Thermodynamic optimization for dissociation process of gas hydrates

Energy 106 (2016) 270e276

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Thermodynamic optimization for dissociation process of gas hydrates Yuehong Bi*, Jie Chen, Zhen Miao Institute of Civil and Architectural Engineering, Beijing University of Technology, Beijing 100124, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 January 2016 Received in revised form 20 February 2016 Accepted 5 March 2016

The dissociation process of gas hydrates is also the discharging process of the gas hydrate cool storage system. In order to reduce the entropy generation rate of the gas hydrate dissociation process, this paper takes the entropy generation minimization as the optimization objective to perform thermodynamic optimization for the related process. By establishing thermodynamic optimization model of the gas hydrate dissolution process based on entropy generation analysis, both the optimal control strategy and the optimal heating rate of the gas hydrate dissolution process are determined. The entropy generation rate related to the optimal heating rate decreases by 7.5% compared with normal situation. The research results can provide important guidelines for optimal design and operation of the dissolution process of gas hydrates related to the gas hydrate cool storage system. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Gas hydrate dissolution process The cool discharging process Thermodynamic optimization Entropy generation minimization Optimal heating rate

1. Introduction Gas hydrates are a class of crystalline inclusion compounds with nonstoichiometric composition, consisting of guest molecules trapped in a lattice of polyhedral water cages [1,2]. Gas hydrates have received increasing attention, mainly due to the natural gas hydrate as a clean carbon-based energy source [3,4], hydrate-based CO2 separation [4e7], potential exploitation of hydrates for gas storage [4,8], transportation and gas separation [4,9], produce gas from gas hydrates [4,9e12], etc. Chatti et al. [13] reviewed the benefits and drawbacks of clathrate hydrates in their interest areas in details. Most of the refrigerants formed with water as refrigerant gas hydrates are particularly attractive for offpeak building cooling, because they freeze at temperatures higher than ice and their phase change latent heat is similar to that of ice [14e30]. Discharging process is the refrigerant gas hydrate dissolution process using the heating medium for heating. The applications of gas hydrates involve complex thermodynamic and kinetic problems which need to establish the relationship between the dissolution rate and thermodynamic variables. The heat transfer in the dissolution process of gas hydrates is somewhat similar to nucleate boiling of liquids. The researchers of Holder's lab firstly obtained measurements on the rate of heat transfer to a solid hydrate phase which decomposed into gas and liquid phases simultaneously [31].

* Corresponding author. Tel./fax: þ86 10 67391608 808. E-mail addresses: [email protected], [email protected] (Y. Bi). http://dx.doi.org/10.1016/j.energy.2016.03.029 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

Kamath et al. [32] put the dissolution process of gas hydrate as nucleate boiling of liquids and established the model of the hydrate dissociation process. Selim et al. [33] developed a mathematical model for hydrate dissociation and the results from the solution of the governing differential equations describing the rate of dissociation can be used to estimate the amount of hydrate dissociated as a function of time. Kim et al. [34] developed an intrinsic model for the kinetics of hydrate decomposition which indicated that the decomposition rate was proportional to the particle surface area and to the difference in the fugacity of methane at the equilibrium pressure and the decomposition pressure. Jamaluddin et al. [35] established the model of decomposition of a synthetic core of methane hydrate by coupling intrinsic kinetics with heat transfer rates. Simulation results indicated that the global rate of decomposition can be affected significantly by moving from a heat transfer controlled regime to a regime where both heat transfer and intrinsic kinetics by changing the system pressure. Clarke et al. [36] developed a new mathematical model which accounted for the distribution of particle sizes in the hydrate phase to determine the rate constant of decomposition. Recently, the research on the decomposition of gas hydrate is still in development. The dissociation kinetics at different heating rates was studied in Refs. [37], where it was shown that even very slow heating can significantly affect the intensity of dissociation. The experiments of dissociation of methane hydrate under external pressure revealed that not the curvature, but the heat flux value to regulate the dissociation rate and the change in diffusion [38]. By applying the CDM “(Consecutive Desorption and Melting Model)”, the process of gas hydrate

Y. Bi et al. / Energy 106 (2016) 270e276

Nomenclature A2

B2 c FH F f Hr K* Kf0 L m_ n2 n n* P

0

coefficient related to the characteristics of the dissolution process of the hydrate medium [J$s½/ (K$m3)] coefficient related to the characteristics of the heat transfer process of the hydrate medium (K/s½) the specific heat [J/(kg$K)] sum of the gas hydrate crystals surface area (m2) area of the heat exchanger (m2) fugacity of the hydration medium (Pa) heat of the hydrate reaction, i.e., the latent heat of liquidesolid phase change (J/mol) dissolution rate constant of gas hydrates [mol/ (m2,s,Pa)] heat transfer coefficient [W/(m2,K)] Lagrange function mass flow rate (kg/s) total mole of generated gas hydrates at different time (mol) total mole of gas hydrates (mol) optimal dependence of the total gas hydrate mole on time (mol) pressure (Pa)

decomposition was assumed to comprise two consecutive and repetitive quasi chemical reaction steps [39]. The visual observation indicated that the model of the methane hydrate dissociation could be a consecutive process of solid dissolution, guest diffusion, and vapor phase formation and growth [40]. Molecular dynamics simulation has been widely applied to the analysis of gas hydrate dissociation process. The dissociation mechanisms of gas hydrates (I, II, H) were revealed by analyzing the structural snapshots, radial distribution functions and diffusion coefficients at different temperatures. The diffusion rates of water molecules and guest molecules increased with the rising of temperature [41]. The analytic model of the mass and heat transfers of hydrate dissociation by depressurization and thermal stimulation in porous media was established, theoretical analysis of the effects of the depressurizing rate and the warm water injection temperature on the gas production and heat transfer characteristics of the methane hydrate dissociation were carried out, and the predicted results were in good agree with the experimental results [42,43]. In addition, the decomposition driving force [44], effects of activated carbon particle sizes [45], using microwave and radio frequency in-liquid plasma methods [46], etc, on methane hydrate dissociation and gas production were reported. In recent years, thermodynamic optimization theory has been applied for optimizing performance of thermodynamic cycles and devices, and has made great progress in the fields of physics and engineering [28,47e57]. The applications of thermodynamic optimization theory include heat engines [47e49], heat pumps [50], refrigerators [51], heat exchangers [52], distillation systems [49], chemical reactions [49], mesoscopic systems [49], quantum systems [49], direct energy conversion devices [52e54], thermal energy storage systems [55e57], and even life processes of animals, superconducting transition phenomena, wind energy systems of the earth [49], etc. However, so far there are a few related references that study on the thermodynamic optimization for solution crystallization process [48,58,59] and crystallization process of refrigerant gas hydrate [57]. There is no related reference that

Pm P‘* Q_ R 0 T Tm T’* t U3 U3*

271

pressure at critical decomposition point (Pa) optimal pressure (Pa) rate of heat transfer (W) universal gas constant [8.314 J/(mol,K)] temperature (K) temperature at critical decomposition point (K) optimal temperature (K) time (s) gas hydrate dissolution rate (mol/s) optimal dependence of the gas hydrate dissolution rate(mol/s)

Greek symbols Lagrange multiplier entropy generation rate of the dissolution process of gas hydrates (W/K) m chemical potential (J/mol) Q‘ phenomenological coefficient [((mol)4/3K/(J$s)]

l s2

Subscripts d cool discharging process eq equilibrium f heat transfer medium

studies on the thermodynamic optimization for dissolution process. In this paper, the thermodynamic optimization will be performed for the dissolution process of refrigerant gas hydrates. 2. Physical model From the gas hydrate dissociation kinetics model established in Refs. [31,32,34], it is learned that hydrate dissociation is a heattransfer-limited process. As gas hydrates (solid) dissociate, they form liquid (water) and gaseous phases. Since all the three phases are present at the dissociating interface, this phenomenon is termed three phase heat transfer. It is reasonable to draw an analogy between nucleate boiling phenomena and heat transfer during hydrate dissociation. Fig. 1 shows schematic diagram of the physical model of gas hydrates dissociation. The overall process of the hydrate decomposition apparently involves two consecutive

Fig. 1. Schematic diagram of the physical model of gas hydrates dissociation.

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Y. Bi et al. / Energy 106 (2016) 270e276

steps: firstly, destruction of the clathrate host lattice at the surface of a particle, and secondly, desorption of the guest molecule from the surface [31,32,34]. Based on the thermodynamic theory [60], the relation of the chemical potential and the fugacity of the hydration medium for the constant temperature is

minðs2 Þ ¼ min

Zt4 Y

0

0

0

dm ¼ RT dðln f Þ

(1)

8 < 1 Zt4 Y0 :t4

0

9  . i2 = 0 fg0 ðn  n2 Þ R ln feq dt ; 2 3

h

 .  2 0 fg0 dt ¼ n Rðn  n2 Þ3 ln feq

(8)

(9)

0

where m is chemical potential (J/mol),f0 is fugacity of the hydration medium (Pa),R is universal gas constant [8.314 J/(mol$K)], and T0 is temperature (K). During the dissolution process of gas hydrates, the entropy generation rate (s2) is

Temperature of liquid phase rising 0 . 0  t < t3 ; n2 ðtÞ ¼ 0; fg ð0Þ ¼ feq Gas hydrate decomposing t3  t  t4 ; n2 ðt3 Þ ¼ 0; n2 ðt4 Þ ¼ n; tde ¼ t4  t3 .

s2 ¼ U3 ðtÞDm2 =T 0

3. Thermodynamic optimal solution

(2)

where U3(t) is the dissolution rate of gas hydrates (mol/s),Dm2 is the chemical potential difference between the end and the start of the hydrate medium dissolution process (J/mol). Substituting Eq. (1) to Eq. (2) yields:

 .  0 fg0 s2 ¼ U3 ðtÞR ln feq

(3)

period: period:

A Lagrange function method is usually used to solve the problem of minimizing entropy generation combining Eqs. (7) and (8) with Eq. (9). The Lagrange function is

hY0 h  . i  . i1 2 0 0 fg0 þ l0 fg0 L ¼ R ln feq Rðn  n2 Þ3 ln feq

(10)

0

where fg0 is the fugacity of the refrigerant at the solid surface (Pa) 0 is the fugacity of refrigerant at the three-phase equilibrium and feq pressure (Pa). From an intrinsic model for the kinetics of hydrate decomposition established by Kim et al. [34], the gas hydrate dissolution rate can be expressed as

U3 ðtÞ ¼

Kd* FH



0 feq



fg0

where l is the Lagrange multiplier. Taking the partial derivative of L with respect to fg0 and setting it equal to zero (vL=vfg0 ¼ 0) yields

  0 . 0  pffiffiffiffi0  qffiffiffiffiffiffiffi Y0ffi 1 ðn  n2 Þ3 ln feq fg ¼ l R

(4)

where is the dissolution rate constant of gas hydrate [mol/ (m2$s$Pa)], and FH is the sum of the gas hydrate crystals surface area (m2). By consulting with Ref. [48], the relation of the sum of the gas hydrate crystals surface area and the mole of the gas hydrate crystals is

qffiffiffiffiffiffiffiffiffiffiffi Y 0

l0

¼ 3=2ðtde Þ1 n3 2

2 3

(5)

where Db is affected by the shapes and the components of the gas hydrate, generally, it is determined by the experiments. n is the total mole of the refrigerant gas hydrates at t ¼ 0(mol). n2 is the total mole of the decomposed refrigerant gas hydrates at different time (mol). The dissolution rate of the refrigerant gas hydrate can be expressed as

 2

dn2 0 ¼ Db Kd* ðn  n2 Þ3 feq  fg0 dt



 3 qffiffiffiffiffiffiffiffiffiffiffi 2 2 0 Y0 2 ,ðt  t3 Þ n*2 ðtÞ ¼ n  n3  l 3

U3 ðtÞ ¼

dn2 ¼ dt

2 3

ðn  n2 Þ R ln

0 feq

fg0

3

¼ n  ntde2 ðt4  tÞ2

for t3  t  t4

(13)

One can obtain the optimal gas hydrate dissolution rate

U3* ðtÞ

dn* ðtÞ 3n pffiffiffiffiffiffiffiffiffiffiffiffi 3 n ¼ 3 ¼ 2 t4  t ¼ dt 2 tde 2 2tde sffiffiffiffiffiffiffiffiffiffiffiffi 3 * t t for t3  t  t4 ¼ U3 4 2 tde

sffiffiffiffiffiffiffiffiffiffiffiffi t4  t tde (14)

*

(6)

Refs. [48,58,59] have provided a simplified way to deal with this problem, i.e., Eq. (6) is expanded to Taylor series and only the first item of Taylor series is reserved, then the dissolution rate of the refrigerant gas hydrate can be approximately given as

Y‘

(12)

Then the optimal total refrigerant gas hydrate mole can be got from Eqs. (9) and (12)

3

U3 ðtÞ ¼

(11)

From Eqs. (7) and (9), one has



Kd*

FH ¼ Db ðn  n2 Þ

for t3  t  t4

where U 3 is the average dissolution rate of the gas hydrate in the interval of tde (mol/s). Moreover, the optimal fugacity of the hydrate medium is

8 > < 0 fg* ðtÞ ¼ feq exp  > :

(7)

where U3(t) is directly related to a phenomenological coefficient Q‘ [(mol)4/3K/(J$s)]. During the dissolution process of gas hydrates, the minimizing entropy generation rate (s2 ) can be written as

0 exp ¼ feq

qffiffiffiffiffiffiffiffiffi Qffi

9 > =

pQ ffiffiffiffiffiffiffiffi ffi 0 0

312 > ;

l0

Q0

2 R4n  2 3

2

0

l

3

ðt  t3 Þ5

! 1 3n3  Q0 pffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi 2 R tde t4  t

for t3  t  t4

(15)

Ref. [61] has established the fugacity model for refrigerant gas hydrate which be verified by the design calculations of the

Y. Bi et al. / Energy 106 (2016) 270e276

273

pffiffiffiffiffiffiffiffiffiffiffiffi t4  t

refrigerant gas hydrate cool storage system engineering. The fugacity model developed in Ref. [61] is written as

T0* ¼ Td  B2

. h  i 0 0 ðRT 0 Þ fg0 ¼ feq exp vH Peq  P0

One has the optimal pressure by substituting Eq. (23) into Eq. (18), i.e.,

(16)

where vH is the specific volume of refrigerant in gas hydrate phase 0 0 0 (m3/kg),T is temperature (K),P is pressure (Pa), and Peq is the 0 equilibrium pressure of refrigerant at temperature T (Pa). The optimal pressure can be got from Eqs. (15) and (16), that is 1

3n3 0 P 0* ¼ Q0 H pffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi,T 0* þ Peq 2 v tde t4  t

for t3  t  t4

(17)

P 0* ¼ A2 Td

for t3  t  t4

(23)

.pffiffiffiffiffiffiffiffiffiffiffiffi t4  t  A2 B2 þ Pm

(24)

0

and t ¼ t3, P *(t3) ¼ Pg0. The optimal control strategies expressed by Eqs. (22)e(24) have been obtained by minimizing the entropy generation rate of the dissolution process of the gas hydrate. The minimizing entropy generation rate (s2min) is given as

0

where T * is the optimal temperature. At the temperature range of refrigerant gas hydrate cool storage 0 system, Peq usually can be approximately substituted byPm, which is the pressure at critical decomposition point, then the above equation is expressed as



. 

0 fg ¼ U3* ðtÞA2 vH s2min ¼ U3* ðtÞRln feq

.pffiffiffiffiffiffiffiffiffiffiffiffi t4  t

(25)

4. Numerical examples and discussions 1

3n3 P ¼ Q0 H pffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi,T 0* þ Pm 2 v tde t4  t 0*

(18)

0

and t ¼ t3, P *(t3) ¼ Pg0 Q pffiffiffiffiffiffi 1 Letting A2 ¼ 3n3 =2 0 vH tde ,A2 is a coefficient depending on the characteristics of the hydrate medium [J$s½/(K$m3)]. Eq. (18) is simply written as 0

0

P * ¼ A2 T *

pffiffiffiffiffiffiffiffiffiffiffiffi t4  t þ Pm

(19)

According to the energy balance equation, the temperature can be calculated by

U3 Hr ¼ Kf0 F DT0f

(20) . .h  i 0 ðTd2  T 0 Þ ln Td1  T

0

DTf ¼ ðTd1  Td2 Þ

where Hr is the latent heat of liquidesolid phase change (kJ/kg), Kf0 and F are the heat transfer coefficient and the area of the heat exchanger in the cold storage tank [W/(m2$K) andm2], respectively. DTf0 is logarithmic mean temperature difference (K). Td1 and Td2 are the inlet and outlet temperatures of the heating medium, respectively (K). Due to the small temperature change of the heat transfer medium in the heat exchanger, logarithmic mean temperature difference (DTf0 ) can be replaced with algebraic temperature difference with small errors, i.e., DTf0 ¼ Td  T 0 , then Eq. (20) can be changed to [62].

U3 H r ¼

Kf0 FðTd

0

T Þ

(21)

where Td is the mean temperature of the heating medium (K), and it can be calculated simply by algebraic average of the inlet (Td1) and outlet temperature of heating medium (Td2), i.e., Td ¼ (Td1 þ Td2)/2. The optimal temperature can be obtained by substituting Eq. (14) into Eq. (21)

T0* ¼ Td  3nHr

. 3 pffiffiffiffiffiffiffiffiffiffiffiffi 2 2Kf0 Ftde t4  t

for t3  t  t4

(22)

0

and t ¼ t3, T *(t3) ¼ Tg0where Tg0 is the initial temperature at the decomposing period (K).  3  2 ,. B2 is a coefficient depending on Letting B2 ¼ 3nHr = 2Kf0 Ftde

the characteristics of the hydrate medium (K/s½). Eq. (22) can be simply written as

In the gas hydrate dissolution process, the heating rate of the heating medium is usually chosen as the external control method to realize the process thermodynamic optimization. The heating rate of the heating medium meets the optimal control strategies, i.e., Eqs. (22)e(24). The heating rate of the heating medium (Q_ d ) is given as

Q_ d ¼ cd m_ d ðTd1  Td2 Þ ¼ U3 ðtÞHr

(26)

where cd is the specific heat [J/(kg$K)],m_ d is the mass flow rate of the heating medium (kg/s), and Q_ d is the heating rate of the heating medium (W). From Eqs. (25) and (26), the ratio of the minimizing entropy generation rate (s2min) and the heating rate of the heating medium (Q_ d ) is given as

s2min Q_ d

¼

A vH p2ffiffiffiffiffiffiffiffiffiffiffiffi Hr t4  t

(27)

Substituting Eq. (14) into Eq. (26) yields

3  Q_ d ¼ U 3 Hr 2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðt4  tÞ=tde

m_ d ðTd1  Td2 Þ ¼



3 U 3 Hr 2 cd

for t3  t  t4

sffiffiffiffiffiffiffiffiffiffiffiffi t4  t tde

for t3  t  t4

(28)

(29)

Simulation tool Matlab has been used to implement the simple numerical model and to carry out the analysis. The heating rate of the heating medium may be regulated using Eq. (28) to agree with the optimal control strategy equations. In practical applications, the inlet temperature of heating medium (Td1) remains constant, the setting value of the outlet temperature of heating medium (Td2) is given, Td2 is monitored and compared with its setting value in real time, and the mass flow rate of the heating medium should be regulated according to Eq. (29) by using the feedback control technology. The pressure and temperature of the hydrate medium for optimal heating rate are shown in Figs. 2 and 3, respectively. In the calculations, the decomposition temperature and pressure of R141b come from Ref. [63], i.e., Tm ¼ 8.44  C andPm ¼ 0.043 MPa. Td ¼ 15  C and t4 ¼ 8 h are measured data by experiments. B2 ¼ 0.04 K/s½ is calculated by the corresponding experimental data. The supposed data is A2 ¼ 50 J$s½/(K$m3). Figs. 2 and 3 show that both the pressure and the temperature rise with the increase in time for the optimal heating rate.

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Y. Bi et al. / Energy 106 (2016) 270e276

Fig. 2. Pressure vs. time for optimal heating rate.

Fig. 3. Temperature vs. time for optimal heating rate.

Eqs. (22)e(24) have some kinetic and heat transfer parameters, Q eg., ‘,Kf0 , F, etc., which reveal that the dissolution process of gas hydrate to be controlled by “kinetics control” and “heat transfer Q pffiffiffiffiffiffi 1 control”. The coefficients A2 ¼ 3n3 =2 0 vH tde and

Fig. 4. Influence of A2 on the pressure vs. time for optimal heating rate.

Fig. 5. Influence of B2 on the pressure vs. time for optimal heating rate.

 3  2 B2 ¼ 3nHr = 2Kd Ftde reflect the characteristics of the dissolution process and the heat transfer process of the gas hydrate medium, respectively. Figs. 4e6 show the influences of A2 and B2 on the pressure and the temperature for the optimal heating rate. In the calculations, Tm ¼ 8.44  C and Pm ¼ 0.043 MPa [63], the mean temperature of the heating medium is measured experimentally, i.e., Td ¼ 15  C, and t4 is also experimentally measured. The coefficient B2 is calculated using experimental data, and coefficient A2 is supposed. Figs. 4 and 5 indicate that the pressure is influenced mainly byA2. The influence of the coefficient B2 on the pressure is only caused by the different gas hydrate decomposition time. Actually, the increase in A2 brings the increase in the decomposition rate of gas hydrates. The pressure rises with the increase in coefficient A2. During most time of the decomposition process, the rate of pressure rise is slightly higher with the increase in A2, however, the pressure suddenly increases significantly with the increase in A2 near the end of the dissolution process. The temperature is influenced only by coefficient B2. The coefficient A2 has no influence on the temperature for the optimal heating rate. Actually, the larger coefficientB2, the higher the heat transfer rate is, and B2 determines the duration of the hydrate

Fig. 6. Influence of B2 on the temperature vs. time for optimal heating rate.

Y. Bi et al. / Energy 106 (2016) 270e276

275

situation (no regulation). Therefore, the effect of thermodynamic optimization is notable. Acknowledgments This paper is supported by National Natural Science Foundation of P. R. China (Project No: 51376012), Beijing Municipal Natural Science Foundation (Project No: 3142003) and Beijing Key Lab of Heating, Gas Supply, Ventilating and Air Conditioning Engineering (NR2013K01). The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript. References

Fig. 7. Ratio of the minimizing entropy generation rate and the optimal heating rate vs. time.

dissolution process. Fig. 6 shows that the rate of temperature goes up faster with the increase inB2. Therefore, the dissolution process of gas hydrates is controlled mainly by “heat transfer control”. The numerical examples chosen coefficient B2(B2 ¼ 0.03, 0.04, 0.08) represented realistic values calculated by three experimental results. However, coefficient A2(A2 ¼ 20, 100, 250, 500) did not represent realistic values because Q0 some phenomenological coefficient included in A2 needed to be determined by further experiments. Therefore, B2 coefficient of real gas hydrates could be given to a certain decomposition process of the gas hydrate, but A2 coefficient of real gas hydrates could not be given in this paper, and these would be the further work. Based on Eq. (27), the ratio of the minimizing entropy generation rate (s2min) and the optimal heating rate of the heating medium (Q_ d ) versus time is shown in Fig. 6. In the calculation, the latent heat of liquidesolid phase change Hr is 344 kJ/kg [63], the specific volume of refrigerant in gas hydrate phasevH is 0.000815 m3/kg [63]. B2 ¼ 0.04 K/s½ and t4 ¼ 8.0 h are calculated by the corresponding experimental data. The supposed data is A2 ¼ 500 J$s½/(K$m3). Fig. 7 shows the ratio of the minimizing entropy generation rate and the optimal heating versus time. It indicates that the ratio goes down rapidly with the increase in time. WithA2 ¼ 500 J$s½/(K$m3),B2 ¼ 0.04 K/s½, t4 ¼ 8.0 h, the same initial condition and the same total mole of gas hydrate decomposed, the entropy generation rate related to the optimal heating rate decreases by 7.5% compared with that corresponding to the normal situation (no regulation). 5. Conclusion In order to reduce the entropy generation rate of the dissolution process of the gas hydrate, this paper established the thermodynamic optimization model for the corresponding process. Based on the thermodynamic optimization model and entropy generation minimization theory, the optimal control strategy equations for the gas hydrate dissolution process are obtained. In the practical engineering, the heating rate of heating medium often acts as the external control way. One can regulate the heating rate of the heating medium with Eqs. (28) and (29). and make the thermodynamic optimization of gas hydrate dissolution process in reality. The entropy generation rate related to the optimal heating rate decreases by 7.5% compared with that corresponding to normal

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