Estimation of filling time for compressed hydrogen refueling

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Energy Procedia 158 Energy Procedia 00(2019) (2017)1897–1903 000–000 www.elsevier.com/locate/procedia

10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China

Estimation of filling time for compressed hydrogen refueling Estimation of filling time for compressed hydrogen refueling The 15th International Symposium on District Heating and Cooling

a

Xin Zhouaa, Tianqi Yangaa, Jinsheng Xiaoa,b, *, Pierre Bénardbb, Richard Chahinebb a,b, Xin Zhou , Tianqi , Jinshengof Xiao *, Pierre Bénard , Richard Chahine Assessing theYang feasibility using the heat demand-outdoor

Hubei Key Laboratory of Advanced Technology for Automotive Components and Hubei Collaborative Innovation Center for Automotive

Components School of Automotive Engineering, Wuhanand University of Technology, Hubei 430070, Hubei Key LaboratoryTechnology, of Advanced Technology for Automotive Components Hubei Collaborative CenterChina for Automotive temperature function for a long-term district heatInnovation demand forecast Hydrogen Research Institute, Université du Québec à Trois-Rivières, QC G9A5H7,Hubei Canada Components Technology, School of Automotive Engineering, Wuhan University of Technology, 430070, China a

b b

Hydrogen Research Institute, Université du Québec à Trois-Rivières, QC G9A5H7, Canada

I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc

Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche & Innovation, Daniel, Limay, hydrogen France In order to cfacilitate the application of hydrogen energy291 andAvenue ensureDreyfous its safety, the 78520 compressed storage tank on board Département Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France In order facilitate the application energy andtoensure its safety, the compressed storage tank on on board needs to betofull of hydrogen gas withinof3 hydrogen minutes. Therefore, meet this requirement, the effectshydrogen of refueling parameters the needs to be full of hydrogen gas within 3 minutes. Therefore, to meet this requirement, the effects of refueling parameters on the filling time need to be investigated urgently. For the purpose of solving this issue, a novel analytical solution of filling time is filling time needa to be investigated purpose of solving a novel analytical of dimensionless filling time is obtained from lumped parameter urgently. model inFor thisthepaper. According to this the issue, equation of state for realsolution gas and obtained fromand a Re lumped model in thisbetween paper. According to theand equation of stateparameters for real gas dimensionless numbers Nu , the parameter function relationships the filling time the refueling areand presented. These Abstract and Reinitial , thetemperature, function relationships between thetemperature, filling time final and temperature the refuelingand parameters are presented. These numbers Nuinclude parameters initial pressure, inflow final pressure. These equations parameters initial temperature, initial of pressure, temperature, finalThen, temperature andoffinal pressure. Theseare equations are used to include fit the reference data, the results fitting inflow show good agreement. the values fitting parameters further District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the are usedsotoasfittothe reference data, of thethese results of fitting good Then, the values of fitting parameters aretime further utilized verify the validity formulas. Weshow believe thisagreement. study can contribute to control the hydrogen filling and greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat utilized so safety as to verify validity these formulas. We believe this study can contribute to control the hydrogen filling time and ensure the duringthe fast fillingof process. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, ensure the safety during fast filling process. prolonging the investment return period. Copyright © 2018 Elsevier Ltd. All rights reserved. The main scope of this paper isby to Elsevier assess the feasibility of using the heat demand – outdoor temperature function for heat demand © 2019 The Published Ltd. Copyright ©Authors. 2018 Elsevier Ltd. Allresponsibility rights reserved. Selection and peer-review under of the scientific committee of the 10th International Conference on Applied forecast. The access districtarticle of Alvalade, in Lisbonlicense (Portugal), was used as a caseth study. The district is consisted of 665 This is an open under thelocated CC BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Peer-review under responsibility of the scientific of ICAE2018 – The 10th International Conference on Applied buildings that vary in both construction periodcommittee and typology. Three weather scenarios (low, medium, high) and threeEnergy. district Energy (ICAE2018). renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: compressed hydrogen storage; hydrogen refueling; filling time; thermodynamics; safety compared with results from a dynamic heat demand model, previously developed and validated by the authors. Keywords: compressed hydrogen storage; hydrogen refueling; filling time; thermodynamics; safety The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.scenarios, Introduction the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1. Introduction The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the Hydrogen been ofconsidered as an important energy source season that can replace on traditional fuels and have the decrease in thehas number heating hours of 22-139h during the heating (depending the combination of weather and Hydrogen has been considered as an important energyintercept source thatstorage, canfor replace fuels and haveonthe greatest development potential inOnthe [1]. hydrogen a kindtraditional of per application technology for renovation scenarios considered). thefuture other hand,Compressed function increased 7.8-12.7% decade (depending the greatest in theused future hydrogen storage, a kind of application for hydrogen energy, has been in [1]. fuel cell to vehicles due to its simplicity infor tank and refueling coupled development scenarios). Thepotential valueswidely suggested could be Compressed used modify the function parameters the structure scenariostechnology considered, and hydrogen energy, hasof been widely usedtointhe fuelproperties cell vehicles due to itsused simplicity in tanktank, structure and refueling improve[2]. the accuracy heat demand estimations. process For safety reasons related of materials in hydrogen the SAEJ2601 has

process [2]. For safety reasons related to the properties of materials used in hydrogen tank, the SAEJ2601 has © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +1-819-376-5011x4478; fax: +1-819-376-5164.

address:author. [email protected]. * E-mail Corresponding Tel.: +1-819-376-5011x4478; fax: +1-819-376-5164. Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]. 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 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/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.438

Xin Zhou et al. / Energy Procedia 158 (2019) 1897–1903 Xin Zhou et al. / Energy Procedia 00 (2018) 000–000

1898 2

established corresponding protocols and regulations that the final hydrogen temperature inside the tank is not allowed to exceed 85℃ during refilling and the filling process should be completed within 3 minutes [3]. To study the temperature rise during refueling, many researches have been done by experiments and numerical simulations [46]. However, few people do research on thermodynamic analysis from the aspect of filling time. In this paper, based on a lumped parameter model, a novel analytical solution of filling time is obtained. According to the equation of state for real gas and dimensionless numbers Nu and Re , the function relationship between the filling time and the refueling parameters is presented. The parameters include initial temperature T0 , initial pressure p0 , inflow temperature T , final temperature T and final pressure p . Then, we express the filling time as functions of them and use these equations to fit the published data. The fitting results show good agreement. The values of fitting parameters are further utilized for the purpose of verifying the validity of these formulas. Nomenclature

af

As cp cv K Nu KRe Din m m0 m Nu p p0 Re RH2

heat transfer coefficient between hydrogen and ambient fluid, W/m2/K internal surface area of tank, m2 constant-pressure specific heat, J/kg/K constant-volume specific heat, J/kg/K coefficient of Nu , K Nu   gas As  /  cv Din  coefficient of diameter, K  0.14  K Nu Re internal diameter, m mass of hydrogen in tank, kg initial hydrogen mass, kg mass flow rate, kg/s Nusselt number of the gas, Nu  Din a f / gas final pressure, MPa initial pressure, MPa Reynolds number of the gas, Re   4m /  πdin  RH2 =4124 J/K/kg

t t T T T0 Tf T u



  gas  ' 

time variable or fill time, s characteristic time, t  = m0 m ,s temperature of hydrogen, K characteristic temperature, K initial temperature in tank, K temperature of ambient fluid, K inflow or outflow temperature, K specific internal energy, J/kg dimensionless heat transfer coefficient,    a f As   cv m    1.9155 K/MPa ratio of specific heats,   c p cv thermal conductivity of the gas, W/m/K initial mass fraction,   m0 m  '  1 dimensionless time,   t t 

2. Model for estimating of hydrogen filling time From general mass and energy balance equations for charge process of high pressure hydrogen gas into a tank, with the assumptions of constant specific heat and constant filling rate, the energy equation can be written as [2]:

dT  dt

1   

T T t  t

(1)

where T    T   T f  1    is a characteristic temperature, t   m0 m is characteristic time, and  =  a f As   cv m  is a dimensionless heat transfer coefficient which represents the ratio of heat transfer ability a f As to heat capacity change cv m  W K  of the system during charge process. Using dimensionless time   t t  , solution of Eq. (1) can be obtained as [2]. 1

T T  1    T   T0  1   

(2)

Then, the solution can be expressed in the form of “rule of mixtures” [7]:

T  'T0  1   ' T 

(3)

1  '  is the weighted factor. Inserting where   m0 m   T   T   T f  1    into Eq. (3) and using Tf  T0 , we obtain 1

the

characteristic

temperature



=

Xin Zhou et al. / Energy Procedia 158 (2019) 1897–1903 Xin Zhou et al. / Energy Procedia 00 (2018) 000–000

1   '  T  T   ' T0

1899 3

(4)

T  T0

We apply a real gas equation of state to the initial and final states of the refuelling procedure [8]: p0V m0 RH2 T0 1   p0 T0  and   pV mRH2 T 1   p T  .Using the above two equations we obtain, for the ratio of the initial mass to the final mass:

=

p T 1   p T  m0  0 m pT0 1   p0 T0 

For simplification, we also use  

1 T  T0

(5)

 '   [9] in Eq. (4). Then the formula can be written as:

 p0T 1   p T   p0T 1   p T   1     T  T  pT0 1   p0 T0   p 1   p0 T0   

(6)

In the Eq. (6), we can further modify dimensionless heat transfer coefficient  . According to the definition and physical meaning of dimensionless numbers Nu and Re , we can assume  =K Nu Nu m =KRe Red m , where ( d 0.67  2 3 ) [10]. Combined with the expression of mass flow rate, we can further assume Nu  0.14Red   =kt t1/3 . Then Eq. (6) becomes: t

 1      T T0  kt

3

 p0T 1   p T   p0T 1   p T     1     T  T    pT0 1  p0 T0   p 1  p0 T0     

(7)

This means the hydrogen filling time can be determined by refueling parameters, such as initial temperature T0 , initial pressure p0 , inflow temperature T , finial pressure p , and other parameters  ,  and kt , which are related to heat transfer coefficient and tank structure. 3. Estimation of hydrogen filling time from different refueling parameters 3.1. Estimating from initial temperature and final pressure In the Eq. (7), we use the initial temperature T0 as an independent variable and the corresponding filling time t as a dependent variable, so Eq. (7) can be turned into: 3

t

   BT0 BT0  1    AT0     T  1       T p T p T 1 1 0 0 0 0 0   1  AT0 T0 kt    





(8)

where AT0  1 T ,  BT0 p0 1   p T  p . Eq. (8) can serve as the function relationship between the initial temperature T0 and filling time t. This formula is used to fit the reference data [11], as shown in Fig.1. The known constants according to the reference[11] are T  358.15K , T  253.15K , p0  10MPa ,  =1.9155K MPa [8]. Fig. 1(a) shows a good agreement. The values of the corresponding fitting parameters under four final pressures are shown in Table 1. To verify the validity of the equation, we substitute the values of fitting parameters into Eq. (8) and process the reference data and then compare the curves with the processed date. The results of the comparison are shown in Fig. 1(b). Through this equation, if the real initial temperature and final pressure are known, we will determine whether the filling process can be completed within 3 minutes or not. For example, as shown in Fig. 1, assuming the filling time is 180 s, when the final pressure in the tank reaches 87.5MPa, a critical initial temperature T0 can be found by ensuring the highest hydrogen temperature is 85℃. If the real initial temperature T0' is higher than the critical initial temperature T0 , the required filling time is higher than the source time. Under this circumstance, we should be careful to prevent accidents caused by reduction of safety performance of hydrogen storage tank.

Xin Zhou et al. / Energy Procedia 158 (2019) 1897–1903 Xin Zhou et al. / Energy Procedia 00 (2018) 000–000

1900 4

3.2. Estimating from initial pressure and final pressure In the Eq. (7), we use the initial pressure p0 as an independent variable and the corresponding filling time t as a dependent variable, so Eq. (7) can be turned into: 3

   (T   p) T0   T   p0 1    T  T     pT0 1   p0 T0   (T  T0 )kt   

t

(9)

We use T  358.15K , T  253.15K , T0  293.15K ,  =1.9155K MPa [8] to fit the data which comes from the reference [11].The fitted parameters are shown in Table 2, and the fitted results are shown in Fig. 2(a). As it’s shown, the fittings agree very well. Fig. 2(b) shows the same kind of comparison as in section 3.1.As shown in it, the curve of t1/3 and initial pressure presents linear trend. Therefore, the function relationship between t1/3 and initial pressure can be further simplified to the form of liner function. For simplification, we rewrite Eq. (9) as:

t1 3

1 (T  T0 )kt

 (T   p) T0   T  T0    1  1     T  T  pT0   1   p0 T0   

According to the reference [12], when -

p0 T0 

1 , there is

(10)

1  p0 1 . Thus Eq. (10) can be modified into: 1+  p0 T0 T0

 t1 3 Ap0 p0  B p0

(11)

where Ap0  (T   p)(T 0   T ) (T  T0 ) (kt pT0 ) , Bp0 ( T  T ) (T  T0 ) kt . This formula is used to fit the processed data, as the same shown in Fig. 2(b). The values of fitted parameters of Ap and Bp for four final pressures are shown in Table 3. In Fig. 2(a), the horizontal line represents the filling time is 180 s. In order to achieve a certain final pressure (for example, 87.5MPa), a critical initial pressure p0 can be obtained. According to the curve of 87.5 MPa, when the real ' initial pressure p0 is higher than the critical initial pressure p0 , the required filling time is lower than the source time. In this case, completing the filling process within 3 minutes can be ensured. 0

0

3.3. Estimating from inflow temperature and final pressure In the Eq. (7), we use the inflow temperature T as an independent variable and the corresponding filling time t as a dependent variable, so Eq. (7) can be turned into:  t

A

T

T  BT



3

(12)

Comparing Eq. (7) with Eq. (12), we have  Tp 1   p T   Tp0 1   p T   1 AT 1  0 , BT  T         1  1 T p p T T T k p p T T T0  kt 0 0 0  0 t 0 0   

The formula can be used to fit the reference date [11] by utilizing T  358.15K , p0  10MPa , T0  293.15K ,

 =1.9155K MPa [8], as shown in Fig. 3(a). Table 2 gives out the values of parameters  and kt . Fig. 3(b) shows

the results of comparison. The curve of t1/3 and inflow temperature also presents linear trend. We use the function relationship between t1/3 and inflow temperature to fit the processed data, and the values of AT and BT are also shown in Table 3. In Fig. 3(a), the horizontal line represents the filling time is 180 s. In order to achieve a certain final pressure (for example, 87.5MPa), a critical inflow temperature T can be obtained. According to the curve of 87.5 MPa, when the real inflow temperature T' is higher than the critical inflow temperature T , the required filling time is higher than the source time, so we can’t complete the filling process within 3 minutes. For safety operation, the inflow hydrogen needs to be pre-cooled. 



Xin Zhou et al. / Energy Procedia 158 (2019) 1897–1903 Xin Zhou et al. / Energy Procedia 00 (2018) 000–000 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0

1901 5

7

87.5MPa

87.5MPa 6

70MPa

70MPa

5

t1/3 (s1/3)

Filling time t (s)



T0'

T0

4

50MPa

3

50MPa

35MPa 2

35MPa 1

270

275

280

285

290

295

300

305

310

315

270

320

Initial temperature T0 (K)

275

280

285

290

295

300

305

310

315

320

Initial temperature T0 (K)

(a)

(b)

300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0

7

87.5MPa

6

70MPa

5

t1/3 (s1/3)

Filling time t (s)

Fig. 1 Effect of initial temperature on filling time under different final pressures. (Symbol: Data [11], Line: Fit)

50MPa

p0

35MPa

87.5MPa

4 3

p0'

70MPa

2

0

2

4

6

8

10

12

14

16

18

0

20

Initial pressure p0 (MPa)

50MPa

35MPa

1 5

10

15

20

Initial pressure p0 (MPa)

(a)

(b)

300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 230

7

87.5MPa

87.5MPa

6

70MPa

70MPa 5

t1/3 (s1/3)

Filling time t (s)

Fig. 2 Effect of initial pressure on filling time under different final pressures. (Symbol: Data [11], Line: Fit)

T' T

50MPa

240

245

250

50MPa

3

35MPa

35MPa

235

4

255

260

265

Inflow temperature T (K)

270

275

2

1 230

280

(a)

235

240

245

250

255

260

265

270

Inflow temperature T (K)

Fig. 3 Effect of inflow temperature on filling time under different final pressures. (Symbol: Data [11], Line: Fit)

275

280

(b)

Xin Zhou et al. / Energy Procedia 158 (2019) 1897–1903 Xin Zhou et al. / Energy Procedia 00 (2018) 000–000

1902 6

Table 1. Value / standard error of fitted parameters for fitting the functions of filling time with initial temperature under different final pressures.



kt

0.00271 / 0.00008

1.80362 / 0.07194

0.20671 / 0.05590

0.00262 / 0.00005

1.99447 / 0.01767

0.23172 / 0.05593

70

0.00260 / 0.00007

1.95475 / 0.03290

0.16612 / 0.06668

87.5

0.00262 / 0.00004

2.00696 / 0.03752

0.15699 / 0.03766

Final pressure p (MPa)

AT0

35 50

Table 2. Value / standard error of fitted parameters for fitting the functions of filling time with initial pressure or inflow temperature. Final pressure p (MPa)

Function of filling time with initial pressure



kt

Function of filling time with inflow temperature



kt

35

1.94532 / 0.04066

0.51929 / 0.04353

1.81348 / 0.01779

0.30376 / 0.01761

50

1.96701 / 0.01993

0.44068 / 0.01739

1.82141 / 0.00700

0.28571 / 0.00565

70

1.96249 / 0.01319

0.35788 / 0.00940

1.79935 / 0.00228

0.23162 / 0.00144

87.5

1.99799 / 0.00578

0.27876 / 0.00317

1.86647 / 0.00262

0.20756 / 0.00143

Table 3. Value / standard error of fitted parameters for fitting the functions of t 1 3 with initial pressure or inflow temperature. Final pressure p (MPa)

 t1 3 AT T  BT

 t1 3 Ap0 p0  Bp0

Ap0

Bp0

AT

BT

35

-0.20357/0.00358

3.95226/0.02340

0.05506/0.00129

12.0727/0.33718

50

-0.19383/0.00173

4.84490/0.01461

0.07033/0.00053

14.8932/0.13439

70

-0.19167/0.00083

5.92028/0.00935

0.09250/0.00042

19.3773/0.10646

87.5

-0.20563/0.00107

7.95976/0.01439

0.11213/0.00043

22.4681/0.10764

4. Conclusions (1) From the perspective of the thermodynamics, a single-zone (hydrogen gas) lumped parameter model about the compressed hydrogen storage system is applied to deduce the correlation between the filling time and the refueling parameters. (2) The hydrogen filling time can be determined by refueling parameters, such as initial temperature, initial pressure, inflow temperature, finial pressure, and other parameters which are related to heat transfer coefficient and tank structure. (3) The presented formulas based on real gas and dimensionless numbers have more physical meanings. The formulas are used to fit published reference data. These results show the effects of initial temperature, initial pressure and inflow temperature on the filling time respectively. The fittings agree very well with the original data. (4) This work helps estimating the hydrogen filling time. To ensure the safety, the filling process can be completed within 3 minutes in the occasions of the real initial temperature being lower than the critical initial temperature, the real initial pressure being higher than the critical initial pressure and the real inflow temperature being less than the critical inflow temperature. Acknowledgements We wish to thank (1) the National Natural Science Foundation of China (No. 51476120), (2) the 111 Project of China (No. B17034), for their financial supports. References [1] Wang GX, Zhou JQ, Hu SJ, Dong SH, Wei P. Investigations of filling mass with the dependence of heat transfer during fast filling of hydrogen cylinders. Int J Hydrogen Energy 2014;39:4380-4388.



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Biography Jinsheng XIAO: 1983 B.S. and 1999 Ph.D. in Engineering Thermophysics, Tsinghua University, China; 1986 M.S. in Marine Engineering, Wuhan University of Technology, China. Assistant (1986-1989), Lecturer (1989-1992), Associate Professor (1992-1996), and Professor (1996-present) in Wuhan University of Technology. Visiting Professor (2008-present) in Hydrogen Research Institute, University of Quebec at Trois-Rivieres, Canada. His current research is on hydrogen storage and purification system.