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Experimental study and kinetic modeling of R410a hydrate formation in presence of SDS, tween 20, and graphene oxide nanosheets with application in cold storage
Journal Pre-proof Experimental study and kinetic modeling of R410a hydrate formation in presence of SDS, tween 20, and graphene oxide nanosheets with application in cold storage
Amir Mohammad Javidani, Saeid Abedi-Farizhendi, Abolfazl Mohammadi, Amir H. Mohammadi, Hussein Hassan, Hassan Pahlavanzadeh PII:
S0167-7322(19)35678-8
DOI:
https://doi.org/10.1016/j.molliq.2020.112665
Reference:
MOLLIQ 112665
To appear in:
Journal of Molecular Liquids
Received date:
13 October 2019
Revised date:
29 January 2020
Accepted date:
8 February 2020
Please cite this article as: A.M. Javidani, S. Abedi-Farizhendi, A. Mohammadi, et al., Experimental study and kinetic modeling of R410a hydrate formation in presence of SDS, tween 20, and graphene oxide nanosheets with application in cold storage, Journal of Molecular Liquids(2020), https://doi.org/10.1016/j.molliq.2020.112665
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© 2020 Published by Elsevier.
Journal Pre-proof
Experimental study and kinetic modeling of R410a hydrate formation in presence of SDS, tween 20, and graphene oxide nanosheets with application in cold storage Amir Mohammad Javidania, Saeid Abedi-Farizhendia, Abolfazl Mohammadib,*, Amir H. Mohammadic,d,#, Hussein Hassana, Hassan Pahlavanzadeha
Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
b
Department of Chemical Engineering, University of Bojnord, Bojnord, Iran
c
Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France
of
a
ro
d
-p
Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa
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Abstract - Gas hydrates, or clathrate hydrates, can be used as a suitable cold/cool storage
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media, due to their large phase change enthalpy. In recent decades, cold production through gas hydrates as a novel and cost-effective method has motivated researchers. Refrigerants have the potential to be used in hydrate-based cold storage systems, because they can form hydrates at moderate pressures and temperatures. Hence, in this work, the kinetics of R410a (50 wt% difluoromethane + 50 wt% 1,1,1,2,2-pentafluoroethane) hydrate formation in the presence of different concentrations of SDS, tween 20, and graphene oxide (GO) was investigated. The experiments were carried out in a 300 cm3 reactor/cell at the initial pressure and temperature of 1 MPa and 279.65 K, respectively. According to the results, at all concentrations of the additives, except tween 20 at a concentration of 1000 ppm, the hydrate formation induction time decreases, compared to pure water. Furthermore, the promotion effects of SDS and GO on the quantity and rate of gas uptake, and the apparent rate constant were observed at the initial minutes of the hydrate growth process. The measured storage capacity and water to hydrate conversion show that the used additives do not change the abovementioned parameters, noticeably.
Keywords - Gas hydrates; Clathrate hydrates; Cold storage; Cool storage; Kinetics; Refrigerant
* Corresponding author: Abolfazl Mohammadi, [email protected] # Co corresponding author: Amir H. Mohammadi, [email protected]
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1. Introduction Cold production is a fundamental part of the strategy to develop in many processes such as food preservation, electronics, air conditioning, etc. However, it accounts for almost 15% of the electricity consumed in industrialized countries and has an increasing trend in all of the world. It has been found that cold storage has the capacity that can be charged during the
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night and discharged during the day using off-peak hours [1-3]. Initially, water and ice were presented as the materials that could be used for cold storage technology, but phase change
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materials (PCMs) as a promising candidate for cold storage application has attracted a great
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deal of attention due to their outstanding properties. PCMs have the potential to absorb
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energy by latent heat during liquefaction. They can take many forms including paraffin
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slurry, microencapsulated slurry, stabilized slurry, and gas hydrate slurry [1, 4-6]. The interaction between the water molecules (called host molecules) and the molecules of
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gases and/or some volatile liquids with appropriate sizes and shapes like methane, ethane,
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propane, carbon dioxide, hydrogen sulfide, cyclopentane, refrigerants, etc (called guest
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molecules) at low temperatures and/or high pressures results in the formation of icy crystalline solids called “gas hydrates” or “clathrate hydrates”. Depending on the sizes of guest molecules, gas composition and thermodynamic conditions, the crystalline structure of hydrates can consist of any combination of three typical categories: structure I, structure II, and structure H [7, 8]. Even though gas hydrates cause blockage in the gas transmission equipment and pipelines, also have the potential for numerous positive applications such as gas storage [9, 10], separation of greenhouse gases [11-15], water desalination [16-19], juice and coffee concentration [20-22], air conditioning systems [1, 23-26], etc.
2
Journal Pre-proof R410a, belonging to the group of hydrofluorocarbons (HFCs) refrigerants, is mainly utilized as a replacement for ozone-depleting substances (ODSs) like R11, R12, and R22. R410a does not contribute to ozone depletion, and therefore, becoming more widely used in air conditioning equipment [27]. R410a forms hydrate with structure II at moderate conditions compared to common gas hydrate formers such as CH4, C2H6 and CO2 [28] and can be used as gas hydrate former in cold storage medium and air conditioning systems.
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However, R410a has a high global warming potential (GWP) of 2088 and about 99 times as
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much as CH4, which includes in the basket of emission controlled by the “Kyoto Protocol” as
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greenhouse gas [29]. Hence, it is necessary to employ methods like gas hydrate technology in
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order to capture and recover the waste R410a gas from emissions.
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In 1982, gas hydrates were presented as new media of cold storage in air conditioning systems, especially due to their large enthalpy of phase change, as mentioned earlier [30]. In
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the past decades, a large number of studies have been done to develop cold storage systems
ur
using gas hydrates. Most of these studies have been carried out with the aim of understanding the thermodynamic (phase equilibrium) and kinetic (growth) behaviors of gas hydrates to be
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used as a suitable medium for cold storage [2, 31]. It was found that refrigerants can form hydrates at moderate pressure and temperature ranges [3]. Hydrate formation and dissociation conditions of different refrigerants (R11, R12, R22, R23, R134a, R141b, R125a, and R410a) and mixed refrigerants were investigated by some researchers [3, 28, 31-36]. Furthermore, enthalpy of hydrate dissociation is a key factor to select suitable gas hydrate former in cold storage applications, because it shows the required enthalpy of hydrate dissociation or cold storage capacity. Hydrate dissociation enthalpy of different gases could be found in the literature [37, 38]. The dissociation enthalpies of R410a and R134a hydrates
3
Journal Pre-proof measured by Ngema et al. was in the range of 69-89, and 124-134 kJ/mol, respectively [39]. Kinetic parameters of gas hydrates such as growth rate and the time needed to form the first crystals (induction time) are crucial factors that play a significant role in the hydrate-based cold storage process [3, 25]. Kinetic promoters improve the kinetics of gas hydrate formation process by shortening the induction time and increasing the gas uptake and the rate of hydrate formation. It has
of
already been proven that surfactants such as sodium dodecyl sulfate (SDS), cetyl
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trimethylammonium bromide (CTAB), linear alkyl benzene sulfonate (LABS), and tween
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promote the kinetic formation of hydrates by decreasing the gas-liquid surface tension [22,
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40-45]. In addition, nanoparticles like Ag, Cu, Al2O3, SiO2 and carbon nanotubes (CNTs)
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play the same role by enhancing the heat and mass transfer due to their high specific surface areas [41, 46-50]. Li et al. reported that Cu nanoparticles enhance the kinetics of R134a
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hydrate formation and dissociation, remarkably [51]. Karamoddin et al. findings indicate that
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SDS greatly increases the rate of R22 hydrate formation at low stirring speed [52]. Kinetics of R404a, R406a, R408a, R427a, R407c, R507c, R410a hydrates formation at different
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degrees of subcooling and in the presence and absence of SDS were investigated by some researchers [3, 28]. According to the reported results, the addition of SDS increases the rate of the hydrates formation for R404a, R406a, R408a, R427a gases and unexpectedly shows a negative effect on the kinetics of R410a, R407c and R507c hydrates [3, 28]. Graphene oxide (GO) nanosheets exhibit excellent mechanical strength in addition to high thermal and electrical conductivities. These nanosheets can promote the hydrate formation kinetics due to their high specific areas to volume ratio. On the other hand, they cause heterogeneous nucleation during crystallization, which helps the hydrate formation to 4
Journal Pre-proof take place more easily. The promotion effects of these nanosheets on the kinetic parameters of methane, propane and ethylene hydrates were studied by Manteghian et al. [49, 53, 54]. According to the related literature, most of the previous researchers have focused on the thermodynamic behaviors of refrigerant hydrates, and the kinetic formation of refrigerants hydrates has received less attention. Therefore, further research is needed on the kinetic of
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refrigerants hydrates formation in the presence of additives.
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In this work, the effects of anionic surfactant, SDS, nonionic surfactants, polysorbate 20 (tween 20) and GO on the kinetic parameters of R410a hydrate formation at initial conditions
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of 279.65 K and 1 MPa were examined. Kinetic parameters include induction time, gas
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consumption, rate of gas uptake, storage capacity, water to hydrate conversion, and apparent
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2.1. Materials
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2. Experimental
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rate constant.
The suppliers, chemical formula and purities of the materials used in this study are presented in Table 1. In all the experiments, to prepare aqueous solutions, a gravimetrical analytical balance and de-ionized water were used.
2.2. Preparation of graphene oxide nanosheets
5
Journal Pre-proof The method used to synthesize and characterize GO, is presented in a previous paper [53]. Briefly, graphite powder (5 g) was added to the sulfuric acid solution (150 mL), followed by adding sodium nitrate (2.5 g) and then potassium permanganate (15 g). Next, the solution was stirred for 24 h. Then, the solution was diluted with de-ionized water (300 mL), and stirred for 2 h. Hydrogen peroxide aqueous solution (100 mL) was added to the solution.
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was sonicated for 20 minutes to produce a GO solution.
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Next, the mixture was washed with HCl and then with de-ionized water. Finally, the mixture
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2.3. Apparatus
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Fig. 1 depicts the schematic diagram of the experimental apparatus used in this work. The
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reactor/cell is made of stainless steel with an inner diameter of 6.2 cm, a height of 10 cm and an effective internal volume of 300 cm3. It has a needle valve, which can withstand up to 10
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MPa for injecting and discharging the gas, and a ball valve for charging the aqueous solution.
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A circulator containing water and ethylene glycol with a volume ratio of 50/50 was employed to keep the reactor temperature at a desired constant value during the tests. A mixer was used
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to agitate the components inside the solution. This helps to increase the gas-liquid contact area and enhances the heat and mass transfer of the aqueous solution. The temperature and pressure of the reactor were monitored continuously along the time during the experiment by means of a platinum resistance thermocouple with an accuracy of 0.1 K and a pressure transducer with an uncertainty of ± 0.01 MPa, which are connected to the top of the reactor. A control panel acquires the temperature and pressure of the reactor and then feeds to the computer and the panel records the obtained data using an in-house software at every 5 seconds.
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2.4. Experimental procedure To ensure that the reactor has no leak, the nitrogen inert gas was injected to the cell up to 10 MPa and left intact for 24 h at 298 K. After a day, the pressure of the reactor remained constant. At the first step of each experimental run, the cell was rinsed and eluted properly
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with distilled water, and then the air and impurities inside the cell were evacuated down to -
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0.07 MPa using a vacuum pump. Thereafter, 100 cm3 of the aqueous solution sample was introduced into the cell. Then, the cell was immersed into the circulator and its temperature
-p
was adjusted to 279.65 K. After reaching the desired temperature value, the R410a
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refrigerant was introduced into the cell up to 1 MPa. In the next step, the mixer was set at a
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speed of 200 rpm in all experiments. During the hydrate formation, the gas molecules transfer to the hydrate cages, and consequently, the cell pressure decreases continuously.
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After the cell pressure variations were reached nearly 0.05 MPa/h, the hydrate formation was
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considered to be over, and the hydrate growth was stopped. R410a hydrate phase equilibrium
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curve reported in the literature [28], as well as the initial conditions of the present study are shown in Fig. 2.
3. Kinetic Model 3.1. Amount of gas consumption In the process of refrigerant hydrate formation, the physical reaction between water molecules and refrigerant can be defined as follows [3]:
7
Journal Pre-proof R
+
MH2O
R.
MH2O
ΔH
+
(1) where, M is hydration number (number of water molecules per refrigerant gas) that depends on the filling size of small and large cavities. R410a molecules form structure II; for this structure, hydration number is calculated by the following equation [7]: 17
(2)
𝑙𝑎𝑟𝑔𝑒 +2𝜃𝑠𝑚𝑎𝑙𝑙
of
M= 𝜃
ro
where θlarge and θsmall represent the fractional occupancy of large and small cavities,
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respectively. R410a molecules cannot enter the small cavities, because of their large size
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[39]. Thus, θsmall for R410a hydrates is zero. The fractional occupancy of large cavities is
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calculated on the basis of Langmuir adsorption theory as follows [7]:
(3)
𝐶𝑙𝑎𝑟𝑔𝑒 𝑓 𝑔 1+ 𝐶𝑙𝑎𝑟𝑔𝑒 𝑓 𝑔
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θlarge=
ur
where Clarge is the Langmuir constant of R410a refrigerant molecules in large cavities, fg is
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the fugacity of the R410a refrigerant in the gas/vapor phase, which is calculated using the Peng-Robinson equation of state [55]. To calculate Clarge, the following formula can be used [56]: Clarge=
𝐴𝑙𝑎𝑟𝑔𝑒
exp
𝑇
𝐵𝑙𝑎𝑟𝑔𝑒
(
𝑇
)
(4) where T is temperature, and Alarge and Blarge are the adjustable parameters for the Langmuir constant, whose values are reported in Table 2 [57]. 8
Journal Pre-proof The amount of R410a gas consumption during the hydrate formation is calculated as follows [58]:
Δn=
𝑃0 𝑉0
𝑃𝑡 𝑉𝑡
-
𝑍0 𝑅𝑇0
𝑍𝑡 𝑅𝑇𝑡
(5) where R represents the universal gas constant, Pt and Tt are the cell pressure and temperature
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at a given time=t, respectively, Vt is the volume of the gas at time=t, V0 represents the
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volume of the gas at the beginning of the reaction, which is equal to 200 cm3, P0 stands for
-p
the initial pressure of the cell, which is 1 MPa, T0 is the initial temperature of the cell, which
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is 279.65 K, and Z represents the compressibility factor of gas, which can be calculated by
Z3-
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the Z form of Peng-Robinson equation of state as follows [55]: (B-1)Z2
(A-3B2-2B)Z
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(6)
+
(𝑅𝑇)2
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(7) B=
(AB-B2-B3)=0
(𝑎𝑐 𝛼)𝑃
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A=
–
𝑏𝑃 𝑅𝑇
(8) 𝑅 2 𝑇𝑐2
ac= 0.45724
(9)
𝑃𝑐2
𝑅𝑇
0.07780 𝑃 𝑐
b=
𝑐
(10)
9
Journal Pre-proof where Pc and Tc refer to the critical pressure and critical temperature of R410a refrigerant that equal to 4.964 MPa and 345.65 K, respectively [59]. α and m are obtained using the following equations: α=
m(1-Tr0.5 ))2
(1+
(11) 0.3746+
0.2669ω2
1.5423𝜔-
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m=
ro
(12)
-p
where, ω is the acentric factor of R410a refrigerant (equals to 0.279) [39], which is an index
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for the non-spherical of their molecules.
(13)
–
Vcell
𝑉𝑠0
+
–
𝑉𝑅𝑊𝑡
𝑉𝐻𝑡
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Vt=
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The volume of the gas inside the cell at a given time, Vt , can be calculated as follows [46]:
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where, Vcell is the reactor volume (300 cm3), 𝑉𝑠0 represents the initial volume of the aqueous
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solution (100 cm3), and 𝑉𝑅𝑊𝑡 and 𝑉𝐻𝑡 are the volume of reacted water and the volume of produced hydrate, respectively. The volume of reacted water at time=t, 𝑉𝑅𝑊𝑡 , is calculated from the following relationship [46]: 𝑉𝑅𝑊𝑡 =
Δn
M×
×
υw L
(14) where υwL is the molar volume of water in the liquid/aqueous phase that is calculated using the following equation [60]:
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Journal Pre-proof υwL = 18.015 × {1- (1.0001 × 10-2) + (1.33391 × 10-4) [1.8(T- 273.15) +32] + (5.50654 × 107 )[1.8(T- 273.15) +32]2 × 10-3 (15) The units of υwL and T are in m3/kmol and K, respectively. The following equation was employed for calculating the molar volume of empty hydrate lattice for structure II [61]: υwMT [sII]= (17.13 + 2.249 × 10-4T + 2.013 × 10-6T2 + 1.009 × 10-9T3) ×
10−30 NA 136
– 8.006 ×
10-9 P + 5.448 × 10-12 P2
(16)
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where, NA is the Avogadro’s number (6.022 ×1023), and P and T are the pressure and
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temperature in MPa and K, respectively. By assuming that the molar volume of hydrate is
-p
equal to the molar volume of empty hydrate lattice, the volume of produced hydrate at time t,
𝑉𝐻𝑡 =
re
can be obtained from the following relationship:
× Δn
υwMT
×
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M
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3.2. Rate of gas uptake
na
(17)
r(t)
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Rate of gas uptake at time=t, r(t), during the hydrate formation can be calculated as: ni−1 −ni+1
=
(ti+1 −ti−1 )n𝑤0
(18) where, ni-1 and ni+1 stand for the gas mole number at time=ti-1 and time=ti+1, respectively, and n𝑤0 is the initial number of moles of water in the liquid phase [46].
3.3. Storage Capacity (SC) 11
Journal Pre-proof Storage capacity (SC) is defined as the volume of entrapped gas into hydrate cages per volume of gas hydrate at the standard conditions. The following equation is used to calculate the SC of R410a [46]: SC
=
𝑉𝑆𝑇𝑃
Δ𝑛 𝑅 𝑇𝑆𝑇𝑃 / 𝑃𝑆𝑇𝑃
=
𝑉𝐻
𝑉𝐻
(19)
of
where subscript STP represents the standard conditions of temperature and pressure, which is
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273.15 K for temperature, and 0.1 MPa for pressure. The proposed algorithm by Mohammadi
re
-p
et al. was used for SC calculation [46].
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3.4. Water to hydrate conversion
Number of moles of water molecules converted to gas hydrate per mole of feed water is
hydrate
conversion
(%)
M × Δn
= n 𝑤0
×
100
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(20)
to
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Water
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known as water to hydrate conversion, which is calculated as follows:
3.5. Hydrate apparent rate constant The following equation is used for the apparent rate constant calculation at a given time [62]: kapp
=
(21)
12
𝑟(𝑡) 𝑓𝑔 −𝑓𝑒𝑞
Journal Pre-proof where, kapp is apparent rate constant, fg represents the fugacity of R410a refrigerant in the gas/vapor phase at the system temperature and pressure, which is calculated using PengRobinson equation of state [55], and feq is the fugacity of R410a refrigerant at the hydrate equilibrium pressure and initial temperature.
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3. Results and Discussion
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4.1. Effects of additives on induction time
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A typical profile of pressure and temperature variations versus time in the (R410a + pure
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water) system during hydrate formation at the initial conditions of 279.65 K and 1 MPa is plotted in Fig. 3. As illustrated, in the initial minutes after gas injecting, a rapid reduction in
na
pressure was observed in the system due to the R410a refrigerant dissolution into the aqueous phase. Then, the cell temperature returned back to the set value until the moment that
ur
primary nucleation started. At this time, the cell temperature was increased instantaneously
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due to the exothermic nature of the crystallization process, and its pressure dropped dramatically as a result of gas falling into the hydrate cages. At this time, the first nuclei of hydrate crystals appeared. The time elapsed between the start of gas injection and observation of significant changes in pressure and temperature is defined as “induction time”. Then, the hydrate crystals begin to grow until the cell pressure reaches approximately a constant value. Table 3 shows the induction times for the systems of R410a + different aqueous solutions at the initial temperature and pressure of 279.65 K and 1 MPa, respectively. The finding 13
Journal Pre-proof induction time indicated that SDS at all concentrations reduced the induction time compared to pure water; however, SDS at the concentration of 500 ppm had the highest reduction in the induction time. In comparison to pure water, tween 20 at concentrations of 50 ppm, 100 ppm, and 250 ppm resulted in a slight decrease in the induction time, but at high concentration (1000 ppm), it increased the induction time. SDS and tween 20 act as surfactants, and it has been established that surfactants alleviate surface tension. Indeed, these surfactants facilitate
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transferring of R410a molecules from the gas phase to the aqueous phase by decreasing the
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surface tension of water molecules. The viscosity of tween 20 is about 400 times more than
-p
that of pure water. Consequently, at a high concentration of tween 20, the viscosity of the
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solution increases significantly. Frank and coworkers showed that the diffusion coefficient of a gas in water decreases by increasing the viscosity of water [63]. Tween 20 aqueous solution
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at 1000 ppm acts as a barrier against the dissolution of molecules of refrigerant into the
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solution, and therefore, results in inhibition effect on the kinetics of R410a hydrate formation. All concentrations of graphene oxide cause a reduction in the induction time
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compared to pure water. GO nanosheets produce lots of nucleation sites, which lead to
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heterogeneous nucleation during the hydrate formation [54, 64]. On the other hand, heterogeneous nucleation needs less work to form hydrate crystals than homogeneous nucleation. It is also be noted that in the case of pure water induction time, R410a can quickly form hydrate without any promoters, and the effect of promoters on induction time is not remarkable. 4.2. Effects of additives on gas consumption and rate of gas uptake Fig. 4 illustrates the quantity of R410a mole consumed changes during the hydrate formation in pure water and various concentrations of SDS at the initial temperature and 14
Journal Pre-proof pressure of 279.65 K and 1 MPa, respectively. As seen in this figure, after 20 min, 50 ppm and 500 ppm SDS have increased the moles of gas consumed. But there is no significant change in the gas consumption of 100 ppm SDS solution, and decreasing the gas consumption of 200 ppm SDS solution is observed. At t=10 min, the amount of gas consumed per mole of feed water for pure water is 0.01010 mole, while 500 ppm SDS has 0.01309 moles. This means that 500 ppm SDS has increased the mole of gas consumption by
of
up to 29.6 mole percentage compared to pure water. In all the solutions, SDS has no effect on
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the final mole of gas consumed and its effect on the changes of gas consumption is more
-p
noticeable in the first 20 min of reaction.
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The effect of tween 20 on the amount of gas consumption of R410a refrigerant is
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depicted in Fig. 5. As shown, all concentrations of tween 20 have a negative effect on the kinetics of R410a hydrate formation and act as a kinetic inhibitor. The reason for the
na
inhibition effect may be due to overcoming the negative effect of high viscosity on the
ur
positive effect of reducing surface tension. Tween 20 is a viscous liquid with the viscosity of 250-450 mPa.s at 298 K. Its high viscosity prevents the diffusion of R410a from the gas
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phase to the solution. Fig. 6 shows the images of R410a hydrate for pure water, 100 and 1000 ppm solutions of tween 20 at the end of the reaction. As illustrated, the 1000 ppm tween 20 produces a high amount of foaming on the surface compared to the100 ppm tween 20 and pure water. It has been established that foam reduces heat transfer and mass transfer coefficients of any solution. Thus, 1000 ppm tween 20 has a more inhibition effect compared to 100 ppm tween 20. Fig. 7 shows changes in the mole consumption of R410a in the presence of GO (50, 100, 200, and 400 ppm). As shown, up to 15 min after the starting of the reaction, as the 15
Journal Pre-proof concentration of GO increases, more promotion effect on the mole consumption is obtained. Compared to pure water, 400 ppm GO increases the amount of R410a consumption by 21.4 mole percentage at t=10 min. GO like SDS, does not change the final mole of the consumed gas significantly. The promotion effect of GO at first 15 min of reaction might be related to the lowering of free energy by providing heterogeneous nucleation of these nanosheets as described earlier and their high specific surface area to volume ratio; this leads to better mass
of
transfer. Contrary to Manteghian and coworkers results regarding the promotion effects of
ro
GO on methane, propane, and ethylene hydrates formation [49, 53, 54], GO has less
-p
promotion effect on R410a gas consumption. It can be due to the higher solubility of R410a
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comparing to the referred gases.
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Figs. 8-10 show the rate of R410a uptake curves during the hydrate formation of different systems, based on Eq. (18) within 20 min. As shown, the maximum rate of gas uptake is
na
observed at the beginning of the reaction due to the sudden drop in pressure and high
ur
solubility of the refrigerant into the aqueous solution. Thereafter, the rate of gas uptake diminishes shortly until the moment that the rate increases sharply. The sudden increase is
Jo
due to the rapid entrapment of the gas molecules into the hydrate cages cavities, and the produced nuclei are at the highest possible. After the peak point, the hydrate crystals begin to grow. As the hydrate growth begins, the number of nuclei decreases. On the other hand, temperature increase arising from the exothermic nature of nucleation decreases the driving force of hydrate formation. These two factors cause a reduction in gas uptake after the induction time. SDS with concentrations of 50 and 500 ppm, and all aqueous solutions of GO enhance the rate of gas uptake at induction time, compared to pure water. Other
16
Journal Pre-proof concentrations of SDS and all concentrations of tween 20 result in reducing the rate of gas uptake at the induction time.
4.3. Effects of additives on storage capacity (SC), water to hydrate conversion, and apparent rate constant of hydrate growth
of
SC and the ratio of water to hydrate conversion are kinetic parameters that are affected by
ro
the amount of entrapped gas molecules (Δn). Table 4 reports the measured SC and water to
-p
hydrate conversion in pure water and additive solutions. As can be seen, the effects of different concentrations of additives on SC and percentage of water to hydrate conversion are
re
similar. According to the results, 1000 ppm tween 20 reduced the aforementioned parameters
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significantly due to its high viscosity as described earlier. Other concentrations of additives
na
had no remarkable effects on the SC and water to hydrate conversion values. These results show that the additives do not change the phase equilibrium curve of hydrate formation, and
ur
the final pressure of the experiments reaches to approximately a constant value. SDS (50
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ppm) had the highest value in SC and percentage of water to hydrate conversion. Figs. 11-13 show the apparent rate constant changes of R410a during the hydrate growth in pure water and in the presence of SDS, tween 20, and GO solutions. As observed, the apparent rate constant decreases after it reaches the maximum value at the induction time. This type of change may arise from decreasing of gas uptake. As shown in Figs. 11-13, all concentrations of SDS increase the apparent rate constant, especially, after 5 min of starting of the growth process. The presence of SDS leads to more captured gas into the aqueous phase by decreasing the gas-liquid surface tension, and consequently, the hydrate growth
17
Journal Pre-proof process is provided easier than pure water. Tween 20 in all concentrations has a negative effect on the apparent growth rate, and GO has no significant effect on enhancing the apparent rate of R410a hydrate growth. Table 5 tabulates the average apparent rate constant of R410a hydrate growth until 10 min after the induction time for different additives at pressure of 1 MPa and the temperature of 279.65 K. The best result for the average apparent rate constant of hydrate growth is seen
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for 50 ppm SDS that is equal to 2.4999 × 10-9 mole gas/mole water. min. Pa. According to our kinetic results, SDS has the best performance in promoting the R410a
-p
hydrate formation. The results also show that GO can be used as an alternative additive to
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promote the kinetics of R410a hydrate for the hydrate-based cold storage systems. In a
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clathrate/ semiclathrate hydrate based cold storage system, enthalpy of hydrate dissociation is a crucial factor that needs further investigation. Therefore, dissociation kinetic and
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measured in the future.
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dissociation enthalpy of R410a hydrate in the presence of SDS and GO nanosheets should be
5. Conclusion
In this study, R410a hydrate was introduced as a cold storage medium and the effects of SDS, tween 20, and graphene oxide on the kinetic parameters of R410a hydrate formation including induction time, gas consumption, rate of gas uptake, apparent rate constant, storage capacity, and water to hydrate conversion were investigated. The experiments were tested at an initial pressure of 1 MPa and an initial temperature of 279.65 K in a stirred batch reactor. The results show that except 1000 ppm tween 20, other concentrations of additives (studied 18
Journal Pre-proof in the current work) reduce the induction time. It was also found that the promotion effects of SDS and GO on the quantity and rate of gas uptake, and apparent rate constant of R410a hydrate formation at the initial minutes of the growth step are significant. In addition, utilization of tween 20 inhibits the kinetics of the R410a hydrate formation process. Furthermore, the effects of additives on the amounts of storage capacity and water to hydrate
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conversion are not significant.
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References [1] A. Delahaye, L. Fournaison, D. Dalmazzone, Gas Hydrates 2: Geoscience Issues and Potential Industrial Applications (2018) 315. [2] X. Wang, M. Dennis, L. Hou, Renewable and Sustainable Energy Reviews 36 (2014) 34. [3] H. Hashemi, S. Babaee, A.H. Mohammadi, P. Naidoo, D. Ramjugernath, International
of
Journal of Refrigeration 98 (2019) 410.
ro
[4] C. Veerakumar, A. Sreekumar, international journal of refrigeration 67 (2016) 271.
-p
[5] G. Li, Y. Hwang, R. Radermacher, International journal of refrigeration 35 (2012) 2053. [6] J. Wu, S. Wang, Energy and Buildings 45 (2012) 99.
re
[7] E.D. Sloan, C.A. Koh, CHEMICAL INDUSTRIES-NEW YORK THEN BOCA RATON-
lP
MARCEL DEKKER THEN CRC PRESS- 119 (2008). [8] E.D. Sloan, Natural gas hydrates in flow assurance. Gulf Professional Publishing, 2010.
na
[9] A. Khokhar, J. Gudmundsson, E. Sloan, Fluid Phase Equilibria 150 (1998) 383.
ur
[10] H.P. Veluswamy, A. Kumar, Y. Seo, J.D. Lee, P. Linga, Applied Energy 216 (2018) 262.
Jo
[11] S. Tomita, S. Akatsu, R. Ohmura, Applied energy 146 (2015) 104. [12] H. Dashti, L.Z. Yew, X. Lou, Journal of Natural Gas Science and Engineering 23 (2015) 195.
[13] E. Kim, S. Lee, J.D. Lee, Y. Seo, Fuel 164 (2016) 237. [14] A. Eslamimanesh, A.H. Mohammadi, D. Richon, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 46 (2012) 62. [15] L. Shi, L. Yi, X. Shen, W. Wu, D. Liang, Journal of Molecular Liquids 229 (2017) 98. [16] H. Fakharian, H. Ganji, A. Naderifar, Journal of the Taiwan Institute of Chemical Engineers 72 (2017) 157. 20
Journal Pre-proof [17] M. Karamoddin, F. Varaminian, Desalination and Water Treatment 52 (2014) 2450. [18] A. Aliev, R.Y. Yusifov, A. Kuliev, Y.G. Yusifov, Russian Journal of Applied Chemistry 81 (2008) 588. [19] P. Babu, A. Nambiar, T. He, I.A. Karimi, J.D. Lee, P. Englezos, P. Linga, ACS Sustainable Chemistry & Engineering 6 (2018) 8093. [20] S. Safari, F. Varaminian, Innovative Food Science & Emerging Technologies (2019).
of
[21] S. Li, Y. Shen, D. Liu, L. Fan, Z. Tan, Chemical Engineering Research and Design 93
ro
(2015) 773.
-p
[22] S. Abedi-Farizhendi, M. Hosseini, M. Iranshahi, A. Mohammadi, M. Manteghian, A.H.
re
Mohammadi, Journal of Dispersion Science and Technology (2019) 1. [23] B. Mahmoudi, P. Naeiji, F. Varaminian, M.M. Ghazi, International Journal of Refrigeration
lP
69 (2016) 17.
na
[24] X. Wang, M. Dennis, Chemical Engineering Science 137 (2015) 938. [25] A. Mohammadi, A. Jodat, Journal of Molecular Liquids 293 (2019) 111433.
ur
[26] B. Mahmoudi, P. Naeiji, F. Varaminian, Journal of Molecular Liquids 214 (2016) 96.
Jo
[27] A. Cavallini, G. Censi, D. Del Col, L. Doretti, G. Longo, L. Rossetto, International Journal of Refrigeration 24 (2001) 73.
[28] H. Hashemi, S. Babaee, A.H. Mohammadi, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 80 (2015) 30. [29] A. Lindley, A. McCulloch, Journal of fluorine chemistry 126 (2005) 1457. [30] J.J. Tomlinson, Presented at the Energy Storage Contractors Rev. Meeting, Arlington, Va., 23 Aug. 1982, 1982.
21
Journal Pre-proof [31] T. Akiya, T. Shimazaki, M. Oowa, M. Matsuo, Y. Yoshida, International journal of thermophysics 20 (1999) 1753. [32] H. Hashemi, S. Babaee, A.H. Mohammadi, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 90 (2015) 193. [33] J. Javanmardi, S. Ayatollahi, R. Motealleh, M. Moshfeghian, Journal of Chemical & Engineering Data 49 (2004) 886.
of
[34] M. Mooijer-van den Heuvel, N. Sawirjo, C. Peters, Fluid phase equilibria 241 (2006) 124.
ro
[35] J.J. Carbajo, ASHRAE Trans.;(United States) 91 (1985).
-p
[36] A. Eslamimanesh, A.H. Mohammadi, D. Richon, Chemical engineering science 66 (2011)
re
5439.
[37] A. Delahaye, L. Fournaison, S. Marinhas, I. Chatti, J.-P. Petitet, D. Dalmazzone, W. Fürst,
lP
Industrial & engineering chemistry research 45 (2006) 391.
na
[38] W. Lin, A. Delahaye, L. Fournaison, Fluid Phase Equilibria 264 (2008) 220. [39] P.T. Ngema, P. Naidoo, A.H. Mohammadi, D. Ramjugernath, The Journal of Chemical
ur
Thermodynamics 136 (2019) 59.
18 (2008) 18.
Jo
[40] B.-Y. Zhang, W. Qiang, D.-L. Sun, Journal of China University of Mining and Technology
[41] H. Pahlavanzadeh, M. Khanlarkhani, S. Rezaei, A.H. Mohammadi, Fuel 253 (2019) 1392. [42] H. Ganji, M. Manteghian, M. Omidkhah, H.R. Mofrad, Fuel 86 (2007) 434. [43] B.R. Lee, J.D. Lee, H.J. Lee, Y.B. Ryu, M.S. Lee, Y.S. Kim, P. Englezos, M.H. Kim, Y. Do Kim, Journal of colloid and interface science 331 (2009) 55. [44] A. Al-Sowadi, H. Roosta, A. Dashti, S.A. Pakzad, R. Ghasemian, M. Rajaei, Journal of Molecular Liquids 294 (2019) 111608.
22
Journal Pre-proof [45] A. Erfani, F. Varaminian, Journal of Molecular Liquids 221 (2016) 963. [46] A. Mohammadi, M. Manteghian, A. Haghtalab, A.H. Mohammadi, M. Rahmati-Abkenar, Chemical Engineering Journal 237 (2014) 387. [47] H. Pahlavanzadeh, S. Rezaei, M. Khanlarkhani, M. Manteghian, A.H. Mohammadi, Journal of Natural Gas Science and Engineering 34 (2016) 803. [48] H. Kakati, A. Mandal, S. Laik, Journal of industrial and engineering chemistry 35 (2016)
of
357.
ro
[49] S. Abedi-Farizhendi, M. Iranshahi, A. Mohammadi, M. Manteghian, A.H. Mohammadi,
-p
Petroleum Science (2019) 1.
re
[50] A. Ghozatloo, M. Shariaty-Niassar, M. Hassanisadi, Iranian Journal of Chemical Engineering 11 (2014).
lP
[51] J. Li, D. Liang, K. Guo, R. Wang, S. Fan, Energy Conversion and Management 47 (2006)
na
201.
[52] M. Karamoddin, F. Varaminian, M. Daraee, Journal of Natural Gas Science and
ur
Engineering 19 (2014) 46.
Jo
[53] S. Abedi-Farizhendi, M. Rahmati-Abkenar, M. Manteghian, J.S. Yekshaveh, V. Zahmatkeshan, Journal of Petroleum Science and Engineering 172 (2019) 636. [54] E. Rezaei, M. Manteghian, M. Tamaddondar, Journal of Petroleum Science and Engineering 147 (2016) 857. [55] D.-Y. Peng, D.B. Robinson, Industrial & Engineering Chemistry Fundamentals 15 (1976) 59. [56] J. Munck, S. Skjold-Jørgensen, P. Rasmussen, Chemical Engineering Science 43 (1988) 2661.
23
Journal Pre-proof [57] P.T. Ngema, C. Petticrew, P. Naidoo, A.H. Mohammadi, D. Ramjugernath, Journal of Chemical & Engineering Data 59 (2014) 466. [58] E. Sloan, C. Koh, Taylor and Francis Group, Boca Raton, 2007. [59] J. Calm, Refrig. Manage. Serv (2008) 1. [60] W. McCain, Tulsa, 1990. [61] J.B. Klauda, S.I. Sandler, Industrial & engineering chemistry research 39 (2000) 3377.
of
[62] P. Englezos, N. Kalogerakis, P. Dholabhai, P. Bishnoi, Chemical Engineering Science 42
ro
(1987) 2647.
-p
[63] M.J. Frank, J.A. Kuipers, W.P. van Swaaij, Journal of Chemical & Engineering Data 41
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(1996) 297.
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[64] Q. Ma, X. Zhu, D. Zhang, S.F. Liu, Journal of Materials Chemistry C 2 (2014) 8956.
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Journal Pre-proof Table 1. Suppliers and purities of the chemicals used. Supplier
Chemical formula
R410a SDS Tween 20 Potassium permanganate Sodium nitrate Sulfuric acid Hydrogen peroxide Graphite powder
Iscon- China Merck- Germany Sigma Aldrich- USA Merck- Germany Merck- Germany Merck- Germany Merck- Germany NGS graphite GmbH
CH2F2/CHF2CF3 (50/50% by weight) C12H25NaO4S C58H114O26 KMnO4 NaNO3 H2SO4 H2O2 C
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Chemical name
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Purity (mass fraction) 0.99 0.99 0.99 0.99 0.99 0.98 0.30 0.99
Journal Pre-proof Table 2. The Langmuir constant parameters of large cavities for R410a. Structure
Alarge (K/MPa)
R410a
II
4.750×10-3
Blarge (K) 5969.68
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Gas
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Journal Pre-proof Table 3. Induction time of R410a hydrate formation in the presence of SDS, tween 20, and graphene oxide. Induction time (min)
Pure water
279.65
1
5.6
SDS (50)
279.65
1
3.5
SDS (100)
279.65
1
3.7
SDS (200)
279.65
1
4.5
SDS (500)
279.65
1
0.6
Tween (50)
279.65
1
3.2
Tween (100)
279.65
1
1.2
Tween (250)
279.65
1
4
Tween (1000)
279.65
1
8.9
GO (50)
279.65
1
1.7
GO (100)
279.65
1
2.1
GO (200)
279.65
1
GO (400)
279.65
1
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P (MPa)
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T (K)
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additive (ppm)
1.8
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0.2
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Journal Pre-proof Table 4. Storage capacity and water to hydrate conversion of R410a hydrate formation in the presence of SDS, tween 20, and graphene oxide. additive (ppm)
T (K)
P (MPa)
Storage
capacity
Water to hydrate conversion (%)
(V/V) 279.65
1
17.45
26.24
SDS (50)
279.65
1
17.79
26.78
SDS (100)
279.65
1
17.50
26.31
SDS (200)
279.65
1
17.15
25.73
SDS (500)
279.65
1
17.54
26.38
Tween (50)
279.65
1
17.02
25.54
Tween (100)
279.65
1
17.17
Tween (250)
279.65
1
16.82
Tween (1000)
279.65
1
3.99
GO (50)
279.65
1
17.05
GO (100)
279.65
1
17.42
GO (200)
279.65
1
17.63
GO (400)
279.65
1
17.41
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Pure water
25.79
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25.21
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5.67
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25.59 26.19 26.53 26.17
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Table 5. Apparent rate constant average of R410a hydrate growth until 10 min after the induction time in the presence of SDS, tween 20, and graphene oxide.
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Pure Water SDS (50 ppm) SDS (100 ppm) SDS (200) SDS (500 ppm) Tween (50 ppm) Tween (100 ppm) Tween (250 ppm) Tween (1000 ppm) GO (50 ppm) GO (100 ppm) GO (200 ppm) GO (400 ppm)
Average of kapp ×109 until t-tind=10 min 2.3125 2.4999 2.2659 2.5228 2.5883 1.3219 1.3783 0.6937 0.0415 2.3918 2.3041 2.3332 2.3127
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Additive
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Fig. 1. The schematic diagram of the experimental set-up used in this study.
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Journal Pre-proof 1.4
1.2
ΔTsubcooling
P (MPa)
1
0.8
0.6
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0.4
0 278
280
282
284
286
288
-p
276
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0.2
290
292
294
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T (K)
Fig. 2. - - , R410a hydrate equilibrium data [28]; , initial condition for the kinetic experiments in this
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study.
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Pressure
Temperature
1
283.5 283
282 0.6 281.5 281 0.4 280.5
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0.2
0 10
20
30
40
Time (min)
-p
0
50
Temperature (K)
282.5
280
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Pressure (MPa)
0.8
279.5 279 60
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Fig. 3. Pressure and temperature variations of the reactor during system hydrate formation for R410a +
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pure water.
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0.014 0.012 0.01 Pure water SDS 50 ppm
0.008
SDS 100 ppm 0.006
SDS 200 ppm SDS 500 ppm
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0.004 0.002
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Mole of gas consumed/ mole of water
0.016
0 5
10
15
20
25
30
35
40
-p
0
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Time (min)
Fig. 4. Effect of different concentrations of SDS on the amount of R410a consumption during hydrate
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formation at an initial temperature of 279.65 K and pressure of 1 MPa.
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0.016 0.014 0.012 Pure water
0.01
Tween 50 ppm 0.008
Tween 100 ppm
0.006
Tween 250 ppm Tween 1000 ppm
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0.004 0.002 0 0
10
20
30
40
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Time (min)
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Mole of gas consumed/ mole of water
0.018
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Fig. 5. Effect of different concentrations of tween 20 on the amount of R410a consumption during
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hydrate formation at an initial temperature of 279.65 K and pressure of 1 MPa.
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(b)
(a)
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(c)
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Fig. 6. The images of hydrate formed at the end of reaction: (a) Pure water, (b) 100 ppm tween 20, (c)
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1000 ppm tween 20.
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0.014 0.012 0.01 Pure water GO 50 ppm
0.008
GO 100 ppm 0.006
GO 200 ppm GO 400 ppm
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0.004 0.002 0 5
10
15
20
25
30
35
40
-p
0
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Mole of gas consumed/ mole of water
0.016
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Time (min)
Fig. 7. Effect of different concentrations of grapheme oxide on the amount of R410a consumption during
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hydrate formation at an initial temperature of 279.65 K and pressure of 1 MPa.
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0.004 Pure water SDS 50 ppm
0.003
SDS 100 ppm SDS 200 ppm
0.002
SDS 500 ppm
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Rate of gas uptake ( ng/ nw .min)
0.005
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0.001
0
5
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0 10
15
20
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Time (min)
Fig. 8. Rate of R410a gas uptake during hydrate formation in the presence of different concentrations of
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SDS at an initial temperature of 279.65 K and pressure of 1 MPa.
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0.004 0.0035 0.003
Pure water Tween 50 ppm
0.0025
Tween 100 ppm
0.002
Tween 250 ppm 0.0015
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Tween 1000 ppm
0.001
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Rate of gas uptake ( ng/ nw .min)
0.0045
0.0005 0 5
10
15
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Time (min)
-p
0
20
Fig. 9. Rate of R410a gas uptake during hydrate formation in the presence of different concentrations of
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tween 20 at an initial temperature of 279.65 K and pressure of 1 MPa.
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0.004 0.0035 0.003
Pure water GO 50 ppm
0.0025
GO 100 ppm
0.002
GO 200 ppm 0.0015
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GO 400 ppm
0.001
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Rate of gas uptake ( ng/ nw .min)
0.0045
0.0005
0
5
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0 10
15
20
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Time (min)
Fig. 10. Rate of R410a gas uptake during hydrate formation in the presence of different concentrations of
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graphene oxide at an initial temperature of 279.65 K and pressure of 1 MPa.
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3.5E-09 3E-09 Pure water
2.5E-09
SDS 50 ppm 2E-09
SDS 100 ppm SDS 200 ppm
1.5E-09
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SDS 500 ppm
1E-09
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kapp (mole G/ mole W.min.Pa)
4E-09
5E-10
0
5
-p
0 10
15
20
re
t- tind (min)
Fig. 11. Apparent rate constant during R410a hydrate growth in the presence of SDS at an initial
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temperature of 279.65 K and pressure of 1 MPa.
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2.5E-09
Pure water
2E-09
Tween 50 ppm Tween 100 ppm
1.5E-09
Tween 250 ppm Tween 1000 ppm
1E-09
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kapp (mole G/ mole W.min.Pa)
3E-09
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5E-10
0 5
10
15
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0
20
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t-tind (min)
Fig. 12. Apparent rate constant during R410a hydrate growth in the presence of tween 20 at an initial
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temperature of 279.65 K and pressure of 1 MPa.
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3.5E-09 3E-09 Pure water
2.5E-09
GO 50 ppm 2E-09
GO 100 ppm GO 200 ppm
1.5E-09
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GO 400 ppm
1E-09
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kapp (mole G/ mole W.min.Pa)
4E-09
5E-10
0
5
-p
0 10
15
20
re
t-tind (min)
Fig. 13. Apparent rate constant during R410a hydrate growth in the presence of graphene oxide at an
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initial temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof Declaration of competing interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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Journal Pre-proof Author statement Amir Mohammad Javidani: Writing- Original draft, Methodology, Validation, Formal analysis, Investigation, Visualization Saeid Abedi-Farizhendi: Formal analysis Abolfazl Mohammadi: Conceptualization, Methodology, Software, Formal analysis, Writing - Review & Editing Amir H. Mohammadi: Writing - Review & Editing Hussein Hassan: Investigation
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Hassan Pahlavanzadeh: Writing - Review & Editing
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Highlights
R410a hydrate is studied as a cold storage medium.
Storage capacity of R410a hydrate is investigated in presence of SDS, tween 20, and graphene oxide nanosheets.
Utilization of 400 ppm GO decreases the amount of induction time from 5.6 min to 0.6
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The addition of 500 ppm SDS, increases the apparent rate constant of hydrate growth up
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to 12%.
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Amir Mohammad Javidani, Saeid Abedi-Farizhendi, Abolfazl Mohammadi, Amir H. Mohammadi, Hussein Hassan, Hassan Pahlavanzadeh PII:
S0167-7322(19)35678-8
DOI:
https://doi.org/10.1016/j.molliq.2020.112665
Reference:
MOLLIQ 112665
To appear in:
Journal of Molecular Liquids
Received date:
13 October 2019
Revised date:
29 January 2020
Accepted date:
8 February 2020
Please cite this article as: A.M. Javidani, S. Abedi-Farizhendi, A. Mohammadi, et al., Experimental study and kinetic modeling of R410a hydrate formation in presence of SDS, tween 20, and graphene oxide nanosheets with application in cold storage, Journal of Molecular Liquids(2020), https://doi.org/10.1016/j.molliq.2020.112665
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© 2020 Published by Elsevier.
Journal Pre-proof
Experimental study and kinetic modeling of R410a hydrate formation in presence of SDS, tween 20, and graphene oxide nanosheets with application in cold storage Amir Mohammad Javidania, Saeid Abedi-Farizhendia, Abolfazl Mohammadib,*, Amir H. Mohammadic,d,#, Hussein Hassana, Hassan Pahlavanzadeha
Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
b
Department of Chemical Engineering, University of Bojnord, Bojnord, Iran
c
Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France
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d
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Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa
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Abstract - Gas hydrates, or clathrate hydrates, can be used as a suitable cold/cool storage
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media, due to their large phase change enthalpy. In recent decades, cold production through gas hydrates as a novel and cost-effective method has motivated researchers. Refrigerants have the potential to be used in hydrate-based cold storage systems, because they can form hydrates at moderate pressures and temperatures. Hence, in this work, the kinetics of R410a (50 wt% difluoromethane + 50 wt% 1,1,1,2,2-pentafluoroethane) hydrate formation in the presence of different concentrations of SDS, tween 20, and graphene oxide (GO) was investigated. The experiments were carried out in a 300 cm3 reactor/cell at the initial pressure and temperature of 1 MPa and 279.65 K, respectively. According to the results, at all concentrations of the additives, except tween 20 at a concentration of 1000 ppm, the hydrate formation induction time decreases, compared to pure water. Furthermore, the promotion effects of SDS and GO on the quantity and rate of gas uptake, and the apparent rate constant were observed at the initial minutes of the hydrate growth process. The measured storage capacity and water to hydrate conversion show that the used additives do not change the abovementioned parameters, noticeably.
Keywords - Gas hydrates; Clathrate hydrates; Cold storage; Cool storage; Kinetics; Refrigerant
* Corresponding author: Abolfazl Mohammadi, [email protected] # Co corresponding author: Amir H. Mohammadi, [email protected]
1
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1. Introduction Cold production is a fundamental part of the strategy to develop in many processes such as food preservation, electronics, air conditioning, etc. However, it accounts for almost 15% of the electricity consumed in industrialized countries and has an increasing trend in all of the world. It has been found that cold storage has the capacity that can be charged during the
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night and discharged during the day using off-peak hours [1-3]. Initially, water and ice were presented as the materials that could be used for cold storage technology, but phase change
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materials (PCMs) as a promising candidate for cold storage application has attracted a great
-p
deal of attention due to their outstanding properties. PCMs have the potential to absorb
re
energy by latent heat during liquefaction. They can take many forms including paraffin
lP
slurry, microencapsulated slurry, stabilized slurry, and gas hydrate slurry [1, 4-6]. The interaction between the water molecules (called host molecules) and the molecules of
na
gases and/or some volatile liquids with appropriate sizes and shapes like methane, ethane,
ur
propane, carbon dioxide, hydrogen sulfide, cyclopentane, refrigerants, etc (called guest
Jo
molecules) at low temperatures and/or high pressures results in the formation of icy crystalline solids called “gas hydrates” or “clathrate hydrates”. Depending on the sizes of guest molecules, gas composition and thermodynamic conditions, the crystalline structure of hydrates can consist of any combination of three typical categories: structure I, structure II, and structure H [7, 8]. Even though gas hydrates cause blockage in the gas transmission equipment and pipelines, also have the potential for numerous positive applications such as gas storage [9, 10], separation of greenhouse gases [11-15], water desalination [16-19], juice and coffee concentration [20-22], air conditioning systems [1, 23-26], etc.
2
Journal Pre-proof R410a, belonging to the group of hydrofluorocarbons (HFCs) refrigerants, is mainly utilized as a replacement for ozone-depleting substances (ODSs) like R11, R12, and R22. R410a does not contribute to ozone depletion, and therefore, becoming more widely used in air conditioning equipment [27]. R410a forms hydrate with structure II at moderate conditions compared to common gas hydrate formers such as CH4, C2H6 and CO2 [28] and can be used as gas hydrate former in cold storage medium and air conditioning systems.
of
However, R410a has a high global warming potential (GWP) of 2088 and about 99 times as
ro
much as CH4, which includes in the basket of emission controlled by the “Kyoto Protocol” as
-p
greenhouse gas [29]. Hence, it is necessary to employ methods like gas hydrate technology in
re
order to capture and recover the waste R410a gas from emissions.
lP
In 1982, gas hydrates were presented as new media of cold storage in air conditioning systems, especially due to their large enthalpy of phase change, as mentioned earlier [30]. In
na
the past decades, a large number of studies have been done to develop cold storage systems
ur
using gas hydrates. Most of these studies have been carried out with the aim of understanding the thermodynamic (phase equilibrium) and kinetic (growth) behaviors of gas hydrates to be
Jo
used as a suitable medium for cold storage [2, 31]. It was found that refrigerants can form hydrates at moderate pressure and temperature ranges [3]. Hydrate formation and dissociation conditions of different refrigerants (R11, R12, R22, R23, R134a, R141b, R125a, and R410a) and mixed refrigerants were investigated by some researchers [3, 28, 31-36]. Furthermore, enthalpy of hydrate dissociation is a key factor to select suitable gas hydrate former in cold storage applications, because it shows the required enthalpy of hydrate dissociation or cold storage capacity. Hydrate dissociation enthalpy of different gases could be found in the literature [37, 38]. The dissociation enthalpies of R410a and R134a hydrates
3
Journal Pre-proof measured by Ngema et al. was in the range of 69-89, and 124-134 kJ/mol, respectively [39]. Kinetic parameters of gas hydrates such as growth rate and the time needed to form the first crystals (induction time) are crucial factors that play a significant role in the hydrate-based cold storage process [3, 25]. Kinetic promoters improve the kinetics of gas hydrate formation process by shortening the induction time and increasing the gas uptake and the rate of hydrate formation. It has
of
already been proven that surfactants such as sodium dodecyl sulfate (SDS), cetyl
ro
trimethylammonium bromide (CTAB), linear alkyl benzene sulfonate (LABS), and tween
-p
promote the kinetic formation of hydrates by decreasing the gas-liquid surface tension [22,
re
40-45]. In addition, nanoparticles like Ag, Cu, Al2O3, SiO2 and carbon nanotubes (CNTs)
lP
play the same role by enhancing the heat and mass transfer due to their high specific surface areas [41, 46-50]. Li et al. reported that Cu nanoparticles enhance the kinetics of R134a
na
hydrate formation and dissociation, remarkably [51]. Karamoddin et al. findings indicate that
ur
SDS greatly increases the rate of R22 hydrate formation at low stirring speed [52]. Kinetics of R404a, R406a, R408a, R427a, R407c, R507c, R410a hydrates formation at different
Jo
degrees of subcooling and in the presence and absence of SDS were investigated by some researchers [3, 28]. According to the reported results, the addition of SDS increases the rate of the hydrates formation for R404a, R406a, R408a, R427a gases and unexpectedly shows a negative effect on the kinetics of R410a, R407c and R507c hydrates [3, 28]. Graphene oxide (GO) nanosheets exhibit excellent mechanical strength in addition to high thermal and electrical conductivities. These nanosheets can promote the hydrate formation kinetics due to their high specific areas to volume ratio. On the other hand, they cause heterogeneous nucleation during crystallization, which helps the hydrate formation to 4
Journal Pre-proof take place more easily. The promotion effects of these nanosheets on the kinetic parameters of methane, propane and ethylene hydrates were studied by Manteghian et al. [49, 53, 54]. According to the related literature, most of the previous researchers have focused on the thermodynamic behaviors of refrigerant hydrates, and the kinetic formation of refrigerants hydrates has received less attention. Therefore, further research is needed on the kinetic of
of
refrigerants hydrates formation in the presence of additives.
ro
In this work, the effects of anionic surfactant, SDS, nonionic surfactants, polysorbate 20 (tween 20) and GO on the kinetic parameters of R410a hydrate formation at initial conditions
-p
of 279.65 K and 1 MPa were examined. Kinetic parameters include induction time, gas
re
consumption, rate of gas uptake, storage capacity, water to hydrate conversion, and apparent
Jo
2.1. Materials
ur
2. Experimental
na
lP
rate constant.
The suppliers, chemical formula and purities of the materials used in this study are presented in Table 1. In all the experiments, to prepare aqueous solutions, a gravimetrical analytical balance and de-ionized water were used.
2.2. Preparation of graphene oxide nanosheets
5
Journal Pre-proof The method used to synthesize and characterize GO, is presented in a previous paper [53]. Briefly, graphite powder (5 g) was added to the sulfuric acid solution (150 mL), followed by adding sodium nitrate (2.5 g) and then potassium permanganate (15 g). Next, the solution was stirred for 24 h. Then, the solution was diluted with de-ionized water (300 mL), and stirred for 2 h. Hydrogen peroxide aqueous solution (100 mL) was added to the solution.
ro
was sonicated for 20 minutes to produce a GO solution.
of
Next, the mixture was washed with HCl and then with de-ionized water. Finally, the mixture
-p
2.3. Apparatus
re
Fig. 1 depicts the schematic diagram of the experimental apparatus used in this work. The
lP
reactor/cell is made of stainless steel with an inner diameter of 6.2 cm, a height of 10 cm and an effective internal volume of 300 cm3. It has a needle valve, which can withstand up to 10
na
MPa for injecting and discharging the gas, and a ball valve for charging the aqueous solution.
ur
A circulator containing water and ethylene glycol with a volume ratio of 50/50 was employed to keep the reactor temperature at a desired constant value during the tests. A mixer was used
Jo
to agitate the components inside the solution. This helps to increase the gas-liquid contact area and enhances the heat and mass transfer of the aqueous solution. The temperature and pressure of the reactor were monitored continuously along the time during the experiment by means of a platinum resistance thermocouple with an accuracy of 0.1 K and a pressure transducer with an uncertainty of ± 0.01 MPa, which are connected to the top of the reactor. A control panel acquires the temperature and pressure of the reactor and then feeds to the computer and the panel records the obtained data using an in-house software at every 5 seconds.
6
Journal Pre-proof
2.4. Experimental procedure To ensure that the reactor has no leak, the nitrogen inert gas was injected to the cell up to 10 MPa and left intact for 24 h at 298 K. After a day, the pressure of the reactor remained constant. At the first step of each experimental run, the cell was rinsed and eluted properly
of
with distilled water, and then the air and impurities inside the cell were evacuated down to -
ro
0.07 MPa using a vacuum pump. Thereafter, 100 cm3 of the aqueous solution sample was introduced into the cell. Then, the cell was immersed into the circulator and its temperature
-p
was adjusted to 279.65 K. After reaching the desired temperature value, the R410a
re
refrigerant was introduced into the cell up to 1 MPa. In the next step, the mixer was set at a
lP
speed of 200 rpm in all experiments. During the hydrate formation, the gas molecules transfer to the hydrate cages, and consequently, the cell pressure decreases continuously.
na
After the cell pressure variations were reached nearly 0.05 MPa/h, the hydrate formation was
ur
considered to be over, and the hydrate growth was stopped. R410a hydrate phase equilibrium
Jo
curve reported in the literature [28], as well as the initial conditions of the present study are shown in Fig. 2.
3. Kinetic Model 3.1. Amount of gas consumption In the process of refrigerant hydrate formation, the physical reaction between water molecules and refrigerant can be defined as follows [3]:
7
Journal Pre-proof R
+
MH2O
R.
MH2O
ΔH
+
(1) where, M is hydration number (number of water molecules per refrigerant gas) that depends on the filling size of small and large cavities. R410a molecules form structure II; for this structure, hydration number is calculated by the following equation [7]: 17
(2)
𝑙𝑎𝑟𝑔𝑒 +2𝜃𝑠𝑚𝑎𝑙𝑙
of
M= 𝜃
ro
where θlarge and θsmall represent the fractional occupancy of large and small cavities,
-p
respectively. R410a molecules cannot enter the small cavities, because of their large size
re
[39]. Thus, θsmall for R410a hydrates is zero. The fractional occupancy of large cavities is
lP
calculated on the basis of Langmuir adsorption theory as follows [7]:
(3)
𝐶𝑙𝑎𝑟𝑔𝑒 𝑓 𝑔 1+ 𝐶𝑙𝑎𝑟𝑔𝑒 𝑓 𝑔
na
θlarge=
ur
where Clarge is the Langmuir constant of R410a refrigerant molecules in large cavities, fg is
Jo
the fugacity of the R410a refrigerant in the gas/vapor phase, which is calculated using the Peng-Robinson equation of state [55]. To calculate Clarge, the following formula can be used [56]: Clarge=
𝐴𝑙𝑎𝑟𝑔𝑒
exp
𝑇
𝐵𝑙𝑎𝑟𝑔𝑒
(
𝑇
)
(4) where T is temperature, and Alarge and Blarge are the adjustable parameters for the Langmuir constant, whose values are reported in Table 2 [57]. 8
Journal Pre-proof The amount of R410a gas consumption during the hydrate formation is calculated as follows [58]:
Δn=
𝑃0 𝑉0
𝑃𝑡 𝑉𝑡
-
𝑍0 𝑅𝑇0
𝑍𝑡 𝑅𝑇𝑡
(5) where R represents the universal gas constant, Pt and Tt are the cell pressure and temperature
of
at a given time=t, respectively, Vt is the volume of the gas at time=t, V0 represents the
ro
volume of the gas at the beginning of the reaction, which is equal to 200 cm3, P0 stands for
-p
the initial pressure of the cell, which is 1 MPa, T0 is the initial temperature of the cell, which
re
is 279.65 K, and Z represents the compressibility factor of gas, which can be calculated by
Z3-
lP
the Z form of Peng-Robinson equation of state as follows [55]: (B-1)Z2
(A-3B2-2B)Z
na
(6)
+
(𝑅𝑇)2
Jo
(7) B=
(AB-B2-B3)=0
(𝑎𝑐 𝛼)𝑃
ur
A=
–
𝑏𝑃 𝑅𝑇
(8) 𝑅 2 𝑇𝑐2
ac= 0.45724
(9)
𝑃𝑐2
𝑅𝑇
0.07780 𝑃 𝑐
b=
𝑐
(10)
9
Journal Pre-proof where Pc and Tc refer to the critical pressure and critical temperature of R410a refrigerant that equal to 4.964 MPa and 345.65 K, respectively [59]. α and m are obtained using the following equations: α=
m(1-Tr0.5 ))2
(1+
(11) 0.3746+
0.2669ω2
1.5423𝜔-
of
m=
ro
(12)
-p
where, ω is the acentric factor of R410a refrigerant (equals to 0.279) [39], which is an index
re
for the non-spherical of their molecules.
(13)
–
Vcell
𝑉𝑠0
+
–
𝑉𝑅𝑊𝑡
𝑉𝐻𝑡
na
Vt=
lP
The volume of the gas inside the cell at a given time, Vt , can be calculated as follows [46]:
ur
where, Vcell is the reactor volume (300 cm3), 𝑉𝑠0 represents the initial volume of the aqueous
Jo
solution (100 cm3), and 𝑉𝑅𝑊𝑡 and 𝑉𝐻𝑡 are the volume of reacted water and the volume of produced hydrate, respectively. The volume of reacted water at time=t, 𝑉𝑅𝑊𝑡 , is calculated from the following relationship [46]: 𝑉𝑅𝑊𝑡 =
Δn
M×
×
υw L
(14) where υwL is the molar volume of water in the liquid/aqueous phase that is calculated using the following equation [60]:
10
Journal Pre-proof υwL = 18.015 × {1- (1.0001 × 10-2) + (1.33391 × 10-4) [1.8(T- 273.15) +32] + (5.50654 × 107 )[1.8(T- 273.15) +32]2 × 10-3 (15) The units of υwL and T are in m3/kmol and K, respectively. The following equation was employed for calculating the molar volume of empty hydrate lattice for structure II [61]: υwMT [sII]= (17.13 + 2.249 × 10-4T + 2.013 × 10-6T2 + 1.009 × 10-9T3) ×
10−30 NA 136
– 8.006 ×
10-9 P + 5.448 × 10-12 P2
(16)
of
where, NA is the Avogadro’s number (6.022 ×1023), and P and T are the pressure and
ro
temperature in MPa and K, respectively. By assuming that the molar volume of hydrate is
-p
equal to the molar volume of empty hydrate lattice, the volume of produced hydrate at time t,
𝑉𝐻𝑡 =
re
can be obtained from the following relationship:
× Δn
υwMT
×
lP
M
ur
3.2. Rate of gas uptake
na
(17)
r(t)
Jo
Rate of gas uptake at time=t, r(t), during the hydrate formation can be calculated as: ni−1 −ni+1
=
(ti+1 −ti−1 )n𝑤0
(18) where, ni-1 and ni+1 stand for the gas mole number at time=ti-1 and time=ti+1, respectively, and n𝑤0 is the initial number of moles of water in the liquid phase [46].
3.3. Storage Capacity (SC) 11
Journal Pre-proof Storage capacity (SC) is defined as the volume of entrapped gas into hydrate cages per volume of gas hydrate at the standard conditions. The following equation is used to calculate the SC of R410a [46]: SC
=
𝑉𝑆𝑇𝑃
Δ𝑛 𝑅 𝑇𝑆𝑇𝑃 / 𝑃𝑆𝑇𝑃
=
𝑉𝐻
𝑉𝐻
(19)
of
where subscript STP represents the standard conditions of temperature and pressure, which is
ro
273.15 K for temperature, and 0.1 MPa for pressure. The proposed algorithm by Mohammadi
re
-p
et al. was used for SC calculation [46].
lP
3.4. Water to hydrate conversion
Number of moles of water molecules converted to gas hydrate per mole of feed water is
hydrate
conversion
(%)
M × Δn
= n 𝑤0
×
100
Jo
(20)
to
ur
Water
na
known as water to hydrate conversion, which is calculated as follows:
3.5. Hydrate apparent rate constant The following equation is used for the apparent rate constant calculation at a given time [62]: kapp
=
(21)
12
𝑟(𝑡) 𝑓𝑔 −𝑓𝑒𝑞
Journal Pre-proof where, kapp is apparent rate constant, fg represents the fugacity of R410a refrigerant in the gas/vapor phase at the system temperature and pressure, which is calculated using PengRobinson equation of state [55], and feq is the fugacity of R410a refrigerant at the hydrate equilibrium pressure and initial temperature.
ro
of
3. Results and Discussion
-p
4.1. Effects of additives on induction time
re
A typical profile of pressure and temperature variations versus time in the (R410a + pure
lP
water) system during hydrate formation at the initial conditions of 279.65 K and 1 MPa is plotted in Fig. 3. As illustrated, in the initial minutes after gas injecting, a rapid reduction in
na
pressure was observed in the system due to the R410a refrigerant dissolution into the aqueous phase. Then, the cell temperature returned back to the set value until the moment that
ur
primary nucleation started. At this time, the cell temperature was increased instantaneously
Jo
due to the exothermic nature of the crystallization process, and its pressure dropped dramatically as a result of gas falling into the hydrate cages. At this time, the first nuclei of hydrate crystals appeared. The time elapsed between the start of gas injection and observation of significant changes in pressure and temperature is defined as “induction time”. Then, the hydrate crystals begin to grow until the cell pressure reaches approximately a constant value. Table 3 shows the induction times for the systems of R410a + different aqueous solutions at the initial temperature and pressure of 279.65 K and 1 MPa, respectively. The finding 13
Journal Pre-proof induction time indicated that SDS at all concentrations reduced the induction time compared to pure water; however, SDS at the concentration of 500 ppm had the highest reduction in the induction time. In comparison to pure water, tween 20 at concentrations of 50 ppm, 100 ppm, and 250 ppm resulted in a slight decrease in the induction time, but at high concentration (1000 ppm), it increased the induction time. SDS and tween 20 act as surfactants, and it has been established that surfactants alleviate surface tension. Indeed, these surfactants facilitate
of
transferring of R410a molecules from the gas phase to the aqueous phase by decreasing the
ro
surface tension of water molecules. The viscosity of tween 20 is about 400 times more than
-p
that of pure water. Consequently, at a high concentration of tween 20, the viscosity of the
re
solution increases significantly. Frank and coworkers showed that the diffusion coefficient of a gas in water decreases by increasing the viscosity of water [63]. Tween 20 aqueous solution
lP
at 1000 ppm acts as a barrier against the dissolution of molecules of refrigerant into the
na
solution, and therefore, results in inhibition effect on the kinetics of R410a hydrate formation. All concentrations of graphene oxide cause a reduction in the induction time
ur
compared to pure water. GO nanosheets produce lots of nucleation sites, which lead to
Jo
heterogeneous nucleation during the hydrate formation [54, 64]. On the other hand, heterogeneous nucleation needs less work to form hydrate crystals than homogeneous nucleation. It is also be noted that in the case of pure water induction time, R410a can quickly form hydrate without any promoters, and the effect of promoters on induction time is not remarkable. 4.2. Effects of additives on gas consumption and rate of gas uptake Fig. 4 illustrates the quantity of R410a mole consumed changes during the hydrate formation in pure water and various concentrations of SDS at the initial temperature and 14
Journal Pre-proof pressure of 279.65 K and 1 MPa, respectively. As seen in this figure, after 20 min, 50 ppm and 500 ppm SDS have increased the moles of gas consumed. But there is no significant change in the gas consumption of 100 ppm SDS solution, and decreasing the gas consumption of 200 ppm SDS solution is observed. At t=10 min, the amount of gas consumed per mole of feed water for pure water is 0.01010 mole, while 500 ppm SDS has 0.01309 moles. This means that 500 ppm SDS has increased the mole of gas consumption by
of
up to 29.6 mole percentage compared to pure water. In all the solutions, SDS has no effect on
ro
the final mole of gas consumed and its effect on the changes of gas consumption is more
-p
noticeable in the first 20 min of reaction.
re
The effect of tween 20 on the amount of gas consumption of R410a refrigerant is
lP
depicted in Fig. 5. As shown, all concentrations of tween 20 have a negative effect on the kinetics of R410a hydrate formation and act as a kinetic inhibitor. The reason for the
na
inhibition effect may be due to overcoming the negative effect of high viscosity on the
ur
positive effect of reducing surface tension. Tween 20 is a viscous liquid with the viscosity of 250-450 mPa.s at 298 K. Its high viscosity prevents the diffusion of R410a from the gas
Jo
phase to the solution. Fig. 6 shows the images of R410a hydrate for pure water, 100 and 1000 ppm solutions of tween 20 at the end of the reaction. As illustrated, the 1000 ppm tween 20 produces a high amount of foaming on the surface compared to the100 ppm tween 20 and pure water. It has been established that foam reduces heat transfer and mass transfer coefficients of any solution. Thus, 1000 ppm tween 20 has a more inhibition effect compared to 100 ppm tween 20. Fig. 7 shows changes in the mole consumption of R410a in the presence of GO (50, 100, 200, and 400 ppm). As shown, up to 15 min after the starting of the reaction, as the 15
Journal Pre-proof concentration of GO increases, more promotion effect on the mole consumption is obtained. Compared to pure water, 400 ppm GO increases the amount of R410a consumption by 21.4 mole percentage at t=10 min. GO like SDS, does not change the final mole of the consumed gas significantly. The promotion effect of GO at first 15 min of reaction might be related to the lowering of free energy by providing heterogeneous nucleation of these nanosheets as described earlier and their high specific surface area to volume ratio; this leads to better mass
of
transfer. Contrary to Manteghian and coworkers results regarding the promotion effects of
ro
GO on methane, propane, and ethylene hydrates formation [49, 53, 54], GO has less
-p
promotion effect on R410a gas consumption. It can be due to the higher solubility of R410a
re
comparing to the referred gases.
lP
Figs. 8-10 show the rate of R410a uptake curves during the hydrate formation of different systems, based on Eq. (18) within 20 min. As shown, the maximum rate of gas uptake is
na
observed at the beginning of the reaction due to the sudden drop in pressure and high
ur
solubility of the refrigerant into the aqueous solution. Thereafter, the rate of gas uptake diminishes shortly until the moment that the rate increases sharply. The sudden increase is
Jo
due to the rapid entrapment of the gas molecules into the hydrate cages cavities, and the produced nuclei are at the highest possible. After the peak point, the hydrate crystals begin to grow. As the hydrate growth begins, the number of nuclei decreases. On the other hand, temperature increase arising from the exothermic nature of nucleation decreases the driving force of hydrate formation. These two factors cause a reduction in gas uptake after the induction time. SDS with concentrations of 50 and 500 ppm, and all aqueous solutions of GO enhance the rate of gas uptake at induction time, compared to pure water. Other
16
Journal Pre-proof concentrations of SDS and all concentrations of tween 20 result in reducing the rate of gas uptake at the induction time.
4.3. Effects of additives on storage capacity (SC), water to hydrate conversion, and apparent rate constant of hydrate growth
of
SC and the ratio of water to hydrate conversion are kinetic parameters that are affected by
ro
the amount of entrapped gas molecules (Δn). Table 4 reports the measured SC and water to
-p
hydrate conversion in pure water and additive solutions. As can be seen, the effects of different concentrations of additives on SC and percentage of water to hydrate conversion are
re
similar. According to the results, 1000 ppm tween 20 reduced the aforementioned parameters
lP
significantly due to its high viscosity as described earlier. Other concentrations of additives
na
had no remarkable effects on the SC and water to hydrate conversion values. These results show that the additives do not change the phase equilibrium curve of hydrate formation, and
ur
the final pressure of the experiments reaches to approximately a constant value. SDS (50
Jo
ppm) had the highest value in SC and percentage of water to hydrate conversion. Figs. 11-13 show the apparent rate constant changes of R410a during the hydrate growth in pure water and in the presence of SDS, tween 20, and GO solutions. As observed, the apparent rate constant decreases after it reaches the maximum value at the induction time. This type of change may arise from decreasing of gas uptake. As shown in Figs. 11-13, all concentrations of SDS increase the apparent rate constant, especially, after 5 min of starting of the growth process. The presence of SDS leads to more captured gas into the aqueous phase by decreasing the gas-liquid surface tension, and consequently, the hydrate growth
17
Journal Pre-proof process is provided easier than pure water. Tween 20 in all concentrations has a negative effect on the apparent growth rate, and GO has no significant effect on enhancing the apparent rate of R410a hydrate growth. Table 5 tabulates the average apparent rate constant of R410a hydrate growth until 10 min after the induction time for different additives at pressure of 1 MPa and the temperature of 279.65 K. The best result for the average apparent rate constant of hydrate growth is seen
ro
of
for 50 ppm SDS that is equal to 2.4999 × 10-9 mole gas/mole water. min. Pa. According to our kinetic results, SDS has the best performance in promoting the R410a
-p
hydrate formation. The results also show that GO can be used as an alternative additive to
re
promote the kinetics of R410a hydrate for the hydrate-based cold storage systems. In a
lP
clathrate/ semiclathrate hydrate based cold storage system, enthalpy of hydrate dissociation is a crucial factor that needs further investigation. Therefore, dissociation kinetic and
Jo
ur
measured in the future.
na
dissociation enthalpy of R410a hydrate in the presence of SDS and GO nanosheets should be
5. Conclusion
In this study, R410a hydrate was introduced as a cold storage medium and the effects of SDS, tween 20, and graphene oxide on the kinetic parameters of R410a hydrate formation including induction time, gas consumption, rate of gas uptake, apparent rate constant, storage capacity, and water to hydrate conversion were investigated. The experiments were tested at an initial pressure of 1 MPa and an initial temperature of 279.65 K in a stirred batch reactor. The results show that except 1000 ppm tween 20, other concentrations of additives (studied 18
Journal Pre-proof in the current work) reduce the induction time. It was also found that the promotion effects of SDS and GO on the quantity and rate of gas uptake, and apparent rate constant of R410a hydrate formation at the initial minutes of the growth step are significant. In addition, utilization of tween 20 inhibits the kinetics of the R410a hydrate formation process. Furthermore, the effects of additives on the amounts of storage capacity and water to hydrate
Jo
ur
na
lP
re
-p
ro
of
conversion are not significant.
19
Journal Pre-proof
References [1] A. Delahaye, L. Fournaison, D. Dalmazzone, Gas Hydrates 2: Geoscience Issues and Potential Industrial Applications (2018) 315. [2] X. Wang, M. Dennis, L. Hou, Renewable and Sustainable Energy Reviews 36 (2014) 34. [3] H. Hashemi, S. Babaee, A.H. Mohammadi, P. Naidoo, D. Ramjugernath, International
of
Journal of Refrigeration 98 (2019) 410.
ro
[4] C. Veerakumar, A. Sreekumar, international journal of refrigeration 67 (2016) 271.
-p
[5] G. Li, Y. Hwang, R. Radermacher, International journal of refrigeration 35 (2012) 2053. [6] J. Wu, S. Wang, Energy and Buildings 45 (2012) 99.
re
[7] E.D. Sloan, C.A. Koh, CHEMICAL INDUSTRIES-NEW YORK THEN BOCA RATON-
lP
MARCEL DEKKER THEN CRC PRESS- 119 (2008). [8] E.D. Sloan, Natural gas hydrates in flow assurance. Gulf Professional Publishing, 2010.
na
[9] A. Khokhar, J. Gudmundsson, E. Sloan, Fluid Phase Equilibria 150 (1998) 383.
ur
[10] H.P. Veluswamy, A. Kumar, Y. Seo, J.D. Lee, P. Linga, Applied Energy 216 (2018) 262.
Jo
[11] S. Tomita, S. Akatsu, R. Ohmura, Applied energy 146 (2015) 104. [12] H. Dashti, L.Z. Yew, X. Lou, Journal of Natural Gas Science and Engineering 23 (2015) 195.
[13] E. Kim, S. Lee, J.D. Lee, Y. Seo, Fuel 164 (2016) 237. [14] A. Eslamimanesh, A.H. Mohammadi, D. Richon, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 46 (2012) 62. [15] L. Shi, L. Yi, X. Shen, W. Wu, D. Liang, Journal of Molecular Liquids 229 (2017) 98. [16] H. Fakharian, H. Ganji, A. Naderifar, Journal of the Taiwan Institute of Chemical Engineers 72 (2017) 157. 20
Journal Pre-proof [17] M. Karamoddin, F. Varaminian, Desalination and Water Treatment 52 (2014) 2450. [18] A. Aliev, R.Y. Yusifov, A. Kuliev, Y.G. Yusifov, Russian Journal of Applied Chemistry 81 (2008) 588. [19] P. Babu, A. Nambiar, T. He, I.A. Karimi, J.D. Lee, P. Englezos, P. Linga, ACS Sustainable Chemistry & Engineering 6 (2018) 8093. [20] S. Safari, F. Varaminian, Innovative Food Science & Emerging Technologies (2019).
of
[21] S. Li, Y. Shen, D. Liu, L. Fan, Z. Tan, Chemical Engineering Research and Design 93
ro
(2015) 773.
-p
[22] S. Abedi-Farizhendi, M. Hosseini, M. Iranshahi, A. Mohammadi, M. Manteghian, A.H.
re
Mohammadi, Journal of Dispersion Science and Technology (2019) 1. [23] B. Mahmoudi, P. Naeiji, F. Varaminian, M.M. Ghazi, International Journal of Refrigeration
lP
69 (2016) 17.
na
[24] X. Wang, M. Dennis, Chemical Engineering Science 137 (2015) 938. [25] A. Mohammadi, A. Jodat, Journal of Molecular Liquids 293 (2019) 111433.
ur
[26] B. Mahmoudi, P. Naeiji, F. Varaminian, Journal of Molecular Liquids 214 (2016) 96.
Jo
[27] A. Cavallini, G. Censi, D. Del Col, L. Doretti, G. Longo, L. Rossetto, International Journal of Refrigeration 24 (2001) 73.
[28] H. Hashemi, S. Babaee, A.H. Mohammadi, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 80 (2015) 30. [29] A. Lindley, A. McCulloch, Journal of fluorine chemistry 126 (2005) 1457. [30] J.J. Tomlinson, Presented at the Energy Storage Contractors Rev. Meeting, Arlington, Va., 23 Aug. 1982, 1982.
21
Journal Pre-proof [31] T. Akiya, T. Shimazaki, M. Oowa, M. Matsuo, Y. Yoshida, International journal of thermophysics 20 (1999) 1753. [32] H. Hashemi, S. Babaee, A.H. Mohammadi, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 90 (2015) 193. [33] J. Javanmardi, S. Ayatollahi, R. Motealleh, M. Moshfeghian, Journal of Chemical & Engineering Data 49 (2004) 886.
of
[34] M. Mooijer-van den Heuvel, N. Sawirjo, C. Peters, Fluid phase equilibria 241 (2006) 124.
ro
[35] J.J. Carbajo, ASHRAE Trans.;(United States) 91 (1985).
-p
[36] A. Eslamimanesh, A.H. Mohammadi, D. Richon, Chemical engineering science 66 (2011)
re
5439.
[37] A. Delahaye, L. Fournaison, S. Marinhas, I. Chatti, J.-P. Petitet, D. Dalmazzone, W. Fürst,
lP
Industrial & engineering chemistry research 45 (2006) 391.
na
[38] W. Lin, A. Delahaye, L. Fournaison, Fluid Phase Equilibria 264 (2008) 220. [39] P.T. Ngema, P. Naidoo, A.H. Mohammadi, D. Ramjugernath, The Journal of Chemical
ur
Thermodynamics 136 (2019) 59.
18 (2008) 18.
Jo
[40] B.-Y. Zhang, W. Qiang, D.-L. Sun, Journal of China University of Mining and Technology
[41] H. Pahlavanzadeh, M. Khanlarkhani, S. Rezaei, A.H. Mohammadi, Fuel 253 (2019) 1392. [42] H. Ganji, M. Manteghian, M. Omidkhah, H.R. Mofrad, Fuel 86 (2007) 434. [43] B.R. Lee, J.D. Lee, H.J. Lee, Y.B. Ryu, M.S. Lee, Y.S. Kim, P. Englezos, M.H. Kim, Y. Do Kim, Journal of colloid and interface science 331 (2009) 55. [44] A. Al-Sowadi, H. Roosta, A. Dashti, S.A. Pakzad, R. Ghasemian, M. Rajaei, Journal of Molecular Liquids 294 (2019) 111608.
22
Journal Pre-proof [45] A. Erfani, F. Varaminian, Journal of Molecular Liquids 221 (2016) 963. [46] A. Mohammadi, M. Manteghian, A. Haghtalab, A.H. Mohammadi, M. Rahmati-Abkenar, Chemical Engineering Journal 237 (2014) 387. [47] H. Pahlavanzadeh, S. Rezaei, M. Khanlarkhani, M. Manteghian, A.H. Mohammadi, Journal of Natural Gas Science and Engineering 34 (2016) 803. [48] H. Kakati, A. Mandal, S. Laik, Journal of industrial and engineering chemistry 35 (2016)
of
357.
ro
[49] S. Abedi-Farizhendi, M. Iranshahi, A. Mohammadi, M. Manteghian, A.H. Mohammadi,
-p
Petroleum Science (2019) 1.
re
[50] A. Ghozatloo, M. Shariaty-Niassar, M. Hassanisadi, Iranian Journal of Chemical Engineering 11 (2014).
lP
[51] J. Li, D. Liang, K. Guo, R. Wang, S. Fan, Energy Conversion and Management 47 (2006)
na
201.
[52] M. Karamoddin, F. Varaminian, M. Daraee, Journal of Natural Gas Science and
ur
Engineering 19 (2014) 46.
Jo
[53] S. Abedi-Farizhendi, M. Rahmati-Abkenar, M. Manteghian, J.S. Yekshaveh, V. Zahmatkeshan, Journal of Petroleum Science and Engineering 172 (2019) 636. [54] E. Rezaei, M. Manteghian, M. Tamaddondar, Journal of Petroleum Science and Engineering 147 (2016) 857. [55] D.-Y. Peng, D.B. Robinson, Industrial & Engineering Chemistry Fundamentals 15 (1976) 59. [56] J. Munck, S. Skjold-Jørgensen, P. Rasmussen, Chemical Engineering Science 43 (1988) 2661.
23
Journal Pre-proof [57] P.T. Ngema, C. Petticrew, P. Naidoo, A.H. Mohammadi, D. Ramjugernath, Journal of Chemical & Engineering Data 59 (2014) 466. [58] E. Sloan, C. Koh, Taylor and Francis Group, Boca Raton, 2007. [59] J. Calm, Refrig. Manage. Serv (2008) 1. [60] W. McCain, Tulsa, 1990. [61] J.B. Klauda, S.I. Sandler, Industrial & engineering chemistry research 39 (2000) 3377.
of
[62] P. Englezos, N. Kalogerakis, P. Dholabhai, P. Bishnoi, Chemical Engineering Science 42
ro
(1987) 2647.
-p
[63] M.J. Frank, J.A. Kuipers, W.P. van Swaaij, Journal of Chemical & Engineering Data 41
re
(1996) 297.
Jo
ur
na
lP
[64] Q. Ma, X. Zhu, D. Zhang, S.F. Liu, Journal of Materials Chemistry C 2 (2014) 8956.
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Journal Pre-proof Table 1. Suppliers and purities of the chemicals used. Supplier
Chemical formula
R410a SDS Tween 20 Potassium permanganate Sodium nitrate Sulfuric acid Hydrogen peroxide Graphite powder
Iscon- China Merck- Germany Sigma Aldrich- USA Merck- Germany Merck- Germany Merck- Germany Merck- Germany NGS graphite GmbH
CH2F2/CHF2CF3 (50/50% by weight) C12H25NaO4S C58H114O26 KMnO4 NaNO3 H2SO4 H2O2 C
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Chemical name
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Purity (mass fraction) 0.99 0.99 0.99 0.99 0.99 0.98 0.30 0.99
Journal Pre-proof Table 2. The Langmuir constant parameters of large cavities for R410a. Structure
Alarge (K/MPa)
R410a
II
4.750×10-3
Blarge (K) 5969.68
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Gas
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Journal Pre-proof Table 3. Induction time of R410a hydrate formation in the presence of SDS, tween 20, and graphene oxide. Induction time (min)
Pure water
279.65
1
5.6
SDS (50)
279.65
1
3.5
SDS (100)
279.65
1
3.7
SDS (200)
279.65
1
4.5
SDS (500)
279.65
1
0.6
Tween (50)
279.65
1
3.2
Tween (100)
279.65
1
1.2
Tween (250)
279.65
1
4
Tween (1000)
279.65
1
8.9
GO (50)
279.65
1
1.7
GO (100)
279.65
1
2.1
GO (200)
279.65
1
GO (400)
279.65
1
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P (MPa)
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T (K)
-p
additive (ppm)
1.8
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0.2
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Journal Pre-proof Table 4. Storage capacity and water to hydrate conversion of R410a hydrate formation in the presence of SDS, tween 20, and graphene oxide. additive (ppm)
T (K)
P (MPa)
Storage
capacity
Water to hydrate conversion (%)
(V/V) 279.65
1
17.45
26.24
SDS (50)
279.65
1
17.79
26.78
SDS (100)
279.65
1
17.50
26.31
SDS (200)
279.65
1
17.15
25.73
SDS (500)
279.65
1
17.54
26.38
Tween (50)
279.65
1
17.02
25.54
Tween (100)
279.65
1
17.17
Tween (250)
279.65
1
16.82
Tween (1000)
279.65
1
3.99
GO (50)
279.65
1
17.05
GO (100)
279.65
1
17.42
GO (200)
279.65
1
17.63
GO (400)
279.65
1
17.41
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Pure water
25.79
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25.21
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-p
5.67
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25.59 26.19 26.53 26.17
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Table 5. Apparent rate constant average of R410a hydrate growth until 10 min after the induction time in the presence of SDS, tween 20, and graphene oxide.
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Pure Water SDS (50 ppm) SDS (100 ppm) SDS (200) SDS (500 ppm) Tween (50 ppm) Tween (100 ppm) Tween (250 ppm) Tween (1000 ppm) GO (50 ppm) GO (100 ppm) GO (200 ppm) GO (400 ppm)
Average of kapp ×109 until t-tind=10 min 2.3125 2.4999 2.2659 2.5228 2.5883 1.3219 1.3783 0.6937 0.0415 2.3918 2.3041 2.3332 2.3127
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Additive
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Fig. 1. The schematic diagram of the experimental set-up used in this study.
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Journal Pre-proof 1.4
1.2
ΔTsubcooling
P (MPa)
1
0.8
0.6
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0.4
0 278
280
282
284
286
288
-p
276
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0.2
290
292
294
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T (K)
Fig. 2. - - , R410a hydrate equilibrium data [28]; , initial condition for the kinetic experiments in this
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study.
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Journal Pre-proof
Pressure
Temperature
1
283.5 283
282 0.6 281.5 281 0.4 280.5
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0.2
0 10
20
30
40
Time (min)
-p
0
50
Temperature (K)
282.5
280
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Pressure (MPa)
0.8
279.5 279 60
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Fig. 3. Pressure and temperature variations of the reactor during system hydrate formation for R410a +
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pure water.
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0.014 0.012 0.01 Pure water SDS 50 ppm
0.008
SDS 100 ppm 0.006
SDS 200 ppm SDS 500 ppm
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0.004 0.002
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Mole of gas consumed/ mole of water
0.016
0 5
10
15
20
25
30
35
40
-p
0
re
Time (min)
Fig. 4. Effect of different concentrations of SDS on the amount of R410a consumption during hydrate
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formation at an initial temperature of 279.65 K and pressure of 1 MPa.
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0.016 0.014 0.012 Pure water
0.01
Tween 50 ppm 0.008
Tween 100 ppm
0.006
Tween 250 ppm Tween 1000 ppm
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0.004 0.002 0 0
10
20
30
40
-p
Time (min)
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Mole of gas consumed/ mole of water
0.018
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Fig. 5. Effect of different concentrations of tween 20 on the amount of R410a consumption during
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hydrate formation at an initial temperature of 279.65 K and pressure of 1 MPa.
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(b)
(a)
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(c)
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Fig. 6. The images of hydrate formed at the end of reaction: (a) Pure water, (b) 100 ppm tween 20, (c)
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1000 ppm tween 20.
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0.014 0.012 0.01 Pure water GO 50 ppm
0.008
GO 100 ppm 0.006
GO 200 ppm GO 400 ppm
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0.004 0.002 0 5
10
15
20
25
30
35
40
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0
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Mole of gas consumed/ mole of water
0.016
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Time (min)
Fig. 7. Effect of different concentrations of grapheme oxide on the amount of R410a consumption during
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hydrate formation at an initial temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof 0.006
0.004 Pure water SDS 50 ppm
0.003
SDS 100 ppm SDS 200 ppm
0.002
SDS 500 ppm
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Rate of gas uptake ( ng/ nw .min)
0.005
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0.001
0
5
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0 10
15
20
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Time (min)
Fig. 8. Rate of R410a gas uptake during hydrate formation in the presence of different concentrations of
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SDS at an initial temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof 0.005
0.004 0.0035 0.003
Pure water Tween 50 ppm
0.0025
Tween 100 ppm
0.002
Tween 250 ppm 0.0015
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Tween 1000 ppm
0.001
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Rate of gas uptake ( ng/ nw .min)
0.0045
0.0005 0 5
10
15
re
Time (min)
-p
0
20
Fig. 9. Rate of R410a gas uptake during hydrate formation in the presence of different concentrations of
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tween 20 at an initial temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof 0.005
0.004 0.0035 0.003
Pure water GO 50 ppm
0.0025
GO 100 ppm
0.002
GO 200 ppm 0.0015
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GO 400 ppm
0.001
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Rate of gas uptake ( ng/ nw .min)
0.0045
0.0005
0
5
-p
0 10
15
20
re
Time (min)
Fig. 10. Rate of R410a gas uptake during hydrate formation in the presence of different concentrations of
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graphene oxide at an initial temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof 4.5E-09
3.5E-09 3E-09 Pure water
2.5E-09
SDS 50 ppm 2E-09
SDS 100 ppm SDS 200 ppm
1.5E-09
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SDS 500 ppm
1E-09
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kapp (mole G/ mole W.min.Pa)
4E-09
5E-10
0
5
-p
0 10
15
20
re
t- tind (min)
Fig. 11. Apparent rate constant during R410a hydrate growth in the presence of SDS at an initial
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temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof 3.5E-09
2.5E-09
Pure water
2E-09
Tween 50 ppm Tween 100 ppm
1.5E-09
Tween 250 ppm Tween 1000 ppm
1E-09
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kapp (mole G/ mole W.min.Pa)
3E-09
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5E-10
0 5
10
15
-p
0
20
re
t-tind (min)
Fig. 12. Apparent rate constant during R410a hydrate growth in the presence of tween 20 at an initial
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temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof 4.5E-09
3.5E-09 3E-09 Pure water
2.5E-09
GO 50 ppm 2E-09
GO 100 ppm GO 200 ppm
1.5E-09
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GO 400 ppm
1E-09
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kapp (mole G/ mole W.min.Pa)
4E-09
5E-10
0
5
-p
0 10
15
20
re
t-tind (min)
Fig. 13. Apparent rate constant during R410a hydrate growth in the presence of graphene oxide at an
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initial temperature of 279.65 K and pressure of 1 MPa.
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Journal Pre-proof Declaration of competing interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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Journal Pre-proof Author statement Amir Mohammad Javidani: Writing- Original draft, Methodology, Validation, Formal analysis, Investigation, Visualization Saeid Abedi-Farizhendi: Formal analysis Abolfazl Mohammadi: Conceptualization, Methodology, Software, Formal analysis, Writing - Review & Editing Amir H. Mohammadi: Writing - Review & Editing Hussein Hassan: Investigation
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Hassan Pahlavanzadeh: Writing - Review & Editing
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Journal Pre-proof
Highlights
R410a hydrate is studied as a cold storage medium.
Storage capacity of R410a hydrate is investigated in presence of SDS, tween 20, and graphene oxide nanosheets.
Utilization of 400 ppm GO decreases the amount of induction time from 5.6 min to 0.6
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The addition of 500 ppm SDS, increases the apparent rate constant of hydrate growth up
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to 12%.
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min.
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