7. Thermodynamic analysis of a latent heat storage system. Comparison with sensible heat

Transcription

1 7. Thermodynamic analysis of a latent heat storage system. Comparison with sensible heat In this section, energy and exergy balances are applied to two different packed beds, one filled with PCM and another with sensible heat storage material. The purpose is not only to assess the applicability of a latent heat storage in the superheating module against traditional sensible heat storage, but also to spot the bottlenecks which, as it will be shown, make latent heat storage a-priori unattractive for such working conditions. This first analysis will help us understand better the behavior of the system and the challenges it presents, setting the base camp for a later parametric study. The thermo-physical parameters of the PCM used are: Density [kg/m3] 2200 Specific heat [J/kg K] 1500 Thermal conductivity [W/m K] 2 atent heat of fusion [J/kg] 800 Melting temperature [ºC] 410 The sensible heat storage material is assumed to have the same properties as the PCM, only with a melting point out of the range of working temperatures. Density [kg/m3] 2200 Specific heat [J/kg K] 1500 Thermal conductivity [W/m K] 2 atent heat of fusion [J/kg] 800 Melting temperature [ºC] T m 310ºC ort m 500ºC In both cases, the properties in liquid and solid state are supposed to be the same. Steam properties are considered constant and equal to those at 100 bar and 400ºC: Density [kg/m3] Specific heat [J/kg K] 3096 Thermal conductivity [W/m K] 6.7 e-4 Kinematic viscosity [m2/s] 6.5e-7 Mass flow [kg/s] 70

2 7.1 Thermodynamic analysis of the charge process The results of the analysis correspond to the fifth cycle of charge-storage-discharge in order to have working conditions closer to the stabilized state. et us look firstly at the evolution of the system during the charge process. For the PCM packed bed we have: Figure 22.- Temperature evolution inside the packed bed between tial -0s- and al -100s-states of charging. Steam in blue and PCM in green. As it can be seen, the charging period is stopped after 100s due to the fact that the steam outlet temperature reaches the maximum value allowed, 320 ºC. Therefore, only a small fraction of the deposit capacity is being used. Figure 23.- Evolution of the steam inlet -red- and outlet -blue- temperatures during charge period.

3 For the sensible heat packed bed, we have: Figure 24.- Temperature evolution inside the packed bed between tial -0s- and al -4190s- states of charging. Figure 25.- Inlet -red- and outlet -blue- steam temperature during charging. See how the steam outlet temperature evolves much more slowly now, thus allowing the deposit to store a greater amount of energy.

4 7.1.1 Energetic analysis of the charge process We will make use of the fuel-product terminology, where fuel refers to the input and product to the desired result of this input. Fuel=Net heat provided by steam=incoming heat -Outgoing heat Q Fuel,ch [J ]= H a H b = ṁ HTF [h a t h b t ]dt ṁ HTF cp HTF [T a t T b t ] t Product=Energy accumulation during charging period=enthalpy change of the packed bed=enthalpy at al state of charging period Enthalpy at tial state of charging period Q Product,ch [ J ]= E PB = E HTF E PCM = E HTF E HTF E PCM t = E PCM Where and refer to the tial and al state of the charging period, respectively. E HTF [ J ]= D 2 HTF 0 h HTF x dx D 2 E HTF [ J ]= D HTF h HTF x dx D 2 2 E PCM E PCM [ J ]= D 2 [ J ]= D 2 1 PCM 0 h PCM 1 PCM 0 h PCM x dx D 2 x dx D 2 HTF cp HTF x=0 HTF cp HTF x=0 1 PCM T HTF x x T HTF x x x=0 1 PCM x=0 h PCM x x h PCM x x Note that the temperature and enthalpy functions only depend on the axial coordinate and not the radial coordinate -assumption of uniform temperature for the same section-. That is why the integral is done only in the axial direction. The energy balance for the charging period states: Q Fuel,ch =Q Product,ch Q oss, ch And the energetic efficiency: en,ch = Q Product, ch Q Fuel,ch In our case, the assumption of null thermal losses will lead to an energetic efficiency equal to one. The results of this analysis are presented together with those from storage and discharging period at the end of this section.

5 7.1.2 Exergetic analysis of the charge process Fuel=Net exergy provided by steam=incoming exergy-outgoing exergy Ex Fuel, ch [ J ]=Ex a Ex b = H a H b T 0 S a S b where S a S b [ J / K ]= ṁ HTF [s a t s b t ]dt ṁ HTF [ s a t s b t ] t The reader is reminded that and refer here to the tial and al states of the charging period, respectively. t= Product=Exergy change of the packed bed=exergy at al state of charging period Exergy at tial state of charging period = E HTF where S HTF E HTF Ex Product, ch [ J ]= Ex PB = Ex HTF Ex PCM = T 0 S HTF [ J / K ]= D 2 S HTF HTF 0 s HTF E PCM E PCM x dx D 2 S HTF [ J / K ]= D HTF s HTF x dx D 2 2 T 0 S PCM HTF x=0 S PCM HTF x=0 s HTF x x s HTF x x S PCM S PCM [ J / K ]= D 2 [ J / K ]= D 2 1 PCM 0 s PCM 1 PCM 0 s PCM x dx D 2 x dx D 2 1 PCM x=0 1 PCM x=0 s PCM x x s PCM x x Exergy balance for the storing period: Ex Fuel, ch =Ex Product,ch Ex oss, ch Ex Cons,ch Since exergy losses are supposed to be null, the exergy consumption can be calculated directly from this balance. Exergetic efficiency: ex,ch = Ex Product,ch Ex Fuel, ch

6 7.2 Thermodynamic analysis of the storage process Different storing times were analyzed in order to determine the time necessary for the system to reach a stable temperature profile, which was found to be of approximately 15 minutes. A storing time of one hour has been chosen in order to guarantee that the system reaches its permanent state. Figure 26.- Steam temperature inside the PCM packed bed at tial -0s- and al states -3600s- of the storing period. It is important to remark here that temperature changes inside the packed bed during the storage period are mainly driven by temperature differences between PCM and steam at a given section and not so much by temperature differences between subsequent sections. Hence, the temperature profile does not tend to flatten as it would happen in a molten salt tank for example. This fact can be seen as an important advantage of packed beds in comparison to the traditional two-tank storage. Due to the lower temperature differences inside the packed bed when a sensible heat storage material is used, the temperature distribution inside the packed bed barely varies after one hour. As it can be seen in the following figure, both lines overlap: Figure 27.- Steam temperature inside the sensible heat packed bed at tial -0s- and al states -3600s- of the storing period.

7 7.2.1 Energetic analysis of the storage process Fuel=Product from previous period=energy accumulation during charging period Q Fuel,sto [ J ]=Q Product,ch = E PB, ch Product=Energy accumulation during charging and storing= Enthalpy change of the packed bed during charging and storing Q Product, sto [ J ]= E PB, ch E PB, sto Where E PB, sto = E HTF E PCM = E HTF E HTF E PCM E PCM Where and refer now to the tial and al states of the storing period. The energy balance for the storing period states: Q Fuel,sto =Q Product, sto Q oss, sto And the energetic efficiency: en, sto = Q Product, sto Q Fuel, sto Once again, the assumption of null thermal losses to the environment results into an energetic efficiency equal to one.

8 7.2.2 Exergetic analysis of the storage process Fuel=Product from previous period = Exergy accumulation during charging period Ex Fuel, sto [ J ]=Ex Product,ch = Ex PB,ch Product=Exergy accumulation during charging and storing Ex Product, sto [ J ]= Ex PB, ch Ex PB, sto Where = E HTF E HTF Ex PB, sto = Ex PB = Ex HTF Ex PCM = T 0 S HTF S HTF E PCM E PCM T 0 S PCM S PCM Where and refer now to the tial and al state of the storing period. The exergy balance for the storing period states: Ex Fuel, sto =Ex Product, sto Ex oss, sto Ex Cons, sto Where exergy losses to the environment are supposed to be null. And the exergetic efficiency: ex, sto = Ex Product, sto Ex Fuel, sto

9 7.3 Thermodynamic analysis of the discharge process The same way it happened for charging, discharging process in the PCM packed bed has to be stopped too soon because of the constraints imposed to the steam outlet temperature. Figure 28.- Temperature evolution inside the packed bed between tial -0s- and al -70s- states of discharging. Figure 29.- Inlet -blue- and outlet -red- steam temperature during discharging of the PCM packed bed

10 The temperature evolution inside the packed bed between tial -0s- and al -4020s-states of discharging is represented in the following figure. Steam in blue and PCM in green. Figure 30.- Temperature evolution inside the packed bed between tial -0s- and al -70s- states of discharging. Figure 31.- Inlet -blue- and outlet -red- steam temperature during charging.

11 7.3.1 Energetic analysis of the discharge process Fuel=Product from previous period=energy accumulation during charging and storing Q Fuel,dch =Q Product,sto [ J ]= E PB,ch E PB, sto Product=Net heat recuperated by steam=outgoing heat-incoming heat Q Product,dch [ J ]= H d H c = ṁhtf [h d t h c t ]dt ṁ HTF cp HTF [T d t T c t ] t t = Where and refer now to the al and tial states of the discharging period. The energy balance for the discharging period states: Q Fuel,dch =Q Product,dch Q oss,dch And the energetic efficiency: en,dch = Q Product, dch Q Fuel,dch

12 7.3.2 Exergetic analysis of the discharge process Fuel=Product from previous period=exergy accumulation during charging and storing Ex Fuel, dch =Ex Product, sto [ J ]= Ex PB, ch Ex PB, sto Product=Net exergy recuperated by steam=outgoing exergy-incoming exergy Ex Product, dch [ J ]=Ex d Ex c = H d H c T 0 S d S c where S d S c [ J / K ]= ṁhtf [ s d t s c t ]dt ṁ HTF [ s d t s c t ] t Exergy balance for discharging period: t = Ex Fuel, dch =Ex Product, dch Ex oss, dch Ex Cons, dch Exergetic efficiency for discharging period: ex,dch = Ex Product,dch Ex Fuel, dch

13 7.4 Thermodynamic analysis of the overall storage process We will now make use of the temperature profiles corresponding to the end of charge -blue- and end of discharge -red-, in order to compare the overall performance of latent vs. sensible heat packed bed. Figure 32.- Evolution of the temperature profile during several subsequent cycles. atent heat storage (left) and sensible heat storage (right). If we focus on the fifth cycle, the energy contained in the deposit at the end of the charging period corresponds to the area below the blue curve #5. On the other hand, the energy contained in the deposit after the discharge is represented by the area below red curve #5. Therefore, the amount of stored energy during charge #5 can be calculated as: Q sto # 5=area below blue curve # 5 area below red curve # 4 Whereas the energy recovered during discharge #5 is: Q recov #5=area below blue curve # 5 area below red curve #5 ooking at both graphs, it is easy to see that the energetic efficiency deed as en,overall = Q recov Q sto energy stored is being recovered. will have rather high values, which tells us that a big amount of the

14 The charge capacity factor, deed as the ratio between Q sto and the total capacity of the deposit, can be seen as: F cap, ch = Q sto areabelow blue curve #5 area below red curve # 4 = Q tot total area refers to the square enclosed by [T min, T max ] and [ x min, x max ]., where the total area The discharge or overall capacity factor is deed analogously: F cap, overall F cap = Q recov areabelow blue curve #5 area below red curve #5 = =F Q tot total area cap, ch en, overall Opposed to en, F cap will have very low values, especially in the case of latent heat storage due to the proximity of blue and red lines. In the case of sensible heat storage, F cap will reach higher values, although still improvable. The understanding and improvement of the overall process via graphic methods is further developed in the "Results and conclusions" subsection number 7.5.

15 7.4.1 Energetic analysis of the overall process Fuel=Net heat provided by steam during charging period Q Fuel,overall [ J ]=Q Fuel,ch =H a H b = ṁhtf [h a t h b t ] dt ṁ HTF cp HTF [T a t T b t ] t Subscripts and refer here to the charging period. t= Product=Net heat recovered by steam during discharging period. Q Product,overall [ J ]=Q Product, dch =H d H c = ṁhtf [h d t h c t ]dt ṁ HTF cp HTF [T d t T c t ] t t = Subscripts referred to the discharging period. Overall energy balance: Q Fuel,overall =Q Product, overall Q oss, overall Where Q oss, overall =Q oss, ch Q oss,sto Q oss, dch =Q oss,dch Overall energetic efficiency: en,overall = en, ch en, sto en, dch = Q Product,dch Q Fuel,ch

16 7.4.2 Exergetic analysis of the overall process Fuel=Net exergy provided by steam during charging period Ex Fuel, ch [ J ]=Ex a Ex b = H a H b T 0 S a S b where S a S b [ J / K ]= ṁ HTF [s a t s b t ]dt ṁ HTF [ s a t s b t ] t t= Subscripts and refer here to the charging period. Product=Net exergy recovered by steam during discharging period. Ex Product, dch [ J ]=Ex d Ex c = H d H c T 0 S d S c where S d S c [ J / K ]= ṁhtf [ s d t s c t ]dt ṁ HTF [ s d t s c t ] t Subscripts referred to the discharging period. t = Overall exergy balance Ex Fuel, overall =Ex Product, overall Ex oss,overall Ex Cons, overall During the first cycles, only the addition Ex oss,overall Ex can be calculated from Cons, overall the overall exergy balance. Eventually, Q oss, overall =0 Ex oss, overall =0 and so the value of can be obtained from the same balance. Ex Cons, overall Overall exergetic efficiency: ex,overall = ex, ch ex, sto ex,dch = Ex Product,dch Ex Fuel, ch

17 7.5 atent vs. sensible heat storage system. Results and Conclusions The results obtained from the thermodynamic calculations previously described are summarized in the following tables. atent heat Q F [MWh] Q P [ MWh] en Ex F [ MWh] Ex P [MWh] ex Charge Storage Discharge Overall Overall capacity factor=0.70/121= Sensible heat Q F [MWh] Q P [ MWh] en Ex F [ MWh] Ex P [MWh] ex Charge Storage Discharge Overall Overall capacity factor=45.76/121=0.378 The results have made clear the fact that the sensible heat storage system studied suits better the superheating module than the one based on latent heat. Namely, the shape of the temperature profile on the sensible heat storage fits better the constraints imposed to the outlet temperature of steam so the charge and discharge do not need to be stopped so prematurely. This leads to higher energetic efficiency and capacity factor and also to smaller exergy losses -in the form of stored energy which cannot be recovered-. Moreover, the sensible heat case presents smaller temperature differences between PCM and steam, so the exergy consumption associated to them is reduced. However discouraging these results might be regarding the use of PCMs, it must be pointed out that that the conclusions here drawn refer exclusively to the two specific cases studied so it would be speculative to extrapolate them to latent vs. sensible storage systems in general. In order to achieve more general results, it would be interesting to further study the performance of a latent heat packed bed via a parametric analysis on the melting temperature and latent heat, which will probably be the most critical parameters affecting the temperature distribution inside the packed bed.

18 7.6 atent heat storage. The optimal shape of the temperature profile Finally, now that the overall process of storage has been studied it is possible to draw some conclusions about the optimal evolution of the temperature inside the packed bed. Continuing with the analysis of the temperature profile and its influence on the overall performance of the system, it seems clear that the maximum stored and recovered energy would be achieved by a packed bed which would present a temperature profile in the following shape: Figure 33.- Optimal temperature profiles inside a packed bed (theoretical) In this ideal packed bed, the charge is performed in such a way that hot steam releases all its energy at the front section, melting it and rising its temperature up to the inlet temperature -500ºC-. After this, steam temperature decreases sharply with axial position, quickly reaching the outlet temperature of 310ºC.

19 This charging process could be seen as one made "section-by-section" i.e. one where the first cold section encountered by steam is heated up absorbing all of its energy, without transferring any of it to the subsequent cold section. This equals to an tely high convective coefficient and a null thermal axial conductivity inside the packed bed. Figure 34.- Optimal charge process (theoretical) The discharge process would take place in an analog way, also equivalent to a heat transfer process dominated by very high convection and presenting a negligibly low conduction. Figure 35.- Optimal discharge process (theoretical) These optimal profiles will be the target to be met when different PCMs will be tested in the parametric analysis.