Efm

MF

a

ARRAA

KGEKFS

1

amacmesu(med

0d

Fluid Phase Equilibria 286 (2009) 33–42

Contents lists available at ScienceDirect

Fluid Phase Equilibria

journa l homepage: www.e lsev ier .com/ locate / f lu id

ffect of various types of equations of state for prediction of simple gas hydrateormation with or without the presence of kinetic inhibitors in a flow

ini-loop apparatus

ohammad Reza Talaghatars Technological and Environmental Research Center, Shiraz, Iran

r t i c l e i n f o

rticle history:eceived 18 July 2009eceived in revised form 1 August 2009ccepted 7 August 2009vailable online 15 August 2009

eywords:as consumption ratequation of state

a b s t r a c t

This paper compares the effects of using various types of equations of state (PR,1 SRK,2 ER,3 PT4 and VPT5)on the calculated driving force and rate of gas consumption based on the Kashchiev and Firoozabadi modelfor simple gas hydrate formation for methane, carbon dioxide, propane and iso-butane with experimentaldata points obtained in a flow mini-loop apparatus with or without the presence of kinetic inhibitors atvarious pressures and specified temperatures. For this purpose, a laboratory flow mini-loop apparatuswas set up to measure gas consumption rate when a hydrate forming substance (such as C1, C3, CO2 andi-C4) is contacted with water in the presence or absence of dissolved inhibitor under suitable temperatureand pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a

ashchiev and Firoozabadi modellow mini-loop apparatusimple gas hydrate

required pressure. Pressure is maintained at a constant value during experimental runs by means of therequired gas make-up. The total average absolute deviation was found to be 15.4%, 16.3%, 15.8%, 17.8%and 17.4% for the PR, ER, SRK, PT and VPT equations of state for calculating gas consumption in simple gashydrate formation with or without the presence of kinetic hydrate inhibitors, respectively. Comparisonresults between the calculated and experimental data points of gas consumption were obtained in flowloop indicate that the PR and ER equations of state have lower errors than the SRK, VPT and PT equations

of state for this model.

. Introduction

Gas hydrates have been known for many years. Gas hydrates,re ice-like crystalline compounds formed by the inclusion of lowolecular diameter non-polar or slightly polar molecules (usu-

lly gases) inside cavities formed by water molecules. Althoughlathrates have similar properties to ice, they differ in that theyay form at temperatures well above the freezing point of water at

levated pressure conditions. They crystallize in three well-knowntructures known as structures I, II and H [1–11]. A clathrate hydratenit crystal of structure I includes two tetrakaidecahedron cavities

512 62) and six dodecahedron cavities (512) for every 46 water

olecules. A clathrate hydrate unit crystal of structure II containsight large hexakaidecahedron (512 64) cavities and 16 dodecahe-ron cavities for every 136 water molecules. For example, as a

E-mail addresses: talaghat@shirazu.ac.ir, talaghat@yahoo.com.1 Peng–Robinson.2 Soave–Redlich–Kwong.3 Esmaeilzadeh–Roshanfekr.4 Patel–Teja.5 Valderrama–Patel–Teja.

378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2009.08.003

© 2009 Elsevier B.V. All rights reserved.

simple hydrate, methane can stabilize the 512 cavities of sI andit occupies all of the large 512 62 cavities of sI. Ethane occupiesthe 512 62 cavities of sI with a diameter ratio of 0.94. A relativelylarge volume of gas can be entrapped under pressure in these cav-ities. Gas hydrates are reviewed in-depth by Sloan [3]. Naturalgas hydrates are a nuisance in the production, transportation andprocessing of natural gases. A variety of methods which prevent for-mation of these solids has been applied for over the last 30 or moreyears. For instance, addition of thermodynamic inhibitors such asmethanol to process streams can stop formation of hydrates. Butwith increasing demands for natural gas, production has shiftedtoward deep, off-shore resources where the hydrate nuisance canbe even more costly to manage. Kinetic inhibition is a recentlyproposed alternative to thermodynamic inhibition. Various modelshave been published on the basis of the crystallization theory forthe prediction of gas hydrate formation. One of the most importantparameters in these models is the driving force. In order to calculatethe driving force of hydrate formation corresponding thermody-

namic models are required for calculation of fugacity of differentcomponents in the gas phase at equilibrium and experimental con-ditions. For example, Gnanendran and Amin [12] used the SRKequation of state to determine the gas phase properties. Sloan [3]used the SRK equation of state to calculate the driving force and

3 se Equ

ptoaaiwsacccpf

faata[mo

2

saotccrrihwtanbtcwfemKscpadwFs

3

oobn

4 M.R. Talaghat / Fluid Pha

redict of hydrate equilibrium pressure. The results indicate thathe prediction of equilibrium pressure by using the SRK equationf state is closer to the experimental data. Kashchiev and Firooz-badi [13] used the PR equation of state to predict induction timend the gas consumption rate by using the calculation of the driv-ng force. They found that the sharp decrease in the induction time,

ith increasing super-saturation, is largely due to the strong super-aturation dependence of the rate of hydrate nucleation. Englezosnd Bishnoi [14] used the Peng and Robinson equation of state toalculate the driving force by using the fugacity coefficient of theomponents in the gas phase resulting in the proposed model’sapability of describing the experimental data quite well with arediction error of less than 11.3%. In addition, at higher drivingorces, the rate of gas consumption is higher.

In this work, the rate of gas consumption for simple gas hydrateormation with and without the presence of kinetic inhibitors in

flow mini-loop apparatus is calculated based on the Kashchievnd Firoozabadi model [15]. In addition, in the proposed model,he effect of using two parameters equations of state, the SRK [16]nd PR [17] and three parameters equations of state, the ER [18], PT19] and VPT [20] for the prediction of the gas consumption rate by

eans of calculating the driving force from the fugacity coefficientf the components in the gas phase is investigated.

. Rate of hydrate formation

Hydrate nucleation is a microscopic process, during whichmall hydrate crystals (nuclei) grow and disperse in an attempt tochieve critical nuclei size for continued growth [3]. The presencef non-polar molecules, such as hydrocarbons, in water, distortshe water molecules inducing them to ‘arrange’ themselves intolusters (nuclei). These clusters increase in number through a pro-ess of continuous fading and growing to a critical size beforeapid hydrate growth proceeds. The time taken for nucleation iseferred to as the induction time. The hydrate nucleation processn practical situations is a heterogeneous nucleation process, asomogeneity is rarely achieved. Hydrate formation occurs at theater–gas interface, as the gas is present at its highest concentra-

ion in the interface, more so than in the bulk liquid. The interfacelso lowers the Gibbs-free energy which is conducive for hydrateucleation. Englezos et al. [21,22] developed a mechanistic modelased on crystallization kinetics and mass transfer effects to predicthe hydrate formation kinetics of methane and ethane hydrates in aonstant pressure stirred-tank gas–water system. Later the modelas simplified by Skovborg and Rasmussen [23] to a mass trans-

er limited model for multi-component gas mixtures. Bourgmayert al. [24] measured the formation rate of methane and ethaneixtures in a semi-batch reactor in the presence of a condensate.

ashchiev and Firoozabadi in 2003 [13] published a comprehen-ive study on hydrate nucleation and growth kinetics based onlassical nucleation and crystallization principles for single com-onent gas hydrate systems. The work also quantified the effects ofdditives in the formation of hydrates when present in water, andistinguished how certain additives acted as hydrate promotershile others acted as hydrate kinetic inhibitors. The Kashchiev and

iroozabadi model was developed based on a single gas componentystem [13].

. Driving forces for gas hydrate formation

Mullin [25] defines the driving force for crystallization in termsf super-saturation. Spontaneous (homogeneous) nucleation willnly occur in a supersaturated solution in the labile region limitedy the super-solubility curve. In the meta-stable zone, spontaneousucleation cannot occur, but growth of crystals is possible. For

ilibria 286 (2009) 33–42

instance, the driving force for nucleation and growth can be definedby the super-saturation ratio: the concentration of the supersatu-rated solution to the equilibrium concentration at the solubilitycurve, both at the same temperature. Sloan [3] suggested an anal-ogy to hydrate formation where concentration is replaced by thelogarithmic pressure giving the hydrate equilibrium curve. Severaldriving forces have been used in modeling of hydrate formationkinetics, and those most frequently used in experimental studiesare related to the hydrate equilibrium curve.

Vysniauskas and Bishnoi [26] used sub-cooling as the driv-ing force for nucleation and growth. Sub-cooling is defined asthe difference between the hydrate equilibrium temperature atthe experimental pressure and the experimental temperature.Sub-cooling is easily determined by measuring the experimentaltemperature and calculating the hydrate equilibrium temperatureusing a thermodynamic model. Englezos et al. [21,22] used the dif-ference in fugacity of the dissolved gas and the hydrate equilibriumfugacity at the experimental temperature as the driving force intheir hydrate formation model. Similarly, Natarajan et al. [27] usedfg/feg − 1, as driving force for nucleation where f is the gas phasefugacity. Skovborg and Rasmussen [23] used the difference in gasmole fraction at the gas–liquid interface and in the liquid bulk phaseas the driving force. They maintain that the formation rate is con-trolled by gas–liquid mass transfer rather than crystal growth, andtherefore, the driving force is not related to the hydrate equilib-rium curve or the hydrate crystal surface, in their study of inductiontimes, Skovborg [28] expressed the driving force as the differencein the chemical potential of water in the hydrate phase and waterin the liquid phase at the experimental pressure and temperature.Kashchiev and Firoozabadi[13] derived a general expression for thesuper-saturation for crystallization of one-component gas hydratesin aqueous solutions. The super-saturation is the driving force ofthe process, since it represents the difference between the chemi-cal potentials of a hydrate building unit in the solution and in thehydrate crystal. Anklam and Firoozabadi [29] presented the expres-sion for driving force of multi-component gas hydrate nucleation inan aqueous phase. In addition, Christiansen and Sloan [30] derivedthe driving force for doubles hydrate formation on the basis ofmolar changes of the total Gibbs free energy of the system whenhydrate crystal forms from water and gas.

3.1. Super-saturation

The driving force for simple or double gas hydrate formation isthe difference between the chemical potentials of the old and newphases. This difference is referred to as super-saturation (��) andis defined for a single gas component system as [31]:

�� = kT ln(˚exp(Pexp, T)Pexp

˚eq(Peq, T)Peq

)+��e(Pexp − Peq) (1)

where �� is the change in chemical potential at operating con-ditions, T is the temperature of the system, k is the Boltzmannconstant, Peq is the hydrate equilibrium pressure at T, Pexp is thepressure of system,˚eq and˚exp are the fugacity coefficient of gascomponent at equilibrium and experimental conditions, respec-tively,��e is calculated using Eq. (2). The fugacity coefficient of gascomponent for equilibrium and experimental conditions should becalculated by a suitable equation of state:

��e = nw�w − �h (2)

�h = �cell (3)

ng

where �cell is the volume of hydrate unit cell, ng the stoichiometricnumber of gas molecules at equilibrium conditions Pe, T. The super-saturation of the system is assumed to be a time-independentparameter regardless of the mode of operation in the reactor, and

M.R. Talaghat / Fluid Phase Equilibria 286 (2009) 33–42 35

Table 1Summary of the cubic equation of states used in this work.

Esmaeilzadeh–Roshanfekr Patel–Teja

p = RTV−b − a

V(V+c)+c(V−c) p = RTV−b − a

V(V+c)+c(V−c)

a =˝aR2T2

cpc˛(Tr) a =˝a

R2T2c

pc˛(Tr)

b =˝bRTcpc

b =˝bRTcpc

c =˝cRTcpc

c =˝cRTcpc

˝b = 2˝c − 1 + 3�c ˝c = 1 − �c

˝a = 3�2c +˝2

c + 2˝b˝c + 2˝c ˝a = 3�2c + 3(1 − 2�c)˝a +˝2

a + 1 − 3�c

˝c is the smallest positive root of the cubic: ˛(Tr) = (1 +m(1 − T0.5r ))

2

˝3c +(

3� − 58

)˝2

c +(

3�2c − 3

4 �c

)˝c + �3

c − 38 �

2c = 0 ˝c is the smallest positive root of the cubic:

˛0.5 = (m1 +m2(1 − T0.5r )) ˝3

b+ (2 − 3�c)˝2

b+ 3�2

c˝2b

+ �3c = 0

T ′r < Tr For �c = 0.32844388 − 0.0690264w + 0.0078711w2 m = 0.452412 + 0.30932w − 0.297935w2

1< Tr < T ′r For �′

c = �c − (�c − Zc) ×(T ′

r−TrTr−1

)2�c = 0.329032 − 0.07699w − 0.2211947w2

T ′r = 0.78921611 + 0.15855814w − 0.1331939759w2 1 < Tr < 0.9

�′c = �c − 10(�c − Zc)(Tr − 0.9)

m1 = 0.999035009 − 0.010618422w − 0.0081744w2

m2 = 0.0.4400108 + 1.5297151w − 0.4710752752w2

Soave–Redlich–Kwong Peng–Robinson

p = RTV−b − a

V(V+b) p = RTV−b − a

V(V+b)+b(V−b)

a =˝aR2T2

cpc˛(T) a =˝a

R2T2c

pc˛(T)

b =˝bRTcpc

b =˝bRTcpc

0.5 2 0.5))2

w + 0.

iaao

ttiLbotaetu

4

igijansf

F

w0s

˛(T) = (1 +m(1 − Tr )) ˛(T) = (1 +m(1 − Trm = 0.480 + 1.574w − 0.176w2 m = 0.3746 + 1.5423˝a = 0.42747 ˝a = 0.45724˝b = 0.08664 ˝b = 0.07780

t depends mainly on the reactor pressure and temperature (whichre assumed constant) along with the hydrate structural propertiess seen above. In this study, the PR, ER, SRK, VPT and PT equationsf state are used to obtain˚eq and˚exp.

Table 1 shows the summery of the equations of state used inhis work. In order to calculate the driving force of hydrate forma-ion by above equation, fugacity coefficient of different componentsn gas phase, corresponding thermodynamic models are required.ow dosage hydrate inhibitors are known as kinetic inhibitors,ecause their concentration in the solution is so low (below 1 wt.%f the aqueous phase) that they have no appreciable influence onhe hydrate/solution/gas thermodynamic equilibrium [32]. As atsufficiently low concentration an additive exerts practically no

ffect on the chemical potentials of the gas and water molecules inhe solution and or the hydrate crystal and �� (Eq. (1)) remainsnchanged [32].

. Nucleus and clusters

Nucleation is perhaps the most challenging step in understand-ng the process of crystallization of gas hydrates. The kinetics ofas hydrate crystallization is covered in a large number of studiesn the literature. Sloan [3] provides an extensive review on the sub-ect. As far as the nucleation aspects of the crystallization processre concerned, a theoretical description of the rate of gas hydrateucleation has been attempted recently by Kvamme [33]. For caphaped and lens-shaped clusters the wetting angles’ are given byollowing equations [13,31,32]:

� − �

or cap-shaped cluster : cos � = ss hs

�(4)

here � is the hydrate/substrate wetting angle with values fromto 180◦, � (J/m2), �ss (J/m2) and �hs (J/m2) are the specific

urface energies of the hydrate/solution, solution/substrate and

2699w2

hydrate/substrate interfaces, respectively. For lens-shaped cluster:

cos � =�2

sg + �2 + �2hg

2�sg�and cos �0 =

�2sg − �2 + �2

hg

2�sg�sg(5)

where �0 and � are the hydrate/gas and hydrate/solution wet-ting angles, with values from 0 to 180◦ respectively, �sg (J/m2),�hg (J/m2) are the specific surface energies of the solution/gas andhydrate/gas interfaces, respectively. The effective specific surfaceenergy of the system is given by

�ef = � (6)

where is the wetting factor (0 < < 1) and for cap-shaped andlens-shape clusters it is given by Eqs. (13) and (14), respectively:

=[(

14

)(2 + cos �)(1 − cos �)2

]1/3(7)

=[(

14

)(2 + cos �)(1 − cos �)2 +

(14

)(2 + cos �0)

× (1 − cos �0)2

(sin �sin �0

)3]1/3

(8)

The nucleus size for hydrate nucleation could be determined fromthe nucleation theory given in Kashchiev [31] as

8c3�2h�

3ef

ns =

27��3(9)

where c = (36�)1/3 assuming spherical nuclei, �h is the volume ofhydrate building unit and�� is super-saturation is defined by Eq.(1) for simple hydrate formation. Nucleation work, W, is the energy

3 se Equ

bw

W

5f

sdd

R

IIpdod

F

F

F

F

TGa

G

Eos

Q

J

IccekmnEtp

A

A

6 M.R. Talaghat / Fluid Pha

arrier needed to achieve the above nucleus size for nucleation,hich is given as Kashchiev and Firoozabadi [13,32]:

= 4c3�2h�

3ef

27��3(10)

. Rate of gas consumption in the early stage of gas hydrateormation

Kashchiev and Firoozabadi [13] developed the rate of gas con-umption based on the early stage of the crystallization theory. Theeveloped gas consumption rate for simple hydrate formation isefined as

(t) = dn(t)dt

=(bhVsG3mJ

Mwh

)t3m (11)

n the following section, different terms of Eq. (11) will be described.n the above equation, R(t) is the rate of gas consumption for aure component in simple gas hydrate formation, h is the hydrateensity, Vs is molar mass of the solution, Mh is the molecular weightf the hydrate, t is time, b is the dimensionless shape factor and isefined as

or spherical crystal : b = 4�3

(12)

or cube crystal : b = 8 (13)

or cap-shaped on a solid substrate with wetting angle � :

b =[

4�3 (�)

](14)

or lens-shaped at the solution/gas interface with angles �, �0 :

b =[ (�) + (�0)

(sin(�)sin(�o)

)3]

(15)

he function (x) is defined by Eqs. (7) and (8), m > 0 is a number,and J are the growth constant and nucleation rate, respectively,

nd are calculated by model kinetics considerations:

= Q (e��/kT − 1) (16)

q. (16) is used for the growth by undisturbed volume diffusionf dissolved gas toward a spherical crystallite [13], Q is the super-aturation-independent kinetic factor given by Eq. (17):

= εahDefcCe (17)

= A e��/kT exp

(−4c3�2h�

3ef

27kT ��2

)(18)

n the above equations, Ce is the equilibrium solubility of the gasomponent, ε≤ 1 is the sticking coefficient of building units to therystallite surface, ah is the surface of hydrate crystal, Defc is theffective diffusion coefficient of gas components in water, A is ainetic parameter and is defined based on the mechanism of attach-ent of hydrate building units to the nucleus and mechanism of

ucleation [32]. For homogeneous nucleation A is calculated byq. (19) and for heterogeneous nucleation on solid substrate or athe solution/gas interface without nucleation active center and thearameter of A is calculated by Eq. (20):

1/2 1/3 1/3

= zε(4�c) �h DcCens

aW(19)

= zε(4�c)1/2�1/3h DcCen

1/3s ApCp

aw(20)

ilibria 286 (2009) 33–42

In the above equations, z = 0.01–1 is the Zeldovich factor, aw is thesurface area of a water molecule. Ap and Cp are the surface area andconcentration of the nucleation active center. The diffusion coeffi-cient (Dc) of gas in water was calculated for the hydrate formingcomponents using the Wilke–Chang correlation, as given in Reid etal. [34]:

Dc = 7.4 × 10−8(�Mww)1/2T

�wv0.6m

(21)

where Dc, Mww and �w are the diffusivity (m2/S), water molecu-lar weight (g/g mol) and water viscosity (cp), respectively. T is theabsolute temperature (k) and �m is the solute molar volume at itsnormal boiling point (cm3/mol). � is the association factor of thesolvent (for water � = 2.6). An average diffusion coefficient for thegas into water was obtained by normalizing the individual diffu-sion coefficient of the hydrate forming gas components, based onthe gas composition of the hydrate forming gas in the natural gasmixture.

5.1. Effect of kinetic inhibitors on the nucleation and growth ratesin crystallization of gas hydrates

Kinetic inhibitors delay hydrate nucleation and/or crystalgrowth for a certain period of time (induction time) exceedingthe free water residence time in the section of the pipeline, withoperation conditions inside the hydrate stability zone [35]. The per-formance of kinetic inhibitors is usually evaluated in autoclavesand/or flow loops in terms of induction time. Understanding thereasons for this effect at the molecular level is of interest becauseof the necessity to avoid hydrate formation during important tech-nological processes. In kinetic inhibition, small quantities (less than1 wt.%) polymers are added to the solution in order to influence thekinetics of hydrate crystallization rather than the thermodynamicequilibrium. Theoretically, the effect of additives on the kinet-ics of hydrate crystallization is poorly understood, especially withregard to the early, nucleation stage of the process. Kashchiev andFiroozabadi [13] developed nucleation and growth rates with thepresence of kinetic inhibitors based on the crystallization theory asfollow:

Ja = J

1 + knCa(22)

Ga = G

1 + kgca(23)

where Ja and Ga are the nucleation rate and the growth constantin the presence of kinetic inhibitors, kn (m3) and kg (m3) are theadsorption constant and Ca (m−3) is the concentration of additivein the solution.

5.2. Rate of gas consumption for simple gas hydrate formationwith the presence of kinetic inhibitors in a flow mini-loopapparatus

Dynamic behavior of the gas flow and component concentra-tion through the flow loop causes the driving force of gas hydrateformation to be variable relative to the position along the pipe andtime.

An element of the pipe segment that is used for the develop-ment of the mathematical models for prevention of gas hydrateformation in a flow mini-loop is shown in Fig. 1. In this figure, Cg is

used for the molar composition of the gas components. Cw, Ch andCa are used for the molar composition of the water content, thehydrate formed, and inhibitor content, respectively. Qw is used forwater flow rate and the nw is used for the hydration number, and ng

is used for number of gas component g. Therefore, nucleation rate

M.R. Talaghat / Fluid Phase Equ

ttEam

J

G

Tt

R

w

mtu

r

Iv

injected into the loop as an aqueous solution to produce the desired

F

Fig. 1. Schematic representation of the flow mini-loop element.

hat is dependent on the driving force is dynamic and variable. Inhis work, time and space dependent nucleation rate as shown inq. (24) is developed based on the work of Kashchiev and Firooz-badi [13,32]. They developed a static nucleation and growth ratesodel for constant driving force:

a(t, z) =[

A

1 + knCa

]exp(��(t, z)kT

)exp

( −4c3�2h�

3ef

27kT ��(t, z)2

)(24)

a(t, z) =[

Q

1 + kgCa

](e��(t,z)/kT − 1) (25)

hen, the gas consumption rate is calculated by the following equa-ion:

h(t, z) =[bh(t, z)Ga(t, z)3mJa(t, z)

Mwh(t, z)

]t3m (26)

here t and z are time and the position along the pipe, respectively.Then, the rate of gas consumption for simple gas hydrate for-

ation is calculated at each time step by integrating Eq. (26) overhe length of the flow mini-loop. Hence, the following equation issed to calculate the gas consumption rate:

h(t)=∫ z=Lpipe

0

((bh(t, z)G3m

a (t, z)J(t, z)Mwh(t, z)

)t3maint(z)

(�d2

pipe

4

)dz

(27)

n the above equation, aint(z) is gas–liquid interfacial area per unitolume of pipe and dpipe is the pipe diameter.

ig. 2. Process flow diagram of a laboratory scale for flow mini-loop apparatus. T: tempera

ilibria 286 (2009) 33–42 37

6. Experiment

6.1. Apparatus and experimental procedure

A laboratory flow mini-loop apparatus was set up to allow thestudy of simple gas hydrate formation with or without the pres-ence of the kinetic inhibitors [36,37]. The equipment is essentiallycomposed of a pipe and a pump. The flow line is made of 316 stain-less steel schedule 80 pipe with an inner diameter of 10.6 mm and apressure rating 10 MPa. The mini-loop layout, shown in Fig. 2, is 2 mwide × 4 m long (four 90◦ elbows) for a total length of 12 m water isinjected to the loop by means of a piston pump (Pump 2) and flowis implemented with a Kracht screw pump (Pump 1) with vari-able rates up to 0.75 m3/h. Temperature control of the flow loop isimplemented using pump fed water (Pump 3) circulation throughinsulated 15 and 32 mm diameter PVC pipes those encompassesthe loop. Cooling is achieved by circulating of ethylene glycol asa coolant prepared in a cooling system operated as a refrigerator.The current temperature range is 2–8 ◦C with a maximum contin-uous cooling rate about 100 ◦C/h. The loop is monitored by threetemperature sensors (platinum resistance thermometers or PT-100, T1–T3), two pressure sensors (P1 and P2), one Endress–Hausermagnetic flowmeter (F) and one Rosemount pressure drop trans-mitter (DP1) arrayed around the flow mini-loop apparatus. Gasinjection rate is monitored by the means of a Rosemount pressuredrop transmitter and an orifice plate (DP2). The pressure of flowmini-loop maintained at a constant value during experimental runsby means of a regulator and gas make-up. All parameters and dataare controlled and recorded every 60 s. The accuracy of the pressureand temperature measurements is estimated to be ±0.05 bar and±0.1 K, respectively.

The materials used for the experiments are fresh water as anaqueous phase, carbon dioxide, methane gas with 99.95% purity,propane gas with 99.9% purity, iso-butane gas with 99.99% purity asthe hydrate former. In the experiments with the presence of kineticinhibitors, the inhibitor is typically (such as PVP and l-tyrosine)

weight percent concentration of inhibitor in the aqueous solution.In this setup, aqueous phase is saturated by the pure gas compo-nent (such as C1, C3, i-C4 and CO2) and is circulated through the flowloop. Saturation of the aqueous phase by the pure gas component

ture gauge; P: pressure gauge; MF: magnetic flow meter; DP: pressure drop gauge.

3 se Equilibria 286 (2009) 33–42

ivoiatbhhGap

f

1

2

3

4

5

7

toflspphiTdafbmtoafflSaocbsebtVwc

et

respectively. According to these figures, by increasing the pressureof the system, the calculated driving forces also increase at pressureabove dew point pressure; the driving force is almost unchangedindicating the negligible effect of pressure on liquid fugacity. As can

Fig. 4. Comparison results between calculated driving force dimensionless for CO2

hydrate formation in presence or absence of kinetic hydrate inhibitors at tempera-ture of 280 K using various types of equations of state in flow mini-loop apparatus.

8 M.R. Talaghat / Fluid Pha

s performed in a mixing tank. The fluid is circulated at a constantelocity. The stream temperature is adjusted by a cooling systemperated as a refrigerator and stream pressure is adjusted by thenjection of the gas from storage tank. The loop and its pump lay incontrolled temperature water bath for controlling the tempera-

ure of the fluid circulating in the loop. The ethylene glycol from aath is circulated through the external jacket of the pipe to ensureaving uniform temperature. As the loop pressure changes or asydrates form, the gas volume in the loop will change accordingly.as pressure drop is monitored while operating the system andbrupt change of the pressure drop in the loop is a measure for theipe plugging by the hydrate crystals.

Investigation of hydrate formation in the flow loop was per-ormed by considering the following conditions.

. The hydrate formers were carbon dioxide, methane, propane andiso-butane.

. Operating temperatures are 7 ◦C for CO2, 4 ◦C for methane andpropane and 2 ◦C for iso-butane.

. Operating pressures for CO2, methane, propane and iso-butaneare in the range of 4–7 MPa, 5–8 MPa, 1–2 MPa and 1–2 MPa,respectively.

. Flow velocity of the aqueous phase inside the flow loop is in therange of 0–2 m/s.

. Two types of the kinetic inhibitors (such as PVP and l-tyrosine)with 100 ppm and 200 ppm concentrations are tested.

. Results and discussion

Several models have been published on the basis of the crys-allization theory for the prediction of gas hydrate formation. Onef the most important parameters in these models is the drivingorce. Various driving forces have been used in order to corre-ate the experimental data with gas consumption data, such asuper-saturation. The super-saturation is the driving force of therocess, since it represents the difference between the chemicalotentials of a hydrate building unit in the solution and in theydrate crystal. In studying the kinetics of hydrate crystallization it

s important to know the mole of hydrate crystallized until time t.he number of moles of gas consumed (N) until time t for simple andouble hydrate crystallization in the solution is an experimentallyccessible quantity which is directly related to the rate of hydrateormation. The overall rate R (mol/s) of gas consumption is definedy the equality R = dN/dt. The temporal evolution of the number ofoles of gas consumed at the post-nucleation stage of hydrate crys-

allization was considered by many authors. In this work, the effectf various types of equations of state on driving force calculationnd gas consumption prediction in early stage of simple gas hydrateormation with or without the presence of kinetic inhibitors in aow mini-loop apparatus, two parameters equations of state, theRK and PR and three parameters equations of state, the ER, PTnd VPT for the prediction of the gas consumption rate by meansf calculating the driving force from the fugacity coefficient of theomponents in the gas phase were investigated. Then, the resultsetween the calculated of diving force and gas consumption forimple gas hydrate formation using the PR, SRK, ER, VPT and PTquations of state for methane, carbon dioxide, propane and iso-utane at different pressures and temperatures were compared. Inhe aim of an unbiased comparison between the PR, SRK, ER, PT andPT equations of state, van der Waals mixing rules were applied

ithout the use of any adjustable parameters (kij = 0). Also, no pure

omponent parameters were adjusted.Driving force is a function of pressure and temperature as

xpressed by Eq. (1) and effective surface energy is dependent onhe wetting angle and hydrate-solution interface energy as shown

Fig. 3. Comparison results between calculated driving force dimensionless formethane hydrate formation in presence or absence of kinetic hydrate inhibitorsat temperature of 277 K using various types of equations of state in flow mini-loopapparatus.

by Eq. (6). The results for the calculation of driving force dimension-less with or without the presence of kinetic inhibitors using the PR,SRK, ER, PT and VPT equations of state at specified temperaturesfor pure component methane (at 277 K), carbon dioxide (at 280 K),propane (at 277 K) and iso-butane (at 275 K) during gas hydrateformation are shown in Figs. 3–6, respectively. In these figures, thesolid curves depict the driving force vs. pressure. The curves weredrawn with the aid of equilibrium pressures at 3.85, 2.84, 0.396 and0.169 MPa for methane, carbon dioxide, propane and iso-butane,

Fig. 5. Comparison results between calculated driving force dimensionless forpropane hydrate formation in presence or absence of kinetic hydrate inhibitors attemperature of 277 K using various types of equations of state in flow mini-loopapparatus.

M.R. Talaghat / Fluid Phase Equilibria 286 (2009) 33–42 39

Fig. 6. Comparison results between calculated driving force dimensionless for iso-bta

beiceoVccaricsslt

driving force in the prediction of the gas consumption rate in simple

TT

utane hydrate formation in presence or absence of kinetic hydrate inhibitors atemperature of 275 K using various types of equations of state in flow mini-looppparatus.

e seen in these figures, for lower pressures, the different types ofquations of state have no noticeable effect on calculation of driv-ng force dimensionless, but for higher pressure, the results for thealculated driving force dimensionless show that the PR and ERquations of state are better than the SRK, PT and VPT equationsf state. In this work, to illustrate the ability of the PR, SRK, ER,PT and PT equations of state to predict the number of moles gasonsumption in simple gas hydrate formation (such as methanearbon dioxide, propane and iso-butane) based on the Kashchievnd Firoozabadi model at various temperatures and pressures, itsesults are compared with experimental data points are obtainedn a flow mini-loop apparatus. For example, the number of molesonsumed variation with time for CO2 hydrate formation at pres-

ure of 7 MPa and temperature of 280 K using these equations oftate are displayed in Fig. 7. Comparison results between the calcu-ated and experimental data points of gas consumed indicate thathe PR and ER equations of state have lower errors than the SRK,

able 2otal average absolute deviation percent for simple gas hydrate formation absence of the

No. Component T (K) P (MPa) No. of data points %ADDY,a PR,b EOS %A

1 CO2 280 4 50 14 142 CO2 280 5 40 14.5 153 CO2 280 6 45 15.1 154 CO2 280 7 50 15.8 16

TAAD% for CO2 gas hydrate 185 14.9 155 C1 277 5 45 14 146 C1 277 6 50 14.8 157 C1 277 7 50 15.4 168 C1 277 8 50 15.8 16

TAAD% for C1 gas hydrate 195 15 159 C3 277 1 50 14.2 1410 C3 277 1.2 45 14.5 1511 C3 277 1.5 45 14.9 1512 C3 277 2 50 15.4 16

TAAD% for C3 gas hydrate 190 14.8 1513 i-C4 275 1 45 14.3 1514 i-C4 275 1.2 45 14.6 1515 i-C4 275 1.5 50 15.1 1516 i-C4 275 2 50 15.5 16

TAAD% for i-C4 gas hydrate 190 14.9 15TAAD% for simple gas hydrate formation 760 14.9 15

a TAAD% = [(1/n)∑

|(gas consumptionexpi

− gas consumptioncali

)|/gas consumptionexpi

]b Peng–Robinson.c Soave–Redlich–Kwong.d Esmaeilzadeh–Roshanfekr.e Patel–Teja.f Valderrama–Patel–Teja.g Equation of state.

Fig. 7. Time dependence of the CO2 consumed during of gas hydrate formation at atemperature of 280 K and pressure of 7 MPa using various types’ equations of statein a flow mini-loop apparatus.

VPT and PT equations of state for this model. The average absolutedeviation percent between the calculated and experimental gasconsumed for methane carbon dioxide, propane and iso-butane atdifferent pressures and temperatures was also obtained. The valuesare demonstrated in Table 2. According to this table, it was foundthat the total average absolute deviation (TAAD) percentages of gasconsumption were found to be 14.9%, 15.6%, 15.2%, 17.2% and 16.7%for the PR, SRK, ER, PT and VPT equations of state, respectively. Inthis comparison, the PR and ER equations of state with TAAD of14.9% and 15.2%, are the best equations of state for calculating the

hydrate formation based on the Kashchiev and Firoozabadi model.Also, for example, comparison results between the calculated andexperimental data of gas consumed for CO2 at pressure of 7 MPaand temperature of 280 K with the presence of PVP (with 100 ppm

kinetic inhibitor in a flow mini-loop apparatus.

DDY,a SRK,c EOS %ADDY,a ER,d EOS %ADDY,a PT,e EOS %ADDY,a VPT,f EOSg

.7 14.3 16.1 15.7

.2 14.8 16.8 16.2

.8 15.4 17.4 16.9

.5 16.1 18.1 17.7

.6 15.2 17.1 16.7

.7 14.3 16.2 15.7

.5 15.1 17.1 16.6

.1 15.7 17.7 17.2

.6 16.1 18.2 17.7

.8 15.3 17.3 16.8

.9 14.4 16.3 15.9

.2 14.8 16.8 16.2

.6 15.2 17.2 16.6

.2 15.7 17.8 17.2

.5 15.1 17.1 16.5

.1 14.6 16.5 16.1

.3 14.9 16.8 16.4

.9 15.4 17.4 16.9

.3 15.8 17.8 17.4

.6 15.2 17.2 16.6

.6 15.2 17.2 16.7

× 100.

40 M.R. Talaghat / Fluid Phase Equilibria 286 (2009) 33–42

Table 3Total average absolute deviation percent for simple gas hydrate formation with the presence of the kinetic inhibitors in a flow mini-loop apparatus.

No. Component T (K) P (MPa) Type of inhibitor Concentration ofinhibitor (ppma)

No. of datapoint

%ADDY,b

PR,c EOS%ADDY,b

SRK,d EOS%ADDY,b

ER,e EOS%ADDY,b

PT,f EOS%ADDY,b

VPT,g EOSh

1 CO2 280 4 PVP 100 45 15.5 16.6 15.9 18.1 17.82 CO2 280 5 PVP 100 45 15.6 16.7 16.1 18.2 17.93 CO2 280 6 PVP 100 45 15.3 16.4 15.7 17.9 17.54 CO2 280 7 PVP 100 45 16.8 17.9 17.3 19.6 19.3

TAAD% for CO2 in presence of 100 ppm PVP 180 15.8 16.9 16.2 18.4 18.15 CO2 280 4 PVP 200 45 15.9 17.1 16.3 18.6 18.26 CO2 280 5 PVP 200 40 15.8 16.9 16.2 18.4 18.17 CO2 280 6 PVP 200 40 15.7 16.8 16.2 18.3 18.08 CO2 280 7 PVP 200 45 17.2 18.4 17.7 20.1 19.7

TAAD% for CO2 in presence of 200 ppm PVP 170 16.2 17.3 16.6 18.9 18.69 CO2 280 4 l-Tyrosine 100 35 15.6 16.7 16.1 18.2 17.910 CO2 280 5 l-Tyrosine 100 35 15.7 16.8 16.2 18.3 18.011 CO2 280 6 l-Tyrosine 100 30 15.4 16.5 15.8 18.0 17.712 CO2 280 7 l-Tyrosine 100 35 16.9 18.1 17.4 19.7 19.4

TAAD% for CO2 in presence of 100 ppm l-tyrosine 135 15.9 17.1 16.3 18.6 18.213 CO2 280 4 l-Tyrosine 200 30 16.1 17.2 16.5 18.8 18.514 CO2 280 5 l-Tyrosine 200 30 15.8 16.9 16.2 18.4 18.115 CO2 280 6 l-Tyrosine 200 30 16.4 17.5 16.8 19.1 18.8616 CO2 280 7 l-Tyrosine 200 35 14.5 15.5 14.9 16.9 16.6

TAAD% for CO2 in presence of 200 ppm l-tyrosine 125 15.7 16.8 16.1 18.3 18.017 C1 277 5 PVP 100 40 14.6 15.6 15.1 17.0 16.718 C1 277 6 PVP 100 40 15.5 16.5 15.9 18.1 17.819 C1 277 7 PVP 100 45 16 17.1 16.4 18.7 18.420 C1 277 8 PVP 100 45 16.4 17.5 16.8 19.1 18.8

TAAD% for C1 in presence of 200 ppm PVP 170 15.6 16.7 16.1 18.2 17.921 C1 277 5 PVP 200 40 14.9 15.9 15.3 17.4 17.122 C1 277 6 PVP 200 40 15.7 16.8 16.1 18.3 18.0523 C1 277 7 PVP 200 40 16.2 17.3 16.6 18.9 18.624 C1 277 8 PVP 200 45 16.4 17.5 16.8 19.1 18.8

TAAD% for C1 in presence of 200 ppm PVP 165 15.8 16.9 16.2 18.4 18.125 C1 277 5 l-Tyrosine 100 35 14.7 15.7 15.1 17.1 16.9026 C1 277 6 l-Tyrosine 100 35 15.5 16.5 15.9 18.1 17.827 C1 277 7 l-Tyrosine 100 35 16.1 17.2 16.5 18.8 18.528 C1 277 8 l-Tyrosine 100 35 16.4 17.5 16.8 19.1 18.8

TAAD% for C1 in presence of 200 ppm l-tyrosine 140 15.7 16.7 16.1 18.3 18.029 C1 277 5 l-Tyrosine 200 30 14.8 15.8 15.2 17.3 17.030 C1 277 6 l-Tyrosine 200 30 15.9 17.0 16.3 18.6 18.231 C1 277 7 l-Tyrosine 200 30 16.2 17.3 16.6 18.9 18.632 C1 277 8 l-Tyrosine 200 30 16.6 17.7 17.1 19.422 19.0

TAAD% for C1 in presence of 200 ppm l-tyrosine 120 15.9 17.0 16.4 18.6 18.233 C3 277 1 PVP 100 40 14.6 15.6 15.1 17.1 16.734 C3 277 1.2 PVP 100 45 15.3 16.3 15.7 17.9 17.535 C3 277 1.5 PVP 100 45 15.7 16.7 16.1 18.3 18.036 C3 277 2 PVP 100 40 16.1 17.2 16.5 18.8 18.5

TAAD% for C3 in presence of 100 ppm PVP 170 15.4 16.4 15.8 18.0 17.737 C3 277 1 PVP 200 40 15.1 16.1 15.5 17.6 17.338 C3 277 1.2 PVP 200 45 15.5 16.5 15.9 18.1 17.839 C3 277 1.5 PVP 200 45 15.9 17.0 16.3 18.6 18.240 C3 277 2 PVP 200 40 16.3 17.4 16.7 19.0 18.7

TAAD% for C3 in presence of 100 ppm PVP 170 15.7 16.7 16.2 18.3 18.041 C3 277 1 l-Tyrosine 100 35 14.8 15.8 15.2 17.3 17.042 C3 277 1.2 l-Tyrosine 100 35 15.4 16.4 15.8 18.0 17.743 C3 277 1.5 l-Tyrosine 100 35 15.8 16.9 16.2 18.4 18.144 C3 277 2 l-Tyrosine 100 35 16.2 17.3 16.6 18.9 18.6

TAAD% for C3 in presence of 100 ppm l-tyrosine 140 15.6 16.6 16.1 18.2 17.945 C3 277 1 l-Tyrosine 200 30 15.2 16.2 15.6 17.7 17.446 C3 277 1.2 l-Tyrosine 200 30 15.6 16.6 16.1 18.2 17.947 C3 277 1.5 l-Tyrosine 200 30 16 17.1 16.4 18.7 18.448 C3 277 2 l-Tyrosine 200 30 16.4 17.5 16.8 19.1 18.6

TAAD% for C3 in presence of 100 ppm l-tyrosine 120 15.8 16.9 16.2 18.4 18.149 i-C4 275 1 PVP 100 45 15.3 16.3 15.7 17.9 17.550 i-C4 275 1.2 PVP 100 45 15.6 16.6 16.1 18.2 17.951 i-C4 275 1.5 PVP 100 40 16 17.2 16.4 18.2 18.452 i-C4 275 2 PVP 100 40 16.5 17.6 17 19.3 18.9

TAAD% for i-C4 in presence of 100 ppm PVP 170 15.9 17.0 16.3 18.6 18.253 i-C4 275 1 PVP 200 45 15.6 16.6 16.1 18.2 17.954 i-C4 275 1.2 PVP 200 45 15.9 17.0 16.4 18.6 18.255 i-C4 275 1.5 PVP 200 45 16.2 17.3 16.6 18.9 18.656 i-C4 275 2 PVP 200 40 16.6 17.7 17.1 19.4 19.1

M.R. Talaghat / Fluid Phase Equilibria 286 (2009) 33–42 41

Table 3 (Continued )

No. Component T (K) P (MPa) Type of inhibitor Concentration ofinhibitor (ppma)

No. of datapoint

%ADDY,b

PR,c EOS%ADDY,b

SRK,d EOS%ADDY,b

ER,e EOS%ADDY,b

PT,f EOS%ADDY,b

VPT,g EOSh

TAAD% for i-C4 in presence of 100 ppm PVP 175 16.1 17.2 16.5 18.8 18.557 i-C4 275 1 l-Tyrosine 100 35 15.4 16.4 15.8 18.0 17.158 i-C4 275 1.2 l-Tyrosine 100 35 15.8 16.9 16.2 18.4 18.159 i-C4 275 1.5 l-Tyrosine 100 35 16 17.1 16.4 18.7 18.460 i-C4 275 2 l-Tyrosine 100 35 16.5 17.6 17 19.3 18.9

TAAD% for i-C4 in presence of 100 ppm l-tyrosine 140 15.9 17.0 16.4 18.6 18.261 i-C4 275 1 l-Tyrosine 200 30 15.7 16.7 16.2 18.3 18.062 i-C4 275 1.2 l-Tyrosine 200 30 16 17.1 16.5 18. 2 18.463 i-C4 275 1.5 l-Tyrosine 200 30 16.1 17.2 16.6 18.8 18.564 i-C4 275 2 l-Tyrosine 200 30 16.6 17.7 17.1 19.4 19.0

TAAD% for i-C4 in presence of 100 ppm l-tyrosine 120 16.1 17.2 16.6 18.8 18.5TAAD% for simple gas hydrate formation in presence of KHIs 2410 15.8 16.9 16.3 18.4 18.1

a Part per million.b TAAD% = [(1/n)

∑|(gas consumptionexp

i− gas consumptioncal

i)/gas consumptionexp

i] × 100.

c Peng–Robinson.d Soave–Redlich–Kwong.e

ccttsegwsata1oswfapo

Fwaa

Esmaeilzadeh–Roshanfekr.f Patel–Teja.g Valderrama–Patel–Teja.h Equation of state.

oncentration) as a kinetic inhibitor were also shown in Fig. 8. Asan be seen in this figure, a good agreement was found betweenhe experimental data were obtained in flow mini-loop appara-us and calculated gas consumed using the PR and ER equations oftate. The average absolute deviations between the calculated andxperimental gas consumed for methane, propane and iso-butaneas hydrate formation with the presence of these kinetic inhibitorsere also obtained. The results are presented in Table 3 for above

imple gas hydrate formation. According to this table, the totalverage absolute deviation (TAAD) percentages of gas consump-ion for simple gas hydrate formation with the presence of PVPnd l-tyrosine as kinetic inhibitors were found to be 16.1%, 17.2%,6.3%, 18.8% and 18.5% for the PR, SRK, ER, PT and VPT equationsf state, respectively. The results show the PR and ER equations oftate with TAAD of 15.8% and 16.3% in simple gas hydrate formation

ith the presence of kinetic inhibitors yield the lowest deviation

or this purpose, respectively. Finally, the results obtained for totalverage absolute deviations for simple gas hydrate formation in theresence or absence of KHIs indicate that the PR and ER equationsf state with 15.4% and 15.8% have the best overall accuracy for pre-

ig. 8. Time dependence of the CO2 consumed during of gas hydrate formationith the presence of 100 ppm PVP as a kinetic inhibitors at a temperature of 280 K

nd pressure of 7 MPa using various types’ equations of state in a flow mini-looppparatus.

diction of gas consumption during the gas hydrate formation usingthis model.

8. Conclusions

The objective of this work was to evaluate the various typesequations of state (PR, SRK, ER, VPT and PT) for predicting gasconsumption in simple gas hydrate formation with or without thepresence of kinetic inhibitors (such as PVP and l-tyrosine) in a flowmini-loop apparatus. For this purpose, the rate of gas consumptionfor simple gas hydrate formation obtained based on the Kashchievand Firoozabadi model using the mentioned equations of state wascompared with the experimental data points were obtained in flowmini-loop apparatus. The results obtained for total average abso-lute deviations for simple gas hydrate formation indicate that thePR and ER equations of state with 14.9% and 15.2% TAAD in absenceof KHIs and 15.8% and 16.3% with the presence of KHIs have thebest overall accuracy for this model. The result showed that the gashydrate formation rate is a strong function of the driving force. Theresults obtained for total average absolute deviations for simple gashydrate formation in the presence or absence of KHIs indicate thatthe PR and ER equations of state with 15.4% and 15.8% have thebest overall accuracy for this mole in prediction of gas consump-tion during the gas hydrate formation. Finally, for lower pressure,the various types of equations of state have no noticeable effecton calculation of driving force or gas consumption, but for higherpressure, this effect is noticeable. It should be noted that the predic-tion of gas consumption does not only depend on equation of state,but also on other things such as type of present hydrate formationmodel.

List of symbolsA kinetic parameter for hydrate formationa surfaceb shape factor of crystalc constant for spherical nucleusC concentration (1/m3), solubility of the gas component

Dc gas diffusivity in the aqueous solutionG growth constant (m1/m/s)J nucleation rateK Boltzmann constant,kn adsorption constant for nucleation (m3)

4 se Equ

kMNnnn

nPQR

Ttvx

z

G��� ε

�˚��D

Skaceeeghsw

A

m

[

[

[

[[

[

[[[[[

[

[

[

[

[[

[

[

[

[

[[[[

[SPE 30420, SPE Offshore Europe Conference, Aberdeen, September 5–8, 1995,

2 M.R. Talaghat / Fluid Pha

g adsorption constant for growth (m3)w molecular weightAva Avogadro’s numbers Number of building units constituting a nucleusw hydration numberg number of gas molecules per unit cell of hydrate crystal

latticek the number of gas molecules

pressuresuper-saturation-independent kinetic factoruniversal gas constant, rate of gas consumation for purecomponenttemperature of systemtimevolumemolar composition, solubility of guest molecule in freewater phase at equilibrium conditionZeldovich factor, position along the pipe

reek symbolsnumber of cavities per water molecule, volume

m solute molar volume at its normal boiling point (cm3/mol)densitywetting angelwetting factor (between 0 and 1)a number ≤1 is the sticking coefficient of building unitsto the crystallite surfaceSurface energy (J/m2)fugacity coefficient of gas at P and T

w water viscosity� super-saturation or driving force of hydrate formationve difference between the volume of nw water molecules in

the solution and the volume of a hydrate building unit inthe hydrate crystal at the equilibrium pressure

uperscripts and subscriptsarbitrary componentpresence of kinetic inhibitor

ell lattice unit cellq equilibriumxp experimentalfc effective

gashydratesolution, substratewater

cknowledgment

The author is grateful to the Fars Technological and Environ-ental Research Center for supporting of this research.

[

[

ilibria 286 (2009) 33–42

References

[1] A.C. Lovell, M. Pakulski, Journal of Petroleum Technology 55 (2003) 65–68.[2] B. Tohidi, R. Anderson, R. Masoudi, M. Arjamandi, R. Burgass, J. Yang, Russian

Chemical Journal 47 (2003) 49–57 (in Russian and English).[3] E.D. Sloan, Clathrate Hydrates of Natural Gases, second ed., Marcel Dekker, New

York, 1998.[4] P. Englezos, Industrial & Engineering Chemistry Research 32 (1993) 1251–

1274.[5] B. Kvamme, T. Kuznetsova, K. Aasoldsen, Molecular Simulation 31 (2005)

1083–1095.[6] E.G. Hammerschmidt, Industrial Engineering Chemistry 26 (1934) 851–855.[7] B. Edmonds, R.A.S. Moorwood, R. Szczepanski, Ultradeep Engineering Supple-

ment to Offshore Magazine (2001) 7–10.[8] A.P. Mehta, P.B. Hebert, E.R. Cadena, J.P. Weatherman, SPE Production & Facili-

ties 18 (2003) 73–83.[9] D.L. Katz, Transactions on American Institute of Mechanical Engineering 160

(1945) 140–148.10] J.M. Herri, J.S. Pic, F. Gruy, M. Cournil, American Institute of Chemical Engineer-

ing Journal 45 (1999) 590–601.11] P.D. Dholabhai, N. Kalogerakis, P.R. Bishnoi, Annual Meeting of the Petroleum

Society of CIM, Calgary, Alberta, June 7–10, 1992.12] N. Gnanendran, N. Amin, Chemical Engineering Science 59 (2004) 3849–

3863.13] D. Kashchiev, A. Firoozabadi, Journal of Crystal Growth 250 (2003) 499–515.14] P. Englezos, P.R. Bishnoi, American Institute of Chemical Engineering Journal

34 (1988) 1718–1721.15] D. Kashchiev, Nucleation: Basic Theory with Applications, Butterworth-

Heinemann, Oxford, 2000.16] G. Soave, Chemical Engineering Science 72 (1972) 1197–1206.17] D.B. Robinson, D.Y. Peng, Industrial Engineering Fundamental 15 (1976) 59–63.18] F. Esmaeilzadeh, M. Roshanfekr, Fluid Phase Equilibria 239 (2006) 83–90.19] N.C. Patel, A.S. Teja, Chemical Engineering Science 37 (1982) 463–473.20] J.O. Valderrama, Industrial Engineering Chemical Research 42 (2003)

1603–1618.21] P. Englezos, N. Kalogerakis, P.D. Dholabhai, P.R. Bishnoi, Chemical Engineering

Science 42 (1987) 2647–2658.22] P. Englezos, N. Kalogerakis, P.D. Dholabhai, P.R. Bishnoi, Chemical Engineering

Science 42 (1987) 2659–2666.23] P. Skovborg, P. Rasmussen, Chemical Engineering Science 49 (1994)

1131–1143.24] P. Bourgmayer, A. Sugier, E. Behar, International Conference on Multiphase

Flow, Nice, France, 1989.25] J.W. Mullin, Crystallization, Butterworth-Heinemann, Oxford, 1997.26] J.W. Vysniauskas, P.R. Bishnoi, Chemical Engineering Science 38 (1983)

1061–1072.27] V. Natarajan, P.R. Bishnoi, N. Kalogerakis, Chemical Engineering Science 13

(1994) 2075–2087.28] P. Skovborg, Gas hydrate kinetics, Ph.D. Thesis, Technical University of Den-

mark, 1993, 238 pp.29] M.R. Anklam, A. Firoozabadi, Journal of Chemical Physics 121 (2004)

11867–11874.30] R.L. Christiansen, E.D. Sloan, Annals of New York Academy of Science 715 (1994)

283–295.31] D. Kashchiev, A. Firoozabadi, Journal of Crystal Growth 241 (2002) 220–230.32] D. Kashchiev, A. Firoozabadi, Journal of Crystal Growth 241 (2002) 476–489.33] B. Kvamme, Annals of New York Academy of Science 715 (1994) 496–501.34] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, fourth

ed., McGraw-Hill, New York, 1987.35] M.A. Kelland, T.M. Svartaas, L. Dybvik, Studies on new gas hydrate inhibitors, in:

pp. 531–539.36] M.R. Talaghat, F. Esmaeilzadeh, F. Fathikalajahi, Fluid Phase Equilibria 279

(2009) 28–40.37] M.R. Talaghat, F. Esmaeilzadeh, F. Fathikalajahi, Chemical Engineering and

Technology 32 (2009) 805–819.