Vafa Feyzi,Vahid Mohebbi

Ahvaz Petroleum Faculty,Petroleum University of Technology (PUT),Ahvaz,Iran

Keywords:Methane hydrate Kinetics Formation Dissociation Mass transfer

ABSTRACT In this work,several experiments were conducted at isobaric and isothermal condition in a CSTR reactor to study the kinetics of methane hydrate formation and dissociation.Experiments were performed at five temperatures and three pressure levels(corresponding to equilibrium pressure).Methane hydrate formation and dissociation rates were modeled using mass transfer limited kinetic models and mass transfer coefficients for both formation and dissociation were calculated.Comparison of results,shows that mass transfer coefficients for methane hydrate dissociation are one order greater than formation conditions.Mass transfer coefficients were correlated by polynomials as relations of pressure and temperature.The results and the method can be applied for prediction of methane production from naturally occurring methane hydrate deposits.

1.Introduction

Increased global demand for energy have triggered efforts to finding new resources of energy,despite the efforts to harness the required energy from renewable resources,the carbon-based energy resources especially natural gas as cleanest and the least carbon-intensive fossil fuel will play an important role to secure the energy of the world.Methane hydrate is the most eminent unconventional source for natural gas.Methane hydrate sources are very abundant in the world.They could be found in the continental margins of the ocean and in the permafrost regions of the Arctic[1].According to a rough estimation,the amount of methane hydrate existing in the world is more than twice the total other kind of fossil fuels on the earth [2].These resources can be found in geological depths where thermodynamic condition favors methane hydrate formation [3].

Different scenarios have been proposed for exploiting the methane hydrate deposits,including depressurization,thermal stimulation,inhibitor injection and CO2-CH4replacement in hydrate structure[4,5].The main strategy for production of natural gas from naturally occurring gas hydrate deposits is based on disturbing the thermodynamic equilibrium to promote hydrate dissociation.Several field experiments were performed to mature the geological knowledge and production technologies for exploiting the methane hydrate resources [6].However,laboratory studies are required to survey the phase equilibria and thermodynamic aspects,thermo-physical properties,and kinetic behavior of methane hydrates.Such a knowledge is required to justify viability,and economical and technical feasibility of production from methane hydrate reservoirs.Many studies are conducted to survey the phase equilibria of methane hydrate formed from pure water,or in the presence of different salts and porous mediums [7–14].According to the literature,the studies that examined the kinetic behavior of both methane hydrate formation and dissociation are limited.Reasonable kinetic models are required for performing numerical simulation and assessment of production from naturally occurring methane hydrate reservoirs [6].In order to perform the numerical simulation of methane production from methane hydrate reservoirs the kinetic equations for hydrate dissociation and formation must be used in conjunction with other governing phenomena such as mass and heat transfer,and multi-phase flow through the sediments [15,16].Several models are proposed to simulate the hydrate dissociation process [17–22].Some considered intrinsic kinetic of hydrate dissociation as rate controlling mechanism [17].Some other assumed that heat transfer be the dominant mechanism [18,19].Several models coupled gas and water flow in porous media with other mechanisms [20,21].

Dissociation of gas hydrates is followed by heat transfer from surrounding to the hydrate particles.Therefore,by hydrate dissociation,local temperature reduces.Local temperature reduction may bring back the thermodynamic condition into the hydrate stability zone and results in methane hydrate re-formation and so frustrate hydrate decomposition [7,23].A rigorous numerical modeling of methane production from methane hydrate must consider the scenario of hydrate re-formation through possible local temperature reduction during hydrate dissociation.Several kinetic models are presented for gas hydrate growth which are comprehensively reviewed by Yin et al.[24].Several models considered mass transfer as the dominant mechanism [25–27],some considered mass transfer through the gas–liquid interface and diffusion into the hydrate particles as limiting steps [25,26]while,some other considered mass transfer through the gas–liquid interface as the limiting step [27].Several models neglected mass transfer resistances and assumed heat transfer and intrinsic kinetic as rate-controlling resistances [28–30].Some studies considered gas and liquid flow in porous media to model hydrate formation in porous mediums [31–33].

In this study,methane hydrate formation and dissociation mechanisms are experimentally studied in a stirred reactor.Experiments conducted at several ranges of temperature and pressure.Rates of methane production and consumption are experimentally measured for each and used to evaluate kinetic parameters from mass transfer limited kinetic models proposed for hydrate formation and dissociation.According to the approach applied to demonstrate kinetic of hydrate dissociation and formation,rates are controlled by mass transfer through gas–liquid interfacial area.Mass transfer coefficients calculated for methane hydrate formation,and dissociation can be used for numerical simulation of methane production from methane hydrate reservoirs.

2.Theory

Englezos et al.[25]proposed a kinetic model for methane and ethane hydrates formation in CSTR reactors in 1987.It was based on the theory of crystallization in conjunction with two filmtheory.Due to the high stirring rate,resistances corresponding to mass and heat transfer through the bulk of the liquid were neglected.Gas-liquid interfacial mass transfer,diffusion into the liquid layer surrounding hydrate species,and intrinsic reaction of hydrate formation were considered as gas consumption ratecontrolling mechanisms.Difference in hydrate former components’fugacity in the liquid bulk(fb)and fugacity at equilibrium temperature and pressure (feq) was considered as driving force and gas consumption rate was modeled as follow:

where D is diffusivity coefficient,K*is overall kinetic constant andis total area of hydrate particles.

In similar work in 1987 Kim et al.[17]proposed a model for kinetic of methane hydrate dissociation in CSTR reactors.They neglected resistances for mass and heat transfer through the liquid bulk due to the high rate of stirring,so truncated the decomposition process to breakage of hydrate hosts and desorption of the released methane molecules into the bulk of liquid.The proposed model evaluates the rate of hydrate decomposition as follow:

where kdis constant for kinetic of hydrate decomposition and fgis the gas phase fugacity.

Skovberg and Rasmussen [27]performed a sensitivity analysis in 1994 to evaluate the validity of Englezos et al.kinetic model.Based on this analysis,Skovberg and Rasmussen [27]concluded that intrinsic kinetic of hydrate formation and mass transfer through liquid film surrounding hydrate species would not be the rate controlling mechanisms.So they proposed a new mass transfer kinetic model which considers the interfacial gas–liquid mass transfer as the rate controlling mechanism during hydrate growth step in stirred reactors.Formalism of this model is as follow:

Recently,Mohebbi et al.[34]proposed a new approach for hydrate formation kinetic modeling in stirred reactors.Their model is an extension for mass transfer limited kinetic model by considering difference in chemical potential as the prime driving force for hydrate formation.By assuming equilibrium between liquid bulk phase and hydrate phase the rate of gas consumption was defined as follow:

As mentioned,equilibrium between liquid phase and hydrate phase was assumed,consequently the liquid phase chemical potential was defined as:

At equilibrium pressure,driving force is equal to zero,so:

By subtracting last two equations:

Finally,the rate of gas consumption due to growth of hydrate is defined as follow:

In this study we apply two versions of mass transfer limited kinetic models (Skovberg-Rasmussen and Mohebbi et al.models)to calculate mass transfer coefficients for methane hydrate formation.Similar to the approach explained for kinetic of hydrate formation,interfacial mass transfer from the liquid phase to the gas phase was assumed to be the rate controlling resistance for methane hydrate decomposition.Gas uptake constant rate during hydrate decomposition experiments confirmed this assumption.It means that,the rate of methane hydrate dissociation would be independent from the hydrate particles total area.Accordingly,the rate of methane hydrate dissociation was modeled by the following relations:

Due to the low solubility of methane in water,Henry’s law can be applied for calculating the mole fraction of methane in water.

where yiand φiare the gas phase mole fraction and fugacity coefficient respectively,P is total pressure and Hiis Henry constant of methane in water.As no mass transfer resistance is considered for the gas phase,methane mole fraction in interface (xint) was calculated at experimental pressure(Pexp)and experimental temperature(Texp).By assuming equilibrium between bulk liquid phase and hydrate particles,methane mole fraction in liquid bulk was calculated at experimental temperature (Texp) and its corresponding equilibrium pressure (Peq).Henry’s law constant that depends on experimental pressure and temperature is represented as follow

Pciis critical pressure and Tciis temperature of methane,R is gas constant and Ceis the water cohesive energy density that is defined as follow

In order to predict the methane hydrate formation equilibrium conditions,a thermodynamic modeling of gas–water–hydrate three phase equilibria was performed.Chen-Guo’s model was used to predict thermodynamic equilibrium conditions [37,38].The model is a modification of well-known van der Waals Platteeuw model [39].In an attempt toward considering the effects of local cavity occupancy on the stability of hydrate a reasonable mechanism was proposed for hydrate formation by Chen and Guo in 1996 [37,38].This new model gives much realistic prospects for kinetic of hydrate formation and is proposed for kinetic studies of hydrate phenomenon.Calculation details and model’s formalism are not presented here.

3.Experimental

3.1.Apparatus

The experimental set up used for this study is a multi-purpose apparatus which can be applied for kinetic and thermodynamic study of pure gas and mixture gas hydrates.The experimental apparatus prepared for this study,was composed of a double wall stirred visual 316.9 cm3reactor which its content is stirred by a 4 cm star covered magnetic bar rotated by an exterior magnetic stirrer (Labinco L-71).Hydrate formation mechanism takes occur at low temperature levels.So continuous heat removal from the reactor during the hydrate formation process is inevitable.The reactor is surrounded by a cooling jacket at which cooling medium is circulated through the jacket constantly using a circulator LAUDA type ALPHA RA8.Ethyl glycol aqueous mixture was used as cooling media.This solution remains liquid on a wide range of temperature(-37 to 127°C)and provide the required heat at operating temperatures.Schematic of the experimental apparatus is presented in Fig.1.Due to the considerable difference between ambient temperature and reactor temperature,insulation of the reactor is very important both to prevent heat loss and more important from temperature control point of view.In order to perform an efficient insulation around the reactor,polyurethane foam was applied as the insulator.Temperature inside the reactor is continuously recorded by a thermocouple type PT100 with accuracy in the range ±0.1 K.Thermocouple consists of two resistances mounted in two different heights in order to measure the experimental temperature in different elevations inside the reactor.Pressure of the gaseous phase is recorded using a SENSYS pressure transmitter with 0.01 bar (1 bar=105Pa) pressure accuracy.

At the beginning of each experiment,inside of the reactor must be vacuumed.It is performed by a PLATINUM pump,complete vacuum of the experimental setup is very crucial.To do this different ports are located on the set up for connecting the vacuum pump.

Methane gas is supplied by a cylinder with high purity (99.9%)purchased from Persian Gas Cooperation.Methane will not be directly inject to the reactor.It is stored in an auxiliary cell with a specific volume (Tank1) and then injected into the reactor.Amount of methane injected to the reactor can be calculated by PVT calculation before and after methane injection.Temperature and pressure inside the tanks are measured by temperature indicator (PT100) and pressure transmitter SENSYS respectively.In this study both formation and dissociation experiments conducted at isobaric condition.To maintain the pressure of gaseous phases inside the reactor a RUSKA hand pump will be applied.The pump composed from a piston which can move through a graduated cylinder.The cylinder is graduated from 0 to 250 ml with 0.01 ml accuracy.Temperature and pressure of the hand pump are recorded by a thermocouple type PT100 with accuracy in the range±0.1 K and an Achcroft pressure transmitter with 0.01 bar(1 bar=105Pa)pressure accuracy.Recording of the measured variables are performed using the data acquisition system implemented on the setup.Data acquisition system composed from 4 temperature loggers and 3 pressure loggers.Rate of data logging can be changed through changing the rate of sampling.All sevendata loggers are connected to a PC which display and store the logged data by Lab View v.16.1 software.

Table 1 Coefficients for Henry’s law constant at standard condition

3.2.Procedure

During the hydrate formation and hydrate dissociation experiments,temperature and pressure maintained constant (isobaric and isothermal).Experiments were conducted at different temperatures (274.15 K,276.15 K,278.15 K,280.15 K,and 282.15 K) and different pressures.Experimental pressures considered by specific values for degree of super-saturation for hydrate formation and degree of sub-saturation for hydrate dissociation.Degree of supersaturation for hydrate formation and degree of sub-saturation for hydrate dissociation are defined as follow:

The equilibrium pressure at any experimental pressure was calculated by the thermodynamic model performed.At the beginning,the reactor evacuated by the vacuum pump.Then the reactor filled by 100 ml of distilled water.Bath temperature was set at the desired temperature and circulator turned on.Then,reactor was pressurized with gas supplied from the auxiliary cell to a pressure(below hydrate equilibrium pressure) and stirrer was set at a low stirring rate (100 r·min-1) and allowed temperature fall to the experiment temperature.After the reactor temperature stabilized,more gas injected to the reactor and gradually pressure raised to the desired value.Next,the stirrer speed adjusted at 300 r·min-1,at lower stirrer rates hydrate layers quickly cover the interface of gas and liquid and hinder further hydrate growth in the liquid bulk.After a while the pressure starts to decrease progressively which indicates the formation of hydrate.In order to maintain the pressure during hydrate formation,gas was continuously injected to the reactor through the RUSKA pump.Experiment was allowed to continue for about 30 minutes and RUSKA pump volume was recorded with time to calculate the rate of methane consumption as follow:

In experiments for studying hydrate dissociation,initially methane hydrate produced with the procedure explained above.Then reactor was depressurized until a pressure slightly above the equilibrium pressure for methane hydrate (about 0.05 bar higher than the equilibrium pressure).After stabilization of the reactor temperature,pressure reduced to a point below the equilibrium point.As the result of decomposition of methane hydrate gas liberated and tended to increase pressure in the gas phase.In order to maintain the pressure at a constant value the hand pumps’piston was gradually displaced.The rate of hydrate dissociation can be calculated as follow:

Fig.1.Experimental set-up scheme.

Table 2 Results for methane hydrate formation experiments

Fig.2.Amount of consumed methane vs time for different DSS at 276.15 K.

Gas-liquid interface area was calculated by taking pictures at different stirrer speed and digitizing the pictures for numerical integration,gas–liquid interface area at the operating stirrer rate(300 r·min-1) was estimated to be 31.2 cm2.

It was observed after one hour from the initial point (hydrate growth),a thin layer is formed in the gas–liquid interface.The consumption rate then start to decrease.Thus,in this study,experiment runs were about 30–40 min after induction time.The amount of water conversion to hydrate was calculated.For the maximum gas consumption,this conversion is less than 2%.Accordingly,it could be concluded the reduction in water contact area is negligible.

4.Results and Discussion

Experiments were performed in two sets at isothermal and isobaric conditions with different pressures and temperatures.In the first series of experiments rates of methane consumption during hydrate formation were evaluated at temperatures 274.15,276.15,278.15,280.15,and 282.15 K and degrees of supersaturations 0.15,0.2,and 0.25 and their corresponding pressures.As the results,methane hydrate formation mass transfer coefficientswere calculated from mass transfer kinetic models for hydrate formation.In the second series of experiments rate of methane uptake during hydrate dissociation were evaluated at temperatures 274.15,276.15,278.15,280.15,and 282.15 K and different sub-saturations (0.05,0.1,and 0.15) for a specific temperature.Methane hydrate dissociation mass transfer coefficientswere evaluated for these data points.

Fig.3.Amount of consumed methane vs time for different DSS at 280.15 K.

4.1.Methane hydrate formation

In order to makes the outputs from this study more practical,it was considered that experimental temperature range selected for experiments to be identical to temperature in the geological depth of naturally occurring methane hydrate reservoirs.Experimental pressures were fixed corresponding to the equilibrium pressures for methane hydrate and degree of super-saturation as defined by Eq.(19).Experimental conditions for methane hydrate formation experiments and results including gas consumption rate and mass transfer coefficients are presented in Table 2.

Fig.4.Amount of consumed methane vs time for different DSS at 282.15 K.

Rates of mole consumption by hydrate formation was calculated by Eq.(22).Moles of methane consumed versus time are presented for some typical temperatures at Figs.2–4.Figs.2–4 show that number of moles consumed during hydrate formation process increases linearly with time.So the rate of mole consumption was approximately constant.This observation is consistent with the results from other literatures [25,27,40–42].As mentioned before,the experiments were performed at isobaric condition,holding pressure at a constant value during methane hydrate growth fixes the driving force.Since the gas–liquid interface remains constant so it is reasonable to observe a constant rate for methane gas consumption under a constant driving force for methane hydrate formations.This behavior validates the mass transfer limited approach for formation of hydrate.Magnitude order for mass transfer parametercalculated by Skovberg and Rasmussen model and their functionality with temperature and pressure are same as data obtained by Englezos et al.[25].

As indicated by Figs.2-4,rates of methane uptake increase with increasing degree of super-saturation at a constant temperature.As degree of super-saturation increases,the operating pressure and driving force for methane hydrate formation increase.As the result more methane is consumed and rate of methane consumption increases.

By increasing temperature,mass transfer coefficient for methane hydrate formation initially decreased and then increased with a minimum at about 276 K.Such a behavior was previously reported by other researchers [25,26,43].Intrinsic rate constants for methane and ethane hydrates formation evaluated by Englezos et al.[25]and mass transfer coefficient calculated by Mohebbi et al.[42]from Englezos data for methane and ethane hydrate formation shows a minimum value at 276 K.similarly,intrinsic rate constants calculated for CO2by Clarke and Bishnoi[26]and Malegaonkar et al.[43]goes from a minimum at 277.15 K and 276 K respectively.It is worth noting that the water density is maximum at about 277 K.

Calculated methane hydrate formation mass transfer coefficients in their generalized formwere correlated on a polynomial as a relation of experimental pressure and temperature.AVis the gas–liquid interfacial area per unit volume of liquid phase.Eqs.(24) and (25) show the relations for methane hydrate formation mass transfer parameters as functions of normalized pressure and normalized temperatureConstant parameters for Eqs.(24)and (25) are presented in Table 3.Sum of squared errors (SSE)and rout mean square error (RMSE) are measures of discrepancy between the experimental data and model predictions,favored at lower values.

Table 3 Constants for Eqs.(24) and (25)

Fig.5.Comparison between experimental data and model predictions for hydrate formation kinetic.

Table 4 Results for methane hydrate dissociation experiments

Fig.6.Amount of produced methane vs time for different DSS at 274.15 K.

Fig.5 shows the accuracy of the applied kinetic models by comparing experimental data points with model predictions for moles of methane consumption during hydrate formation.It shows that there is a reasonable agreement between the model results and the experimental data.

4.2.Methane hydrate dissociation

Experiments for dissociation of methane hydrate were performed at five temperatures (274.15,276.15,278.15,280.15,and 282.15 K) and different of sub-saturation degrees (0.05,0.1,and 0.15).Initially methane hydrate slurry was produced in the reactor and then,according to the amount of sub-saturation degree,gas phase pressure lowered under equilibrium pressure for methane hydrate formation.Due to the relatively higher rate of methane hydrate dissociation,the experiments were carried out at limited degrees of sub-saturation.Methane hydrate dissociation experiments were performed at constant temperature and constant pressure condition with fixed stirring rate of magnet stirrer(300 r·min-1).Experimental results indicated that by methane hydrate dissociation,methane deliberated with a constant rate.This observation shows that rate of methane hydrate dissociation would be independent of the total area of hydrate particles so mass transfer through hydrate particles and intrinsic kinetic of hydrate dissociation would not be the prime resistances during hydrate dissociation.If rate of methane hydrate dissociation be controlled by the mass transfer through hydrate particles and intrinsic kinetic of hydrate dissociation reaction on the surface of hydrate particles,by passing time and reduction in total area of hydrate particles,the rate of methane hydrate dissociation must decrease.While in this study we observed a constant rate for methane hydrate dissociation.According to this observation we assumed that mass transfer resistance in gas–liquid interface be the rate limiting resistance for hydrate dissociation in the CSTR reactor.So we applied the mass transfer limited kinetic models and modeled the experimental data by models similar to Skovberg and Rasmussen and Mohebbi et al.kinetic models.As the results of methane hydrate dissociation kinetic modeling mass transfer coefficient for methane hydrate dissociationwere calculated and presented in Table 4.

Fig.7.Amount of produced methane vs time for different DSS at 276.15 K.

Fig.8.Amount of produced methane vs time for different DSS at 282.15 K.

Table 5 Constants for Eqs.(26) and (27)

Fig.9.Comparison between experimental data and model predictions for hydrate dissociation kinetic.

Methane consumption rates are illustrated in Figs.6–8.By increasing degree of sub-saturation at a constant temperature,rate of methane production by hydrate decomposition increases.As degree of sub-saturation increase,driving force for hydrate dissociation increases,so consequently rate of methane production increases.

It can be observed from Table 4 and Figs.6–8 that increase in degree of sub-saturation substantially increases the rate of methane production.In addition,rate of methane production increases by increasing temperature (especially at higher temperatures),such a behavior would be due to the endothermic nature of hydrate dissociation reaction.

Calculated methane hydrate dissociation mass transfer coefficients in their generalizedwere correlated on a polynomial as a relation of experimental pressure and temperature.Eqs.(26) and (27) show the relations for methane hydrate dissociation mass transfer parameters as functions of normalized pressure and normalized temperature.Constant parameters for Eqs.(26) and (27) are represented in Table 5.

Fig.9 shows comparison between model predictions with experimentally measured data points for methane mole production during hydrate dissociation.It shows that the applied kinetic model predicts the experimental data with an acceptable accuracy.To evaluate the repeatability of methane hydrate dissociation experiments,two tests were repeated again.

5.Conclusions

In this study,kinetics of methane hydrate formation and dissociation were studied at isobaric and isothermal condition.Experiments were conducted at different temperatures and different degrees of super-saturation and degrees of sub-saturation.Results indicated that by increasing degree of super-saturation for methane hydrate formation experiments and degree of subsaturation for methane hydrate dissociation experiments rates of gas consumption and gas production increases respectively.At lower temperatures rates of hydrate formation and dissociation were slightly affected by temperature although,at higher temperatures increasing temperature increased rates of methane hydrate formation and dissociation.It was observed that the rates of gas consumption and gas production remained constant during hydrate formation and hydrate dissociation experiments respectively.This observation confirms the validation of mass transfer limited kinetic approach.Accordingly,the results for hydrate formation and hydrate dissociation were modeled via two mass transfer limited kinetic models.Comparison the formation and dissociation mass transfer coefficients for methane hydrate revealed that mass transfer coefficients for methane hydrate dissociation are one order of magnitude greater than formation mass transfer coefficients.It means that rate of methane hydrate dissociation is higher than rate of methane hydrate formation.Obviously,values of kinetic parameters for hydrate formation and dissociation evaluated experimentally are dependent on the reactors configuration and other experimental conditions.

Nomenclature

Ag-larea between gas and liquid phases,m2

C concentration,mol·m-3

Cecohesive energy density of water,kJ·m-3

Cw0concentration of water,mol·m-3

D diffusivity coefficient,m2·s-1

（DSS）dissociationsub-saturation degree

（DSS）formationsuper-saturation degree

fbfugacity in the bulk phase,MPa

feqfugacity at hydrate equilibrium condition,MPa

kdoverall kinetic parameter for hydrate dissociation,mol·s-1·m-2·MPa-1

K*overall kinetic parameter for hydrate formation,mol·s-1·m-2·MPa-1

n moles,mol

nHmole in hydrate phase,mol

npumpmole of gas in the pump,mol

P pressure,MPa

Pcicritical pressure,MPa

Peqhydrate formation equilibrium pressure,MPa

Pexpexperimental pressure,MPa

Ppmppump pressure,MPa

R universal gas constant,m3·MPa·mol-1·K-1

T temperature,K

Tcicritical temperature,K

Texpexperimental temperature,K

Tpmppump temperature,K

t time,s

Vpmppump volume,m3

Vwmolar volume of water,m3·mol-1

xbliquid bulk phase mole fraction

xintgas–liquid interface mole fraction

yigas phase concentration in mole fraction

Z compressibility factor

φifugacity coefficient in the gas phase

μgchemical potential in the gas phase,kJ·mol-1

μlchemical potential in the liquid phase,kJ·mol-1