Study of Thermocline Tank Performance in Dynamic Processes and Stand-by Periods with an Analytical Function Academic research paper on "Materials engineering"

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Energy Procedía 49 (2014) 725 - 734

SolarPACES 2013

Study of thermocline tank performance in dynamic processes and stand-by periods with an analytical function

Rocío Bayón*, Esther Rivas, Esther Rojas

CSSU-Thermal Storage-CIEMAT-PSA, Av. Complutense 40, 28040 Madrid (Spain)

Abstract

The behavior of an Andasol-like thermocline tank with and without solid filler has been predicted with an analytical Logistic Cumulative Distribution Function not only during dynamic processes of charge/discharge but also during stand-by periods of no operation. The evolution of thermocline thickness with dwelling time in stand-by periods has been studied under the condition of energy conservation when thermocline zone is total or partially inside the tank. Thermocline degradation is faster for the tank with molten salt and solid filler than for the tank with only molten salt because thermal diffusivity of the molten salt is lower than thermal diffusivity of the solid material. The strong decrease in tank efficiency with consecutive charge/discharge cycles when thermocline zone is left inside the tank can be relieved if a certain percentage of thermocline zone is extracted. Actually, if 50% thermocline is extracted, efficiency after a second process can be as high as 96% comparing with the 77% obtained if thermocline is not extracted. However, extracting thermocline zone implies a decrease of outlet temperature in discharge or an increase of outlet temperature if the process is a charge. Therefore, temperature limits and operation strategies should be defined for the solar thermal power plant that includes a thermocline storage tank in order to establish which amount of thermocline zone can be extracted.

© 2013 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selectionandpeerreviewbythescientificconference committeeofSolarPACES2013underresponsibilityofPSEAG. Final manuscript published as received without editorial corrections.

Keywords: sensible heat; thermocline storage; analytical function; charge/discharge cycles; stand-by degradation; themocline extraction

* Corresponding author. Tel.: +34-913466048; fax: +34-913466037. E-mail address: rocio.bayon@ciemat.es

1876-6102 © 2013 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/Kcenses/by-nc-nd/3.0/).

Selection and peer review by the scientific conference committee of SolarPACES 2013 under responsibility of PSE AG. Final manuscript published as received without editorial corrections. doi: 10.1016/j.egypro.2014.03.078

1. Introduction

The reduction of the storage system cost in Solar Thermal Power Plants (STPP's) is one of the key points that could increase their utility and lead to a wider adoption of this kind of plants around the world [1]. In this way, the replacement of the conventional molten salt two-tank system by a single thermocline tank is being seriously considered since this could reduce around 33% the thermal storage system cost provided a quantity of the molten salt (between 50% and 75%) is substituted by a cheaper solid filler material [2].

Although thermocline tanks have a great potential to decrease thermal storage costs, they still present challenges in terms of control strategy and storage efficiency. From a practical point of view the best way to understand thermocline tank behavior and establish optimal control strategies, is to simulate the annual performance of a STPP in which this kind of storage has been implemented. For that purpose, an analytical expression that provided tank outlet fluid temperature as a function of time and fluid mass flow would be strongly desirable.

In a recent work still under revision we have introduced a Logistic Cumulative Distribution Function (CDF) for describing the behavior of thermocline storage tanks. This function results to be a good approximation to the solutions obtained with a single-phase one-dimensional numerical model [3] and has been validated with experimental results reported in the literature [4, 5] for thermocline tanks with different storage media.

In the present work this Logistic-CDF has been used for describing the performance of an Andasol-like thermocline tank with and without solid filler not only during dynamic processes of charge and discharge but also during the stand-by periods when the tank is not in operation. The evolution of thermocline thickness with dwelling time in stand-by periods has been studied when thermocline zone is either total o partially inside the tank. It has been found that thermocline degradation is faster for the tank with molten salt and solid filler than for the tank with only molten salt because the thermal diffusivity of the molten salt is lower than the thermal diffusivity of the solid material.

The variation of characteristic parameters like stored energy and tank efficiency with consecutive charge/discharge processes in which thermocline is partially extracted has been evaluated. It has been found that the storage efficiency strongly decreases with charge/discharge cycles if thermocline zone is left inside the tank but this decrease can be somehow relieved if a certain percentage of thermocline zone is extracted.

2. Logistic CDF as analytical function for describing thermocline tank behavior

In previous works [3, 6] we presented a single-phase one-dimensional numerical model for simulating thermocline storage tanks with an effective storage medium formed by either a liquid or both a liquid and a solid filler. This model neglected thermal losses, was expressed in dimensionless coordinates and its numerical results were successfully validated with experimental data found in the literature for different kinds of thermocline storage tanks [3]. This numerical model was developed for solving the following dimensionless energy balance equation valid for the dynamic processes of charge and discharge:

8d , 8d d2S

-T + v -T = —¡7 (1)

dt dz dz 2

The expressions for the dimensionless variables are displayed below and the correlations of physical parameters are recorded in the Appendix A. The numerical solutions obtained for this equation are sigmoid curves representing dimensionless temperature distribution, ^ , along the dimensionless tank height, z , for different dimensionless time values, t* (or z'c positions). In a more recent work we have proposed a Logistic Cumulative Distribution Function (CDF) for describing the behavior of thermocline storage tanks. In this way the numerical solutions of Eq. 1 can be approximated with a good degree of accuracy to a Logistic CDF curve expressed as:

№ ; zc*, S) =^mn + (2)

1 + e S

Where ^max and represent maximum and minimum dimensionless temperatures, z'c is the dimensionless location of thermocline zone center and also the position of the inflection point, whereas S parameter indicates the amplitude of thermocline zone since it is related to the Logistic-CDF slope at that inflection point [7]. With the numerical model we already demonstrated that the evolution of thermocline zone thickness depended on the working conditions (i. e. dimensionless velocity, v*, and time, t*) [3]. Therefore the dependence of S parameter with these working conditions was obtained for the analytical function with the help of the numerical results. It has been obtained that S parameter for dynamic processes can be expressed as a product of two factors: one depending on t* and another depending on v*:

For the case of stand-by processes, some previous studies have demonstrated that thermal losses to the environment can be neglected [2], which means that the tank can be treated as adiabatic. Therefore since only degradation by thermal diffusion is considered, the energy balance equation is similar to Eq. 1 but without the dynamic term with v* . The stand-by energy equation was numerically solved for the case in which whole thermocline region is confined within the tank, and the corresponding temperature distribution solutions were approximated to the Logistic-CDF of Eq.2. In this particular case, thermocline location, zc, remains constant and it has been obtained that S parameter varies dimensionless time, t * by means the expression:

Similarly, Bharathan et al. [8] observed that thermocline zone spreading was proportional to the square root of time and thermal diffusivity. In this way, Eq. 4 displays the same dependence since t* is proportional to dimensional time and effective thermal diffusivity (see below) and thermocline thickness is proportional to S parameter. However, if thermocline zone is at tank edge or has been partially extracted in a previous dynamic process, both S and z'c will vary with dimensionless time and since the stand-by degradation is adiabatic, degradation must be studied under the condition of energy conservation.

For calculating the stored energy in a thermocline tank, temperature profile of Eq. 2 must be integrated along the whole tank height (i. e. from z* = 0 to z* = 1 ). The resulting equation for the energy fraction expressed in dimensionless coordinates is:

1 + e S

q; = i+s in

1 + eS

This expression is valid for any dimensionless temperature profile, which is defined by thermocline location, z'c, and the parameter S. Therefore, if the variation of S with time is given by Eq. 4 and we assume an adiabatic stand-by degradation process for which the initial Q* is constant, the time variation of z"c can be worked out from Eq. 5:

2Qf 2 e5^ _

1 - e5^

Dimensionless correlations

Temperature: $ =

Minimum temperature: ^ = -^á-

Velocity:

s(pC I Lv

V p) liquid '

liquid

Thermocline position: in discharge:

Maximum temperature: ^max = 1

Height: z* =

Time: t = -

z, = v t

in charge: z* = 1 -v t

2.1. Application to the particular case of an Andasol-like thermocline tank

Being formulated in dimensionless form and parameterized in terms of working conditions, all equations presented in the previous sections can be used for characterizing dynamic processes and stand-by periods of any kind of thermocline tank, independently on the size and the storage medium (i. e. only liquid or liquid with solid filler). Moreover, the advantage of having an analytical equation for describing the behavior of a thermocline tank is that all calculations are dramatically simplified. In this way, one of the most important parameters to be controlled when a thermocline tank is studied or when it is implemented in a STPP, is the outlet temperature as a function of time for every instantaneous inlet/outlet velocity. This temperature can be obtained from Eq. 2 taking into account that in discharge it is measured at tank top ( z = 1) and in charge it is measured at tank bottom ( z* = 0 ).

Therefore, the equations have been applied to the particular case of a thermocline tank similar in size and performance to the storage tanks of Andasol I commercial plant [9] that contains either solar salt as storage liquid (e=1) or a combination of solar salt and a solid filler of quartzite rock and sand (e=0.22) [10]. In Fig. 1 the outlet temperature (at tank top, L=14 m) for a discharge process of an Andasol-like thermocline tank is plotted for an arbitrary velocity profile generated with the only requirement that velocity values are similar to the ones expected for a tank operating in a solar thermal plant. As we can see, outlet temperature remains constant until thermocline zone is extracted, which implies a temperature decrease. Also we observe that the period between 350-450 min corresponds to a stand-by process (vm=0) during which liquid temperature at tank top slightly decreases due to thermocline degradation.

400 380-O 360-2[ 340-Jd 320-1 T300

0 100 200 300 400 500 600 t [min]

Fig. 1 Outlet temperature in discharge (i. e at tank top, L=14 m) of an Andasol-like thermocline tank for a certain velocity profile.

In order to have an idea of the stand-by behavior of an Andasol-like thermocline tank, various initial temperature profiles have been considered and their evolution after 12 h has been recorded in Fig. 2. All these initial profiles have the same S value (0.025) but different thermocline zone positions: zc= 7 m (i. e. at half tank height), zc=12.7 m (i. e. at tank top border ), zc=0.28 m and zc=14.14 m (i. e. thermocline partially out of the tank). In this figure we observe that thermocline degradation after 12 hours is higher if the tank contains a solid filler of quartzite rock+sand (e=0.22), whereas the initial temperature profile remains almost constant for the tank with only molten salt (s=1). This happens because the thermal diffusivity of the molten salt is lower than the thermal diffusivity of the quartzite rock filler [5]. The contrary would be observed if the diffusivity of the solid filler were lower than the diffusivity of the liquid medium.

Fig. 2. Stand-by degradation of different intial temperature profiles for an Andasol-like thermocline tank with only molten salt (s=1) or with

molten salt and a solid filler of quartzite rock (s=0.22).

3. Consecutive charge/discharge processes

In this section, the Logistic-CDF has been used for predicting the behavior of an Andasol-like thermocline tank when consecutive charge and discharge processes are carried out. In this way tank performance has been evaluated in terms of two characteristic parameters: stored energy, Qf , calculated with Eq. 5 and tank efficiency, rj, defined as the percentage ratio between the stored or delivered energy by the thermocline tank and the ideal total energy [3].

3.1. Without thermocline extraction

With the help of the Logistic-CDF and its parameterization it is possible to calculate tank efficiency at the end of consecutive charge/discharge cycles, with no stand-by periods in between and assuming that thermocline is never extracted from the tank. In our previous work, it was demonstrated that tank efficiency increases with dimensionless velocity up to a maximum for v* > 2350 [3]. For the particular case of an Andasol-like thermocline tank, charge/discharge cycles have been performed at v* = 8000 , which corresponds to vm=0.40 m/h for the case of a tank with only molten salt (s=1) and vm=1.47 for the case of a tank with quartzite rock+sand solid filler (g=0.22) (see dimensionless correlations box and Appendix A section). The variation of both stored energy and efficiency with the consecutive charge/discharge cycles has been plotted in Fig. 3. Since the dimensionless velocity used is well over the limiting value of 2350, the results are independent on the kind of tank that is considered and hence valid for thermocline tanks with and without solid filler.

In Fig. 3 we can see that the stored energy by the thermocline tank in charge decreases with the cycles whereas the energy inside the tank after every discharge is increased. Therefore, as charge/discharge cycles are performed, more energy that cannot be extracted remains in the tank. This happens because the available thermal energy at maximum temperature decreases with subsequent charging/discharging cycles due to a continuous increase of thermocline thickness [3], which leads to a decrease in tank efficiency. In this way, Fig. 3 clearly shows that if charge/discharge cycles are performed without thermocline zone extraction and even if the tank is operated under optimum efficiency conditions (i. e. at v* > 2350), it could deliver only about half of the ideal total energy after 5 days operation.

Charge/discharge

Fig. 3. Evolution of stored energy and tank efficiency after consecutive charge/discharge processes performed at v" = 8000 and without

thermocline zone extraction.

3.2. With partial thermocline extraction

It is clear that thermocline storage tanks meant to be implemented in STPP's cannot be operated in the way described in previous section because thermocline thickness increases not only with charge and discharge cycles but also during stand-by periods. In both cases, the storage system exergy is decreased and so is the potential useful power that can be extracted. One solution to this problem is to perform charge/discharge cycles in which thermocline zone is either partial or totally extracted.

In Fig. 4, we observe how the efficiency of an initial process of either charge (i.e. from a totally discharged tank at Tmin) or discharge (i. e. from a totally charged tank at Tmax), dramatically increases when thermocline zone is extracted. Actually if we extract half of thermocline, the 90% efficiency obtained without its extraction is increased to 98%.

However, extracting thermocline zone implies a decrease of outlet temperature for discharge processes or an increase of outlet temperature if the process is a charge. This can be clearly seen in Fig. 5 where outlet temperature with time has been plotted for a discharge process and in which the temperature decrease with the increasing percentage of extracted thermocline is also indicated.

TC extracted [%]

Fig. 4. Evolution of tank efficiency with the percentage of thermocline zone extracted.

If outlet temperature of the storage system decreases during a discharge process, this will imply a temperature decrease of the steam feeding the power block and hence the turbine efficiency will decrease as well. Therefore this effect must be considered if thermocline zone is to be extracted during storage system discharge. On the other hand, if outlet temperature of the storage system increases during a charge process, this will lead to a temperature increase of the heat transfer fluid entering the solar field and hence the collector efficiency will be decreased. Moreover, this temperature increase can also affect the performance of different components located prior to solar field inlet like pumps or control instrumentation. Therefore all these effects must be taken into account as well if thermocline zone is to be extracted during storage system charge.

In conclusion, the special behavior of thermocline tanks in terms of variable outlet temperature has to be taken into account when defining the control & operation strategies, which might be different from the ones used in solar thermal power plants with the conventional molten-salt two-tank storage system.

Fig. 5. Outlet temperature with time for a discharge process. Temperature decrease with the percentage of extracted thermocline zone is also

indicated

Another question to be considered when thermocline zone is extracted during a charge or discharge deals with the behavior of temperature profiles generated in the subsequent process. In Fig. 6 we can see the evolution of temperature profiles for a charge process performed after a discharge with different final scenarios of extracted thermocline: 100% (flat initial profile), 65%, 50%, 37%, 24% and 0%. In this case, temperature profiles have been

obtained with the numerical model [3] using the profiles established at the end the precedent discharge, as intial conditions. In Fig. 6 we can see that at the beginning of the process, temperature profiles starting from a partially extracted thermocline scenario are not symmetrical, but as they approach the tank bottom (i. e. end of charge) they become more symmetrical so they can quite well be fitted to a Logistic-CDF curve. This allows calculating the energy stored in the tank with the help of Eq. 5.

At the end of a charge process for which thermocline zone is not extracted (i. e. temperature profiles at tank bottom, z=0, in Fig. 6), the profiles lay between the two extreme cases: 100% and 0% thermocline extraction in the precedent discharge. Actually temperature profiles starting from thermocline extraction lower than 50% are more similar to the profile of 0% extraction and the profiles starting from extractions higher than 50% are more similar to the starting from 100% extraction. The reverse case, i. e. discharge process after previous discharges behaves the same way.

Fig. 6. Time evolution of temperature profiles for charge process performed from final discharge profiles resulting from different thermocline

extraction percentages: 100%, 65%, 50%, 37%, 24% and 0%.

Finally we have calculated the tank efficiency as a function of thermocline percentage extracted in charge processes performed from various final temperature profiles and the results are displayed in Fig. 7. The efficiency for each case has been calculated with the help of Eq. 5 as the difference between the energy remaining in the tank after the discharge and the stored energy after the charge. In Fig. 7 we observe that the highest efficiencies are obtained for the case in which thermocline was totally extracted in the precedent discharge (100%) and the lowest efficiencies are obtained for the case in which thermocline remained inside the tank (0%). It is interesting to note that by extracting 25% thermocline in the precedent discharge the efficiency of the subsequent charge already improves 4% in all cases and this improvement attains 8% when the charge is performed from a temperature profile in which 50% thermocline has been extracted. However if 75% thermocline is extracted in discharge the efficiency improvement in the subsequent charge is only 10% and the curve is very close to the corresponding to 100% thermocline extraction in discharge. This means that it might not be worth extracting the whole thermocline since extracting only 75% would already lead to similar efficiency results.

Charge process after previous discharge

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

On the other hand, the table included in Fig. 7 shows the effect of thermocline extraction strategies on the efficiency of subsequent charge/discharge processes. In this way, if thermocline is neither extracted in discharge nor in charge, the efficiency after the second process will be about 77%. However, if 25% thermocline is extracted in both processes this efficiency will attain 88% and this value can be as high as 96% if 50% thermocline is extracted. This means that the strong decrease in tank efficiency due to consecutive dynamic processes can be somehow relieved by partially extracting thermocline zone. As pointed out before, thermocline extraction will imply a variation (increase or decrease) in the storage system outlet temperature and this effect has been indicated in the table of Fig. 7 as well. In this way we can see for example that if 50% thermocline is extracted this would imply 350 °C as outlet temperature in both charge and discharge processes. Whether these temperature values can be used or not will depend on the limits determined by the other power plant components, which will help to define operation strategies and establish the amount of thermocline zone that can be extracted.

Fig. 7. Tank efficiency as a function of extracted thermocline percentage for charge processes performed from different final discharge temperature profiles (i. e. % of TC extracted). A table with charge efficiency and outlet temperatures for some particular cases has been included.

4. Conclusions

In this work a Logistic-CDF has been used for predicting the behavior of an Andasol-like thermocline tank when consecutive charge and discharge processes are carried out and also during stand-by periods of no operation.

For stand-by period, the tank is considered to be adiabatic and hence degradation of thermocline zone takes place only by diffusion and has been studied under the condition of energy conservation. We have observed that thermocline degradation after 12 hours is higher if the tank contains a solid filler of quartzite rock+sand (e=0.22), whereas the initial temperature profile remains almost constant for the tank with only molten salt (e=1). This happens because the thermal diffusivity of the molten salt is lower than the thermal diffusivity of the quartzite rock material.

For the dynamic case, if charge/discharge cycles are performed without thermocline extraction, the exergy of the storage system is decreased and so are the potential useful power that can be extracted and the tank efficiency. One solution to this problem is to perform charge/discharge cycles in which thermocline zone is either partial or totally extracted. In this way, if 50% thermocline is extracted, efficiency after a second process can be as high as 96% comparing with the 77% obtained if thermocline is not extracted. This means that the strong decrease in tank efficiency due to consecutive dynamic processes can be somehow relieved by partially extracting thermocline zone.

However since thermocline extraction implies a variation in the storage system outlet temperature (i. e. increase in charge or decrease in discharge), temperature limits should be defined in order to establish which amount of thermocline zone can be extracted. This special behavior of thermocline tanks requires the development of control &

operation strategies that may differ from the ones used in solar thermal power plants with the conventional molten-salt two-tank storage system.

Acknowledgements

The authors would like to acknowledge the E. U. through the 7th Framework Programme for the financial support of this work under the O.P.T.S. project with contract number: 283138.

References

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[6] Bayon R, Rojas E, Rivas E, Effect of storage medium properties in the performance of thermocline tanks, SolarPACES 2012 Conference, Marrakech (Morocco), September 2012.

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Appendix A. Nomenclature and physical properties

p density

Cp heat capacity

pCp volumetric heat capacity

k thermal conductivity

viiquid velocity of the liquid inside the tank

vm=evuquid velocity of the liquid at tank inlet/outlet

L tank height

s porosity of the storage medium

Tmax maximum temperature of the tank (inlet temperature in charge or outlet temperature in discharge) Tmin minimum temperature of the tank (outlet temperature in charge or inlet temperature in discharge) ef sub index referring to the effective storage medium liquid sub index referring to the liquid

(pC\ =e(pC) +(1 -e)(pC) Effective volumetric heat capacity: V P'eff V P'liquid V P'solid

Effective thermal conductivity: kf ~ skliquid +(1 ~s)ksolid

™ - keff

ioC "I

Effective diffusivity: P ef