Thermocline stability criterions in single-tanks of molten salt thermal energy storage

Applied Energy 97 (2012) 816–821

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Thermocline stability criterions in single-tanks of molten salt thermal energy storage Frank G.F. Qin a,⇑, Xiaoping Yang b, Zhan Ding a, Yuanzhi Zuo a, Youyan Shao a, Runhua Jiang a, Xiaoxi Yang a a b

Key Laboratory of Distributed Energy Systems of Dongdong Province, Dongguan University of Technology, Dongguan 523808, China South China University of Technology, Guangzhou 510640, China

a r t i c l e

i n f o

Article history: Received 25 July 2011 Received in revised form 16 February 2012 Accepted 19 February 2012 Available online 17 March 2012 Keywords: Molten salt Thermal energy storage Thermocline Stability criterions Solar energy

a b s t r a c t Thermal storage with molten salt is considered to be an important subsystem for solar thermal power stations due to the fluctuation of sunshine over time. A molten salt thermal storage tank, in which the fluid is stratified in temperature with ‘‘hot’’ on the upper level and ‘‘cold’’ in the lower level due to the density difference of the fluids (Criterion 1), is preferred for the system efficiency. Porous media, such as quartzite rock or silica sand, are used to fill the tank in order to reduce the inventory of the molten salt and manage the mixing between the hot and cold molten salt, so as to form a stable layer of thermocline. However, in the flow of molten salt, either the hot fluid displaces the cold one or vice versa, phenomena of viscous fingering and/or channeling are likely to occur, which may disturb the stability of the thermocline, resulting in an over widened temperature transitional zone. To circumvent the problems, criterions are proposed in this work based on the analysis of Darcy’s flow in porous medium, i.e. Criterion 2, when hot molten salt displaces cold molten salt, the flow velocity must be under the critical value (vc); Criterion 3, when cold molten salt displaces hot molten salt from the top down, though this is unusual, the flow velocity must exceed a critical value (wc); and Criterion 4, in the thermocline region, if the mobility ratio is less than 1, displacement is stable, otherwise it is unstable. Criterion 1 concerns the hydrostatics factor, i.e. density and gravity. Criterion 2–4, however, takes hydrodynamics into consideration as well, which involve velocity, density and viscosity of the fluid, and porosity and permeability of the porous medium. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Thermal energy storage (TES) has been proved an important sub-system for the solar energy generation systems (SEGSs) because it considerably increased the SEGS performance. This distinguishes the solar thermal power plants from the conventional fossil fuel thermal power plants. A well designed, operated and managed molten salt TES system for SEGS achieves several goals: (1) To release energy for electricity generation after sunset for several hours to meet the power consumption peak without the fossil fuel backup, and make the SEGS more independent of the weather fluctuations over time so that it increases the efficient annual usage of sunlight. (2) To generate higher temperature steam, e.g. over 450 °C, for turbines so that it raise the Rankine cycle efficiency up to 40%. In comparison, the expensive high-temperature oils generate steam around 390 °C, which gives only 37% Rankine cycle efficiency, as shown in Fig. 1. ⇑ Corresponding author. Tel.: +86 0769 22862619; fax: +86 0769 22861808. E-mail address: [email protected] (F.G.F. Qin). 0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2012.02.048

(3) To improve the system performance and economic index, such as reduce the levelized electricity cost, for the SEGS due to the above two points. Two types of TES system, in which molten salt was used as the heat transfer fluid (HTF) and also served as the energy storage medium (ESM), have been investigated at Sandia National Laboratories for large scale SEGS application. One of them is the so called two-tank molten salt thermal storage. It was also successfully used for parabolic trough solar plants and tower solar plants as well [1– 4]. Though the two-tank TES system was found to substantially benefit the performance of the SEGS plant and made it operate much more economically, the system investment cost was up to $24/kW ht [5,6]. To cut costs, the single-tank molten salt TES, in which porous fillers, such as a mixture of quartzite rock and silica sand, was used as a packed bed in the tank to reduce the molten salt inventory, was then investigated. A single tank TES used thermocline to separate the hot and cold fluids [7]. It was estimated the single tank TES system can save 35% of investment cost compared to a two-tank storage system [8–11]. A critical aspect that determines the performance of a singletank TES is the thermocline thickness and its stability. Energy

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Nomenclature ds g H K M P T v w

particle diameter, m gravity acceleration constant, ms2 height of the TES tank, m permeability, m2 K =l mobility ratio, M ¼ K 21 =l2 1 pressure, Pa temperature, K velocity of hot molten salt displacing cold one, ms1 velocity of cold molten salt displacing hot one, ms1

Greek

 g u

porosity discharging efficiency stratification efficiency

stored in the tank with molten salt and filler materials may not be fully retrieved in the discharging phase. Mixing of the hot and cold molten salt fluids broadens the thickness of the thermocline and reduces the useful amount of the hot fluid, with which the discharging molten salt must be above a certain temperature to generate superheated steam. Zhen et al. proposed to use discharge efficiency, g, to characterize the single-tank performance, which was defined as [12]:

g¼

Output energy with Hl > H0 Total energy initially stored in the thermocline tank

ðaÞ

where Hl is the a threshold value determined by the application of interest. A value of 0.95 for H0 was chosen for the calculation/simulation in their work, implying that thermal energy delivered at temperatures greater than a certain value is qualified as useful energy. They found that the discharge efficiency varies depending on the height of the tank (H) and the Reynolds number (Re), and could be expressed as

g ¼ 1  0:1807Re0:1801 ðH=100Þm

ðbÞ

where m = 0.00234Re0.6151 + 0.00055Re0.485. On the other hand, the thermocline thickness in the mixing zone of the hot and cold molten salt is a measure of the charge/discharge efficiency of the single-tank TES system. Mixing or de-stratification of the two HTFs always results in entropy generation, in other words the internal exergy loss of the TES system. Therefore, exergy loss can be used as a measure of the ability of the TES. Haller et al. proposed to use stratification efficiency, u, to depict this process [13]. It can be written as:

l q n

viscosity, Pa s density, kg m3 exergy, kJ kg1

Subscript 1 2 c l exp irr mix int

and superscript molten salt located below the thermocline molten salt located above the thermocline critical velocity liquid experiment irreversible mixing internal

u¼

Exergy loss of fully mixing  actual Exergy loss Exergy loss of fully mixing

¼1

Dnexp irr;int

ðcÞ

Dnmix irr;int

where Dnexp irr;int is the actual exergy loss in the experiment/operation. Dnmix is the exergy loss when the two fluids are fully mixed. u = 0 irr;int represents a fully mixing state and u = 1 represents an ideal stratification of the two HTFs with different temperatures. Beside the above two ‘‘technical’’ analysis, a mathematical analysis, TOPSIS, for better operation and management of SEGS was proposed by Cavollaro, in which fuzzy multi-critical method is used to compare different heat transfer fluids (HTFs) in order to investigate the feasibility of utilizing a molten salt [14]. In recent decades, studies on the phenomenon of fluids mixing in porous media revealed an important mechanism: viscous fingering [15–17]. There is justification to believe that the viscous fingering also plays an important role in the formation or destruction of thermocline between the hot and cold HTF in the single-tank TES system. However up to now we still lack of information about how or when the viscous fingers occur in a single-tank thermocline molten salt TES, in which filler material is used to form a packed bed inside. To the best of authors’ knowledge there is no thermocline stability criterion for single-tank TES has been studied or reported yet. In this paper several thermocline stability criterions were proposed from preliminary results of the analysis for the thermocline stability. 2. Problems with thermocline stability In the flow of molten salt, either the hot fluid displaces the cold one or vice versa, the phenomena of channeling and viscous

hot fluid

cold fluid

Fig. 1. Live steam temperature vs Rankine cycle efficiency.

Fig. 2. Schematic diagram of the viscous fingering in porous medium when hot molten salt displace cold molten salt.

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fingering are likely to occur, which may disturb the stability of the thermocline, resulting in a over widened temperature transition zone. Viscous fingering is the formation of patterns in a morphologically unstable interface between two fluids in a porous medium [18,19]. Fig. 2 illustrates this phenomenon, where a hot fluid is displacing a cold one from the top down. The phenomenon has been widely observed and reported either for miscible fluids or nonmiscible fluids. In fact the majority of liquids mixing in porous media involves or starts with viscous fingering. Flow channeling typically contains a single stream or several interconnecting streams, producing a braided flow pattern, as shown in Fig. 3. The scope of viscous fingering/channeling are both developing from small to large. When this happens in a molten salt TES tank, it can destroy the thermocline, resulting in undesirable mixing, which is the main reason for the entropy generation or internal exergy loss concerned with in Ref. [13]. To understand the conditions of maintaining a stable thermocline is vitally important for TES tanks.

hot molten salt

H

ρ

B

A

D

cold molten salt I

During the operation of charging a TES tank, the hot molten salt is charged in from the top inlet of the tank. When the hot molten salt displaces the cold one in the porous medium of the tank, viscous fingering is likely to occur as mentioned above. Suppose that the interface between hot and cold, A B C D E, as shown in Fig. 4, has a local random disturbance to form a small bulge B C D. The two lines F C G and H B I are both perpendicular to the interface. Because the hot molten salt is less viscous than the cold one, i.e. l2 < l1, the flow resistance along F C G will be less than that of H B I, resulting in a further development of the bulge B C D, which eventually produces a extended finger tip of the hot molten salt into the cold one, which is shown as the dot line in Fig. 4. The thermocline is unstable. On the other hand, however, gravity is a stabilizing factor that tends to keep the interface horizontal due to the density difference of the two fluids. Therefore, from the consideration of these two factors: viscosity and density, the process of the hot molten salt displacing the cold one downwards may be stable or unstable depending on which of the two factors is predominant.

ρ

G

μ

Fig. 4. Schematic diagram of the development of the viscous fingering.

hot molten salt

ρ2, μ2

A

δx

v

C cold molten salt

3.1. Thermocline stability Criterion I

3.2. Thermocline stability Criterion II

E

v

C

3. Stability criterions

Hydrostatically, it is obvious that under the gravity field on the earth, a hot fluid, which is normally lighter, sitting on a cold one, is a more stable configuration than vice versa. It is the gravity that makes this the prime criterion for the stability of the thermocline of thermal storage tanks.

μ

ρ

μ

Fig. 5. Pressure analysis in front of the bulge.

A further analysis can be given in this way, the hot molten salt of viscosity l2 and density q2 displaces a cold molten salt of viscosity l1 and density q1 by downward flow (Fig. 5) with the flow velocity = v. Suppose that a shallow depression C, of depth dx, develops in the horizontal interface A B. Let:

P0 ¼ pressure at the level AB; P1 ¼ pressure just below C; P2 ¼ pressure just above C; The depression will finally disappear if P1 > P2, but it will increase in depth if P2 > P1. According to Darcy’s law,

P1 ¼ P0 þ g q1 dx  P2 ¼ P0 þ g q2 dx 

l1 v dx

ð1Þ

K

l2 v dx

ð2Þ

K

where K is the permeability of the porous medium in the tank, and g is the gravity acceleration. The condition for stable flow is therefore expressed as:

P1  P2 ¼ gðq1  q2 Þdx 

v ðl1  l2 Þ K

dx > 0

ð3Þ

This gives:

gðq1  q2 Þ >

v ðl1  l2 Þ K

ð4Þ

That is:

v < gK 

Fig. 3. A typical two dimensional water channeling phenomenon found on ground surface.

q1  q2 l1  l2

ð5Þ

Apart from K all of the quantities in this expression are known. q2 K must be determined experimentally. gK  lq1  will be termed as 1 l2 the critical velocity, vc:

F.G.F. Qin et al. / Applied Energy 97 (2012) 816–821

v c ¼ gK 

q1  q2 l1  l2

ð6Þ

If q1 > q2 and l1 > l2, which is the case of hot molten salt displacing cold one in a downward flow (charging), the flow is stable if v is lower than the critical value, vc. 3.3. Thermocline stability Criterion III During the operation of discharging, the hot molten salt is withdrawn out of the tank from the top inlet, while cold molten salt is fed back into the tank at the lower inlet, resulting in an upward flow in the tank. An analysis of the situation is shown in Fig. 6, where the condition of stable flow is opposite to the operation of charging, which is formulated as:

p1 ¼ p0  g q1 dx 

p2 ¼ p0  g q2 dx 

l1 wdx

ð7Þ

K

l2 wdx

ð8Þ

K

p1  q2 ¼ gðq1  q2 Þdx 

wðl1  l2 Þ dx < 0 K

ð9Þ

This gives:

gðq1  q2 Þ <

wðl1  l2 Þ K

ð10Þ

or:

w > gK 

q1  q2 l1  l2

ð11Þ

Since q1 > q2 and l1 > l2, the value of the right-hand side of in Eq. (11) is negative. Since a discharging flow is normally bottomup, giving a positive flow velocity, so that it always complies with in Eq. (11). The thermocline interface is stable. There is no velocity limit in this case if only the flow current is upward. However, in a situation when the cold molten salt is introduced into the tank from the top inlet (rather than the lower inlet) to displace the hot molten salt in a downward flow, though this is unusual, now q2 > q1, and l2 > l1, the flow is stable if (and only if) the velocity exceeds the critical value:

w > wc ¼ gK 

q2  q1 l2  l1

ð12Þ

That is to say the conditions that yield stable downward flow of hot displacing cold cause unstable downward flow of cold displacing hot, and vice versa. Note also that laboratory experiments designed to test these must be done at the correct linear velocity.

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3.4. Thermocline stability Criterion IV The hot and cold molten salts are miscible flow currents. When one displaces another in a porous medium, viscous fingering takes place when the viscous force of a displacing phase has greater momentum than that of the displaced phase. An important criterion for a stable front of displacement is that the mobility ratio M < 1 [18]. M is defined as:

M¼

K 2 =l2 K 1 =l1

ð13Þ

where l2 and l1 are the viscosities of the displacing and displaced fluid, K2 and K1 are permeability of the porous medium of the displacing and the displaced fluid, respectively. Viscous fingers often occur when a less viscous liquid displaces a more viscous one, i.e. in the condition of l2 < l1. Therefore, the thermocline is intrinsically unstable when charging the TES tank, and viscous fingering is more likely to occur during the charging phase in a TES system, where the displacing fluid is the hot molten salt and the displaced fluid is the cold molten salt. In a uniform porous medium, where the permeability is supposed to be the same everywhere, i.e. K1 = K2. Permeability depends on the equivalent diameter of the filler materials and the porosity of the packed bed. Since l2 < l1 when charging the TES tank, mobility ratio, M, would be greater than 1. The displacement tends to be unstable. Therefore, the Criterion II, i.e. Eq. (6), indicates that the downward flow velocity must be lower than the critical velocity, vc, implying that during the charging phase when hot HTF displaces cold, the interstitial velocity of the HTF must be controlled under the critical value to avoid viscous fingering. To surpass this velocity limit, a possible strategy is to form a porosity gradient packed bed with lower permeability in the upper level and higher permeability in the lower level, leading to a result that K2 is greater enough than K1, resulting in M < 1. In this way the downward flow of hot molten salt displacing cold would be able to break the threshold of the criterion velocity, vc, given by Eq. (6). 4. Preliminary calculations and discussion 4.1. Critical velocity of hot molten salt displacing cold Owing to lack of exact data and difficulties of the experiment under such a harsh condition for molten salt, the critical velocities could only be roughly estimated at the current state. The reported molten salts used in the solar-two project and other SEGS plants are nitrate salts and eutectic salts [5,8]. The physical properties of the molten salt HITEC varying with temperature are given by the following formulas [12]:

q ¼ 1938:0  0:732ðT l  200:0Þ

ð14Þ

l ¼ exp½4:343  2:0143ðln T l  5:011Þ

ð15Þ

hot molten salt

ρ

w

μ

C

δx

A

B

cold molten salt

ρ

μ

Fig. 6. Pressure analysis in front of the bulge for upward flow.

Table 1 lists the properties of the several salts and eutectic salts. In this paper the simulating calculation uses quartzite rock and silica sand as filler materials in the TES tank. Sandia National Laboratories, US, has tested a number of mineral matters for their compatibility with nitrate salts as potential filler materials in TES tanks. Therefore the preliminary calculations in this paper use quartzite rock and silica sand as filler materials. Their physical properties are listed in Table 2. The permeability of the packed bed can also be estimated by the Kozeny–Carman equation in terms of the effective/equivalent diameter, ds, of the filler material [9,20,21]:

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Table 1 Composition, density and viscosity of molten salts. Solar salt

HITEC

HITEC XL

Composition

NaNO3 KNO3 NaNO2 Ca(NO3)2

60% 40%

7 53 40

7 45

Density, q (kg m3)

@300 °C, q1 @400 °C, q2

1899 1843

1640 1592

1992 1934

Viscosity, l (Pa s)

@300 °C, l1 @400 °C, l2

3.26  103 1.84  103

3.16  103 1.78  103

6.37  103 3.59  103

48

Table 2 Filler materials physical properties.

6. Conclusion

 (%)

ds (m) Quartzite rock Silica sand 2:1 mixture of Qr and Ss Note: The data of ds and Ss = Silica sand.

0.05 0.005 0.035

25 26 22

 are obtained from Refs.

K (m2) 7

3.97  10 4.59  109 1.23  107

[1,2,5,12]. Qr = Quartzite rock,

Table 3 The critical velocity when displacement is from the top down. Critical velocity*,

Quartzite rock Silica sand 2:1 mixture Qr and Ss

vc and wc (ms1)

Solar salt

HITEC

HITEC XL

0.15336 0.00177 0.04735

0.13373 0.00155 0.04129

0.08114 0.00094 0.02505

*

Note: (1) when hot molten salt displaces cold molten salt, the velocity must be lower than vc; when cold molten salt displaces hot molten salt, the velocity must be greater than wc. (2) Qr = quartzite rock, Ss = Silica sand.

2

K¼

ds e3 175ð1  eÞ2

ð16Þ

where ds is the particle diameter,  the porosity of the packed bed, and K the permeability of the porous packed bed. During charging phase, based on the Eq. (6), the critical flow velocity, which is the maximum interstitial velocity without inducing viscous fingering, is presented in Table 3.

Stability of the thermocline plays an important role in the maintenance of the stratification of hot and cold molten salt in a singletank TES system. Viscous fingering developed in the interfacial region broadens the thickness of the thermocline and cause mixing of the hot and cold molten salt, which is the main reason for entropy generation or internal exergy loss of the thermal storage tank. However, it can be prevented under certain hydrostatics and hydrodynamics conditions in a porous medium. Four thermocline stability criterions are proposed in this paper. Criterion I—hot molten salt with less density must sit on top of the cold molten salt allowing a stable hydrostatic state. Criterion II—when hot molten salt is displacing cold from the top down in charging a TES tank, the interstitial flow velocity must be less than the critical velocity to prevent viscous fingering. Criterion III—when cold molten salt is displacing hot from the bottom up in the discharging phase, there is no interstitial flow velocity limit. Whereas when cold molten salt is displacing hot from the top down, the interstitial flow velocity must exceed the critical velocity. Criterion VI—the mobility ratio in charging the TES tank is naturally greater than 1. So the thermocline is intrinsically unstable. The interstitial flow velocity must be controlled to be below the critical velocity given by Criterion II unless the displacement is done under a gradient porosity packed bed. The mobility ratio is less than 1 in discharging the TES tank. So the displacement of cold to hot from the bottom up is intrinsically stable. There is no interstitial flow velocity limit unless the displacement is from the top down.

4.2. Critical velocity of cold molten salt displacing hot As mentioned above the velocity of cold molten salt displacing hot would not have a critical threshold if it is a rising flow. However, if this displacement is from the top down, though this is unusual, a critical velocity, wc, exists given by Eq. (12). The interstitial velocity of the molten salt must exceed wc to form a stable thermocline (Table 3).

Acknowledgements This research was supported by 973 program (2010CB227306) of China, and the key laboratory project (2009A060800022) of Guangdong Province, China. The authors appreciate the help from Miss Jenni Qin in finalizing this article. References

5. Discussion The Reynolds number in the flow of hot molten salt displacing cold from the top down in TES tanks in current large scale SEGS, according to the technical report of Sandia National Laboratories, is in the magnitude of 200–300, giving a interstitial flow velocity about 0.012–0.017 ms1 [5,12]. This is under the critical velocity calculated in this work, which is 0.025 ms1 (Table 3), if a mixture of quartzite rock and silica sand is used as filler materials. Therefore the viscous fingering/channeling can well be prohibited.

[1] Pacheco JE, Showalter SK, Kolb WJ. Development of a molten-salt thermocline thermal storage system for parabolic trough plants. J Sol Energy Eng 2002;124:153–9. [2] Brosseau Doug A, Hlava Paul F, Kelly MJ. Testing thermocline filler materials and molten-salt heat transfer fluids for thermal energy storage systems used in parabolic trough solar power plants. US: Sandia National Laboratories; 2004. p. 95. [3] Dersch Jurgen et al. Trough integration into power plants—a study on the performance and economy of integrated solar combined cycle systems. Energy 2004;29:947–59. [4] Herrmann Ulf, Kelly Bruce, Price H. Two-tank molten salt storage for parabolic trough solar power plants. Energy 2004;29:883–93.

F.G.F. Qin et al. / Applied Energy 97 (2012) 816–821 [5] Kelly BD. Advanced thermal storage for central receivers with supercritical coolants. US: Abengoa Solar Inc.; 2010. June 15, p. 184. [6] Peng Qiang et al. The preparation and properties of multi-component molten salts. Appl Energy 2010;87(9):2812–7. [7] Flueckiger Scott, Yang Zhen, Garimella Suresh V. An integrated thermal and mechanical investigation of molten-salt thermocline energy storage. Appl Energy 2011;88(6):2098–105. [8] Kearney D et al. Assessment of a molten salt heat transfer fluid in a parabolic trough solar field. J Sol Energy Eng 2003;125:170–6. [9] Yang Zhen, Garimella SV. Molten-salt thermal energy storage in thermoclines under different environmental boundary conditions. Appl Energy 2010;87:3322–9. [10] Price H. A Parabolic Trough Solar Power Plant Simulation Model. . [11] Kearney DW. Engineering evaluation of a molten salt HTF in a parabolic trough solar field. . [12] Yang Zhen, Garimella SV. Thermal analysis of solar thermal energy storage in a molten-salt thermocline. Sol Energy 2010;84. [13] Haller Michel Y et al. Methods to determine stratification efficiency of thermal energy storage processes – Review and theoretical comparison. Sol Energy 2009;83:1847–60.

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[14] Cavallaro Fausto. Fuzzy TOPSIS approach for assessing thermal-energy storage in concentrated solar power (CSP) systems. Appl Energy 2010;87(2):496–503. [15] Ghesmat Karim, Azaiez Jalel. Effect of medium dispersivity on the viscous fingering instability in porous media. In: 21st International symposium on high performance computing systems and applications [1550-5243]. IEEE Computer Society: Ghesmat; 2007. [16] Coskuner Gokhan. Onset of viscous fingering for miscible liquid–liquid displacements in porous media. Trans Porous Med 1993;10:285–91. [17] Vitovskii OV, Kuznetsov VV, Nakoryakov VE. Stability of the displacement front and development of ‘‘fingering’’ in a porous medium. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5; September–October, 1989. p. 101–106. [Original article submitted August 31, 1988, 1990]. [18] Sahimi M. Flow and transport in porous media and fractured rock: from classical methods to modern approaches. Weinheim: VCH Verlagsgesellschaft mbH; 1995. [19] Homsy GM. Viscous fingering in porous media. Annu Rev 1987;19:271–311. [20] Beckermann C, Viskanta R. Natural convection solid/liquid phase change in porous media. Int J Heat Mass Transfer 1988;31(1):35–46. [21] Saghir MZ, Chaalal O, Islam MR. Numerical and experimental modeling of viscous fingering during liquid–liquid miscible displacement. J Petrol Sci Eng 2000;26:253–62.