Growth and decomposition mechanism of clathrate hydrates in

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Catalysis and Kinetics

Growth and decomposition mechanism of clathrate hydrates in presence of porous media and seawater: Experimental validation Avinash V Palodkar, and Amiya K. Jana Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b03245 • Publication Date (Web): 22 Jan 2019 Downloaded from http://pubs.acs.org on January 26, 2019

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Growth and Decomposition Mechanism of Clathrate Hydrates in Presence of Porous Media and Seawater: Experimental Validation Avinash V. Palodkar and Amiya K. Jana* Energy and Process Engineering Laboratory, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, India - 721302

ABSTRACT The natural gas entrapped in the hydrate reservoirs can meet the global energy demand for the forthcoming centuries. For exploiting this vast energy source at a commercial rate, it is required to forecast the amount and physical behavior of the natural gas hydrates contained in the reservoirs. In this direction, we formulate a rigorous mathematical model to interpret the clathrate hydrate kinetics in reservoir mimicking environment. The formulation precisely considers the effects of the central elements existed in the marine and permafrost regions i.e., seawater and porous medium. Usually, the salt ions present in the seawater impede the hydrate growth by interfering in the formulation of strong hydrogen-bonded water molecules network, and they counteract during the hydrate decay by facilitating the breakage of the hydrate associated water network. This multifaceted behavior is taken into account by introducing the general activity term in the newly proposed dynamic driving force i.e., chemical potentials difference of the cavity building water molecules in the liquid and hydrate phase. The same term *Corresponding

author. Fax: +91 3222 282250.

E-mail address: [email protected] (A. K. Jana).

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accounts for the irregularities in the size and shape of the porous sand particles and their internal pores. This apart, we propose to use the active surfaces of unconsolidated porous materials as the interface for the phase transition. The formulation is finally implemented to predict the methane and carbon dioxide hydrates formation, growth and decomposition in presence of the synthetic and natural seawater and the silica sand of distributed particle size at the wide range of operating pressure and temperature. It appears that the proposed formulation is reliable and accurate enough in predicting the clathrate hydrate kinetics in the reservoir like situation.

Keywords: Clathrate hydrate; formation; decomposition; seawater-silica sand; modeling; validation

1. INTRODUCTION Natural gas hydrates (NGH) present in the permafrost and marine sediments are the vast source of upcoming primary fuel – natural gas.1 The organic carbon contained in these regions is 53.1% of the global organic carbon content, which is twice of all the fossil fuels reserves combined.2 The conventional mining methods undermine the equilibrium of the hydrates entrapped in the reservoirs, which lead to free the natural gas and water with sand as a byproduct. The direct decomposition of NGH in the reservoirs invites the potential environmental damages.3-5 Thus, there is a need to find a convenient route for exploiting the natural gas hydrates at a commercial scale from their reservoirs by avoiding the environmental risks. In this context, the methane (CH4) - carbon dioxide (CO2) (pure/mixed) gas exchange mechanism offers an eco-friendly solution without interfering the stability of the regions.2,6,7


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There are a few field trials have already been performed in the onshore8 and offshore9 locations. These tests are conducted with the use of thermal stimulation, depressurization, inhibitor injection and gas swapping technologies. Among them, the gas exchange mechanism is perceived as a commercially feasible and stable technique.10,11 This scheme transforms the natural gas hydrate to more stable mixed gas hydrates (MGH) of CH4, CO2 and the mixture of CO2 and nitrogen (N2) or hydrogen (H2) without interrupting the seafloor equilibrium. This process involves simultaneous formation and decomposition of the MGH, and its efficiency gets improved with the introduction of a gas mixture. The suitable combination of the replacement agent is a mixed gas having 20% CO2 and 80% N2, which has close composition to the flue gas.10,12 This opens up an additional advantage of directly sequestrating the flue gas in the hydrate reservoirs. The researchers are evaluating the physical behavior of the gas exchange process for its effective application in the actual field. These attempts are majorly related to the experimental conduct. However, a relatively small number of efforts have been made to predict the same.13-16 The gas exchange process involves the hydrate formation and decay. To properly understand this process, one needs to have the knowledge on hydrate characteristics. In this light, the transport of unsaturated groundwater and heat (TOUGH) simulator with EOSHYDR2 module has analyzed the production scenario of one of the most concentrated NGH reservoirs in the world.17 This formulation combines the mass and energy balance equations to interpret the gas recovery. Their simulations recommend that the natural gas production is strongly dependent on the hydrate saturation, the initial temperature of hydrates, the temperature of heat transforming medium and the thermal conductivity of the system.17 Besides, a subsurface transport over multiple phases (STOMP) simulator has been developed to predict the methane recovery from


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the gas exchange process.18 In which, the contribution of the saline water is ignored during the simulation. Then, Tang et al.19 have used TOUGH-Fx/Hydrate for analyzing the gas hydrate decomposition controlling mechanisms in the laboratory to field scale hydrate-bearing cores. Oyama et al.20 have proposed a theoretical model for describing the methane hydrate decomposition in presence of pure water and porous Toyoura sand. However, this formulation neglects the dynamics involved in the reaction interface and driving force. Fitzgerald et al.21 have performed the formation and thermal based dissociation of CH4 hydrate as a function of the initial hydrate saturations. Further, they have used COMSOL for predicting their experimental data. In this simulation, the uniform hydrate saturation is assumed throughout the bed, which is quite unusual in practice. Afterward, Yuan et al.22 have put forward a formulation for the CH4CO2 (pure) gas exchange mechanism based on their laboratory scale experiment, which comprises of the aqueous brine and quartz sand. Besides, Yonkofski et al.23 have employed the modified version of the STOMP family simulator i.e., STOMP-HYDT-KE to describe the MGH (CH4-CO2-N2) kinetics. However, it has under-predicted the recovered volume of the associated components (i.e., water, CH4, CO2 and N2 gases, and sand).11 Note that the performance of the abovementioned modeling studies is system oriented and highly dependent on the process parameters. Besides, a clear relationship is yet to be developed between the laboratory-derived model parameters and the actual field parameters, which is essential to ensure their application in the gas hydrate technology at a commercial level. It is with this intention that the present work has been undertaken. The marine sediments hold more than 90% of the natural gas hydrates reserves on the planet.24 The porous silica sand and seawater are the central characters of these hydrate reservoirs. Thus, one has to realize their contribution to interpret the influence on the gas hydrate


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kinetics. Here, we begin with the contribution of a porous medium, i.e., silica sand. It provides a platform for the transformation of the gas-water mixture from aqueous to hydrate phase.25 The particle size of the silica sand significantly affects the guest gas consumption during the hydrate growth. The small size sand particles provide a large surface area for the phase transformation, which can substantially improve the guest gas uptake.26 However, the tiny size particles obstruct the guest gas from penetrating into the small interstitial pore spaces present between them, which delays the gas hydrate growth rate.27 Apart from this, the porous material itself has some internal pores, where the hydrates form and grow, and the size and shape of these pores are instrumental in evaluating the hydrate formation and subsequent growth.28 In this context, Zhao et al.29 have examined the microstructural characteristics of the NGH formed in the interstitial and internal pores of the silica sand bed by using X-ray computed tomography (CT). In which, they have observed the uniform distribution of the NGH throughout the packed bed (including the internal pores of the silica sand). Apart from silica sand, there are few other porous materials, like silica gel,30 hollow silica,30 activated carbon,30 zeolite,31 silicon SBA-15,32 cellulose and polyurethane foam30 and hydrogels30. To enhance the rate of gas hydrate formation and decomposition kinetics, the use of additives, such as tetrahydrofuran (THF),31,32 tetra-n-butyl ammonium bromide (TBAB),31,32 tetra-n-butyl ammonium fluoride (TBAF)33 and sodium dodecyl sulphate (SDS),34 among others, are noticed. As the hydrate formation progresses, the amount of water molecules present in the liquid phase decreases. Besides, the salt ions do not participate in the hydrate formation reaction which costs an enhancement of their concentration in the liquid state.35 Naturally, the opposite behavior is true during the hydrate decay. However, the role played by the salt ions in the gas hydrate kinetics is still at an immature level of research. Mekala et al.36 have reported that the presence of


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salt can significantly slow down the hydrate growth; whereas, Yang et al.37 have investigated a little inhibition effect on the CO2 hydrate formation and growth in presence of seawater. In fact, they have observed that the salt has improved the formation rate during the initial period of the hydrate growth.37 At the beginning, the CO2 hydrates are nucleated faster in the salt water system (SWS) than the pure water system (PWS). This is because the salt ions can act as an additional nucleation source along with the porous medium. Afterwards, they alter their role by interfering in further CO2 hydrate growth.37 The probable reason behind this is that in the SWS, the interaction via Coulombic forces between the dissolved salt ions and water molecules dominates. During this interaction, the water molecules arrange themselves around the salt ions. Naturally, this will hinder the development of the strong hydrogen bond between the water molecules, which is essential to form the stable hydrate cages.38 This apart, the salt ions and water molecules are slightly polar; thus their attaching tendency is higher as compared to the non-polar hydrateforming guest molecules (i.e., CH4 and CO2).38 Based on the review made on hydrate modeling, it becomes clear that there is a lack of mathematical formulation in explaining the physical insight into the process of hydrate formation and decay in reservoir mimicking environment. To bridge this gap, one needs to develop a rigorous framework for hydrate dynamics with considering the stated practical issues. With this, we put forward a formulation for predicting the gas hydrate formation, growth and decay by accounting the crucial aspects involving the hydrate-bearing sediments and salts. Combining these proposed growth and decay models, one can formulate the gas-swapping mechanism in straightforward way. In this contribution, attempt is made to predict the gas hydrate formation, growth and decay in presence of the seawater and porous silica sand. The influence of natural porous medium (i.e.,


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unconsolidated silica sand) is accounted for through the effective reaction interface area. Besides, the effect of salt ions38 present in the seawater during the hydrate growth and their counteraction in the decay is considered by introducing the novel time-dependent driving force. Moreover, the same term takes into account the practical issues associated with the porous medium such as the hydrate formation in the irregular shape of pores, and the surface tension between the hydrate and aqueous phase in those pore networks. The proposed formulation is finally evaluated by comparing with the existing models20,39 with reference to the experimental data at various conditions. They include the CH4 and CO2 hydrates formation, growth and dissociation in the unconsolidated silica sand and bentonite clay with the distributed particle size and the seawater with distinct salinity for the wide range of operating pressure and temperature.

2. MODEL DEVELOPMENT The usual hydrate formation process requires plenty of the water molecules.40,41 The number of free water molecules drops with the hydrate growth, which causes deceleration in the phase transformation rate. Besides, the system containing the ionic solution (especially, salt) can increase the resistance to the clustering of water molecules around the guest gas, as depicted in Figure 1. This apart, the NGH present in the reservoirs acts like the cement in unconsolidated sands or sandstones or clay layers.42 Therefore, the gas hydrate kinetics is profoundly affected by the physical properties of the associated porous medium. With this, we propose here a mathematical formulation that accounts for the crucial aspects of the gas hydrate formation, growth and decay in the saline environment with the porous medium.


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2.1. Hydrate Formation and Growth. The governing equation is proposed for the consumption of guest gas during the hydrate formation and the associated growth in presence of the saline environment and the porous medium as,

dngg, H dt

 K Ae μ nH2O, L

(1)

Here, ngg, H is the moles of guest gas in hydrate phase, Ae the effective reaction surface area,

 the driving force and K the temperature dependent rate constant given as,

K  K 0 exp  Ea / RT 

(2)

in which, K 0 is the pre-exponential factor, Ea the activation energy for the reaction, R the universal gas constant and T the operating temperature. Now, to solve Equation (1), we have presented the moles of residual water in liquid phase,

nH2O,L in terms of the overall moles of water ( nH2O,T ), the moles of water required to encapsulate a single mole of guest gas ( nH ) and ngg, H (i.e., nH2O,L  nH2O,T  n H ngg,H ). With this, we further introduce an adjustable parameter (  ) to relate the maximum value of the guest gas ingested in the course of the hydrate formation and the possible amount of guest gas engaged in the entire hydrate cages. Naturally, in an ideal case with the completely filled hydrate cages, the value of

 will be unity. Accordingly, one can simplify the above equation to the final form of the proposed model,

ngg, H 

α nH2O, T   nH K 0  Ae exp  ΔEa / RT   t   1  exp   nH   RT 

(3)

2.2. Hydrate Dissociation. The basic objective of gas hydrate decomposition is to unsettle the hydrogen-bonded cages of the water molecules, which contain the guest gas. With this, the 8 ACS Paragon Plus Environment

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entrapped guest gas gets released, for which, we formulate the governing equation for predicting that guest gas dynamics in the hydrate phase in presence of seawater and porous medium as,



dngg, H dt

 K Ae  nH2O,H

(4)

Substituting Equation (2) and the moles of water in hydrate phase, nH2O,H as n H ngg,H in the above equation, 

dngg, H dt

 K 0 exp  Ea / RT  Ae  n H ngg,H

(5)

Solving the above equation,

 ln(ngg,H )   n H K 0 exp  Ea / RT  Ae  t   IC

(6)

Now, the integration constant, IC is estimated based on: at t  0 , ngg,H  n0 and IC   ln (n 0 ) , in which, n 0 is the total moles of guest gas present in the hydrate phase at the beginning of hydrate dissociation. Further, substituting IC into Equation (6)

 ln (ngg,H )   n H K 0 exp   Δ Ea / RT  Ae  t   ln (n 0 )

(7)

Multiplying both sides by  1 and simplifying,





ln ngg,H / n 0   n H K 0 exp   Δ Ea / RT  Ae  t

(8)

Further simplification of the above equation leads to the final form of the proposed model for the gas hydrate decomposition in saline environment with porous medium as,

 n H K0 ngg,H  n 0 exp  Ae exp   Δ Ea / RT    RT 

 t 


(9)

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2.3. Constituents of the Proposed Model. The proposed formulation (Equations (3) and (9)) has a couple of constituent elements i.e., the reaction interface and driving force. In the following, their estimation procedure is presented.

2.3.1. Interstitial reaction surface area. Usually, the hydrates are entrapped in the interstitial space available between the unconsolidated porous sediments, considering of sand or clay.11,17 Besides, in the formation or dissociation of hydrates, these porous surfaces play a vital role by acting as a phase transformation medium.25 Perceiving this, we introduce an effective surface area of porous material as,

Ae   A

(10)

in which,  is a correction factor to the overall surface area of the porous material, A . Now, A is a function of the total number of particles ( n p ) present in the bed and the individual particle surface area ( A pi ) as: A  np Api . This n p is estimated by dividing the individual particle volume (

Vpi ) from the total volume of the porous material ( Vp ). For this, the Vp is obtained by subtracting the injected water volume to completely saturate the bed ( Vs ) from the total volume of that bed (

Vb ). Furthermore, one gets A pi from its diameter ( d p ) as: A pi   d p2 . At this point, it should be noted that as material size increases, the total available surface area decreases, which in turn, reduces the effective reaction surfaces ( Ae ) for the phase transformation and the guest gas uptake during the hydrate growth.


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2.3.2. Driving force. The driving force for the gas hydrate kinetics is considered as a function of the chemical potentials of water in the filled hydrate (  wH ) and the liquid phase (  wL ) as, (  wH   wL ) / RT    L H (  w   w ) / RT

Formation and growth Decomposition

(11)

in which, the  wH and  wL have the following forms,

μwH  μw0  Δ μwH &

μwL  μw0  ΔμwL

(12)

Here, μw0 is the chemical potential of water in empty hydrate cages and Δ μwH the difference in chemical potentials of water between the empty and filled hydrate cages in hydrate phase, and

Δ μwL the chemical potential difference of water between the unfilled cavities in hydrate phase and the liquid phase. Now, Δ μwH is evaluated from van der Waals-Platteeuw equation,40

 2  Nc    wH     v j ln 1    ji   RT  i 1    j 1

(13)

Here,  j is the number of cages of type j per water molecule in the hydrate phase and N c the number of hydrate forming components. The fractional occupation of j type cage by i type guest gas molecule (  ji ) is a function of the fugacity of species i in the hydrate phase ( f i ) and the Langmuir constant for the same species in an j type cage ( C ji ) as,

   C f  ji i    ji   Nc   1   C ji fi   i 1 

(14)


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The value of f i is supposed same with that of the fugacity of species i in gas phase, which is computed from the Soave-Redlich-Kwong equation of state (SRK-EoS),43 and the C ji is obtained from,44 R

4π C ji  exp   (r ) / KT  r 2 dr  KT 0

(15)

where, K indicates the Boltzmann's constant, R the cell radius of hydrate and  (r ) the spherically symmetric cell potential, which is obtained from the Kihara type of potential parameters.40 Then, the Δ  wL is estimated from,40,41 P ΔμwL T,P  Δμw0 (T,0) T ΔhwL T  ΔVwL   dT  dP  ln (aw ) 2 2  RT RT0 RT RT T0 0

(16)

Here, T0 is the temperature of a reference point, Δ  w0 (T , 0) the difference in standard chemical potential of water for gas hydrate at reference temperature and absolute zero pressure, Δ hwL the enthalpy difference between empty hydrate cavities and liquid water, P the operating pressure,

ΔVwL the difference between molar volume of the water in hydrate and liquid phase, and aw the absolute activity of water in aqueous phase.

2.3.2.1. Activity. The salt ions present in the seawater do not participate in the hydrate formation. However, they impede the growth by interfering with the formation of strong hydrogen bonding network of the water molecules.38 This dynamic characteristic of the hydrate growth and decay can be tracked by the change in the activity of water during the process.45 This apart, there are some practical issues associated with the porous material i.e., the unevenness in 12 ACS Paragon Plus Environment

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size and shape of the internal and interstitial pore edges and spaces available in unconsolidated porous medium, the hydrate growth and decomposition in these complicated structures, and the capillary effect can be accounted through the activity term.46,47 Basically, the water molecules involved in the gas hydrate kinetics are linked to the (i) guest gases, (ii) salt ions and (iii) porous media, and this association can be computed from their respective activities i.e., aw,gg , aw,SI and aw,PM .

2.3.2.1.1. estimating aw,gg . The activity of water associated with the guest gas is estimated from,44

ln (aw,gg )  ln ( w (1  xgg ))

(17)

in which, the activity coefficient of water in the water-gas mixture,  w is supposed as unity,48,49 and the mole fraction of guest gas, xgg is estimated by estimating the molality of the guest gas,

mgg .50

2.3.2.1.2. estimating aw,PM . The contribution of porous material is computed from,44 ln (aw,PM ) 

Vw (  ΔP) RT

(18)

Here, Vw is the molar volume of water and P the difference in pressure between the liquid and hydrate phases, which is a function of interfacial tension between hydrate and liquid water,  H-W , the contact angle between the liquid water and porous material,  (assumed as zero), and the perimeter, L and area S of pore edges of the irregular pores porous material as,51

P  ( H-W L cos  ) / S

(19) 13 ACS Paragon Plus Environment

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Here,  H-W is estimated from,

σ H-W  σ 0 / 1  κδ

(20)

where,  0 is the surface tension for a plane surface of separation between the two phases of a one component fluid system (0.0267 J.m-2)42 and, δ the Tolman length (0.4186 nm)51. Moreover,

κ , the hydrate-liquid interface curvature, is a function of the hydrate core radius, rcore and the 2 D

fractal dimension, D f as: κ  2k / rcore f . Furthermore, for evaluating L and S , we assume that Df

the irregular pores possess the fractal geometry:51 L  2 k rpore and S   rpore , in which, k is the 2

fractal parameter of pore shape and rpore the pore radius. Concerning the hydrate present in the irregular pores of porous material, one can assume that all these irregular pores are filled with the hydrates and on the surface of these hydrates, a monolayer of water (with thickness 0.4 nm) is present.51 Now, one can evaluate the hydrate core radius, rcore by subtracting the bound water layer thickness from the pore radius.47 Then, the Df

perimeter of hydrate core, l can be expressed as: l  2 k rcore , and accordingly, the P is simplified as,

P  2 D f

rcore

2k  0  2 k 1  2 D f  rcore

  



2k  0

(21)

2 D f

rcore  2k

Finally, substituting Equation (21) into (18), one can obtain the simplified form of aw,PM as,

V ln(aw,PM )   w RT

 2k  0  2 D f r  core  2k

   

(22)


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It is worth noticing that as the size of porous material increases, the activity of water in aqueous phase ( a w ) gets affected [see Equation (16) through (22)], which leads to decrease the driving force.

2.3.2.1.3. estimating aw,SI . The activity of water that accounts for the influence of the salt ions is computed from the Pitzer model as,





ln aw,SI  

Mw   ml     1000  l 

(23)

The aw,SI is strong function of the molality of solutes (i.e., cations: c, anions: a and neutrals: n) present in the electrolytic solution ( ml ) and the molar mass of water ( M w ). Further, the proportionality osmotic coefficient,  is governed by the ionic strength ( I ), the temperature and pressure dependent computable groupings of the second ( B ,  ,  ) and third (C,  ,  ) virial coefficients and the one third of Debye-Huckel limiting slope ( A ) as,

  1 

 A I 1.5      mc ma Bca  ZCca   mc mc  cc   ma cca    0.5    1  1.2 I c a c  c a     ml   l  2





      m  a  a

aa

a

c

aac



(24)

     mn mc nc   mn ma na   mn mc ma nca  n a n c a  n c 

In the above equation, the single summation index c, a and n indicate sum over all solute species, and the double summation index c  c' and a  a ' refer to all the pairs of dissimilar cations and anions. Additionally, the function Z is computed from the concentration and charge ( zl ) of the 

involved solutes as: Z   ml zl . Furthermore, the second ( Bca and  ) and third ( Cca ) virial l

coefficients are computed from the following equations.


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Bca   ca(0)   ca(1) e ca

I

  ca(2) e 12

I

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(25)

mn  mn  E mn ( I )  I E mn ( I )

(26)

Cca  Cca / 2 zc za

(27)

(0) Here,  is a single factor for each pair of positively or negatively charged ions, and  ,  (1)

and  (2) are the temperature dependent empirical constants, which are available in literature.52 Besides, the electrostatic asymmetrical mixing effects based on the ionic strength and the type of electrolyte pair are accounted through E mn ( I ) and E mn ( I ) . Note that the value of  ca is equal to 2.0 for univalent and 1.4 for higher valence pairs. Moreover, the ionic strength of solution ( I ) is estimated as, I

1 ml zl2  2 l

(28)

During the hydrate growth, the water molecules in the liquid phase convert into the solid hydrate phase. For the hydrate formation in electrolytic solution, the salt ions (like, Na+ and Cl-) do not participate in the hydrate building process, which results in improving their strength in the liquid state. This change of ionic strength in the course of hydrate growth can be interpreted by evaluating the molality of salt ions from the number of moles of salt ions ( nSI ) and the amount of water remaining in the aqueous phase (WRA) as,

ml 

nSI WRA

(29)

Further, WRA is computed from the water present in the beginning of the hydrate growth (Win) and the water conversion to hydrates (WC) during the hydrate growth as,

WRA  Win (1  WC )

(30)


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Energy & Fuels

Ultimately, the sum of these activities (Equations (17), (22) and (23)) provide a combined influence of the guest gas solubility, seawater and porous material on the gas hydrate growth and decay (i.e., aw ) as:





2 D f   aw   w (1  xgg )  exp 2k Vw  0 / RT (rcore  2k )  exp   M w   ml /1000  l  

(31)

3. RESULTS Here, we investigate the performance of the proposed framework to interpret the gas hydrate formation, growth and decay in variety of conditions that mimic the NGH reservoirs. These variations include (i) the type of hydrate-forming and -dissociating guest gases (i.e., pure CH4 and CO2), (ii) quantity, size and type of the porous medium, (iii) salinity of saltwater (0-3.55 wt%), and (iv) operating pressure and temperature. The proposed formulation has typically three adjustable parameters, namely K0,  and  , which are linked with the intrinsic reaction rate constant, deviation from the ideal hydrate cage occupation of the guest gases and the active surface area of the porous media, respectively. These parameters are tuned through the generalized reduced gradient nonlinear optimization technique in Solver tool (inbuilt in Microsoft Excel 2010) and they are reported in Tables 1 and 2.

3.1. Formation Kinetics. 3.1.1. CH4 hydrate in synthetic seawater and silica sand. We start the performance evaluation of the proposed and existing39 formulations for the CH4 hydrate formation and growth in presence of synthetic seawater and porous silica sand. Here, we compare the model prediction with the available experimental data53 of the CH4 hydrate growth in the sand environment. In this, the synthetic seawater has 3.55 wt% salinity, and the process is 17 ACS Paragon Plus Environment

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operated at a pressure of 11.54 MPa and temperature of 272.27 K. We have simulated the formulation by using the optimized set of tuning parameters. Figure 2 depicts the performance of the proposed and existing models. Here, we quantify the prediction accuracy of these formulations by evaluating their average absolute relative deviation (AARD) defined as, AARD (%) 

100 ngg,e  ngg,p ndp ngg,e

(32)

in which, ndp is the total number of data points, and ngg,e and ngg,p are the respective experimental and model predicted moles of the guest gas during the gas hydrate reaction. Note that Figure 2 shows the performance of the concerned models for 300-500 μm particle size distribution of silica sand. It is evident that the proposed model has outperformed the existing model. This observation is supported by the percent AARD reported in the same figure. The noticeable accuracy of the proposed formulation is obtained mainly because of considering the influence of the salt ions and porous medium. Besides, the proposed model includes a less number of tuning parameters than the existing model, which will improvise the reliability of the proposed framework.

3.1.2. CH4 hydrate in synthetic seawater and mixture of silica sand and bentonite clay. Now, we evaluate the performance of the proposed and existing39 models for the CH4 hydrate formation and subsequent growth in presence of the synthetic seawater (3.55 wt% salinity) and a mixture of silica sand (with various particle size distributions) and bentonite clay (particle size range: 30-3200 nm). Figure 3 shows the comparative predictions with reference to the experimental data53 of the CH4 hydrate growth conducted at the pressure of 11.54 MPa and


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temperature of 272.91 K. Here, the particle size of the silica sand is distributed between 300 and 500 μm. In the similar fashion, Figures 4 and 5 are produced to depict the comparative model predictions. In these cases, only the particle size distribution of the employed silica sand is different than the previous case [i.e., 250-300 μm (for Figure 4) and 150-250 μm (for Figure 5)], and rest of the operating conditions are remained identical. From these figures, it becomes obvious that the proposed formulation is functioning better than the existing one. Further, this observation is confirmed through the percent AARD values provided in the respective figure.

3.1.3. CH4 hydrate in seawater and silica sand. Here, we investigate the potential of the proposed formulation for the CH4 hydrate formation and growth in the natural seawater with porous silica sand. Figure 6 compares the performance of the proposed model and the existing model39 with reference to the experimental data36 of CH4 gas intake during the hydrate formation in presence of natural seawater (3.03 wt% salinity). Besides, the silica sand having 100-500 μm particle size distribution is used in the process, which is operated at pressure and temperature of 8 MPa and 277.2 K, respectively. From this plot, it is obvious that the proposed formulation is accurate enough to predict the CH4 hydrate formation. We have also observed that the existing model deviates from the experimental data. Note that the simulation run time is close to 20 hours, which is somewhat close to the period that is needed to form the natural gas hydrates in the reservoir.

3.1.4. CH4 hydrate in pure water with silica sand. Now, we compare the performance of the proposed and existing model with the experimental54 CH4 gas intake during the hydrate


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formation in pure water with silica sand (particle size range: 100-500 μm) at 7.9 MPa and 277.2 K. Figure 7 portrays that the proposed formulation is capable enough to predict the CH4 hydrate growth in pure water. However, the available model39 has under predicted the experimental data. These observations are well reflected through the values of the percent AARD provided in Figure 7.

3.1.5. CO2 hydrate in natural seawater and silica sand. Next, the proposed formulation is evaluated for the CO2 hydrate formation followed by growth in the natural seawater (3.3 wt% salinity) and silica sand (with three different particle size distribution). Here, CO2 forms hydrates at the pressure and temperature of 6 MPa and 276.15 K, respectively. Figure 8 compares the model and experimental data26 of CO2 gas uptake during the hydrate growth in the silica sand bed of particle size distribution as 0.15-0.18 mm. Additionally, Figures 9 and 10 show the comparison for the CO2 hydrate growth with two sets of particle size distribution i.e., 0.43-0.46 mm and 0.85-1.00 mm, respectively. Apart from the developed model, we have tested the available kinetic model of Palodkar et al.39 for these cases. Here, the proposed framework has shown a decent agreement with the experimental data and better response than the existing one in every situation. This can also be recognized by the percent AARD provided in the respective figure.

3.2. Decomposition Kinetics. 3.2.1. CH4 hydrate in natural seawater and silica sand. Here, we investigate the performance of the developed formulation for the CH4 hydrate decomposition in presence of the natural seawater (3.03 wt% salinity) and silica sand (100-500 μm of particle size distribution). Figure 11 compares the model predictions and experimental data36 of CH4 gas


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recovery during the hydrate decomposition at an operating pressure of 4.8 MPa and temperature of 297.15 K. Additionally, we have simulated the available theoretical model20 for this case. The tuning parameters of the proposed and existing models are identified and reported in Table 2. From the plot, it appears that the proposed formulation works better than the existing model. We quantify the performance based on the percentage AARD given in the figure. In the concerned situation, the methane gas is recovered from the hydrates present between the silica sand particles and surrounded by the natural seawater. The similar kind of environment is witnessed in the hydrate reservoirs.40

3.2.2. CH4 hydrate in pure water with silica sand. Figure 12 depicts a comparison in between the proposed and existing20 models with reference to the experimental54 CH4 gas recovery in water with Toyoura silica sand at 4.8 MPa and 297.2 K. In this case, the proposed model outperforms the existing model, which is reflected in their respective AARD presented in Figure 12. This shows that the proposed model is equally useful in predicting the CH4 decomposition in pure and sea water with silica sand.

3.2.3. CO2 hydrate in saltwater and silica sand. The simulation run is conducted for the CO2 hydrate decomposition in the saltwater of 1.5 wt% salinity and the silica sand of 100-500 μm particle size distribution. The CO2 hydrate is decomposed at the pressure of 2.2 MPa and temperature of (a) 280.5 K and (b) 286.5 K. Figures 13 and 14 compare the model predicted value with the experimental data37 of the normalized CO2 gas recovery during the hydrate decay at 280.5 K and 286.5 K, respectively. It is evident from these figures that the proposed model


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predicts the decomposition kinetics better than the model of Oyama et al.20. And, this observation is supported by the percent AARD of the proposed and existing formulations.

4. CONCLUSIONS This work formulates a mathematical model to predict the gas hydrate formation and decomposition at the reservoir representative condition. The proposed model takes into account the combined influence of porous medium and seawater on the gas hydrate kinetics. The salt ions present in seawater affect the hydrate growth and decay, and this behavior is interpreted by tracing their ionic strength in the course of the process. Besides, the effective surface area of silica sand participating in the phase transition of the water-gas mixture from liquid to hydrate is treated as a reaction interface. This formulation has typically three adjustable parameters, which are tuned by using the generalized reduced gradient nonlinear optimization technique in Solver tool. The proposed framework is validated for the CH4 and CO2 gas hydrate formation, growth and decomposition in the variety of experimental conditions. These variations include (i) the type of guest gas molecules, (ii) the particle size distribution of the porous silica sand, (iii) the salinity of water and (iv) the operating pressure and temperature. For all of the cases, the proposed model has shown better performance than the existing ones. Seeing the performance of the proposed model at the conditions that represent the hydrate field environment, it seems that this formulation is capable of predicting the formation and decomposition mechanism of naturally occurring gas hydrates.


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AUTHOR INFORMATION *Corresponding

author

E-mail address: [email protected] (A. K. Jana). Fax: +91 3222 282250

ORCID Avinash V. Palodkar: 0000-0001-8080-7354 Amiya K. Jana: 0000-0003-1367-5480

Competing Interests: The authors declare that they have no competing interests.

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(30) Linga, P.; Clarke, M. A. A review of reactor designs and materials employed for increasing the rate of gas hydrate formation. Energy Fuels 2017, 31 (1), 1-13. (31) Zhao, Y.; Zhao, J.; Liang, W.; Gao, Q.; Yang D. Semi-clathrate hydrate process of methane in porous media-microporous materials of 5A-type zeolites. Fuel 2018, 220, 185-191. (32) Zhao, J.; Zhao, Y.; Liang, W.; Song, S.; Gao, Q. Semi-clathrate hydrate process of methane in porous media-mesoporous materials of SBA-15. Fuel 2018, 220, 446-452. (33) Zheng, J.; Zhang, P.; Linga, P. Semiclathrate hydrate process for pre-combustion capture of CO2 at near ambient temperatures. Appl. Energy 2017, 194, 267-278. (34) Kumar, A.; Sakpal, T.; Linga, P.; Kumar, R. Influence of contact medium and surfactants on carbon dioxide clathrate hydrate kinetics. Fuel 2013, 105, 664-671. (35) Ghaedi, H.; Ayoub, M.; Bhat, A. H.; Mahmood, S. M.; Akbari, S.; Murshid, G. The effects of salt, particle and pore size on the process of carbon dioxide hydrate formation: A critical review. AIP Conf. Proc. 2016, 1787 (1), 1-10. (36) Mekala, P.; Babu, P.; Sangwai, J. S.; Linga, P. Formation and dissociation kinetics of methane hydrates in seawater and silica sand. Energy Fuels 2014, 28 (4), 2708-2716. (37) Yang, S. H. B.; Babu, P.; Chua, S. F. S.; Linga, P. Carbon dioxide hydrate kinetics in porous media with and without salts. Appl. Energy 2016, 162, 1131-1140. (38) Holzammer, C.; Finckenstein, A.; Will, S.; Braeuer, A. S. How sodium chloride salt inhibits the formation of CO2 gas hydrates. J. Phys. Chem. B 2016, 120, 2452-2459. (39) Palodkar, A. V.; Mandal, S.; Jana, A. K. Modeling growth kinetics of gas hydrate in porous media: Experimental validation. Energy Fuels 2016, 30 (9), 7656-7665. (40) Sloan, E. D.; Koh, C. A. Clathrate hydrates of natural gas, 3rd ed.; CRC Press: Florida, 2008.


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(41) Uchida, T.; Hirano, T.; Ebinuma, T.; Narita, H.; Gohara, K.; Mae, S.; Matsumoto, R. Raman spectroscopic determination of hydration number of methane hydrates. AIChE J. 1999, 45 (12), 2641-2646. (42) Clennell, M. B.; Booth, S.; Winters, J.; Henry, P.; Winters, W. J. Formation of natural gas hydrates in marine sediments: 1. Conceptual model of gas hydrate growth conditioned by host sediment properties. J. Geophys. Res. 1999, 104 (B10), 22985-23003. (43) Akberov, R. R. Calculating the vapor-liquid phase equilibrium for multicomponent systems using the Soave-Redlich-Kwong equation. Theor. Found. Chem. Eng. 2011, 45 (3), 312318. (44) Klauda, J. B.; Sandler, S. I. Modeling gas hydrate phase equilibria in laboratory and natural porous media. Ind. Eng. Chem. Res. 2001, 40 (20), 4197-4208. (45) Barbosa-Cánovas, G. V.; Fontana, A. J.; Schmidt, S. J.; Labuza, T. P. Water activity in foods: Fundamentals and applications; IFT Press Blackwell Publishing Professional: Iowa, USA, 2007. (46) Casco, M. E.; Silvestre-Albero, J.; Ramírez-Cuesta, A. J.; Rey, F.; Jordá, J. L.; Bansode, A.; Urakawa, A.; Peral, I.; Martínez-Escandell, M.; Kaneko, K.; Rodríguez-Reinoso, F. Methane hydrate formation in confined nanospace can surpass nature. Nat. Commun. 2015, 6, 6432-1-8. (47) Palodkar, A. V.; Jana, A. K. Formulating formation mechanism of natural gas hydrates. Sci. Rep. 2017, 7 (1), 6392-1-11. (48) Sun, R.; Hu, W.; Duan, Z. Prediction of nitrogen solubility in pure water and aqueous NaCl solutions up to high temperature, pressure, and ionic strength. J. Solution Chem. 2001, 30 (6), 561-573.


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Figure captions Figure 1. The interaction of salt ions with water molecules in electrolytic solution. Figure 2. Comparing the performance of the proposed and existing39 models with the experimental data53 of CH4 gas uptake during the hydrate formation in the seawater of 3.55 wt% salinity and the silica sand of particle size 300-500 μm, at operating pressure of 11.54 MPa and temperature of 272.27 K, respectively. * represents %AARD. Figure 3. Comparing the performance of the proposed and existing39 models with the experimental data53 of CH4 gas uptake during the hydrate formation in the seawater of 3.55 wt% salinity and the mixture of silica sand (particle size range: 300-500 μm) and bentonite clay (particle size range: 30-3200 nm) at operating pressure of 11.54 MPa and temperature of 272.91 K. * represents %AARD. Figure 4. Comparing the performance of the proposed and existing39 models with the experimental data53 of CH4 gas uptake during the hydrate formation in the seawater of 3.55 wt% salinity and the mixture of silica sand (particle size range: 250-300 μm) and bentonite clay (particle size range: 30-3200 nm) at operating pressure of 11.54 MPa and temperature of 273.65 K. * represents %AARD. Figure 5. Comparing the performance of the proposed and existing39 models with the experimental data53 of CH4 gas uptake during the hydrate formation in the seawater of 3.55 wt% salinity and the mixture of silica sand (particle size range: 150-250 μm) and bentonite clay (particle size range: 30-3200 nm) at operating pressure of 11.54 MPa and temperature of 274.55 K. * represents %AARD. Figure 6. Comparing the performance of the proposed and existing39 formulations with the experimental data36 of CH4 gas uptake during the hydrate growth in the silica sand (100-500 μm


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size range) and the seawater of 3.03 wt% salinity at the operating pressure and temperature of 8 MPa and 277.2 K, respectively. * represents %AARD. Figure 7. Comparing the performance of the proposed and existing39 formulations with the experimental data54 of CH4 gas uptake during the hydrate growth in the Toyoura silica sand (100500 μm size range) and pure water at the operating pressure and temperature of 7.9 MPa and 277.2 K, respectively. * represents %AARD. Figure 8. Comparing the performance of the proposed and existing39 model with the experimental data26 of CO2 gas uptake during the hydrate growth in presence of the silica sand (particle size range: 0.15-0.18 mm) and seawater (3.3 wt% salinity) at the operating pressure and temperature of 6 MPa and 276.15 K, respectively. * represents %AARD. Figure 9. Comparing the performance of the proposed and existing39 model with the experimental data26 of CO2 gas uptake during the hydrate growth in presence of the silica sand (particle size range: 0.43-0.49 mm) and seawater (3.3 wt% salinity) at the operating pressure and temperature of 6 MPa and 276.15 K, respectively. * represents %AARD. Figure 10. Comparing the performance of the proposed and existing39 model with the experimental data26 of CO2 gas uptake during the hydrate growth in presence of the silica sand (particle size range: 0.85-1.00 mm) and seawater (3.3 wt% salinity) at the operating pressure and temperature of 6 MPa and 276.15 K, respectively. * represents %AARD. Figure 11. Comparing the performance of the proposed and existing20 model with the experimental data36 of CH4 gas recovery with the hydrate decomposition in the fixed bed containing the silica sand (particle size range: 100-500 μm) and seawater (3.03 wt% salinity) at the operating pressure of 4.8 MPa and temperature of 297.15 K. * represents %AARD.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 12. Comparing the performance of the proposed and existing20 model with the experimental data54 of CH4 gas recovery with the hydrate decomposition in the fixed bed containing the Toyoura silica sand (particle size range: 100-500 μm) and pure water at the operating pressure of 4.8 MPa and temperature of 297.2 K. * represents %AARD. Figure 13. Comparing the performance of the proposed and existing20 models with the experimental data37 of CO2 gas recovery with the hydrate decay in presence of Toyoura silica (particle size distribution of 100-500 μm) and saltwater (1.5 wt%) at operating pressure of 2.2 MPa and temperature of 280.5 K * represents %AARD. Figure 14. Comparing the performance of the proposed and existing20 models with the experimental data37 of CO2 gas recovery with the hydrate decay in presence of Toyoura silica (particle size distribution of 100-500 μm) and saltwater (1.5 wt%) at operating pressure of 2.2 MPa and temperature of 286.5 K. * represents %AARD.


Page 32 of 49

Page 33 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figures

Figure 1. The interaction of salt ions with water molecules in electrolytic solution.


Energy & Fuels

0.030

-1

CH4 consumed (mol of CH4. mol of H2O )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 49

0.025 0.020 0.015 53

Experimental data * Proposed model (1.70) 39 * Model of Palodkar et al. (4.30)

0.010 0.005 0.000

0

20

40

60

80

100

120

140

160

180

200

Time (min)

Figure 2. Comparing the performance of the proposed and existing39 models with the experimental data53 of CH4 gas uptake during the hydrate formation in the seawater of 3.55 wt% salinity and the silica sand of particle size 300-500 μm, at operating pressure of 11.54 MPa and temperature of 272.27 K, respectively. * represents %AARD.


Page 35 of 49

0.07

-1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.06 0.05 0.04 0.03 53


0.02 0.01 0.00

0

20

40

60

80

100

120

Time (min)

140

160

180

200

Figure 3. Comparing the performance of the proposed and existing39 models with the experimental data53 of CH4 gas uptake during the hydrate formation in the seawater of 3.55 wt% salinity and the mixture of silica sand (particle size range: 300-500 μm) and bentonite clay (particle size range: 30-3200 nm) at operating pressure of 11.54 MPa and temperature of 272.91 K. * represents %AARD.


Energy & Fuels

0.08

-1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 49

0.07 0.06 0.05 0.04 0.03 53


0.02 0.01 0.00

0

50

100

150

Time (min)

200

250



-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels


Page 37 of 49

0.08 0.07 0.06 0.05 0.04 0.03 53


0.02 0.01 0.00

0

20

40

60

80

100

Time (min)

120

140

160



Energy & Fuels

0.012

-1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 49

0.010 0.008 0.006 0.004

36


0.002 0.000

0

180

360

540

720

Time (min)

900

1080

1260

Figure 6. Comparing the performance of the proposed and existing39 formulations with the experimental data36 of CH4 gas uptake during the hydrate growth in the silica sand (100-500 μm size range) and the seawater of 3.03 wt% salinity at the operating pressure and temperature of 8 MPa and 277.2 K, respectively. * represents %AARD.


Page 39 of 49

0.16 -1

CH4 gas uptake (mol of CH4. mol of H2O )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.14 0.12 0.10 0.08 0.06

54


0.04 0.02 0.00

0

1200

2400

3600

4800

6000

Time (min)

Figure 7. Comparing the performance of the proposed and existing39 formulations with the experimental data54 of CH4 gas uptake during the hydrate growth in pure water with Toyoura silica sand (100-500 μm size range) at the operating pressure and temperature of 7.9 MPa and 277.2 K, respectively. * represents %AARD.


Energy & Fuels

0.08 -1

CO2 consumed (mol of CO2. mol of H2O )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 49

0.07 0.06 0.05 0.04 26


0.03 0.02 0.01 0.00

0

120

240

360

Time (min)

480

600

720

Figure 8. Comparing the performance of the proposed and existing39 model with the experimental data26 of CO2 gas uptake during the hydrate growth in presence of the silica sand (particle size range: 0.15-0.18 mm) and seawater (3.3 wt% salinity) at the operating pressure and temperature of 6 MPa and 276.15 K, respectively. * represents %AARD.


Page 41 of 49

0.045 -1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.040 0.035 0.030 0.025 0.020 26


0.015 0.010 0.005 0.000

0

120

240

360

Time (min)

480

600

720

Figure 9. Comparing the performance of the proposed and existing39 model with the experimental data26 of CO2 gas uptake during the hydrate growth in presence of the silica sand (particle size range: 0.43-0.49 mm) and seawater (3.3 wt% salinity) at the operating pressure and temperature of 6 MPa and 276.15 K, respectively. * represents %AARD.


Energy & Fuels

0.040 -1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 49

0.035 0.030 0.025 0.020 26


0.015 0.010 0.005 0.000

0

120

240

360

Time (min)

480

600

720

Figure 10. Comparing the performance of the proposed and existing39 model with the experimental data26 of CO2 gas uptake during the hydrate growth in presence of the silica sand (particle size range 0.85-1.00 mm) and seawater (3.3 wt% salinity) at the operating pressure and temperature of 6 MPa and 276.15 K, respectively. * represents %AARD.


Page 43 of 49

0.40 0.35

CH4 recovered (mol of CH4)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.30 0.25 0.20 0.15 36

Experimental data * Proposed model (7.13) 20 * Model of Oyama et al. (17.46)

0.10 0.05 0.00 0

10

20

30

40

Time (min)

50

60

70

80

Figure 11. Comparing the performance of the proposed and existing20 model with the experimental data36 of CH4 gas recovery with the hydrate decomposition in the fixed bed containing the silica sand (particle size range: 100-500 μm) and seawater (3.03 wt% salinity) at the operating pressure of 4.8 MPa and temperature of 297.15 K. * represents %AARD.


Energy & Fuels

0.6 0.5

CH4 recovered (mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 49

0.4 0.3 54


0.2 0.1 0.0

0

5

10

15

20

Time (min)

25

30

35

40

Figure 12. Comparing the performance of the proposed and existing20 model with the experimental data54 of CH4 gas recovery with the hydrate decomposition in the fixed bed containing the Toyoura silica sand (particle size range: 100-500 μm) in pure water at the operating pressure of 4.8 MPa and temperature of 297.2 K. * represents %AARD.


Page 45 of 49

1.2 1.0 Normalised CO2 recovery

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.8 0.6 37


0.4 0.2 0.0

0

30

60

90

120

150

Time (min)

180

210

240

270

Figure 13. Comparing the performance of the proposed and existing20 models with the experimental data37 of CO2 gas recovery with the hydrate decay in presence of Toyoura silica (particle size distribution of 100-500 μm) and saltwater (1.5 wt%) at operating pressure of 2.2 MPa and temperature of 280.5 K. * represents %AARD.


Energy & Fuels

1.2 1.0

Normalised CO2 recovery

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 49

0.8 0.6 37


0.4 0.2 0.0

0

30

60

90

120

150

Time (min)

180

210

240

270

Figure 14. Comparing the performance of the proposed and existing20 models with the experimental data37 of CO2 gas recovery with the hydrate decay in presence of Toyoura silica (particle size distribution of 100-500 μm) and saltwater (1.5 wt%) at operating pressure of 2.2 MPa and temperature of 286.5 K. * represents %AARD.


Page 47 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Energy & Fuels

Table 1. Model parameters for the CH4 and CO2 hydrate formation kinetics. Case CH4 || Synthetic seawater (3.55 wt%) || Silica sand (300-500 μm)† || 11.54 MPa || 272.27 K CH4 || Synthetic seawater (3.55 wt%) || Silica sand (300-500 μm)† & Bentonite clay (30-3200 nm)†|| 11.54 MPa || 272.91 K CH4 || Synthetic seawater (3.55 wt%) || Silica sand (250-300 μm)† & Bentonite clay (30-3200 nm)† || 11.54 MPa || 273.65 K CH4 || Synthetic seawater (3.55 wt%) || Silica sand (150-250 μm)† & Bentonite clay (30-3200 nm)† || 11.54 MPa || 274.55 K CH4 || Natural seawater (3.03 wt%) || Silica sand (100-500 μm)† || 8 MPa || 277.2 K CH4 || Pure water || Silica sand (100-500 μm)† || 7.9 MPa || 277.2 K CO2 || Natural seawater (3.3 wt%) || Silica sand (0.15-0.18 mm)† || 6 MPa || 276.15 K CO2 || Natural seawater (3.3 wt%) || Silica sand (0.43-0.50 mm)† || 6 MPa || 276.15 K CO2 || Natural seawater (3.3 wt%) || Silica sand (0.85-1.00 mm)† || 6 MPa || 276.15 K a

Palodkar et al.39

Proposed model K 0a



×10-13





K 0a

Eab

× 10-10

×10-3



0.1469

2779.34

0.9975

0.1575

99969.8

83.1239

0.4899

0.3568

0.0916

0.4278

0.3443

99.9613

83.2511

0.4795

0.4077

0.0726

0.3397

0.3986

99.8993

84.3181

0.4762

0.4474

0.0913

0.4262

0.4406

99.2573

83.3072

0.4648

0.0476

0.1296

0.9998

0.0576

0.2452

67.5346

0.6222

0.8323

0.6018

0.3009

0.7624

993.51

84.7865

0.4563

0.4526

0.1583

0.6105

0.4926

0.0197

60.9518

0.6237

0.2643

0.9612

0.8956

0.2926

0.0998

60.8847

0.6014

0.2299

3.7009

0.9667

0.2599

0.2457

59.8027

0.6232

mol of guest gas. mol of H2O-1. m-2. min-1; b J. mol-1; † the particle size distribution.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 48 of 49

Table 2. Model parameters for the CH4 and CO2 hydrate dissociation kinetics.



CH4 || Natural seawater (3.03 wt%) || 645.16 g Silica sand (100-500 μm)† || 4.8 MPa || 297.15 K CH4 || Pure water || 645.16 g Silica sand (100-500 μm)† || 4.8 MPa || 297.2 K CO2 || Saltwater (1.5 wt%) || 645.16 g Silica sand (100-500 μm)† || 2.2 MPa || 280.5 K CO2 || Saltwater (1.5 wt%) || 645.16 g Silica sand (100-500 μm)† || 2.2 MPa || 286.5 K a

Oyama et al.20

Proposed model

Case

mol of guest gas. mol of H2O-1. m-2. min-1. † the particle size distribution. Here,

K 0a

×10-12





0.4559

148.97

0.4105

1.00

0.5277

2.3418

0.5354

41.15

0.3344

0.0593

0.5837

30.92

0.3962

0.0607

0.6279

11.20

 is the percentage contribution to the dissociation of the total heat input to the

system. …..


Page 49 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

For Table of Contents Graphic


Growth and decomposition mechanism of clathrate hydrates in

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