case, the above equations can be interpreted as being Favre-averaged. Then, if suitable eddyviscosity turbulence model is used to close the unknown correlations,µ s can be regarded as an eective shell-side viscosity, andΓ s as an eective shell-side Prandtl number for h s . Both can be calculated from the model parameters.

The ow in utility boiler is clearly turbulent; in the application shown in

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Section 6 below, the Reynolds number based on an average velocity and a boiler transversal dimension is in excess of 500,000. Turbulence in such a highly complex physical domain is correspondingly a complex issue. Given the impossibility to mesh the individual tubes in the banks, we have resorted to the use of a kturbulence model, with some modications to impose a length scale within the tube bank. While more sophisticated turbulence models are available, their use for the problem addressed in this paper does not justify the substantial additional computational expense, since the tube bank is nevertheless represented as a subgrid feature.

In the tube side, the ow is considered (locally) one-directional (viz in the direction of the tube orientation), which allows to obtain the local mass-ow rate by simple geometrical calculations (see below). Regarding the tube-side momentum equations, their only use would be to calculate tube-side head losses. However, if head losses in the tube-side circuit are quantity of interest, they can be calculated using simpler alternative methods, e.g. pipe-ow formulae. Thus, in the current application, the tube-side momentum equations are not required. The only relevant conservation equation for the tube side is therefore the one for enthalpy (h t ), which reads:

∂ ( t ρ t h t ) ∂t + ∇ • ( t ρ t v t h t ) = α t→w (T w -T t ) ( 4
)
where t is the fraction of local space occupied by the tube-side uid; v t is the (one-directional) tube-side-uid velocity vector; α t→w is a volumetric heattransfer coecient (from the shell uid to the tube wall), with unitsW/m 3 K; and T t is the (bulk) tube-side-uid temperature.

Streamwise heat conduction (molecular or turbulent) has been neglected in the above equation, since in all cases it will be much less important than convection. (Cross-stream conduction is accounted for in the volumetric heattransfer coecient α t→w ).

Finally, for the metal (the tube wall), the only relevant equation is the energyconservation one, which, neglecting axial heat-conduction, reads:

∂ ( w ρ w h w ) ∂t = α s→w (T s -T w ) + α t→w (T t -T w ) ( 5
)
where w is the fraction of local space occupied by the tube wall.

An alternative framework to that presented here for addressing the spacesharing feature of the ow under consideration is the use of dierent computational spaces for each of the co-existing worlds. Beale and Zhubrin [START_REF] Beale | A distributed resistance analogy for solid oxide fuel cells[END_REF] apply this concept in their simulation of Solid Oxide Fuel Cells.

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F i = ξ u i ρ s u i U (6)
where u i is the i th component of the velocity vector, U is the absolute value of the velocity vector, and the friction factors ξ u i are calculated similarly to Rhodes and Carlucci [START_REF] Rhodes | Predicted and measured velocity distributions in a model heat exchager[END_REF] as:

ξ u i = 2 f P 1 -s 1 - ( 7
)
for the parallel-ow direction and

ξ u i = 2 f ⊥ P P s P -D o 2 1 -s 1 - ( 8
)
for the crossow direction.

In equations ( 7) and ( 8), the factors f and f ⊥ are functions of the local Reynolds number [START_REF] Rhodes | Predicted and measured velocity distributions in a model heat exchager[END_REF]; P is the tube pitch in the cross-ow direction; P is an average pitch; D o is the tube outer-diameter; s is the local void fraction, and is the void fraction in the local tube-bank. These both can be readily calculated from geometrical data.

An alternative means of combining the contributions from the principal directions to the pressure loss is the tensorial approach suggested by Butterworth [START_REF] Butterworth | The development of a model for three-dimensional ow in tube bundles[END_REF].

Heat-transfer coecients

For the calculation of the volumetric heat transfer coecientα t→w in equation ( 4), we rst compute the (per-unit-surface) heat-transfer coecient α t→w by considering the heat-transfer resistances due to heat convection and fouling:

1 α t→w = R t + R f t (9)

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The convection resistance R t is obtained using a Nusselt-number correlation:

1 R t = N u k t D i ( 10
)
with k t being the tube-side-uid thermal-conductivity and N u = 0.023Re 0.8 t P r 0.4

t ([19]

). Transport and thermodynamic properties for this correlation are calculated at the local tube temperature, which is an output from the model.

Finally, the dimensions of α t→w in equations ( 4) and ( 5), ie W/m 3 K, are recovered from those of α t→w (W/m 2 K) by multiplying the coecient by the surface-to-volume ratio in the bank, ie by the local ratio of heat-exchanging surface S to physical volume V :

α t→w = α t→w S V ( 11
)
The shell-to-wall heat-transfer coecient α s→w is calculated in a similar manner:

1 α s→w = R s + R f s ( 12
)
with the resistance coecient R s now calculated using the correlation proposed by Zhukauskas [START_REF] Zhukauskas | Heat transfer from tubes in crossow[END_REF] for the Nusselt number:

N u = CRe m s P r 0.36 s P r s P r w 1/4 (13)
Here, the Reynolds number is calculated with the tube external diameter and the maximum gas velocity within the tube bank. The gas Prandtl numbers P r s and P r w are calculated respectively at the local gas temperature and at the wall temperature, both obtained from the model.

The constants C and m depend on tube-bank conguration and Reynolds number; see Zhukauskas [START_REF] Zhukauskas | Heat transfer from tubes in crossow[END_REF] for details and for the range of validity for the correlation.

It is dicult to reliably calculate the shell-side fouling-resistance from other ow parameters, despite past and on-going research eorts on fouling modelling and prediction (Erickson et al [START_REF] Erickson | Modelling of fouling and slagging in coal-red utility boilers[END_REF]; Zibas and Idem, [START_REF] Zibas | Boiler heat transfer modeling using cems data with application to fouling analysis[END_REF]; Bergeles et al [START_REF] Bergeles | Eects of fouling on the eciency of heat exchangers in lignite utility boilers[END_REF]; Wang and Harb [START_REF] Wang | Modeling of ash deposition in large-scale combustion facilities burning pulverized coal[END_REF]; Isdale et al [START_REF] Isdale | Integrated modelling of process heat transfer with combustion and fouling[END_REF]; Kaer et al [START_REF] Kaer | Towards a CFD-based mechanistic deposit formation model for straw-red boilers[END_REF]). In the present work, empirical values, calculated from plant data, will be used.

Turbulence

The modication of the turbulence in the presence of tube bundles has been addressed by several authors in the past. When eddy-viscosity models are used,

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a common approach is to modify the turbulent viscosity in the tube bundle, eg by using a length scale (typically proportional to the clearance between tubes) and a velocity uctuation to obtain an eective viscosity or thermal diusivity (Rhodes and Carlucci [START_REF] Rhodes | Predicted and measured velocity distributions in a model heat exchager[END_REF]). Another approach (see eg Prithiviraj and Andrews [START_REF] Phrithiviraj | Three-dimensional numerical simulation of shelland-tube heat exchangers. Part I: Foundation and uid mechanics[END_REF]) modies the source term in thek and equations to account for the enhanced production and dissipation of turbulence in the tube bundle.

In this work, a version of the rst approach is used. The gas eective-viscosity for points located within the tube bundle is calculated considering that the tube clearance is a characteristic length scale l. For the uctuating velocity, k 1/2 is used. Thus:

µ T = C µ ρ s lk 1/2 (14)
where C µ is a standard constant in the kmodel [START_REF] Launder | Mathematical Models of Turbulence[END_REF]; the turbulent kinetic energy k is calculated from the standard equation [START_REF] Launder | Mathematical Models of Turbulence[END_REF]; and the characteristic length-scale l is set within the tube bundle as l = P -D o , with P being the average local pitch.

Outside the tube bundle, the eective viscosity is calculated as usual with the Prandtl-Kolmogorov formula and the kmodel.

The eective diusivity Γ s in equation ( 3) is calculated as Γ s = µ T /P r s . The turbulent Prandlt number for the shell-side enthalpy is taken asP r s = 0.9.

Steam properties

The tube-side of the convective zone often consists of steam in greatly-diering thermodynamic conditions. Thus, properties such as density, thermal conductivity or specic heat cannot be regarded as constant, and for an accurate calculation of shell-to-tube heat transfer they must be computed as a function of the local temperature and pressure. In this work, the IAPWS-IF97 formulation for water and steam [START_REF] Wagner | The IAPWS Industrial Formulation 1997 for the thermodynamic properties of water and steam[END_REF] has been attached to the simulation code for this purpose.

Geometrical description

One of the main diculties in simulating heat exchangers and convective zones is often their geometrical complexity, since they are often composed of a large number of interconnected tube banks. This is certainly true of the convective zone of a power-station boiler.

The approach embodied in the equations introduced above implies the treat-

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ment of tubes as subgrid features. This somehow alleviates the problem, since it circumvents the need for meshing individual tubes; but some signicant difculties still remain, and this section describes how they have been addressed in the present model.

The geometrical description used in this model considers essentially two types of element: tube banks and manifolds. The tube bank is the main heatexchanging item. They can be two-dimensional (ie, a single plane of tubes) or three dimensional. In either case, they can additionally be present in the form of arrays of identical structures regularly arranged in space. Tube banks are characterised by geometrical, physical and topological properties. Among the geometrical properties, the main relevant ones are pitch, external and internal diameters, position and dimensions. The physical properties include all the tube-side-uid properties, the tube material (and hence its properties), and the mass-ow rate per tube. The all-important topological properties are two: the ow direction within the tubes, by reference to the simulation axes, and the bank connectivity, ie to which other bank(s) each bank is connected and how.

One type of such connection (but not the only one) is the manifold (or header). This is dened as a virtual element (ie without a geometrical representation in the model) where the tube-side ow from one or several banks is collected, and probably mixed and distributed to other banks. The inlet manifold is a special type of manifold, which is used to distribute to the appropriate tube banks the tube-side uid arriving from other plant devices not included in the simulation (eg, the steam fed to the reheater from the turbine). Several inlet manifolds are allowed in the model, so that several independent (not interconnected) steam and water circuits can be present in the calculation, as is the case in power-generation boilers.

5 Solution

Simultaneous treatment of the three phases

Equations ( 1)-( 5) can be discretised and solved using any CFD technique. The solution procedure is however complicated by the presence of three distinct phases: the shell-side gas-phase; the tube-side vapor-(or liquid-) phase; and the metal, solid phase. An economical and easy-to-implement method can be used when quasi-steady-state is assumed in the metal-side enthalpy-equation [START_REF] Zhang | A quasi-three-dimensional approach to predict the performance of steam surface condensers[END_REF]. In these circumstances, the left-hand side of the equation vanishes, and the equation can be used to calculate the metal temperature:

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T w = α s→w T s + α t→w T t α s→w + α t→w ( 15
)
This value for T w can then be used in equations ( 3) and (4).

A further simplication in the numerical solution can be achieved if the tube-side ow in the heat-exchanging banks is always considered to be onedirectional, and aligned with any of the mesh directions. Then equation ( 4) for h t can be discretised as:

V P ∆t (ρ tP h tP -ρ tT h tT ) -max [A t u tw ρ tW h tW , 0] + + max [-A t u tw ρ tP h tP , 0] + max [A t u te ρ tE h tE , 0] - -max [-A t u te ρ tP h tP , 0] = α t→w Cp t V P (h w tP -h tP ) (16)
where it has been assumed (without loss of generality) that the tube is oriented in the x (West-to-East) direction (see gure 1); the max function expresses the upwinding practice for the enclosed quantity (ie, the value convected into the cell through the cell face is the value in the upwind cell center);A t is the total cross-sectional area of the tubes in the cell; g = A t u tP ρ tW and similar terms are the tube-side mass-ow-rate per cell, constant along the cells in the same tube bank on mass-conservation grounds; andV P is the cell volume.

Compared to the dierential equation ( 4), the right-hand-side uses enthalpies, rather than temperatures. Thus, h t = Cp t T t is the tube-side-uid enthalpy, and h w t = Cp t T w is the tube-side-uid enthalpy at the wall temperature.

Since the tube-side mass-ow-rate g is known for each cell in the bank from the geometrical model, equation ( 16) can be cast into simple, source-only, linear equation in the form:

0 = S 1 -S 2 h tP ( 17
)
with S 1 and S 2 being appropriate coecients, variable from cell to cell, but not explicitly dependent on h tP . After this manipulation, the convective term in equation ( 16) has been transferred to the source term in [START_REF] Beale | A distributed resistance analogy for solid oxide fuel cells[END_REF]; and, since the latter does not (formally) have a convection term, it can be easily solved alongside the discretised versions of the shell-side equations ( 1), ( 2) and ( 3), which in general of course do have a convection term.

Tube-side mass-conservation

The model conservation equations do not include a three-dimensional, tubeside continuity-equation because the ow in each tube is one-directional and

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conned. The geometrical model thus ensures mass conservation within the same tube bank, and also when a bank is directly linked to another one. However, some provisions must be made to calculate the ow distribution when a manifold is fed by, and in turn feeds, several tube banks.

The mass-ow rate m i through element i (be it a tube bank or a manifold) is given by the equation

m i = j =i m j δ ij n j + b i (18)
where m j is the mass-ow rate through element j, δ ij is 1 if element i feeds element j and 0 otherwise, n j is the number of (equal) elements fed from j, and b i is the mass ow-rate if i is an inlet manifold, and 0 otherwise.

Equation ( 18) is cast into a matrix form

[A][m] = [b],
which is solved by LU decomposition to calculate the vector of the unknown mass-ow rates[m].

Numerical details

The equations and algorithms described above have been coded by the authors into the nite-volume CFD-code PHOENICS ( [START_REF] Spalding | A general purpose computer program for multi-dimensional one and two phase ow[END_REF]); version 2.2 has been used. For accuracy and eciency, structured, Cartesian grids are employed, and porosities are selectively used were needed to account of the fraction of local space occupied by tubes and thus unavailable to the ue gas. Second-order interpolation schemes are used for shell-side velocities, turbulence statistics and enthalpy.

A typical discretisation for a convective zone, such as that shown in Results section below, involved around 700,000 cells, and takes around 10 hours CPU time to converge on a Pentium IV at 3 GHz. A parametric analysis was performed with a ner grid of 1.1 million cells to conrm that results are grid independent.

6 Results

Validation tests

Validation tests have been performed mainly in respect of two dierent aspects of the model. The rst aspect is the correct working of the several features of the geometrical model, such as the dierent connectivity options and the

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conservation of overall tube-side-uid mass. These tests will not be reported here.

The second validation initiative has consisted in predicting of the overall heattransfer rates in geometrically-simple congurations. The results of this validation exercise are reported in this section.

The simple congurations considered are single-pass, cross-ow heat exchangers, which can be analysed alternatively using either the Log Mean Temperature Dierence (LMTD) method or the eectiveness-NTU (Number of Transfer Units) method [START_REF] Incropera | Fundamentals of Heat and Mass Transfer[END_REF]. While these alternative theoretical methods are also approximations, the similarity of the results with both the numerical and theoretical approaches adds condence in the accuracy of the former.

A general schematic of the conguration is represented (in cross-section) in gure 2, where the main heat-exchanger and ow parameters are shown. Table 2 presents the values of these parameters for the dierent cases used in the validation. The test cases include a range of tube diameters, pitch values, gas velocities and gas and tube-side inlet temperatures. Cases with constant and variable tube-side temperature are both considered.

Validation results are presented in table 3, and show a good agreement between both calculation methods. For instance, discrepancies in outlet temperatures in both calculation methods are normally around 1%, with only one case (case 4) yielding dierences around 4%.

Convective-zone modelling

The model has been applied to the simulation of the convective zone of a power station boiler. This is one of the three 350 MW(e), wall-red boilers of the Teruel power station located at Andorra (Teruel, Spain). The unit is a sub-critical coal-red utility boiler, with natural circulation and balanced draft. The boiler possesses three stages of superheat, a single reheat a two economisers. The combustion and heat transfer in the furnace zone has been already investigated numerically in the past by one of the present authors [START_REF] Fueyo | An Eulerian-Eulerian model of coal combustion, NOx formation and reburning[END_REF].

A schematic of the convective zone is shown in gure 3. After leaving the furnace, the ue gas ows across radiant superheater (wing walls) and nal superheater (FS). Downstream the nal superheater, the gas enters the convective zone separated in two parallel passes. Two independent water-steam circuits can be found in the boiler. In the shorter one, steam is drawn from the high-pressure turbine through the reheater (RH) and sent back to the power cycle. The other one is the main water-steam circuit. The water is fed into this circuit through the lower economiser (LE) and then through

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the upper economiser (UE). From there, the hot water is sent to the drum separator, where liquid water and steam are at equilibrium conditions. The liquid phase from the drum circulates through down-comers to the furnace water-walls where the phase change from liquid to steam takes place using the heat released in the combustion zone, and then returns as a two-phase mixture to the drum. From there, dry steam is distributed through the tubes that line the ceiling and walls of the convective zone (which therefore serve as a preliminary superheater), and then collected in a manifold and circulated successively through the primary superheater (PS), the wing walls (WW) and the nal superheater (FS). From this last heat exchanger, the steam is sent to the high-pressure turbine. The gas ow-rates through the parallel passes of the convective section are adjusted to maintain the steam temperature at reheater outlet by means of regulating dampers, located under the lower economiser.

The reheater is located in the rear pass of the boiler, whereas the primary superheater and upper economiser are located in the frontal one. Aside from the main gas outlet at the cold end of the lower economiser, there is a secondary extraction of hot gases (between the reheater and the lower economiser) to regulate the gas temperature at each of air preheater inlets.

Some plant measurements in the convective zone are available, and will be used for comparison with computed results in this section. This type of utility boilers are conventionally instrumented, providing of course enough measurements for their safe operation and control. However, such information is neither complete nor reliable enough to be used in the validation of thermouid-dynamical models. In part to remedy this situation, a plan for the improvement and extension of instruments and measurement procedures was designed and implemented in this case-study boiler. The rationale and details of this plan can be found in [START_REF] Díez | Combustion and heat transfer monitoring in large utility boilers[END_REF]. As for the variables used for validation in the present paper, discussed in this section, a grid of eight gas thermocouples was installed at the lower economiser outlet, and six water and steam thermocouples were installed at upper economiser, primary superheater and reheater outlets; the former were installed to reduce the uncertainty due to temperature stratication in the ow and the latter to obtain more reliable data by taking additional measurements at ends of the external headers. Serious technical problems arose when attempting to instrument headers located inside the boiler enclosure. Thermowells equipped with armoured outt can be installed in this situation, but this possibility was discarded owing to doubts about integrity of the pressure circuit. In consequence, the water temperature at lower economiser outlet (ie upper economiser inlet) and the steam temperature at primary superheater inlet were not measured.

The operating conditions change considerably depending on the load, or fraction of the nominal power at which the boiler operates. For instance, the pressure at economiser inlet varies from 166 bar to 183 bar, and the range of temperatures at the reheater inlet from 595 K to 640 K. Table 4 presents

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the operating conditions for dierent loads, which are used as input data in the simulations carried out to validate the model. Most of these data are directly-available measurements, but some of them are indirectly estimated using other operating data. This is the case of gas mass-ow-rate (obtained by closing the overall mass balance in the boiler), steam mass-ow-rate leaving the drum (mass balance in the main steam circuit) and steam mass-ow-rate at reheater inlet (mass balance considering the high-pressure extractions to the water heaters in the cycle).

For these convective-zone calculations, tube-side heat-transfer resistances are neglected. For the shell side, values calculated from the application of semiempirical heat-transfer models are used. The direct measurement of ash fouling rates in this type of equipment is technically unfeasible, and therefore one has to resort to indirect thermal calculations. In this case, a semi-empirical approach was proposed in [START_REF] Cortés | Modeling large-size boilers as a set of heat exchangers: tips and tricks[END_REF], aiming at the on-line estimation of these thermal resistances. The method basically consists in the formulation of a lumped model for large heat exchangers, such as those found in utility boilers, coupled with energy balances in a separated per-section analysis. Typical mean values for the shell-side heat-transfer resistances, calculated in this way to account for ash fouling, have been used in the CFD simulations: for the reheater R f s = 0.00459 Km 2 /W ; for the primary superheater R f s = 0.004163 Km 2 /W ; for the lower economiser R f s = 0.00173 Km 2 /W ; for the upper economiser R f s = 0.002062 Km 2 /W . Figure 4 is a three-dimensional view of the geometry as generated directly from the geometrical model (tube banks are represented as solid boxes for simplicity, but uid ow is of course allowed through them in the model). The simulation domain starts at the end of the combustion zone, just under the nose, where uniform velocity and temperature proles are presumed. (The convective-zone model can be coupled with models for the combustion zone, which would allow this presumption to be relaxed by using calculated results in the absence of detailed experimental data.)

Figures 5 and6 represent the shell-side temperature and (superimposed) the shell-side velocity vectors in a 2D view of the mid-plane for 60% and 100% load respectively, showing how the gas temperature gradually decreases along the ow path. The ow pattern is very similar in both cases, as it can be expected; and the temperature map is also similar, albeit the temperatures are lower for the lower load as expected.

Figures 7 and8 are the corresponding tube-side temperatures. The interconnection of the tube banks in both steam circuits is apparent from the gradual change in the tube-side temperature even when the interconnected banks are not contiguous in physical space.

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The graph in gure 9 compares the total heat heat exchanged in the convective zone (reheater, primary superheater, lower and upper economiser) with the measured one for several loads. The agreement is generally good, but the case for 100% load shows a more signicant discrepancy, with the model tending to follow more closely the linear behaviour found for lower loads. Figure 10 is the corresponding graph for the calculated and measured average outlet temperatures of water or steam in the upper economiser, reheater and primary superheater outlets, and the computed and measured mean temperature of the gas at the outlet of the convective zone. There is a good agreement in both gures between calculated and experimental data.

7 Conclusions and future work

The present paper has introduced a means of simultaneously calculating the shell-side ow-eld, the shell-side and tube-side thermal elds and the tubewall temperature in the convective zone of a power station boiler. The model allows for several arbitrarily-interconnected heat-exchanging elements to be simulated in a exible manner. The model has been validated with the simulations of a real power-station convective zone for dierent loads, and the agreement between calculated and plant data has been satisfactory. These results are indicative of the capability of the model to deal with the dierent operating conditions of a real plant and the its usefulness in the study of the performance of convective zones.

The model described here can be extended with relative ease to account for additional physical processes. Firstly, heat transfer by radiation is bound to relevant in the convective surfaces which are exposed to the ame. Heat transfer by radiation can be accounted for in the model either as a direct ame-tosurface phenomenon (eg by use of viewfactors), or by considering the gas as a participating media, by use of a full radiation model. In the absence of other data, incoming radiation from the ame zone to the convective one can be estimated from furnace-combustion models. These can be usefully coupled to the present convective-zone model to obtain other relevant boundary conditions which are dicult to obtain experimentally (eg, velocity or temperature distributions on the convective-zone inlet-plane). A two-way coupling would allow, among other things, to account for the possible eect of pressure losses in the convective zone on the ow pattern in the furnace.

Shell-side fouling has been modelled in the present work using experimental values for the associated heat-transfer resistance. Research work, such as that cited in the introduction, can be with some eort integrated in the model to simulate the motion of the y-ash in the convective section, the build-up of deposits, and their impact on heat transfer. Work along these lines has been

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recently published by Kaer et al [START_REF] Kaer | Towards a CFD-based mechanistic deposit formation model for straw-red boilers[END_REF].

In respect of the tube-side submodels, an extension can be devised to calculate head losses in the tube-side circuits. The ow distribution from the manifolds to the individual tubes can then be calculated, if required, in a more accurate manner using this information.

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3. 1

 1 Pressure lossesPressure losses ( F in equation (2)) are calculated by means of friction factors ξ, as follows:

u i i th component

  of velocity vector (m/s) u te Tube-side-uid velocity across the East cell-face (m/s) u tw Tube-side-uid velocity across the West cell-face (m/s) ACCEPTED MANUSCRIPT U Absolute value of velocity vector (m/s) v s Shell-side-uid velocity-vector (m/s) v t Tube-side-uid velocity-vector (m/s) V P Volume of cell P (m 3 ) Greek Letters α t→w Volumetric heat-transfer coecient from the tube-side uid to the tube wall (W/m 3 K) α s→w Volumetric heat-transfer coecient from the shell-side uid to the tube wall (W/m 3 K) α " s→w Heat-transfer coecient from the tube-side uid to the tube wall (W/m 2 K) α " t→w Heat-transfer coecient from the tube-side uid to the tube wall (W/m 2 K) δ ij Connectivity parameter (=1 if element i feeds element j and 0 otherwise) ∆t Time interval (s) Dissipation rate of the turbulent kinetic energy (m 2 /s 3 ) s Fraction of local space occupied by the shell-side uid t Fraction of local space occupied by the tube-side uid w Fraction of local space occupied by the tube wall Γ s Eective diusivity in the shell-side enthalpy-equation (kg/ms) µ s Molecular (dynamic) or eective (molecular plus turbulent) viscosity of the shell-side uid (kg/ms) µ T Turbulent viscosity of the shell-side uid (kg/ms) ρ s , ρ t , ρ w Density of shell-side uid, tube-side uid and tube wall respectively (kg/m 3 ) ξ u i Friction factor for the i th component of velocity vector (m

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Three-cell schematic showing the discretisation of the tube-side enthalpy equation (for tubes aligned with the x direction)

Fig. 9 .

 9 Fig. 9. Comparison between calculated and measured exchange heat for dierent loads.

Fig. 10 .

 10 Fig. 10. Comparison between calculated and measured mean temperatures at the outlets of RH, PS, UE and the gas exit.

8

  AcknowledgementsThis work was partly supported by the European Union under Contract ECSC 7220/ED/096 to Grupo ENDESA. The cooperation of Dr Juan Francisco Gonzalez and Mess Enrique Perez and Mariano Lacarta of Grupo ENDESA is gratefully acknowledged. We also thank CHAM (London, UK), for granting us the use of their PHOENICS CFD code, in which the models outlined in this paper have been coded by the authors.

	h tT	ACCEPTED MANUSCRIPT Specic enthalpy of tube-side uid at the previous time-
		step (J/kg)
	h tW	Specic enthalpy of tube-side uid in the West cell (J/kg)
	h w t	Specic enthalpy of tube-side uid at the tube-wall tem-
		perature (J/kg)
	k	Turbulent kinetic energy (m 2 /s 2 )
	k t	Thermal conductivity of tube-side uid (W/mK)
	l	Characteristic length scale in the tube bundle (m)
	m i	Mass ow rate through element i (kg/s)
	N u	Nusselt number ()
	n j	Number of elements fed from element j ()
	P	Pressure (P a)
	P	Tube pitch in the cross ow direction (m)
	9 Nomenclature P Average pitch in the tube bundle (m)
	P r s , P r w	Prandtl numbers of shell-side uid calculated at the local
		uid temperature and at the wall temperature respectively
	A t P r t	Cross-sectional surface-area of tubes in a cell (m 2 ) Prandtl number of tube-side uid calculated at the local
	b i	Inlet mass-ow rate through element i (if a manifold) uid temperature
	R f s	(kg/s) Shell-side fouling resistance (m 2 K/W )
	Cp t R f t	Specic heat of tube-side uid (J/kgK) Tube-side fouling resistance (m 2 K/W )
	C µ R s	Constant in the k -turbulence model Shell-side convection resistance (m 2 K/W )
	D i R t	Inner tube diameter (m) Tube-side convection resistance (m 2 K/W )
	D o F i Re s , Re t	Outer tube diameter (m) Local Reynolds number of the shell-side and tube-side u-i th component of friction term (kg/m 2 s 2 ) ids
	F S/V	Friction term accounting for shell-side pressure-losses in Ratio of tube surface-area to volume in the bank (m 2 /m 3 )
	t	the tube bank (kg/m 2 s 2 ) Time (s)
	g T s , T t , T w	Tube-side mass-ow-rate per cell (kg/s) Shell-side-uid temperature, tube-side-uid temperature
	h s , h t , h w	Specic enthalpy of shell-side uid, tube-side uid and and tube-wall temperature (K)
		tube wall respectively (J/kg)
	h tE	Specic enthalpy of tube-side uid in the East cell (J/kg)
	h tP	Specic enthalpy of tube-side uid in the current cell
		(J/kg)

Table 2

 2 Validation cases. All cases solved with LMTD method, except Case 5 with eectiveness-NTU.

		L	N T	N L	P T	P L	D	V ∞	T in s	T out s	T in t	T out t
	Case (m) (--) (--)	(m)	(m)	(m) (m/s) ( o C)	( o C)	( o C)	( o C)
	1	0.75	20	15	0.038 0.038 0.019	8	325	341.95	375	375
	2	1.0	12	8	0.0285 0.057 0.019	7	293.15 303.8 328.15 328.15
	3	1.0	14	14	0.015 0.015 0.01	5	298.15 344.21 373.15 373.15
	4	1.0	5	20	0.02	0.02	0.01	10	1200	615	400	400
	5	4.0	10	10	0.05	0.05 0.025	5	800	625	300	345.04

Table 3

 3 Validation cases. Comparison of theoretical and simulation results.

		T out s	T out s	T out t	T out t	W	W	α s→w	α s→w
		(K)	(K)	(K)	(K)	(kW) (kW) (W/m2K) (W/m2K)
	Case theor	simul	theor	simul	theor simul	theor	simul
	1	341.95 341.21 (Const) (Const) 91.80 91.64	167.0	168.5
	2	303.80 303.38 (Const) (Const) 33.41 33.98	199	203.6
	3	344.21 341.88 (Const) (Const) 62.39 62.26	210	211.9
	4	615	641	(Const) (Const) 201.1 241.3	148.5	150.8
	5	625.0	634.4	345.0	343.5	885.0 910.8	81.0	83.3

Fig. 4. Geometry of the convective zone, as represented in the model.

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Fig. 6. Shell-side temperature and shell-side ow-eld on a middle plane for100% load. Fig. 8. Tube-side temperature on a middle plane for 100% load.

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