Computationalmodelingofmethanehydratedissociationinasandst ...static.tongtianta.site/paper_pdf/cbf93e40-6822-11e9-a69f-00163e08… · Gas hydrates (gas clathrates) are solid compounds

Chemical Engineering Science 62 (2007) 6155–6177www.elsevier.com/locate/ces

Computational modeling of methane hydrate dissociation in a sandstone core

Kambiz Nazridoust∗, Goodarz AhmadiDepartment of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA

Received 12 June 2006; received in revised form 30 April 2007; accepted 27 June 2007Available online 6 July 2007

Abstract

Hydrate dissociation in a porous sandstone core was studied using a computer modeling approach. It was assumed that the hydrate wasdispersed in the pores of the core. Using FLUENTTM code, an axisymmetric model of the core was developed and solved for multiphase flowsduring the hydrate dissociation. The core model contained three separate phases: methane hydrate, methane gas, and liquid water. At the startof simulation, the valve at one end of the core was opened exposing the core to low pressure; hydrate began to dissociate and methane gasand water began to flow. The depressurization was controlled by adjusting the pressure of the outlet valve.

A comprehensive Users’ Defined Subroutine (UDS) for analysis of hydrate dissociation process into the FLUENT code was developed.The new UDS uses the kinetic model introduced by Kim et al. [Kim. H.C., Bishnoi, P.R., Heidemann, R.A., Rizvi, S.S.H., 1987. Kinetics ofmethane hydrate decomposition. Chemical Engineering Science 42, 1645–1653.] and can model multiple zones dissociation and multiphaseflows. Variations of relative permeability of the core were included using Corey’s model. The new model allows for variation of the porositywith hydrate saturation.

For different core temperatures and various outlet valve pressures, the spatial and temporal variations of temperature, pressure, and flow fieldsin the core were simulated. The time evolutions of methane gas and water flow rate at the outlet were also evaluated. It was shown that the rateof hydrate dissociation in a core was a sensitive function of surrounding environment temperature, outlet pressure condition, and permeability.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Gas hydrate; Methane hydrate; FLUENTTM; CFD; Porous core; Dissociation; Depressurization

1. Introduction

Gas hydrates (gas clathrates) are solid compounds of nat-ural gas molecules that are encaged within a crystal structurecomposed of water molecules. In physical appearance, gashydrates resemble packed snow or ice (Sloan (1990, 1998)).Both hydrocarbon and non-hydrocarbon hydrates occur natu-rally in the deep ocean (Kvenvolden et al., 1993c).

Gas hydrates are stable only under specific thermodynam-ical pressure–temperature conditions. Under the appropriatepressure, they can exist at temperatures significantly above thefreezing point of water. The maximum temperature at which agas hydrate can exist depends on its pressure and gas compo-sition. Edmonds et al. (1996) have studied the influence of dif-ferent factors such as salinity on hydrate stability. Gas hydratescontain a tremendous amount of natural gas per unit volume.

∗ Corresponding author. Tel.: +1 315 268 2322.E-mail address: [email protected] (K. Nazridoust).

0009-2509/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2007.06.038

According to Kvenvolden, (1993a–c), 1 m3 of hydrate dissoci-ating at atmospheric temperature and pressure forms 164 m3 ofnatural gas and 0.8 m3 of water.

In the 1960s, natural gas hydrate reservoirs were discov-ered in the oceanic sediments and in the permafrost regionsof the earth (Katz, 1971; Makogon, 1965). World reserves ofnatural gas trapped in the hydrate state have been estimatedto be several times the known reserves of conventional naturalgas and oil combined (Makogon, 1997; Kvenvolden, 1993a–c,MacDonald, 1990b). Therefore, hydrates have the potential tobecome a major source of energy in the second half of the 21stcentury. Thus, developing methods for commercial productionof natural gas from hydrates has attracted considerable atten-tion(Collett, 1993a,b, 1997, 2002; Iseux, 1992; Kvenvolden,1993a–c; Milkov and Sassen, 2003). Last 30 years have seenconsiderable efforts for the commercial production of naturalgas from hydrate reservoirs (Englezos et al., 1993). Until nowall efforts have been limited to laboratory and bench-scale stud-ies (Collett, 2002); the exception being the gas hydrate field in

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6156 K. Nazridoust, G. Ahmadi / Chemical Engineering Science 62 (2007) 6155–6177

Western Siberia, which was exploited successfully (Makogon,1997).

Hammerschmidt (1934) discovered that natural gas hydratewas responsible for the blockage of natural gas pipelines. Sloan(1990) discussed the occurrence of blockage of flow lines andgas pipelines in Arctic regions due to gas hydrate formation.Various methods have been developed and used to preventhydrate formation in petroleum production and transportationequipment or to remove hydrate plugs in oil and gas pipelines(Behar et al., 1994; Yousif and Dunayevsky, 1997; Paez et al.,2001; Reyma and Stewart, 2001).

Gas hydrates are also of interest because of their potentialrole in climate change. Gas hydrates in continental shelf sedi-ments can become unstable either as a result of warming bot-tom water, or as a result of a pressure drop due to a reduction insea level (such as during the ice age). When these marine gashydrates begin to dissociate, the methane trapped in the gas hy-drates is released into the atmosphere. Methane is a greenhousegas which is far worse than CO2. Sufficient flux of methaneto the atmosphere from hydrate dissociation can cause a ma-jor global warming. This process is believed to have influencedpast climate changes (MacDonald, 1990a; Kvenvolden, 1991;Englezos and Hatrikiriakos, 1994; Henriet, 1998; Haq, 1998;Hesselbo et al., 2000).

There are other potential industrial applications of gashydrate. Rogers (1997, 1999) presented the process to store andtransport natural gas in the hydrate form, which is approachinga commercial stage. Some scientists investigated the relationbetween earth environment and natural gas hydrate reservoir(Kvenvolden, 1994). Extensive reviews of gas hydrate weregiven by Makogon (1997) and Sloan (1998). Englezos et al.(1993) also reported a detailed account of the recent researchefforts on hydrates.

Several processes for large-scale natural gas production fromhydrates have been suggested that can be divided broadly intothree categories: depressurization, thermal stimulation, and in-hibitor injection. In depressurization technique, a well is drilledinto hydrate reservoir lowering the pressure to below the ther-modynamic equilibrium condition causing the hydrate to disso-ciate. Because no extra heat is introduced into the reservoir, theheat of the dissociation must be supplied from the surroundingformation. Selim and Sloan (1990), Hong and Pooladi-Darvish(2003), Hong et al. (2003), among others have suggested thatthis could be the rate-controlling step in the overall dissociationprocess. Therefore, this technique could be attractive primarilywhen the thermal conditions of the reservoir are favorable forproviding the needed heat transfer. The presence of a free-gaszone beneath the hydrate may be essential to the success of thedepressurization method. The most common depressurizationtechnique is drilling through the hydrate layer and completingthe well in the free-gas zone. Gas production from this layerleads to pressure reduction and dissociation of the overlyinghydrate supplies the reservoir with fresh natural gas. Makogon(1981) discussed gas production from the Messoyakha fieldbased on this depressurization technique. Collett and Kuskra(1998) and Kamath (1998) believed that the depressurizationmethod is the most economically feasible method.

There have been a number of studies on simulating the gashydrate dissociation and formation process. Thermodynamictechniques as well as kinetic approaches have been developedin these studies. Holder et al. (1982) showed that the energyvalue of the produced gas is approximately 10 times the energyrequired to dissociate hydrate in typical reservoirs. Englezosand Bishoni (1988a,b) used the models of Van der Waals andPlatteeuw (1959) and Patwardhan and Kumar (1986a,b) topredict the formation of gas hydrates in solutions of aqueouselectrolytes. Sun and Mohanty (2006) simulated formationand dissociation of methane hydrates in porous media. Theyincluded four components (hydrate, methane, water, and salt)and five phases (hydrates, gas, aqueous-phase, ice, and saltprecipitate) in their simulation.

Ji et al. (2001) presented a parametric study of naturalgas production from the dissociation of methane hydrate in aconfined reservoir using the depressurization method. The one-dimensional linearized model suggested by Makogon (1997)was used in the analysis. For different well pressures andreservoir temperatures, distributions of temperature and pres-sure in the methane hydrate reservoir were evaluated. Timeevolutions of the resulting temperature and pressure profiles inthe reservoir under various conditions were presented. Effectsof variations in reservoir porosity and zone permeability werealso studied. They showed that the gas production rate was asensitive function of well pressure, reservoir temperature, andzone permeability.

In a related work, Ji et al. (2003) studied production ofnatural gas at a constant rate from a well drilled into a con-fined methane hydrate reservoir. They assumed that the poresin the reservoir were partially saturated with hydrate. A lin-earized axisymmetric model with a fixed well output conditionwas used in the analysis. For different reservoir temperaturesand various well outputs, time evolutions of temperature andpressure profiles, as well as the gas flow rate in the hydrateand gas zones were evaluated.

Ahmadi et al. (2004, 2007) described one-dimensional andaxisymmetric models for natural gas production from thedissociation of methane hydrate in a confined reservoir by adepressurizing well. They accounted for the heat sink from hy-drate dissociation and solved the convection–conduction heattransfer in the gas and hydrate zones. Using a finite-differencescheme, they evaluated the gas flow and hydrate dissociationprocess inside the reservoir. For different well pressures, andreservoir temperatures and pressures, they simulated the pres-sure and temperature conditions in the reservoir. It was shownthat the gas production rate was a sensitive function of wellpressure. In addition, both heat conduction and convectionin hydrate zone were important. The simulation results werecompared with the linearization approach and discussed.

Vysniauskas and Bishnoi (1983) performed a series of thestudies of the kinetics of gas hydrate formation. The rate ofhydrate formation was modeled from the consumption rate ofgas. Isothermal and isobaric experiments were carried out ina semi-batch stirred tank reactor using methane and ethane.It was found that pressure and temperature driving force andgas–liquid interfacial area were the most important parameters

K. Nazridoust, G. Ahmadi / Chemical Engineering Science 62 (2007) 6155–6177 6157

Fig. 1. Schematic of hydrate core sample, the computational grid, locations of different sections, and the boundary conditions.

Table 1Initial conditions

Core temperature (K) 275.45Initial pressure (MPa) 3.75Initial hydrate saturation 0.465Initial water saturation 0.351Initial gas saturation 0.206Initial porosity 0.182Initial absolute permeability (mD) 97.98

Table 2Boundary and ambient conditions

Ambient temp. (K) Outlet valve pressure (MPa)Case 1 274.15 2.84Case 2 275.15 2.84Case 3 276.15 2.84Case 4 275.15 2.99Case 5 275.15 3.28

Table 3Locations of sections of the core

Sections Distance from outlet valve (cm)a 0.375b 15.0c 22.5d 29.625

affecting the gas consumption rate. Increased stirring rate andpressure resulted in an increased consumption rate of gas, whilean increase in temperature resulted in decreased consumptionrate.

Englezos et al. (1987a, b) related the gas consumption ratewith hydrate crystal growth rate. Experiments were carriedout in the same equipment as was used by Vysniauskas andBishnoi (1983). Hydrate growth was modeled using crystalliza-tion theory, and a two-film model was adapted for the gas–liquidinterfacial mass transfer. It was assumed that hydrate particleswere spherical, and the number of moles of gas consumed perparticle per second was proportional to the fugacity drivingforce and the surface area of the particle. Their experimentaldata suggest that the rate constants have weak dependence onthe temperature.

Kim et al. (1987) developed a model to describe the kineticsof methane hydrate dissociation. The model assumed that, ata constant temperature, a two-step process could describe gashydrate dissociation; the first is the destruction of the clathratehost lattice at the surface of a particle and the second step isdesorption of the guest molecule from the surface. These stepsoccur at the solid surface, not within the bulk of hydrate. As thedecomposition continues, particles shrink and gas is releasedand enters the bulk gas phase. Hydrate was assumed invariantin composition and density. Assuming constant number of par-ticles during decomposition, they expressed the particle area asa function of the moles of hydrate.

The kinetic model developed by Kim et al. (1987) was usedin several studies in the past. Masuda et al. (1999) developedformed methane hydrate in a core-shape vessel and measuredthe amount of gas generation due to hydrate dissociation usinga depressurization method. They also performed a computermodel study and compared their simulation results with theexperimental data for different cases. Recently, Moridis et al.(2005) reported the results of their computer model for the gasgeneration in a hydrate core due to dissociation by heating.They also compared their numerical simulation results with theexperimental data of Kneafsey et al. (2005).

Clarke and Bishnoi (2000 and 2001) measured the rate of de-composition of gas hydrates formed from mixtures of methaneand ethane. The experimental procedure of Kim et al. (1987)was modified to include a particle size analyzer. A new mathe-matical model was developed which could account for the initialparticle size distribution. This model was used to determine theintrinsic rate constant and activation energy for methane/ethanehydrate decomposition. They extended their model to hydratesthat were formed from gas mixtures.

In this paper, dissociation of methane hydrate in a core isstudied. It was assumed that the hydrate is partially saturatedin the pores of the core. An axisymmetric computer model ofthe hydrate core was developed and solved for the multiphaseflow and thermal field during the hydrate dissociation. One ofthe goals of this study was to develop a computational hydratemodule for a commercially available CFD package such asFLUENT code. Currently these CFD packages do not have thecapability to simulate hydrate decomposition/formation. Withthe computational module developed in this study, the capability


Fig. 2. Pressure contours in the core sample at different times for the reference case (case 2).

for simulating hydrate dissociation for different complex three-dimensional geometries is provided. The written user definedcode accounts for the dissociation process of hydrate includingthe rate of dissociation, amount of heat absorbed and the gasand water generated. The UDS included the effects of relativepermeabilities of water and gas and effective porosity of thecore. The code allows for time variation of these quantities anduses appropriate functions to account for these variations.

For different core initial temperatures and various outletvalve pressures, time evolutions of temperature and pressureprofiles, as well as the cumulative amount of natural gas pro-duced were evaluated. The simulation results showed that theprocess of natural gas production was a sensitive function oftemperature and pressure, as well as core permeability. Thesimulation results were compared with available experimentaldata and qualitative agreement was found.

2. Hydrate core dissociation

Consider a methane hydrate core that is partially saturatedwith hydrate, and contains pressurized natural gas. Assume thatthe initial pressure and temperature in the core are Pc and Tc.At this temperature, the pressure Pc is larger than the hydrateequilibrium pressure Pe. When one end of the core is opened,the pressure in the core drops to a certain value less than Pe.

This causes the hydrate to become unstable and dissociate in theregion near the open end. A dissociation front forms that movesfrom the exposed end toward the closed end with time. Near theend that is exposed to the environment, only gas and water arepresent, while in the rest of the core, solid hydrate, together withgas and water exists. In addition, dissociation of hydrate is anendothermic process, which causes the temperature to decreasenear the dissociation front. However, heat transfer from thesurrounding thermal bath increases the temperature in the coreuntil it reaches the surrounding temperature.

In this study, the kinetic model of Kim et al. (1987) wasused to simulate the hydrate dissociation process. The intrinsicrate constant and activation energy for decomposition of themethane hydrate were found from Clarke and Bishnoi (2001).Accordingly, for an invariant hydrate composition, the hydratedissociation rate depends on hydrate saturation and the differ-ence between local pressure and the equilibrium pressure.

3. Model formulation

3.1. Hydrate core model

The governing equations used to solve for the multiphaseflow conditions during the hydrate dissociation process are out-lined in this section. The continuity equations for different


Fig. 3. Temperature contours in the core sample at different times for the reference case (case 2).

species are given by

−∇ · �kuk + mk = �

�t(�0�kSk) (k = H, g, w), (1)

where mk is the rate of generation/dissociation of species k, �0is the porosity of the core, Sk is the saturation of phase k, �k

is the phase density, t is time, and uk is fluid velocity vector(with uH = 0 since hydrate is stationary). Here H, g, and w

stand for hydrate, gas, and water phases.For saturations of various phases, the following equality

holds:

Sg + Sw + SH = 1, (2)

where Sg, Sw, and SH are, respectively, saturation of gas, water,and hydrate phases. The effective porosity of the medium isgiven as

�eff = �0(1 − SH ). (3)

Darcy’s law for flow in porous media is given by

uk = −KDKrk

�k

∇p (k = g, w), (4)

where Krk is relative permeability of phase k and �k is thephase viscosity. Here, KD is the absolute permeability of themedia and is modeled as (Masuda et al., 1999)

KD = KD0(1 − SH )N , (5)

where KD0 is the absolute permeability at zero hydrate satura-tion, and N is the permeability reduction index which dependson the pore structure of the medium. Note that Eq. (5) satisfiesthe expected limiting conditions at SH = 0 or 1, and the valueof the permeability index N is determined experimentally.

The relative permeability of water and gas are evaluated byCorey (1954) formula given as

Krw = S4, (6)

and

Krg = (1 − S)2(1 − S2), (7)

where

S = Sw − Swr

1 − Sgr − Swr

. (8)

In Eqs. (6)–(8), Krw and Krg are, respectively, the relative per-meability of water and gas, and Swr and Sgr are the irreduciblesaturations of water and gas.

The equation of energy balance for the effective mediummay be written as

�

�t[(1 − �0)�RCRT

+�0SH �H CH T +�0Sw�wUw+�0Sg�gUg]=∇ · (Ko∇T )

− ∇ · (�whwuD,w + �ghguD,g) − QH , (9)


Fig. 4. Hydrate saturation contours at different times for the reference case (case 2).

where T is the temperature, C is the heat capacity, U is theinternal energy, and h is the enthalpy. Subscripts R, H, w andg, respectively, indicate rock, hydrate, water, and gas. Here, Ko

is the effective thermal conductivity and is defined as

Ko = (1 − �0)KR + �0(SH KH + SgKg + SwKw), (10)

where KR, KH , Kg , and Kw, are respectively, thermal con-ductivity of rock, hydrate, gas and water. In Eq. (9), QH

is heat-sink/source rate due to hydrate dissociation. Themodel for latent heat of dissociation is presented in the nextsection.

3.2. Hydrate dissociation by depressurization

As the hydrate dissociates into gas and water, a dissociationfront forms that divides the core into two regions, one contain-ing solid hydrate, and the other containing dissociated gas andwater. Kim et al. (1987) developed a model for the molar gen-eration rate of methane gas due to hydrate dissociation, ngp.Accordingly,

ngp = kBAp[Pe(T ) − P ], (11)

kB = kod exp

(−�E

RT

), (12)

where Pe is the equilibrium pressure, P is the local pressure inthe core and Ap is the surface area of hydrate per unit volume.The surface area of hydrate particles was expressed as a func-tion of the number of moles of methane in the hydrate (nH ).This function satisfies several conditions such as invariant com-position of hydrate, constant number of moles of methane perunit volume of hydrate, uniform decomposition rate, constantnumber of particles during decomposition, and so on (for moredetails please refer to Kim et al., 1987). The dissociation rateconstant, kB , is given by Eq. (12), where �E is the activationenergy, R is the gas constant, and T is the temperature. Theconstant ko

d is an intrinsic dissociation constant and is indepen-dent of pressure and temperature. In practice, these parame-ters are evaluated by curve fit to the experimental kinetic data.Values of �E = 77 330 J/kmol and ko

d = 8.06 kmol/Pa/s/m2

were suggested by Clarke and Bishnoi (2001).If hydrate is of the form, CH4 − (NH )H2O, where NH

corresponds to the number of water molecules in the hydrate(also known as hydrate number), it follows that

nH2O = NH ng = −NH nH , (13)

where n denotes the number of moles of each compound. Sincehydrate dissociates, a negative sign is used in Eq. (13) for nH .Relating the number of moles to the mass of each substance


Fig. 5. Methane gas saturation contours at different times for the reference case (case 2).

using their molecular weights, Eq. (13) gives

mw = MwNH mg/Mg , (14)

− mH = MH mg/Mg , (15)

where Mg , Mw, and MH are molecular weights of gas, water,and hydrate phases.

If hydrate exists in a porous medium with saturation SH andconsists of spherical particles having a surface area AHS , thetotal surface area of hydrate per unit volume of the porousmedium (Ap) is equal to �0SH AHS . Then, the mass generationrate of gas and water per unit volume of the porous mediumby hydrate dissociation are given by

mg = kBMgAHS�0SH [Pe(T ) − P ], P �Pe. (16)

The heat of hydrate dissociation affects hydrate dissociationbehavior because of changes in equilibrium pressure. Masudaet al. (1999) have suggested the following expression for thedissociation heat-sink rate:

QH = −mH (c + dT )

MH

, (17)

where c = 56, 599 J/mol and d = −16.744 J/mol K.The relation between equilibrium temperature Te and pres-

sure Pe is given as (Makogon, 1997)

log10(Pe) = A(T − To) + B(T − To)2 + C, (18)

where To is 273.15 K and A, B, and C are empirical constantsthat depend on hydrate composition. Values of A, B, and Care obtained using the least squares error fit to the equilibriumpressure–temperature data for methane hydrate (Ji et al., 2001),i.e.,

A = 0.0342 K−1, B = 0.0005 K−2, and C = 6.4804.

In Eq. (18), Pe is in Pascal and T is in Kelvin.

3.3. Axisymmetric core model

An axisymmetric computational model for analyzing thedissociation of a sandstone hydrate core was developed andthe corresponding multiphase flows of water and gas wereanalyzed. The core was assumed to be 30.0 cm in length and5.1 cm in diameter. The computational model was created inGambitTM pre-processor, and was meshed using structuredrectangular cells. A computational mesh with 800 cells asshown in Fig. 1 was used. The core is assumed porous withvariable porosity. The local relative permeabilities of water andgas were also allowed to vary with time as hydrate dissociates.An ideal gas model for the gas phase was assumed and thevolume of fluid (VOF) model was used for the simulation ofwater and gas flows.

At the start of each simulation, for duration of 10 min, thepressure at the outlet valve was decreased at a constant rate


Fig. 6. Water saturation contours at different times for the reference case (case 2).

Fig. 7. Comparison of temperature variations from simulation to experimental data for the reference case (case 2).


Fig. 8. Cumulative gas generation for the reference case (case 2) compared to the experimental data.

Fig. 9. Variations of pressure, temperature, equilibrium pressure, and porosity profiles along the core axis with time for the case 1.


Fig. 10. Time variations of the pressure at sections (a)–(d) of the core sample for different cases.

until it reached the desired pressure boundary condition whereit remained constant afterwards. Hydrate core was also assumedto be kept in a constant temperature air bath where the onlyheat transfer mode was free convection between the core andthe surrounding. A heat transfer coefficient of 16.6 W/m2/K assuggested by Masuda et al. (1999) was used. A hydrate number(NH ) of 6.0 was also assumed in the simulations.

3.4. Initial and boundary conditions

As shown in Fig. 1, pressure outlet boundary condition wasdefined on the right side of the core, which represented theopening of outlet valve. On all the walls, no-slip boundarycondition was assumed. Free convection heat transfer betweenall the walls of the core and the surrounding was also assumed.In this section, the simulation results for five different cases

are presented. Table 1 shows the summary of initial conditionsused for hydrate core sample in these simulations.

The permeability reduction index (N) is assumed to be 15 assuggested by Masuda et al. (1999). Table 2 summarizes the cor-responding boundary conditions used for the outlet valve andthe surroundings. Case 2 is considered as the reference caseand cases 1 and 3 show the effects of variation of ambient tem-perature on the hydrate dissociation process and gas generationin the core sample. Cases 4 and 5 show the effects of pressurevariation at the outlet valve on the flow field and evolution ofnatural gas generation in the core sample.

4. Results and discussions

For different boundary conditions, the flow fields inside thecore sample were simulated and time evolutions of pressure


Fig. 11. Variations of the core pressure and equilibrium pressure with temperature at section (a) of the core sample for different cases.

Fig. 12. Time variations of the temperature at sections (a)–(d) of the core sample for different cases.


Fig. 13. Time variations of hydrate saturation at sections (a)–(d) of the core sample for different cases.

and temperature profiles and the rate of gas/water generationdue to hydrate dissociation were evaluated. Four sections alongthe core sample as shown in Fig. 1 were considered and thetime variations of different parameters at these sections wereevaluated and compared. Table 3 shows the distances of thesesections from the outlet valve. The simulation results are pre-sented in this section and the effects of various parameters arediscussed.

4.1. General behavior

Computational modeling results for the reference case(case 2) are presented and discussed in this section. Fig. 2shows the time evolution of the static pressure contours inthe core sample at different times after the outlet valve opens.

This figure shows that the pressure in the core graduallydecreases from an initial value of 3.75 MPa to the outlet pres-sure of 2.84 MPa. Hydrate dissociation is initiated as soon asthe pressure in the core sample becomes less than the equi-librium pressure. Then the generated gas and water begin tomove toward the outlet valve. The low-pressure front con-tinues to move from the outlet valve into the core samplecausing the hydrate to dissociate along the core. After 200 min,Fig. 2d shows that the pressure in the core reaches to aboutthe surrounding pressure.

Fig. 3 displays the contours of temperature in the coresample at four different times. The core sample is assumedto be in air with constant temperature. The temperature at theoutlet valve is the same as the surrounding air temperature.Free convection heat transfer between the core walls and the


Fig. 14. Time variations of the methane gas saturation at sections (a)–(d) of the core sample for different cases.

surrounding is included in the model. As noted before, hydratedissociation is an endothermic process, which results in ab-sorption of heat. Fig. 3 shows that as the hydrate in the coresample dissociates, heat is absorbed from the surrounding,which results in decreasing the local temperature in the core.The low temperature regions in Fig. 3 represent the areas thathydrate is dissociating. As noted before, hydrate dissociationgenerates natural gas and liquid water that flow toward theoutlet valve. Natural convection heat transfer increases the tem-perature of the core sample on the right-hand side of the disso-ciation region (toward the outlet valve). Fig. 3d shows that thecore temperature approaches the surrounding air temperaturewith time.

Figs. 4–6, respectively, display the saturation contours ofhydrate, gas, and water, in the core sample at different times.The initial values of saturations in the core sample are listed in

Table 1. Fig. 4 shows that hydrate dissociation starts from theoutlet valve where the pressure is lower than the equilibriumpressure. The dissociation front is roughly planar at the ini-tiation of the dissociation process. As the front moves awayfrom the outlet region it develops a curvature due to the non-uniformity of the temperature field. Fig. 4d shows that the ma-jority of hydrate is dissociated after 200 min. As the hydratedissociates, methane and water are generated. From Figs. 5and 6 it is seen that the saturations of methane and water in-crease as the saturation of hydrate in the core sample decreasesdue to dissociation.

4.2. Comparison with experimental data

Masuda et al. (1999) have reported several experiments ondissociation of hydrate in a vessel that is similar to the present


Fig. 15. Time variations of the core effective porosity at (a)–(d) of the core sample for different cases.

core sample. They have reported their approximate initial sat-urations for gas, hydrate, and water in their experiment, whichare listed in Table 1. For the simulation, we have used identicalvalues of the parameters and the resulting simulation results arecompared with the experimental data of Masuda et al. in thissection.

Fig. 7 shows the simulated time variations of the tempera-ture at sections (b)–(d) of the core sample for case 2. Here thesimulated temperatures are averaged across the respective sec-tions. The experimental data for time variation of temperatureas reported by Masuda et al. (1999) are shown in this figure forcomparison. It is seen that the simulation results are in goodagreement with the experimental data. The temperatures in allthe sections of the core sample for both simulation and exper-imental data decrease to a minimum as the hydrate dissociatesand then increase and approach the surrounding temperature.

As noted before, hydrate dissociation is an endothermic processand absorbs heat that causes the drop in the temperature. Thefree convection heat transfer then causes the core temperatureto approach the surrounding air temperature.

While Fig. 7 shows good agreement between the model pre-dictions and the experimental data, there are some quantitativedifferences. It is seen that the minimum temperature in all sim-ulations occurs slightly later than the respected experimentaldata. In all the simulations, overall heat transfer coefficientsfor natural convection to the surrounding and typical materialproperties were used. It is conjectured that the differences be-tween the simulation results and the experimental data are dueto these approximations.

Fig. 8 compares the cumulative gas generated as predictedby the present simulation for case 2 and the experimentallymeasured values of Masuda et al. (1999). This figure shows


Fig. 16. Cumulative generation/dissociation in the core for cases 1–3. (a) Cumulative gas generation in standard cm3. (b) Cumulative hydrate dissociation ingrams. (c) Cumulative water generation in grams. (d) Cumulative heat absorbed by hydrate in kJ.

that the predicted monotonically increasing trend in the cumu-lative gas generation is comparable to that of the experimentaldata. The simulation predicts that the core sample generatesabout 9014 standard cm3 of methane gas when all the hy-drate in the core dissociates. Masuda et al. (1999), however,reported generation of about 9067 standard cm3 of methanegas, which is slightly higher than the simulation results.This small difference could be due to numerical round offerrors.

4.3. Effect of surrounding air (Bath) temperature

The effect of surrounding thermal condition on hydratedissociation in the core sample is studied in this section. Sim-ulation results for cases 1–3 for different surrounding tempera-tures are described and compared. Time evolutions of pressureand temperatures at different sections and along the core axis,

as well as hydrate dissociation and methane generation ratesin the core sample are plotted and discussed.

For case 1, Fig. 9 shows time evolutions of different ther-modynamical properties and porosity along the core axis.Fig. 9a shows the time variations of pressure profile in the core.Near the outlet valve, the pressure decreases rapidly to thesurrounding ambient pressure, and a dissociation front seem toform that moves to left toward the closed side of the core withtime. The pressure variation is quite similar to those reportedby Makogon (1997) and Ahmadi et al. (2004), among others.As the hydrate dissociates, the permeability of the core sampleincreases that causes the pressure to drop faster. Time varia-tions of temperature profile along the core axis are shown inFig. 9b. The drop in the temperature due to hydrate dissociationand the subsequent increase of the core temperature caused bythe free convection heat transfer from the surrounding thermalbath can be seen from this figure. While the movement of the


Fig. 17. Core pressure variations at sections (a)–(d) versus time for cases 2, 4, and 5.

dissociation front can also be seen, the heat transfer from theambient fluid to the core distorts the profiles to certain extents.

Variations of the equilibrium pressure along the core axisare shown in Fig. 9c. These profiles are similar to those fortemperature shown in Fig. 9b. This is as expected since theequilibrium pressure as given by Eq. (18) relates directly totemperature. Fig. 9d shows the variations of porosity along thecore axis with time. When hydrate dissociates, the pore spacingincreases, which results in an increase in the local porosity as isgiven by Eq. (3). The porosity profiles clearly show the locationof the dissociation front and their movement away from theoutlet value toward the core center.

Fig. 10 shows variations of pressure at sections (a)–(d) of thecore sample versus time. Here the time evolutions of the av-eraged pressure across different sections are shown. (The time

interval used is 10 min.) This figure shows that the pressure inthe core decreases gradually from the initial value of 3.75 MPato the outlet valve pressure of 2.84 MPa. Section (d) is the clos-est to the outlet valve and the pressure at this section quicklydecreases to the surrounding pressure. The simulation resultsfor time variations of pressure at sections (c), (b) and (a) inFig. 10 show that the depressurization process slows down asthe distance from the outlet valve increases. The effect of sur-rounding temperature can also be seen from Fig. 10. As thesurrounding temperature increases, the pressure at all sectionsin the core decreases faster. As the hydrate dissociates, the per-meability of the core sample increases that causes the pressureto drop faster. Also increasing the surrounding temperature in-creases the heat transfer, which causes the hydrate to dissociatemore rapidly and results in a faster depressurization in the core.


Fig. 18. Core temperature variations at sections (a)–(d) versus time for cases 2, 4, and 5.

For different ambient temperatures, Fig.11 shows the varia-tions of equilibrium pressure versus temperature at section (a)in the core sample. This figure shows that the equilibrium pres-sure decreases with a decrease in temperature. This is as ex-pected since Eq. (18) implies that the equilibrium pressure isa function of temperature. The equilibrium pressure decreasesdue to hydrate dissociation and reduction of temperature andthen increases due to increase of temperature due to naturalconvection. Fig. 11 shows that the hydrate dissociation startswhen the pressure of the core drops to values less than theequilibrium pressure of the hydrate.

Fig. 12 shows the temperature time histories at sections(a)–(d) of the core sample. Here the temperatures are averagedacross respective sections. It is seen that the temperature inall sections of the core sample decreases to a minimum as thehydrate dissociates and then increases and approaches the sur-rounding temperature condition. The drop in the temperature

due to hydrate dissociation and the subsequent increaseof the core temperature due to the free convection heat transferare clearly observed from this figure for cases 1 and 2. Forcase 3 with relatively high surrounding temperature, however,the temperature of the core first increases for a short period,due to the heat transfer from the surrounding to the core.

For section (d), which is closest to the outlet valve,Fig. 12 shows that the temperature decreases to a minimumvery rapidly. Comparing the temperature variations in sections(a)–(d) in Fig. 11, it is seen that as the distance from the outletvalve increases, the temperature reaches the minimum value ata slower rate. In addition, higher the surrounding temperature,the faster the temperatures at core sections decrease to theirminimum values. This is because the hydrate in core sampledissociates more rapidly due to a higher rate of heat transfer.

Figs. 13 and 14, respectively, display time variations of hy-drate and gas saturations. Fig. 13 shows that the saturation of


Fig. 19. Variation of Hydrate saturation at sections (a)–(d) versus time for cases 2, 4, and 5.

hydrate at section (d) decreases sharply. Similarly, Fig. 14 in-dicates that at section (d) gas is produced rapidly as hydratedissociates. As the distance from the outlet valve increases, therate of hydrate dissociation decreases and the rate of the gen-eration of gas and water increases. Figs. 13 and 14 show thatsaturation of different phases at sections (a)–(c) remain roughlyunchanged at the beginning when the dissociation front is nearthe outlet valve. It is also seen that increasing the surroundingtemperature causes saturations of hydrate, gas, and water toreach to their final values faster. This is again due to a higherrate of heat transfer to the core sample, causing faster dissoci-ation of hydrate and generation of water and gas. As the hy-drate dissociates, increase in the porosity of the core sampleand permeability of the gas and water contribute to more rapiddepressurization of the core. Careful examination of Figs. 13and 14 also shows that the sum of all phase saturations at any

time is unity as is required by Eq. (2), which is a good checkon the accuracy of the computer model.

Figs. 15 and 16 show time variations of effective porosity andrelative permeability at different sections of the core sample.As the hydrate dissociates, the pore spacing increases, whichresults in an increase in core sample porosity as is given byEq. (3). It is seen that in section (d), the effective porosity ofthe core increases quickly. As the distance from outlet valveincreases, the rate at which hydrate dissociates decreases andthe rate of increase in porosity decreases accordingly. This isclearly seen from Fig. 15 for sections (a)–(c). An increase inthe surrounding temperature will result in a faster increase inporosity, which is due to a more rapid dissociation of hydratein the core.

For the entire core sample, Fig. 16 shows the cumulativegas and water generation, cumulative hydrate dissociation, and


Fig. 20. Variation of methane gas saturation at sections (a)–(d) versus time for cases 2, 4, and 5.

the total heat absorbed by hydrate dissociation. The negativevalues of the y-axis in Fig. 16b and d indicate the reductionof mass of hydrate due to dissociation and the correspondingamount of heat absorbed. This figure shows that the core samplegenerate about 9000 standard cm3 of methane and about 39 gof water, when 44 g of hydrate in the core dissociates. Theheat absorbed is about 19 kJ. It is also seen that increasing thesurrounding temperature increases the rate of gas and waterproduction due to a faster rate of hydrate dissociation. As isexpected, the long-term cumulative values, however, remainconstants.

4.4. Effect of outlet valve pressure

The effect of outlet valve pressure on hydrate dissociation inthe core sample is studied. Simulation results for cases 2, 4, and

5 for different surrounding pressure are described and comparedin this section. Time evolutions of pressure and temperaturesat different sections in the core sample, as well as hydratedissociation and methane generation rates in the core are plottedand discussed.

Fig. 17 shows the variations of pressure versus time atsections (a)–(d) of the core sample for different cases. Herethe time evolutions of the averaged pressure across differentsections are shown. This figure shows that the core pressuredecreases gradually from its initial value of 3.75 MPa to theoutlet valve pressures of 2.84, 2.99, and 3.28 MPa, respec-tively, for cases 2, 4, and 5. The simulation results for the timevariations of pressure at sections (a)–(d) in Fig. 17 show thatthe depressurization of the core sample and the correspondinghydrate dissociation process slows down as the outlet pres-sure increases. Similar to Fig. 10, as the distance from the


Fig. 21. Cumulative generation/dissociation in the core for cases 2, 4, and 5. (a) Cumulative gas generation in standard cm3. (b) Cumulative hydrate dissociationin grams. (c) Cumulative water generation in grams. (d) Cumulative heat absorbed by hydrate in kJ.

outlet valve increase, the pressure variation at the core sectionevolves at a slower pace.

Variations of the temperature versus time at sections (a)–(d)of the core sample are shown in Fig. 18. Like Fig. 12, thisfigure shows that the temperature in all the core sections de-crease as the hydrate dissociates and then the temperaturesapproach the surrounding thermal condition. As noted be-fore, hydrate dissociation absorbs heat and cools down thecore sample. The free convection heat transfer then causesthe core temperature to approach the surrounding tempera-ture. Comparison of the time variations of the temperatureat sections (a)–(d) shows that as the distance from the out-let valve increases, temperature reaches to its minimum at aslower rate. An increase in the outlet valve pressure leads toa lower magnitude for the minimum temperature at the coresection, which also occurs after a longer time. This is because

hydrate dissociates at a slower rate at higher values of corepressures.

Figs. 19 and 20, respectively, display time evaluations ofhydrate and gas saturations at different sections in the coresample. As the distance of the section from the outlet valveincreases, the rate at which the hydrate dissociates decreases.It is also seen that decreasing the outlet valve pressure causesthe saturations of hydrate, gas, and water to reach their finalvalue faster. This is because the dissociation of the hydrateaccelerates as the pressure decreases. Comparison of Figs. 19and 20 with Figs. 13 and 14 shows that the time variationsof hydrate saturations are quite similar, with the effect of anincrease in the outlet valve pressure being comparable with areduction in the bath temperature. It should be noted here thatthe presented results for phase saturations in Figs. 19 and 20satisfy the constraint imposed by Eq. (2).


Fig. 21 shows the cumulative gas and water generations,cumulative mass of the dissociated hydrate, and the total heatabsorbed by hydrate dissociation in the entire core sample. Thisfigure shows that when the hydrate dissociation is completed,the cumulative values reach to their maximum saturation values.Increase in the outlet valve pressure, results in lower methanegas and water production rates. Trends of variations in thisfigure are similar to Fig. 16 for decreasing bath temperature.

5. Conclusions

Dissociation of methane hydrate in a porous core sampleincluding methane gas and water generations as well as thethermal and multiphase flow conditions are studied. Usingthe FLUENTTM code augmented with a newly developedUsers’ Defined Subroutines (UDS), an axisymmetric modelof the core was formulated and solved. The correspondingmultiphase gas–liquid flows during hydrate dissociation pro-cess were analyzed. For different surrounding temperaturesand various outlet valve pressures, time evolutions of gas andwater generations during hydrate dissociation were evaluatedand variations of temperature and pressure and flow conditionsin the core were simulated. The simulation results were com-pared with the experimental data of Masuda et al. (1999) andfavorable agreement was observed. On the basis of the resultspresented, the following conclusions are drawn:

• Hydrate dissociation rate is sensitive to physical and ther-mal conditions of the core sample, the heat supply from theenvironment, and the outlet valve pressure.

• Porosity and relative permeability are important factors af-fecting hydrate dissociation and gas generation processes.

• For the core studied, the temperature near the dissociationfront decreases due to hydrate dissociation and then increasesdue to thermal convection.

• Increasing the surrounding temperature increases the rateof gas and water production due to a faster rate of hydratedissociation.

• Decreasing the outlet valve pressure increases the rate ofhydrate dissociation and therefore the rate of gas and waterproduction increases.

• The developed UDS for the FLUENTTM Code provides areasonable tool for computational modeling of hydrate dis-sociation in core samples.

This study was the first step in developing a computationalhydrate module for a commercially CFD packages such asFLUENT code. These CFD packages do not have the capa-bility to model Hydrate decomposition/formation at present.Using the computational module developed in this work, thecapability for simulating hydrate dissociation different com-plex three-dimensional geometries are provided.

Notation

A empirical constants in Eq. (18)Ap surface area of hydrate per unit volume

B empirical constants in Eq. (18)C empirical constants in Eq. (18)CR heat capacity of rockCH heat capacity of hydrateKo effective thermal conductivityKD absolute permeability of the mediaKD0 absolute permeability at zero hydrate saturationKg thermal conductivity of gasKH thermal conductivity of hydrateKrk relative permeability of phase k

KR thermal conductivity of rockKrw relative permeability of waterKrg relative permeability of gasKw thermal conductivity of waterMg molecular weights of gasMH molecular weights of hydrateMw molecular weights of waterN permeability reduction indexNH hydrate numberPe equilibrium pressureP local pressure in the coreQH heat-sink rate of hydrate dissociation.R gas constantSwr the irreducible saturations of waterSgr irreducible saturations of gasSk saturation of phase k

T TemperatureU internal energyc empirical constants in Eq.(17)d empirical constants in Eq. (17)h enthalphykod intrinsic dissociation constant

kB dissociation rate constantmk rate of generation/dissociation of species k

ngp molar generation rate of methane gasnk number of moles of phase k

t timeuk fluid velocity vector

Greek letters�0 porosity of the core�eff effective porosity of the medium�k density of phase k

�E activation energy�k viscosity of phase k

SubscriptsR rockH hydratew waterg gask phase k

Acknowledgments

The support of the US Department of Energy under grantDE-FC26-00-NT40916 is gratefully acknowledged.


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