Jacek Kasperski
email: jacek.kasperski@pwr.wroc.pl

Two kinds of gravitational ejector refrigerator stimulation

Keywords:

Temperatures and levels of refrigerant in the heat exchangers of a gravitational ejector refrigerant make a combined system of numerous mutual couplings. It has some significant properties of self-regulation. There are three kinds of reaction on the selfregulation system of the refrigerator: thermal-type when it is stimulated by changing the temperature of exchangers surrounding, ejector-type stimulated by changing the ejector's geometry or refrigerant kind, volume-type stimulated by changing the amount of refrigerant. The predicting of a specific reaction of a system balance is difficult but it may be obtained by a mathematical model and calculating experiments.

Introduction

The ejector refrigerators have been known in engineering since the beginning of the 20 th century thanks to the works of LeBlanc and Parsons [START_REF] Sun | Recent developments in the design theories and application of ejectors a review[END_REF]. At first, water was used as a refrigerant, later the refrigerants known from compressor refrigerators were used [START_REF]Steam Jet Refrigeration Equipment, Equipment Handbook[END_REF].

In the works concerning ejectors Alexis, Katsanis [START_REF] Alexis | Performance characteristics of a methanol ejector refrigeration unit[END_REF] used alcohols, Selvaraju, Mani [START_REF] Selvaraju | Analysis of a vapour ejector refrigeration system with environment friendly refrigerants[END_REF], Pridasawas, Lundqvist [START_REF] Pridasawas | An exergy analysis of a solar-driven ejector refrigeration system[END_REF][START_REF] Pridasawas | A year-round dynamic simulation of a solar-driven ejector refrigeration system with iso-butane as a refrigerant[END_REF], Boumaraf, Lallemand [START_REF] Boumaraf | Modeling of an ejector refrigerating system operating in dimensioning and off-dimensioning conditions with the working fluids R142b and R600a[END_REF] hydrocarbons.

There are few publications concerning the gravitational ejector refrigerators. In a publication Nguyen, Riffat, Doherty [START_REF] Nguyen | Development of a solar-powered passive ejector cooling system[END_REF] described a refrigerator in a form of a 5-meter high tower with water as a refrigerant. The refrigerator used a one-way valves at the inlet of a steam generator and an evaporator. Additionally an expansion valve was fixed.

Ling [START_REF] Ling | A study on the new separate heat pipe refrigerator and heat pump[END_REF] described an gravitational ejector refrigerator in a vertical arrangement with water as a refrigerant and a pump supply of a steam generator. In some research (Srisastra, Aphornratana, Sriveerakul [START_REF] Srisastra | A circulating system for a steam jet refrigeration system[END_REF][START_REF] Srisastra | Development of a circulating system for a jet refrigeration cycle[END_REF], Huang, Hu, Lee [START_REF] Huang | Development of an ejector cooling system with thermal pumping effect[END_REF]) double tanks or valves with a cyclic steam generator feeding system have been used. The applied systems of thermal pumping allowed to decrease the refrigerators height to some significant extent. Technical literature does not provide descriptions of the gravitational refrigerators working without pumps, one-way valves, tanks and cyclic feeding system.

The unique research concerning this area has been published [START_REF] Kasperski | Mathematical model of thermal and substance equilibrium in installation of gravitational ejector refrigerator[END_REF] by the author of this publication.

A conception of a gravitational refrigerator

In a pump version of the ejector refrigerator (Fig. 1a) a disposition of devices in a vertical axis is optional. Heat exchangers may be placed on different levels towards one another. The flows of liquid refrigerant are forced by the pump work, which, as the only one part, contains movable parts. A structure of the gravitational ejector refrigerator (Fig. 1b) does not allow to put the exchangers in any way, because of the pressures which balance at the bottom pipe of the refrigerator. The lowest pressure in the refrigerator installation is obtained in the evaporator. It causes the inflow of liquid to the highest installation level. The highest pressure is obtained in a steam generator, which forces the lowest liquid level. The specific of the work of the gravitational system is isentropic expansion of the refrigerant into a liquid pipes and evaporator volume. This effect should theoretically slightly increase the efficiency of the refrigerator but practically is insignificant.

The ejector cycle allows to build a hermetic gravitational refrigerators, like, much better known absorptive cycle with inert gas [START_REF] Srikhirin | A review of absorption refrigeration technologies[END_REF]. The hermetic refrigerators are regarded as exceptionally durable and reliable because they do not contain movable parts. Moreover, they are quiet. The size of gravitational refrigerators and especially their height depend on the applied refrigerant and levels of temperature in particular parts of the device.

The usefulness of the refrigerant for the gravitational refrigerator

Low pressure refrigerants are used the most effectively for work in the gravitational refrigerator. Low pressure and high density of saturated liquid allow to construct the refrigerators of small height. The specific parameter which proves the usefulness of the refrigerant is the value of liquid height changed due to saturation temperature. The liquid level is pushing down (according to the gravitational forces), as a result of the saturated steam pressure in a specific temperature which has been shown in the Fig. 2.

A negative derivative value means that the level of refrigerant decreases with the increase of temperature:

g t v dt t dp g t v t v dt t dp dt dh liq vap liq ) ( ) ( ) ( ) ( ) ( ⋅ - ≈ - ⋅ - = [mK -1 ] (1)
Large value of the derivative (1) proves usefulness of the refrigerant (for ex. ammonia).

Small value of the derivative (water, alcohols, heavier hydrocarbons) means that the refrigerator works at small differences of pressures between a steam generator and an evaporator causing the small height of device. It is worth noticing that even for the best refrigerant the derivative value (1) strongly depends on the temperature. In the range of temperatures 0÷100 o C the derivative value changes from 10 to 100 times for most refrigerants. In the ejector device the highest temperature level occurs in the steam generator and the value of eq. ( 1) is the highest there as well. The large value of derivative means that the changes of the temperature of refrigerant are going to cause the changes of liquid level in the heat exchanger. Cross-section, heat transfer area and heat transfer coefficient are going to change with the change of filling height. The correct work of the refrigerator depends on the proper liquid level in all three heat exchangers. The phenomena of the changing levels may be advantageous or disadvantageous for the work of refrigerator -it needs analyzing.

Self-regulation of the steam generator

The strongest dependence (1) of the height of liquid on the saturation temperature occurs the steam generator. The coefficient values dh/dt obtained for water as a refrigerant at the temperature +80 o C amount to -0.2 mK -1 . The increase of temperature t g_ext of the generator surrounding causes the increase of temperature t g of boiling refrigerant. Steam pressure p g pushes down the h g liquid level, decreasing area F g of heat transfer. Total liquid push-out from the generator is not possible as it would stop a steam generation. It makes a back coupling causes the liquid level goes up again (Fig. 1).

The described phenomenon may be advantageous. The heat transfer in the generator is self-regulating: while increasing the surrounding temperature the heat transfer is limited, while decreasing the surrounding temperature the heat transfer is intensified.

Condenser's self-regulation

The boiling phenomenon occurs below liquid surface, the condensation phenomenon occurs above liquid surface. In the condenser the heat transfer area concerns an area filled with steam as shown in the Fig. 3. During temperature increase of condenser's surrounding t c_ext the temperature t c inside the condenser, pressure p c of condensed steam increases as well and liquid level h c is pushed down increasing simultaneously the F c area of the heat exchange. Inversely, a drop of condensation temperature increases liquid level and decreases the area of the heat transfer with the condenser's surrounding. The described phenomenon is beneficial, the heat transfer in the condenser has self-regulation: while increasing the surrounding temperature the heat transfer process is intensified and while decreasing the surrounding temperature the heat exchange is limited. The obtained coefficient (1) values dh/dt for water as a refrigerant at temperature +35 o C amount to -0.033 mK -1 .

Evaporator's self-regulation

In the evaporator the lowest temperatures of refrigerating cycle occur and contrary to the generator the dh/dt values are insignificant here. For water as a refrigerant at temperature +15 o C this coefficient amounts to -0.012 mK -1 . Increase of temperature t e_ext of the evaporator surrounding causes the increase of t e temperature of evaporating refrigerant. The pressure p e of vapour pushes down the liquid level h e , decreasing area F e of the heat transfer (Fig. 2). The described phenomenon is not advantageous, the surface of heat transfer in the evaporator diminishes when the surrounding temperature increasing. The total push-out of the liquid from the evaporator is not possible as it would stop the evaporation. It makes the back coupling and the liquid level goes back to the appropriate level.

The phenomena of the evaporator's self-regulation should be analyzed together with the flow ejector characteristic. The evaporation limitation decreases also the stream of vapour sucked up by the ejector. In reaction to this the ejector decreases pressure in a suction area and thanks to this, increases h e level in the evaporator, enlarges the heat transfer area F e and intensifies evaporation. Inversely, the increase of evaporation pressure pushes down the liquid level decreasing the heat transfer with simultaneous increase of the stream of steam sucked up from the evaporator.

Model of self-regulation for the gravitational ejector refrigerator

A significant phenomenon taking place in the described device is constant amount of the refrigerant. The refrigerant pushed out from one of the heat exchangers is forced into the other two exchangers. This phenomenon has serious consequences especially for the liquid pushed out from the steam generator because the derivative value dh/dt is the highest for the temperatures in the steam generator. It is difficult to predict whether the liquid pushed out from the steam generator flows in the most part to the evaporator or to the condenser. This phenomenon demands the analyse of plenty of phenomena taking place in gravitational ejector refrigerator.

In the previous publication [START_REF] Kasperski | Mathematical model of thermal and substance equilibrium in installation of gravitational ejector refrigerator[END_REF] the calculating model for the phenomena taking place in the gravitational ejector refrigerator has been presented. In the model assumptions six independent variables have been taken into account. For each of three heat exchangers there are: temperature and the height of filling of refrigerant liquid.

Mathematical calculating model is based on six balance equations: The way of formulating the model equations is the best given by the matrix form of the eq. ( 2), where the matrix contains coefficients a 0 ÷a 35 , which are strongly non-linearly Fig. 4 presents a scheme of couplings occurring in the gravitational ejector refrigerator. Numbered denotations on the scheme are in accordance with the way of the balance equations numeration (2). The eq. marked as 1 defines energetic relations of three heat exchangers of the refrigerator. Eq. 2 defines flow relations in ejector and refrigerant's properties. Eq. 3 defines relations between the liquid pushed out from the one of exchangers and forced in to two others. The eq. 4,5,6 define the balance between the liquid height in the generator, evaporator and condenser. The whole refrigerator's system is full of mutual couplings and predicting the refrigerant's reactions is difficult.

•
independent
The right side of the eq. ( 2

Calculating experiment with the thermal-type stimulation

The special software for calculations was developed and several calculating experiments have been done. The aim of the experiments was comparison of the model's reaction on changes of temperatures outside the steam generator, condenser and evaporator and comparing the obtained results of temperature changes and liquid levels with the values of derivative dh/dt from the formula [START_REF] Sun | Recent developments in the design theories and application of ejectors a review[END_REF]. The conditions of experiment fulfill previously described way of thermal-type of stimulation on the gravitational ejector refrigerator.

The standard working conditions for the ejector were: the temperature +80 o C in steam generator, +35 o C in condenser, +15 o C in evaporator has been used in the calculating experiment with the gravitational ejector refrigerator. The water was used as a refrigerant and allowed in this case to build a gravitational refrigerator. The dimensions of considered device are rather small size (about 5m height similar to [START_REF] Nguyen | Development of a solar-powered passive ejector cooling system[END_REF]) and theoretically reached COP 0,16. The results of calculating simulations have been put in the Fig. 5, 6, 7.

In the case of steam generator (Fig. 5) a decreasing of liquid level along with temperature increase is visible. The curve of decreasing is inclined less than the derivative value dh/dt for a particular temperature. It may mean that except for selfregulation of the liquid level resulting from pressures inside the generator, the other heat exchangers react here, as well as characteristic of ejector and allocations of the refrigerant.

In the case of condenser (Fig. 6) a strongly changeable dependence of the liquid level in the function of temperature changes is visible. A decreasing curve in the centre is inclined inversely than the derivative value dh/dt relation for the given temperature. It may mean that self-regulation of liquid level resulting from a system of pressures inside the condenser is too weak towards to other reactions.

In the case of evaporator (Fig. 7) a decrease of liquid level along with an increase of temperature is visible. A decreasing curve is inclined less than the derivative value dh/dt line for a given temperature. It may mean that except for a self-regulation of liquid level resulting from the system of pressures inside the evaporator the other heat exchangers, ejector characteristic and allocations of the refrigerant react in here.

Calculating experiment with the volume-type stimulation

According to a patent application [START_REF]Patent application[END_REF] it is possible to make a special tank with changeable volume, for instance by using a compensatory metal bellows (Fig. 8). Using a tank does not increase a leak of the refrigerant. Changing the tank's value may be a result of external interactions (for ex. a squeeze), and internal ones (for ex. refrigerant's pressure). Generally, an enlarging of the refrigerant's tank causes outlet of refrigerant simultaneously from all three heat exchangers, reduction of a tank causes the increase of these levels. It strongly disturbes a system of balance and a simple defining of a refrigerator's reaction on the change of the refrigerant's amount is not possible. What is possible, however, is doing a calculating experiment in order to test the reaction of a cycle on changes of the amount of the refrigerant in refrigerator's installation.

The conditions of experiment fulfill the previously described way of volume-type stimulation on the gravitational ejector refrigerator. The same parameters as in the previous experiment have been applied to the calculating experiment. The results of calculating simulations have been put in the Fig. 9, 10. The obtained results show that the decrease of refrigerant's amount is associated with temperatures decrease (Fig. 9) in all three exchangers of the refrigerator, a reverse process takes place with the increase of refrigerant's amount. The temperature change is the strongest in the case of the evaporator, the weakest in case of the steam generator -it is in accordance with a size of derivatives dh/td in particular exchangers.

In the Fig. 10 the dependence of cooling capacity and COP (coefficient of performance) have been shown for the analyzed refrigerator depending on amount of refrigerant. This dependence is strongly changeable and a loss 0.03dm 3 of the refrigerant The method of thermal-type and volume-type do not increase a leak of installation and the changes may take place in a continuous way. The method of ejector-type, by the change of ejector's geometry, is difficult to realize but it may take place in a continuous way. The change of refrigerant's kind may be realized only in a abrupt way. 5. The calculating experiment proved that the decrease of the amount of refrigerant decreases the temperatures in all three refrigerator's exchangers: the strongest in the evaporator, the weakest in the steam generator.

6. The calculating experiment proved that by changing the amount of refrigerant the maximum cooling capacity may be obtained. It appears that with help of the model the optimal amount of refrigerant in the installation may be determined. The cooling capacity achieves maximum with this optimal amount. 7. The calculating experiment proved that by changing the amount of refrigerant the maximum COP value may be obtained. It appears that with help of the model the optimal amount of refrigerant in the installation may be determined. COP achieves maximum with this optimal amount.

Figure Captions

  the equation of balance of refrigerant cycle energy the equation of the balance of flows in ejector the equation of balance of amount of refrigerant the equation of balance of pressures between generator and evaporator the equation of balance of pressures between generator and condenser the equation of balance of pressure between condenser and evaporator

  ) contains three non-zero values : w en , w ej , w ref . Those values define three basic ways of influencing on parameters inside refrigerator: thermal-typestimulated by changing the temperature around the exchangers, ejector-type -by changing the ejector's geometry and volume-type -by changing the refrigerant's amount. The specific characteristic for each of these reaction types are as following: • Thermal-type: ACCEPTED MANUSCRIPT 10 Expression w en is linear function of surrounding temperature t g_ext , t c_ext , t e_ext for all three exchangers. Changing the conditions of surrounding the system of refrigerator's coupling is evoked by the value of expression w en . This change may be realized in a continuous way. • Ejector-type: Expression w ej is linear function of the ejector characteristic and properties of the refrigerant. The change of ejector's geometry is difficult to realize. The change w ej may also be realized by the change of refrigerant. The refrigerant change may be realized only in a abrupt way, never continuous. • Volume-type: Expression w ref is equivalent to total amount of the liquid refrigerant in the installation. If the refrigerator was made of metal and is hermetic than the simple change of the amount of refrigerant is not possible. The problem is more explained in section 9.

10 . Conclusions 1 .

 101 It is possible to predict the changes of liquid levels as a reaction on the temperature changes of the refrigerant in the heat exchangers of the gravitational refrigerator only for the separated alone heat exchanger. An indicator of these changes is a derivative value dh/td for the refrigerant's temperature. 2. Three kinds of the reaction on the gravitational refrigerator have been proposed and described: • thermal-type -stimulated by the change of temperatures of exchanger's surrounding • ejector-type -stimulated by of the change of ejector's geometry or refrigerant change • volume-type -stimulated by of the change of the amount of refrigerant.

3 .

 3 The calculating experiment showed that the temperature change in the steam generator evokes the change of liquid level. This change is definitely weaker than it would result from the derivative value dh/td for the temperature in a steam generator.The temperature change in the evaporator causes the change of liquid level in it. This change is significantly weaker than it would result from the derivative value dh/td for the temperature in the evaporator. The change of temperature in the condenser evokes the change of liquid level but it is inverse to expectations resulting from the derivative values dh/td for the temperature in the condenser (the liquid level increases along with the temperature instead of decreasing).4. The change of the amount of refrigerant in the refrigerator makes the establishment of a new system of balance parameters. Predicting the reaction of the system on the changes of filling with the refrigerant is difficult. The calculating model allows to check refrigerator's reaction in a simple way.

Fig. 1 .

 1 Fig. 1. Pump and gravitational ejector refrigerator.

Fig. 2 .

 2 Fig. 2. Reaction of refrigerant level in the steam generator and the evaporator on

Fig. 3 .

 3 Fig. 3. Reaction of refrigerant level in the condenser on temperature change.

Fig. 4 .

 4 Fig. 4. System of mutual reaction in the gravitational ejector refrigerator

Fig. 6 .

 6 Fig.6. Changes of liquid level as a reaction on the change of refrigerant temperature in

Fig. 7 .

 7 Fig. 7. Changes of liquid level as a reaction on the change of refrigerant temperature in

Fig. 8 .

 8 Fig. 8. Additional tank with changeable volume for liquid refrigerant.

Fig. 9 .

 9 Fig. 9. Changes of temperatures in the exchangers as a reaction on the change of

Fig. 10 .

 10 Fig. 10. Changes of a cooling capacity and COP of the refrigerator as a reaction on the

  from the variables t g , t c , t e , h g , h c , h e .

	1.	eq.	of	energy	balance	...
	2.eq.	of	s ejector'	flow	balance	...	...
	4.eq. 3.eq.	of of	balance balance evaporator volume s t' -refrigeran generator	... ...	... ...	×	=	0
	5.eq.	of	generator	-	condenser	balance	..	...	0
	6.eq.	of	condenser	-	evaporator	balance	...	0


Kosman Wojciech
email: wojciech.kosman@polsl.pl

Roskosz Maciej

Nawrat Krzysztof

Thermal elongations in steam turbines with welded rotors made of advanced materials at supercritical steam parameters

Keywords:

may come

Thermal elongations in steam turbines with welded rotors made of advanced materials at supercritical steam parameters

Introduction

Significant improvements in the efficiency of a power generating unit may be achieved by increasing the live steam parameters. Power generation efficiency increases (by 1.5 -1.7 percentage points) by moving from the traditional values (a pressure of [START_REF] Ch | Von COMTES 700 zu 50plus -Entwicklungsschritte auf dem Weg zum Kohlekraftwerk mit 50% Wirkungsgrad[END_REF] MPa and a temperature of 535 0 C) to supercritical ones (a pressure of 25.8 and a temperature of 540 o C) [START_REF] Wichtmann | Ultra-supercritical Steam Turbine Turbosets Best Efficiency Solution for Conventional Steam Power Plants[END_REF]. Increasing of the live steam parameters to a pressure of 28.5 MPa and a temperature of 600 o C (620 o C for the reheat steam) results in another increase of efficiency of 1.8 -2.2 percentage points [START_REF] Kolev | A new type of a gas-steam turbine cycle with increased efficiency[END_REF]. A pressure of 30-35 MPa and a temperature of 700°C (720°C reheat) are the parameters currently tested and lead to an efficiency increase above the 50% level [START_REF] Kjaer | The Advanced Supercritical 700 o C Pulverised Coal-Fired Power Plant[END_REF].

Advancement into ultra-supercritical parameters raises many new issues that must be resolved with regard to design [START_REF] Ulm | The situation in steam turbine construction and current development trends[END_REF], materials and operation [START_REF] Prisyazhniuk | Alternative trends in development of thermal power plants[END_REF]. The increases in the live steam parameters would not have been possible without the application of the new materials [START_REF] Engelke | Turbine designs with new steels for high steam parameters. II: manufacturer-specific design characteristics[END_REF]. Analysis of the available design data (see, for example, Jensen [START_REF] Jensen | Experience gained from commissioning a new 411 MW coal-fired plant with advanced steam data[END_REF]) indicates that this is a crucial condition for the development of supercritical steam turbines. Significant achievements have already been made in the engineering of the new materials. A new series of advanced materials have been developed that may successfully operate at high temperature values [START_REF] Mayer | New Materials for Fossil-Fired Thermal Power Stations[END_REF]. New material development has concentrated on martensitic steels [START_REF] Birks | Very heavy section 9Cr martensitic steel castings of USC applications: Developments for 700 C applications[END_REF]; however nickel alloys have also been tested [START_REF] Knoedler | KOMET 650 -Investigation of Materials for Use in Steam Turbines at Temperatures up to 650 o C[END_REF].

Besides applying new materials, the second characteristic feature of supercritical steam turbines is the presence of cooling systems that protect turbine components in the areas with the highest temperatures. Specific cooling system designs may vary. Cooling in the reaction turbines [START_REF]Tachibana-wan unit 2 takes a supercritical step forward for Japan[END_REF] differs from cooling in impulse turbines [START_REF] Retzlaff | Steam Turbines for Ultrasupercritical Power Plants[END_REF]. The cooling steam may be supplied from the appropriate superheater stages (external steam) [START_REF] Wieghardt | Siemens Steam Turbine Design for AD700 Power Plants[END_REF] or taken from the same turbine part (internal steam) [START_REF] Oeynhausen | Steam Turbines for the New Generation of Power Plants[END_REF].

The temperature of the steam decreases rapidly along the turbine due to the expansion process. For example in a high-pressure turbine part [START_REF] Wieghardt | Siemens Steam Turbine Design for AD700 Power Plants[END_REF] the steam temperature at the inlet is 600 o C, while the outlet temperature is 350 o C. For the ultrasupercritical live steam temperature of 700 o C, the temperature of the outlet steam is 400 o C.

Thus turbine components are often manufactured from various welded materials [START_REF] Pirschter | Alstom Steam Turbine Designs for AD700 Power Plant[END_REF], which allows turbine production costs to be reduced. Such a solution is preferred mainly for the rotors of high-and intermediate-pressure parts. In addition, some designs offer welded casings. Due to improved strength properties of the new materials, a noticeable change may also be observed in the smaller thicknesses of components made from the new materials [START_REF] Ch | Von COMTES 700 zu 50plus -Entwicklungsschritte auf dem Weg zum Kohlekraftwerk mit 50% Wirkungsgrad[END_REF].

When a turbine operates, a temperature difference occurs between the rotor and the casing that leads to different thermal elongations in these two components. This results in altered axial clearances that are set during the assembly process.

In each section of the steam path and glands, reliable operation must ensure that any unsafe decreases in axial clearances are avoided. Therefore, it becomes essential to determine and examine the elongation of the stationary and rotating components under various heating conditions.

The research described in this paper concerns the axial elongations of the components of the model turbine shown in Fig. 1. The research involves mostly welded rotors that consist of disks made of several materials (in practice, two materials). The analysis concerns thermal loads occurring in the components exposed to steam at ultrahigh temperatures.

This research was motivated by the following issues:  the properties of the new materials differ from traditional ones, i.e., there are different heat expansion and conduction coefficients,  the thicknesses of the components, made from the new materials, are smaller due to higher limiting stresses, and  the operation of the supercritical steam turbines does not include long enough periods of time and the experience gained so far is insufficient to formulate adequate recommendations for the maintenance of the turbines.

This analysis compliments and extends the knowledge base regarding research in the area of supercritical steam turbine operation. The analysis involves four research tasks, presented below:

1. Development of a model for the thermal elongations analysis. The model is required to integrate:  the possibility to build the component of an arbitrary material with a known thermal and mechanical properties,  various design forms of the rotor (welded or forged rotor),  external cooling of the components (mainly the rotors) [START_REF] Kosman | Thermal analysis of cooled supercritical steam turbine components[END_REF].

2. The determination of the axial elongations in steady and transient states for the welded rotors made of traditional and advanced materials within the area covered by the inner casing.

3. Assessment of the advanced materials behavior under various operating conditions of the supercritical steam turbines.

4. Analysis of new design solutions -welded rotors consisting of discs made from various materials -under transient operation conditions (start-up, heating, cooling, and alteration of the power output).

The results obtained from the numerical simulations (task number 2) are used in research tasks that concern the applications of advanced materials (tasks 3 and 4). In the latter stages of the research, the results are to be prepared in the form that may easily be written to data and knowledge bases and then applied to turbine assembly and operation control processes.

Model of the thermal states and axial elongations of the turbine components

Assumptions a)

. The analyzed object are the high pressure rotor (R), internal casing (IC) and external casing (OC) of a supercritical steam turbine. The fixed point of the rotor is located at the axial bearing. In Fig. 1 it is assumed to be at point 0. The fixed point of the internal casing assembly is located on the axis of the steam inlet (cross-section A-D-F in Fig. 1). b). The distributions of temperature T and pressure p along the steam path are obtained from a detailed analysis of the expansion process in consecutive stages, i.e., from the first stage to the last (Fig. 2):

  n 2 , ... , 4 , 3 , 2 i p , T i , s i , s  (1)
where: n is the number of stages.

The developed model involves the algorithms and numerical codes described in [START_REF] Chmielniak | Expansion Line Modeling and Strength Diagnostics of Internally Cooled Gas Turbine[END_REF], which calculate the steam parameters at the outlets in consecutive stages. The input data for the calculations consists of the steam flow, the pressure and the temperature (m s,0 ,T s,0 , p s,0 ) at the turbine inlet. c). The steam temperature distributions in the internal and external casings glands are determined by the well-known relationships that describe the steam flow through seals [START_REF] Chmielniak | Thermal Loads of Stream Turbines[END_REF]. d).The heat transfer between the steam and the components of the turbine involves a convection process with a known convective heat-transfer coefficient. The substitute coefficients [START_REF] Kosman | Solution of inverse heat conduction problem for thermal stresses analysis in turbomachinery rotors[END_REF] are applied to the locations where the rotor or casings interact with other components. In this way the surface of the rotor is divided into the areas exposed to the steam and the areas that interact with a row of blades.

In transient problems, it is assumed that the convective heat-transfer coefficients on the surfaces of the analyzed components change along the axis of the turbine -zand are dependent also on time in -t -by:

    m , ... , , j t , z f j j 2 1    , (2)
where: m -the number of distinguished characteristic surfaces. During a start-up the heat transfer coefficients may be related to the steam flow by [START_REF] Chmielniak | Thermal Loads of Stream Turbines[END_REF]:

    m , ... , 2 , 1 j m , z f 0 , s j j    (3)
e). The rotor and casing model is assumed to be a structure of revolution under axisymmetrical load. The displacements of each point of the deformed component (rotor or casing), which are in a cylindrical coordinate system (r, z, ) and are related to the initial configuration (assembly, cold state) are described by the displacement vector, u, [START_REF] Chmielniak | Expansion Line Modeling and Strength Diagnostics of Internally Cooled Gas Turbine[END_REF]:

    t , z , r u u , u u z r   , (4)
which is related to the strain tensor ε ij = ε ij (r, z, t), (i, j = r, z) through the geometrical relationship:

  z , r j , i i u j u j i ij                 2 1 ( 5
)
If it is assumed that the component is fixed in the cross-section 0-0 (Fig. 1), then the thermal elongations are equal to the axial component of the displacement vector:

    t , z , r u t , z , r w z  , (6)
From the equations ( 5) and ( 6) the thermal elongation of a component at coordinate z is equal to:

         z 0 z d t , , r t , z , r w (7)
f). Finite element method is applied to the temperature, strains and stresses calculations.

The ANSYS package is used in the calculations.

Design forms of the analyzed rotors

First, the numerical analysis involves welded rotor that is made of two discs (see Fig. 3). Three characteristic cross-sections are marked in figure 3: A is the steam inlet, B is the inner casing outlet, and C is the outer casing outlet. In these cross-sections the elongations time trends are analyzed.

Three types of material are considered and applied to the rotors, casings and valves of the turbine. In later sections of this paper, the materials are referred to as:  ferrite steel -symbol: F,  martensitic steel -symbol: M,  nickel alloys -symbol: Ni.

The discs of the welded rotors may be made of one of the above-mentioned materials. For the increased live steam parameters, the first disc (at the steam inlet area) may be made of nickel alloys, while the outlet section may be made of either martensitic or ferrite steel.

Thermal and strength properties of ferrite and martensitic steel and nickel alloys

The increased parameters of the live steam drive the application of the advanced materials. Thus, an examination was conducted of the available materials currently applied in the area of power engineering that satisfy the requirements of supercritical steam turbines. In each of the groups F, M and Ni, a model steel was chosen.

According to Kosman and Roskosz [START_REF] Kosman | Solution of inverse heat conduction problem for thermal stresses analysis in turbomachinery rotors[END_REF], the new martensitic-ferrite steel with 9-12.5% chromium, is highly resistant to creep and may be applied up to a temperature of 620 o C. According to [START_REF]Cases of ASME Boiler and Pressure Vessel Code[END_REF] the martensitic steel VM12 may even be applied up to a temperature of 630 o C.

The group of analyzed also includes ferrite steels, which may be applied up to a temperature of 540 o C. However in the parametrical calculations it is assumed that the temperature of the live steam equals T p,0 = 600 o C. Thus, under such a condition, the results for the components made of ferrite steel may only be treated as a reference values for other materials.

The coefficient of thermal expansion, , is lower for the martensitic steels than for the ferrite steels and nickel alloys (Fig. 4), which affects the elongations of the components. The convective heat transfer coefficients  are shown in Fig. 4. In this case, the thermal convection in the nickel alloys is definitely smaller, which affects the temperature differences at the components walls and the stresses within the material.

The influence of the type of material on the thermal elongations of the turbine components in the steady state

The components under analysis are the rotor and inner casing of the model turbine shown in Fig. 1. This figure presents the constraints and the fixed points of the casings and rotor. On this basis, thermal elongations may be tracked for each component.

The internal casing elongates from the fixed point "0" along the turbine axis. The absolute elongation of the casing in the X-Y-Z cross-section of the turbine equals w OC = Z -Z1. Similarly the absolute elongation of the rotor is defined as w R = X -X1. The elongations of both the external casing and the rotor increase along the axis to reach a maximum values at the outlet, while:

1 G G w max , OC   and 1 C C w max , R   (8)
The fixed point of the internal casing is located in the cross-section A-D-F presented in Fig. 1. In the cross-section X-Y-Z of the turbine, the elongation of the internal casing is w IC = Y -Y1.

The selection process for axial clearances must determine the relative elongations: rotor to internal casing w R-IC and rotor to external casing w R-OC . The relative elongations of the rotor and the casing in the X-Y-Z cross-section equal respectively (Fig. 1)

1 Z 1 X w OC R     and 1 Y 1 X w IC R     (9)
Likewise, for an arbitrary cross-section that is located at the coordinate "z"

    z w z w w OC R OC R     and     z w z w w IC R IC R     (10)
Modeling of the temperature distribution in the rotor and the casing assumes that the outer surface of the rotor and the inner surface of the casing are exposed to the same steam flow, which changes temperature T s,i along the turbine axis (see Fig. 2 and equation ( 1) ). The heat exchange rate differs for both components and is characterized by the convective heat coefficients  R,j and  IC,j . These coefficients vary along the turbine axis and depend on the live steam flow (3).

In the steady state, the temperature distributions in the rotor and the casing are first calculated, then the absolute elongations are calculated, followed by the relative elongations between the rotor and the inner casing.

The results of the calculations are shown in figs. 5 and 6. The steam temperature at the turbine inlet (cross-section A in Fig. 5) equals 600 o C and decreases to 380 o C (cross-section B) along the steam path due to the expansion process. The maximal rotor temperature is just slightly lower than the maximal steam temperature and equals 595 o C. The absolute elongation of the rotor increases with the distance of the cross-section from the fixed point and reach the maximal value at the opposite end (Fig. 5). Similar calculations were conducted for the inner casing, which then allows the relative elongation from the rotor to the inner casing to be determined. The distribution of the relative elongations along the turbine axis is shown in Fig. 6. The graph compares the elongations calculated for cases in which the rotor is made of the F steel, M steel or the Ni alloys. In each case, the inner casing is made of the ferrite steel F. The values of the relative elongations in the outlet cross-section of the inner casing (cross-section B) for various materials are shown in Table 1.

Based on Fig. 6 and Table 1, it is possible to determine the influence of the type of material on thermal elongations. The M and Ni materials behave differently than the ferrite steel F. The relative elongations are negative for the rotor made of the martensitic steel, which means that the absolute elongation of the rotor is smaller than the casing elongation. For the two remaining materials the situation is quite the opposite. However, this does not cause any problems for the turbine as long as the elongations are taken into consideration at the design stage, when the axial clearances are chosen.

Time trends of the thermal elongations during a start-up

The start-up process is conducted according to the start-up characteristic, which defines the changes in the live steam temperature, the flow rate and the rotational speed:

      t f n , t f m , t f T 0 , s 0 , s    (13)
A start-up characteristic from a cold state is developed for the model turbine that has been analyzed (Fig. 7). The live steam flow change is described by the values related to the design flow rate -m s,0,nom -at full turbine load.

The characteristic serves as a base for modeling the expansion process in the steam path during the start-up. The calculations assumed a constant time step t.

For an arbitrary start-up time the live steam parameters (T s,0 and p s,0 ) and the flow rate -m s,0 -are determined from Fig. 7. For these values, further calculations are conducted as described in the section 3.1.c. The results of the calculation provide the parameters of the steam at the outlets of the consecutive rows of blades for time steps t j = j t.

   

j i p j , i , s j i T j , i , s t , z f p , t , z f T   ( 14
)
where: n is the number of stages, k is the number of time steps, i = 2, 3, 4, ...., 2n and j = 1, 2, ..., k. An example of the time trends for the relative elongation -w w-kw -from the rotor to the inner casing during a start-up is shown in figs. 8 and9. During the first stage of the start-up the relative elongation quickly reaches a maximum value. Later on, as the temperature of turbine components increases, the relative elongations decrease. After a longer period of heating the thermal elongations become stable and reach steady state. Such a tendency occurs in each of the analyzed cross-section (Fig. 8 and9).

The relative elongations clearly depend on the distance from the fixed point of the turbine (point 0 in Fig. 1). In the outlet cross-section of the inner casing (crosssection B in figs. 1 and3) the elongations w R-IC are larger than in the cross-section A (compare trends shown in Fig. 8 and9). Depending on the material type, the relative elongation of the cross-section B not only changes in value but also in sign.

The influence of the type of material on the thermal elongations is most visible the in the outlet cross-section of the inner casing (Fig. 9). The materials M and Ni behave differently when compared to the ferrite steel F. The smallest relative elongations occur in the rotor made of martensitic steel, while the largest occur in the rotor made of nickel alloys. The maximal difference between the elongations for rotor made of martensitic steel and nickel alloys reaches 2 mm. These conclusions should be taken into consideration when the axial clearances are set in the turbine.

As mentioned in section 3.2, the welded rotor may consist of two different materials that are chosen with respect to the temperature and the stress levels of the rotor. In the presented research it is assumed that the first disc (in the steam inlet area) is made of nickel alloys and that the outlet section is made of martensitic steel.

Figure 10 compares the time trends of the relative elongations for the two rotors. The first rotor is only made of nickel alloys (Ni), while the second one consists of nickel alloys and martensitic steel (Ni+M). The elongations time trends for the rotor made of nickel alloys are the same as in Fig. 8. A characteristic feature of the Ni+M rotor is that the relative elongations are close to zero in the steady state. The elongations values in the steady state are also given in the Table 1.

The relationship between the relative elongations and the heating process

The values of the relative elongations presented so far correspond to a start-up conducted according to the characteristics shown in Fig. 7. Different results are obtained for a shortened start-up, when the rates of change of the steam parameters and the flow are assumed to be twice as fast.

The results of the calculations are shown in Fig. 11. For such shortened start-up conditions the heating process is much more intensive, the temperature of the components increases faster and as a result the relative elongations are more dynamic.

Additional analysis concerns the thermal elongations of the turbine components in the transient state of operation, i.e., when the load changes immediately from zero to its nominal level (a "step change"). The heating is the most intensive in this case and the relative elongations have the most dynamic time trends. The results obtained from this additional analysis describe the most inconvenient state of the elongations.

Figure 11 compares the time trends of the relative elongations at the outlet crosssection of the inner casing (cross-section B in Fig. 3) for various start-up cases. The rotor under investigation is welded. It is made of nickel alloys at the steam inlet area (the first disc in Fig. 3) and martensitic steel in the remaining sections (the second disc). For the start-up conducted according to the characteristic in Fig. 7 the relative elongations are only positive, which means that the absolute elongations of the rotor are always larger than the elongations of the casing. For the shortened start-up and for the load step change the relative elongations are negative during the first stage of the startup.

The step change in the load causes a near step change in the casing elongations and an almost identical change in the relative elongations. The maximal absolute value of the negative elongations is higher than the positive values, which occur later during the start-up.

The influence of the rotor design form on the relative elongations

In order to assess the influence of the rotor design on the relative elongations it is relevant to repeat the calculations for the rotor forged as a single piece. These results may be compared to the previous ones that correspond to the welded rotor. It is assumed here that both rotors are made of the ferrite steel F (as is the casing). The analysis of the thermal elongations involves the start-up, which is conducted according to the characteristics shown in Fig. 7.

The results of the calculations are presented in Fig. 12. The results refer to the outlet cross-section of the inner casing because in this location the influence of the design form is the most evident. Generally it must be noted that this influence is significantly smaller in comparison to the influence of the type of the material, which was described earlier.

Differences between the elongations in the rotors appear during the first stage of the turbine start-up. In later stages of the heating process the time trends tend towards the steady state, which is almost identical for both forms of the rotor.

Relative elongation rotor -outer casing

The final stage of this research is related to the thermal elongations of the rotor and the outer casing. The analysis again concerns the heating process conditions described by the start-up characteristics in Fig. 7.

Figure 13 presents the relative elongations between the end of the outer casing on the steam outlet side (cross-section C in Fig. 1) and various models of the rotor. This figure corresponds to Fig. 9 for the inner casing. In this case the most intensive change in thermal elongations occurs during the first stage of the start-up. Materials M and Ni perform differently than the ferrite steel F. The smallest relative elongations occur in the rotor made of martensitic steel, while the biggest for nickel alloys. The relative elongations between the rotor and the outer casing (Fig. 13) are much larger than the elongations between the rotor and the inner casing (Fig. 9). This fact must be taken into consideration when the axial clearances are set for a turbine.

Comparison between the calculation results and measurement data

In order to verify the developed model a comparison is performed between the calculated and measured relative elongations of the rotor and the outer casing. The elongations is measured at the end of the casing on the steam outlet side. The analyzed machine is not a supercritical steam turbine but a conventional one, since this turbine is available for testing. The turbine type, however, has no effect on the verification of the model.

The modeling of the thermal elongations for the rotor and the casing is based on the measurements of the rotational speed (n), the live steam temperature (T), the pressure (p) and the flow (m). The measurement results gathered in Fig. 14 correspond to the start-up from a cold state.

The results of the calculations of relative elongations are shown in Fig. 15, where they are plotted against the measurement data. The comparison proves that the numerical simulation reflects the measured trend in a satisfactory manner. The maximal difference between the measured and calculated trend does not exceed two percent. Therefore the verification proves that the model developed for the calculations of the elongations is correct.

Conclusions

The axial elongations measurement is relatively easy in the outlet cross-section of the outer casing (cross-section C in Fig. 1). This represents the relative elongations between the outer casing and the rotor. During standard operation, the elongations are not supervised "inside the turbine" (neither in the steam path nor in the external glands), which is the reason why the research presented here primarily analyzed the relative elongations between the rotor and the inner casing. Since the experience gathered from the operation of supercritical steam turbines with components made of new materials is so far insufficient, numerical simulations may significantly complement the knowledge bases. This analysis focused on determining the effects of the material type, design form and start-up heating process on the thermal elongations of the turbine components.

The obtained results presented in this paper prove that the advanced materials and their range of applications significantly affect the values of the relative elongations between the rotor and the inner casing as well as the axial clearances set during the assembly process. It is shown here that the materials M and Ni perform much differently than the ferrite steel F. This difference is best represented for the steady state by the results shown in Fig. 6 and Table 1. Even larger differences occur for transient conditions (figs. 8 -10). A very small relative elongations may be obtained for a welded rotor made of two different materials (nickel alloys and martensite steel), shown in Fig. 10. All of the presented results indicate that the advanced materials change the operational conditions of supercritical steam turbines when compared to traditional materials.

The influence of the rotor design form is small when compared to the influence of the material type.

This research proves that the immediate load change from zero to its nominal level (a "step change") results in the most intensive heating process in the turbine components. The time trends of the relative elongations are the most dynamic. The obtained results are relevant to the most inconvenient elongation state, which is important to consider when axial clearances are selected.

The conclusions in this paper provide essential information as well as procedures to support the assembly and operation control processes of the supercritical steam turbines. 8 The relative elongations in cross-section A (Fig. 3) during a start-up Fig. 9 The relative elongations in cross-section B during a start-up.

Figure captions

Fig. 1 .Fig. 2 .Fig. 4 .Fig. 6

 1246 Fig. 1. The model turbine

Fig. 10

 10 Fig. 10 Comparison of the relative elongations in cross-section B for the rotor made of one and two materials.

Fig. 11

 11 Fig.11The relative elongations in the cross-section B during a start-up for various startup cases.

Fig. 12

 12 Fig.[START_REF] Retzlaff | Steam Turbines for Ultrasupercritical Power Plants[END_REF] The relative elongations in the cross-section B during a start-up for (1) a forged rotor and (2) a welded rotor

Table 1

 1 Comparison of the elongations for various design cases

	Case number	Unit	1	2	3	4
	Rotor material	-	F	M	Ni	Ni+M
	Casing material	-	F	F	F	F
	Rotor absolute elongation	mm	13.92	13.02	14.91	13.64
	Casing absolute elongation	mm	13.49	13.49	13.49	13.49
	Relative elongation	mm	0.43	-0.43	1.42	0.15

Acknowledgements

This research was financed by the Polish Ministry of Science and Higher Education, grant No G 005/T02/2007 (PBZ-MEiN-4/2/2006), 2007-2010.


A Ruiz Celma

F López-Rodríguez

A Ruiz Celma

Cogeneration plant in an olive sludge industry

Keywords: Combined heat and power (CHP), Sludge, Olive husk, Economic analysis

Spain is the world's main producer of olive oil, with an annual production approaching one million tons. A great amount of wet residues are generated -mainly sludge-, thus favouring the development of energy plants for their treatment and/or elimination. Such installations require a simultaneous electric and thermal energy demand, and combined heat and power (CHP) systems might be the most adequate in certain cases. The economic viability of a CHP system in a sludge processing plant (sludge obtained from olive oil extraction industry) is analysed in the present work. Special attention is paid to the analysis and discussion of energy savings and environmental benefits.

Kyoto Protocol came into force on February 16th 2005, after ratification by at least 55 countries that represent 55% of the world's greenhouse gas emissions, in order to achieve a 5.2% reduction (from 1990 levels) in such global emissions by 2008-2012.

According to the Directive 2004/8/CE [1] of the European Parliament, the promotion of cogeneration on the basis of useful heat demand is priority, provided their benefits. Some of the most relevant among these are: (i) primary energy savings, (ii) elimination of energy loss in the electrical network and (iii) reduction of greenhouse gas emissions. Also, positive contribution to safe energy supply is also favoured.

Non-cogeneration systems involve heat produced in the boiler and electricity purchased from a utility, whereas cogeneration combines heat and electricity production from a single energy source. Overall cogeneration efficiencies (based on both the electrical and thermal energy products) of over 80% are achievable [START_REF] Rosen | Reductions in energy use and environmental emissions achievable with utility-based cogeneration: simplified ilustrations for Ontario[END_REF]. Besides, energy savings may reach 15-40% of the primary energy needs, if compared to the separate production of electric and thermal energy. The main limitation of the combined heat and power (CHP) scheme lies in its economic viability, since a high simultaneous utilisation of heat and power is required in most applications [START_REF] Hinojosa | A comparison of combined heat and power feasibility models[END_REF].

According to the statistics of the International Olive Council, Spain is the world's main olive oil producer, followed by Italy and Greece. The combined production of these three countries exceeds 70% of the world's total. Fig. 1 shows the percentage contributions of the main producer countries for the season 2006-2007. The average annual virgin olive oil production in Spain approaches one million tons, which corresponds to approximately 5.5 million tons of olives processed in extraction plants. The most currently used extraction system in Spain is the two-phase centrifugation, which is characterised by a relevant generation of sludge as a semi-solid residue. It is composed of olive husk (OH), of remaining oil in a proportion between 2.5% and 3.5% by weight, and of olive mill wastewater (OMW). The strong seasonality of olive oil production -mainly from November to February-, the high rates of sludge generationapproaching 80% by weight from the total olive mass processed in industry-, its high moisture content -normally 70% by weight (wet basis)-, as well as the presence of polyphenols and other organic compounds, make the treatment of this residue to be actually problematic.

Mechanical separation by centrifugation is commonly one the first operations in the processing of sludge. This way, solid (OH) and liquid (OMW) phases, as well as oil, are obtained, and then specific actions are performed for each product. OH is composed of pulp, olive stones, residual oil and water in variable quantities within the range 50-55% [START_REF] Civantos | Obtención del aceite de oliva virgen[END_REF][START_REF] Baeta-Hall | Bio-degradation of olive oil husks in composting aerated piles[END_REF]. Once the added moisture content is reduced, OH is characterised by an average heating value in the range 18-22 MJ kg -1 [START_REF] Jenkins | Combustion properties of biomass[END_REF], which is sold on the market as solid fuel for small boilers. Taralas and Kontominas [START_REF] Taralas | Pyrolysis of solid residues commencing from the olive oil food industry for potential hydrogen production[END_REF] analysed some other potential applications for OH, like hydrogen production by pyrolysis. OMW comes from the vegetable water of the fruit and the fresh water used during the process, and it contains olive pulp, mucilage, pectin, certain dissolved mineral salts, etc. The typical weight composition of OMW is [8]: 83-96 % water, 3.5-15 % organics and 0.5-2 % mineral salts. Vitolo, Petarca and Bresci [START_REF] Vitolo | Treatment of olive oil industry wastes[END_REF] proposed different ways to treat OMW, such as evaporation, ultra filtration/reverse osmosis, anaerobic and aerobic digestion, specific chemical and biochemical treatments, manufacture of animal foods and incineration. In practice, the most common method to eliminate OMW is that of evaporation pools, provided low cost and favourable climate in the Mediterranean area. However, this procedure presents a series of objections such as bad smell, increase of insect population, flooding, filtration, need of vast areas and strong visual impact.

Caputo, Scacchia and Pelagagge [START_REF] Caputo | Disposal of by-products in olive oil industry: waste to energy solutions[END_REF] proposed a simultaneous energetic use of OH and OMW in centralised-combined scenarios, in order to achieve an integral management of this kind of sub-products. In particular, those authors described gasification, combustion (after mixing) and drying processes, followed by vapour cycles.

The direct drying process of high moisture content residues like sludge is subject to high energy costs. For this reason, small-and mid-sized cogeneration plants appear as an excellent alternative, using heat engines (internal combustion engines or gas turbines) to generate electric power apart from the thermal power required in the drying process. The use of a cogeneration plant for the processing of the sludge from olive oil industry is analysed in the present work. Primary energy savings in the production process, environmental benefits, as well as the most relevant economic magnitudes involved are pointed out, according to the new legislative framework set in the Spanish Royal Decree 661/2007 May 25th [11] which regulates the activities for electric power production subject to special regime.

Configuration of the cogeneration plant

One of the optional operations for the treatment of sludge are the extraction of the remaining olive oil and the drying of OH, so that it can be used as fuel. The OMW generated in these processes must be reduced in order to lessen the environmental impact. However, among some other disadvantages, their main limitation lies in their poor profitability.

A cogeneration scheme based on internal combustion engines was integrated to the previous technology with the aim of overcoming the economic limitations of the treatment of sludge. Fig. 2 shows a scheme of the olive sludge industry under study. The process described here was structured in three main steps: three-phase centrifugation, thermal drying of OH and concentration of OMW.

The thermomixer was the first device in the centrifugation line, and it was fed with sludge from the reception basin, after an olive pulp/pit separation process. The sludge was then mixed and heated in order to maximise enzyme activity and the antiemulsifying power of temperature. This way, further oil extraction was favoured. The thermal energy needed to raise the temperature of the sludge into the thermomixer was supplied by the cooling circuit of the internal combustion engines.

Once the sludge had been warmed up to about 35ºC, it was taken to the three-phase decanter, where the components were separated according to their densities (1.2, 1.05 and 0.91 g/cm 3 for OH, OMW and oil [START_REF] Civantos | Obtención del aceite de oliva virgen[END_REF], respectively) by centrifugal action. Water supply into the decanter might be necessary in order to achieve an appropriate separation, in a rate of about 0.03 to 0.06 litre water per kilogram sludge, although the recirculation of OMW might allow a reduction of such value. Finally, the depletion of OMW took place in a vertical centrifuge.

The olive oil obtained after centrifugation was stored for further sale. OH was then taken to the drying unit, so that moisture content was reduced down to an approximate value of 15% by weight (wet basis). Provided efficiency and economic advantages, the selected setup was a direct contact rotary dryer. The biomass and the drying airflow were arranged in equiflow, in order to minimise volatility and to prevent fire risk. A gas-to-air heat exchanger allowed to reach an inlet-air temperature of about 400ºC. Exhaust gases from the engines (at temperatures over 500ºC) acted as hot fluid in the heat exchanger, and were channelled towards the chimney after cooling. The cold fluid was set to be an airflow pre-warmed to about 75ºC in the air-coolers of the engine water circuit. Finally, the wet airflow was channelled across the cyclones, leaving the drying unit towards the OMW concentration tower.

Moreover, OMW was stored in an intermediate basin to feed the concentration tower, where a recirculation process until OMW got a final moisture content of about 60% by weight (wet basis) was performed. The drying agent in the concentration tower was on the one hand the wet airflow from the rotary dryer (at about 110ºC), and on the other hand a 75ºC hot airflow from the water-to-air heat exchanger of the engine jackets. The outlet of the OMW concentration tower was connected to the chimney so that wet air was emitted to the surroundings. The power of the plant's engines was maximized as stipulated by the Spanish Royal Decree 661/2007, with the corresponding bonus to the annual electric energy production. The thermal energy supplied by such engines exceeds the energy needs of the OMW drying process, which regards this simple OMW dehydration device as being an economically favourable alternative if compared with other ones -like, for instance, the use of heat pumps-.

The power plant consisted of three internal combustion engines, powered by natural gas. In particular, two TBG620V16K model by Deutz (1355 kW unitary power according to DIN ISO 3046 code, 3393 kW ISO fuel consumption and 2.04 kg/s exhaust gas flow at 542ºC) and one QSV81G model by Cummins Power Generation Ltd. (1639 kW unitary power, 4051 kW fuel consumption and 2.49 kg/s exhaust gas flow at 503ºC).

Mass-energy balance and legislative framework

Plants operating in cogeneration mode during determined periods and as a strict electric power production plant during the rest of time are regulated by the European Directive 2004/8/CE, as well as by the Spanish Royal Decree 661/2007. In order to receive the corresponding subvention, 9.35 c€/kWh for all programming periods in this particular case, the plant should show a mean annual equivalent electric efficiency (EEE) equal or greater than that of table 1. In this situation, the minimum EEE (EEE min ) of the plant under study should be 55%. The EEE associated to the installation was calculated as:

ref V Q E EEE    (1)
where E represents the electric energy generated -measured at the alternator terminals-, Q the primary energy consumption with respect to the low heating value (LHV) of the fuel, V the useful thermal energy demand during the process and  ref the reference value for the efficiency in separated heat production published by the Commission of European Communities on December 21 st 2006 [START_REF]por la que se establecen valores de referencia de la eficiencia armonizados para la producción por separado de electricidad y calor de conformidad a lo dispuesto en la Directiva 2004/8/CE[END_REF].

The analysis of the annual operation of the plant was based on mass and energy balances, assuming an annual reception of 25000 t sludge to be the reference value for dimensioning. However, it must be brought into mind that olive production -and hence sludge generation-generally presents significant annual variations. This is mainly caused by crop rotation: an abundant harvest is usually followed by a low flowering period. The storing pool capacity was then dimensioned as 22962 m 3 .

The criterion considered in the programming of the cogeneration plant operation was that of satisfying the thermal energy demand at EEE min . The operation process was divided in two well-defined periods: cogeneration mode (in which all the sludge was processed) and strict electric power production (until EEE min was reached). The initial values for the mass balance analysis were obtained either from previous experiments or from equipment manufacturers:

(i) Sludge reception basin: 70% by weight (wet basis) initial moisture content of sludge; 3.5% by weight (wet basis) remaining oil in sludge.

(ii) Pit/pulp wet separation: pit separation 12% by weight from pit content of sludge (around 15%); 22% by weight (wet basis) moisture content of pit. (iii) Centrifugation phase: 5.66 t/h operating rate; 3% by weight (wet basis) fresh water added into the decanter (referenced to total sludge weight); recovered oil 45% by weight (referenced to total oil in sludge); non-recovered oil was retained in WOH (65%) and in OMW (35%); 60% by weight (wet basis) moisture content of WOH. (iv) Thermal drying phase: 15% by weight (web basis) final moisture content of dried olive husk (DOH). (v) OMW concentration tower: 60% by weight (wet basis) final moisture content of concentrated OMW.

The mass balance analysis was carried out for annual values of the main variables, according to a specific model developed by the authors. The most relevant results are shown in table 2.

Electric energy was used for:

 Wet husk/pulp separator.  Internal transport of sludge.  Centrifugation section (including thermomixer, horizontal and vertical centrifuges, vibrofilters and racking pumps).  Thermal drying section (including rotary drier, fans, worm gears and pneumatic transport systems).  OMW concentration tower (including pumps and fans).  Internal combustion engine section (including pumps and fans).  Lighting and general administration facilities.

The total electric power of the plant was 615 kW. In order to estimate the electric power demand for the different sections of the plant, a utilisation coefficient was associated to each installed electric power, which was defined as direct function of the daily working time and of the operating regime of each device (values determined experimentally). The electric power demand for each section is shown in Fig. 3.

Thermal energy was used for:

 Thermomixer; as hot water flow.  Drier; as high temperature (400ºC) airflow.  OMW concentration tower; as low temperature (100ºC) air/gas flow.

A detailed analysis of the electric and thermal energy demand of the system under study is a crucial task for further calculations [START_REF] Hinojosa | A comparison of combined heat and power feasibility models[END_REF]. Energy demand profiles can be estimated hourly, monthly or yearly, depending on accuracy needs for each particular system. In this sense, no fluctuations of the energy charge were observed for the installation reported here; instead, seasonal energy demand profiles followed an almost constant pattern. Therefore, according to the results of the energy analysis performed for an annual period, Table 3 shows the electric and thermal energy demanded/produced by the different sections of the process. The total electric energy demand of the plant reached about 8.68 TJ/year, 54.28% of which was consumed in the processing of the sludge, and the rest by the internal combustion engine auxiliaries.

The total thermal energy demand for the sludge treatment reached 60.61 TJ/year, and additional consumption of natural gas (5.394•10 6 Nm 3 /year) by the internal combustion engines should also be considered. Therefore, the average energy supply rate required for the treatment of sludge was found to be 0.188 MJ/kg electric energy and 2.424 MJ/kg thermal energy.

The thermal energy required for the treatment of sludge represented 77% of the useful thermal energy supplied by the cogeneration plant (excluding the periods of strict electric power generation), while the electric power demand represented only 11.77%thus favouring the marketing of the excess energy-.

Energy-environmental analysis

The energy and environmental benefits derived from the use of cogeneration systems in the processing of sludge from the olive oil industry were analysed in order to evaluate the primary energy savings and the reduction of CO 2 equivalent emission.

If the thermal and electric energy separated production was considered, the primary energy needed to generate the electric energy equivalent to that of the producing process demand was found to be 9.95 TJ, assuming the sludge annual reception as 25000 t and reference value for the efficiency in separated electric production as  el ref = 0.4733, according to the guidelines published by the Commission of European Communities [START_REF]por la que se establecen valores de referencia de la eficiencia armonizados para la producción por separado de electricidad y calor de conformidad a lo dispuesto en la Directiva 2004/8/CE[END_REF]. Such value for the electric efficiency was determined in terms of: (i) the type of fuel, natural gas; (ii) the date (year) of construction of the plant, 2002; (iii) the correction factor to account for the mean values of the weather parameters, which leads to a 0.3% reduction in the electric efficiency for the particular location of the plant referred to in the present work (Extremadura, Spain); (iv) the correction factor to account for the avoided loss to the electric network, based on the generation voltage (380 V) as well as on the electricity percentage consumed in situ (11.77%) and that transferred to the electric network (88.23%).

A primary energy of 73.91 TJ was required to generate the thermal energy equivalent to that needed in the process, provided that the harmonised thermal energy reference for separated production was  th ref = 0.82 [START_REF]por la que se establecen valores de referencia de la eficiencia armonizados para la producción por separado de electricidad y calor de conformidad a lo dispuesto en la Directiva 2004/8/CE[END_REF]. As a consequence, the total primary energy need for separated production of electric and thermal energy for the industry was 83.86 TJ.

The total primary energy demand in cogeneration mode corresponds to natural gas consumption (LHV 38.52 MJ/Nm 3 ), and reached a value of 207.79 TJ. The electric energy to be transferred to the electric network -after the thermal and electric energy demands of the plant were satisfied-reached 65.04 TJ. If such electric energy had been generated under ordinary energy production regime conditions ( th ref = 0.4733), an equivalent 137.43 TJ primary energy consumption would have been achieved. Consequently, the net primary energy needs associated to the cogeneration mode could be evaluated as 70.36 TJ, thus achieving a significant energy saving (16%) if compared to the separated-production mode.

The CO 2 emission saving will depend on the base case scenario. According to the specifications of the Spanish Renewable Energies Plan for 2005-2010 [START_REF]Plan de Energías Renovables en España[END_REF], the CO 2 emission factor associated to the thermal use of natural gas is 55.80 kg CO 2 /GJ. Similarly, the CO 2 emission factor for electric energy production was determined according to the technologies involved in the electricity production process from the same energy source -natural gas-(372 t CO 2 /GWh indicated value for combined-cycle power plants and 54% electric efficiency). In the particular case reported here, the value for the CO 2 emission factor of the electric energy production process was estimated as 117.90 t CO 2 /GJ).

The CO 2 emission factor for power and thermal use is applied, respectively, to the amount of electric energy considered at end-use and to the amount of gas burned. This way, the CO 2 equivalent emission of greenhouse gases were estimated according to the energy use in the plant. The reduction of CO 2 emission achieved by the cogeneration system in the plant was found to be about 753 annual tons. See results in Table 4 for further details.

Economic feasibility of cogeneration

A comparative economic analysis of a conventional sludge processing installation (separated production of thermal and electric energies) versus an installation incorporating the cogeneration system under study is carried out in the present section. Two possible scenarios were considered: Scenario-1: additional cost of 12 €/t incoming sludge, according to the average price for 2006 campaign. Scenario-2: no additional cost for incoming sludge, provided that transport costs are covered by olive oil industries. This analysis was based on the following parameters: total capital investment (TCI, M€), total operating cost (TOC, M€/year), revenues from electric energy sale (R ee , M€/year), revenues from olive oil sale (R oo , M€/year) and revenues from dried OH (R oh , M€/year). The TCI was evaluated as the sum of all direct and indirect costs of the plant. The former include purchased equipment cost (PE, M€), equipment installation cost (10% PE), control equipment cost (5% PE), pipes and tubes (5% PE), auxiliary facilities (7% PE), and civil work and buildings (15% PE), whereas the latter cover engineering, setting up of equipment and contractor fee (10% PE) (all percentages derived from the specific literature [START_REF] Peters | Plant design and economics for chemical engineers[END_REF][START_REF] Turton | Analysis, synthesis and design of chemical processes[END_REF]). The TOC including maintenance, insurance and personnel vary for different technologies, and annual costs range from 3% to 6% of TCI [START_REF] Dornburg | Efficiency and economy of wood-fired biomass energy systems in relation to scale regarding heat and power generation using combustion and gasification technologies[END_REF]. In particular, a value of 4% was used in this study.

The following values were considered for the cogeneration installation under study: direct costs 3.544 M€ (main and secondary basins 0.375 M€, centrifugation phase 0.270 M€, thermal drying phase 0.127 M€, OMW concentration tower 0.170 M€, engines 1.553 M€) and TCI 3.793 M€.

A value of 1.837 M€ was obtained for TOC, including natural gas and incoming sludge costs (only in scenario-1, as explained before). The reference price for natural gas was taken as 6.666 €/GJ. The revenues from sale of electric energy (R ee , M€/year), were calculated as the product of the net electric power transferred to the main supply (kW) times the annual operating hours (h/year) times the estimated sale price of the electric power (€/kWh). Two alternatives for the sale of net electric energy are allowed by Spanish legislation: (i) to transfer the electric power to a distributing company (in this case, the price will be set by means of a unique rate valid for all the programming periods); (ii) to sell the electric power in the free market (price will be that arising from the free market complemented by an incentive and/or an extra payment). In this situation, a price of 9.35 c€/kWh for all programming periods is established by the Royal Decree 661/2007, which regulates the installations for the treatment and reduction of sludge from olive oil industry.

Direct costs reached 1.289 M€ for the conventional plant, and only 1.432 M€ were devoted to the TCI. The value for the TOC was 0.7861 M€, which included: cost of natural gas to satisfy the thermal energy demand (6.666 €/GJ), cost of the electric energy demand (7.00 c€/kWh), and cost of incoming sludge (only in scenario-1).

The marketing of the olive oil obtained from a second centrifugation is not so relevant as that of the virgin oil. In fact, it has been subjected to significant price fluctuations for certain reasons along the years: from more than 0.78 €/kg before the 2001 crisis of the sector down to 0.42 €/kg in 2003. The price considered in the present analysis was approximated as 1€/kg (as for the last two years).

Dried OH are usually sold in bulk for thermal use at domestic and industrial scales, or even for animal feed production. A sale price of 0.0576 €/kg was considered here for wet husk, and 0.048 €/kg for OH. Finally, the concentrated OMW obtained in the process is sold as organic fertilizer, at a very reduced sale price (0.0060 €/kg).

The parameters used for the economic evaluation [START_REF] Pérez-Carballo | Control de la gestión empresarial[END_REF] of the proposal are the following:

(i) Net present value (NPV), defined as:

NPV =  k=1 N F k / (1+i) k -TCI, ( 2
)
where N is the economic life (in years) of the plant, i the annual interest percentage rate and F k the annual cash flow in the year k evaluated as follows:

F k = R ee + R oo + R oh + R co -TOC (3)
(ii) Profitability index (PI), obtained through the equation:

PI =  k=1 N F k / (1+i) k / TCI (4)
(iii) Internal rate of return (IRR), defined as the value of the interest rate that cancels the NPV.

(iv) Payback time (PBT), the period of time after which the investment is recovered.

The results obtained for the economic parameters relating to the comparison of the conventional plant versus that including the cogeneration system are shown in Table 5 for the two possible above-mentioned scenarios.

In scenario-1, the NPV associated to the conventional plant showed a negative value, which indicates a poor profitability for the traditional second-centrifugation oil extraction operation. The TCI showed a 164.87% increase for the cogeneration plant; however, a low -positive-NPV was found. Therefore, cogeneration appears as an efficient energy technique for the integral management of by-products. A negative NPV was also found for the conventional plant in scenario-2, although a 660% increase with respect to that of scenario-1 was observed. In this case, a 4.5-year period for the PBT was achieved, with a 17.7% generated interest rate.

The economics of CHP are very sensitive to fuel and electricity prices. Provided that price fluctuations are quite unpredictable, a specific parameter should be included to test the sensitivity of such changes. Therefore, an additional sensitivity analysis was carried out in order to evaluate possible fluctuations in the economic and operating variables from the results achieved in the present study. The variation range for each of the parameters involved as well as their influence on the NPV values are shown in Table 6.

Conclusions

The feasibility of CHP system for the industrial sludge treatment was studied from technical, environmental and economic points of view. Reductions in the primary energy demand (over 16%) as well as in the CO 2 equivalent greenhouse gases emission were achieved. Moreover, this kind of energy recovery system allows a profitable integral treatment of by-products from olive oil industry in small-and mid-sized plants.

Figure 1 .

 1 Figure 1. Olive oil world production (2006-2007).

Figure 2 .

 2 Figure 2. Cogeneration plant for the treatment of sludge from olive oil industry.

Figure 3 .

 3 Figure 3. Sharing of the electric power demand (kW).

  FIGURE 1

TABLE CAPTIONS Table 1 .

 CAPTIONS1 Minimum values of EEE for different fuels and technologies.

Table 2 .

 2 Results for annual mass balance of the plant.

Table 3 .

 3 Results for annual energy balance of the cogeneration plant.

Table 4 .

 4 Primary energy demand and CO 2 equivalent emission of greenhouse gases.

Table 5 .

 5 Economic indexes for the plant under study.

Table 6 .

 6 Values of the sensitivity analysis parameters.

TABLE 2

 2

	Equipment	Input	Mass flow	Amount of	Output	Mass flow	Amount of
			rate (t/h)	input (t)		rate (t/h)	output (t)
	Basin	Sludge	-	25000	Sludge	8.39	25000
	Wet husk	Sludge	8.39	25000	Wet husk	0.15	450
	separator				Sludge	8.24	24550
	Three-phase	Sludge	5.50	24550	Olive oil	0.09	400
	decanter	Fresh water	0.16	715	Olive husk	2.19	9820
					OMW	3.37	15045
	Dryer	Olive husk	2.20	9820	Dry olive husk	1.03	4604
	Concentration	OMW	3.38	15045	Concentrated	1.58
	tower				OMW

TABLE 4

 4

	Separate production		Cogeneration
	Energy
	Electric energy (TJ)	9.95	Electric energy transferred to the	137.43
			network (TJ)
	Thermal energy (TJ)	73.91	Natural gas burned (TJ)	207.79
	Total (TJ)	83.86	Net (TJ)	70.36
			Annual saving (TJ)	13.50
	Greenhouse gases emissions
	Electric energy (t CO 2 /year)	556	Associated to electric energy	7669
			transferred to the network (t
			CO 2 /year)
	Thermal energy (t CO 2 /year)	4124	Natural gas burned (t CO 2 /year) 11595
	Total (t CO 2 /year)	4680	Net (t CO 2 /year)	3926
			Annual saving (t CO 2 /year)	754

TABLE 5

 5

	System	TCI (M€)	NPV (M€)	PI	IRR (%)	PBT (months)
	Scenario-1
	Conventional	1.432	-2.57	-	-	-
	Cogeneration	3.793	0.35	1.09	6.85	85
	Scenario-2
	Conventional	1.432	-0.25	-	-	-
	Cogeneration	3.793	2.66	1.70	17.7	54