spe-167259-pa (simulation of hydrate dynamics in reservoirs)

Simulation of Hydrate Dynamics inReservoirs

M.T. Vafaei, B. Kvamme, A. Chejara, and K. Jemai, University of Bergen

Summary

Gas hydrates in reservoirs are generally not in thermodynamicequilibrium, and there may be several competing phase transitionsinvolving hydrate. Formation of carbon dioxide (CO2) hydratesduring aquifer storage of CO2 involves roughly 10 vol% increasecompared with groundwater. Dissociation of hydrate towardundersaturated fluid phases involves the same level of contraction.Hydrate phase transitions are generally fast (scales of seconds)compared with mineral dissolution and precipitation, and it isunlikely that a time-shifted explicit coupling to geomechanicalanalysis will be able to capture the appropriate dynamic couplingsbetween flow and changes in stress. The need for geomechanicalintegrity of the storage site therefore requires a reservoir simulatorwith an implicit solution of mass flow, heat flow, and geome-chanics. And because CO2 involved in hydrate is also involved indifferent geochemical reactions, we propose a scheme where allpossible hydrate formation (on water/ CO2 interface, from watersolution, and from CO2 adsorbed on mineral surfaces) and all dif-ferent possible dissociations are treated as pseudoreactions, butwith kinetics derived from advanced theoretical modeling. Themain tools for generating these models have been phase-field-theory (PFT) simulations, with thermodynamic properties derivedfrom molecular modeling. The detailed results from these types ofsimulations provide information on the relative impact of masstransport, heat transport, and thermodynamics of the phase transi-tion, which enable qualified simplifications for implementationinto RetrasoCodeBright (RCB) (Saaltink et al. 2004). The primarystep was to study the effect of hydrate growth or dissociation witha certain kinetic rate on the mechanical properties of the reservoir.Details of the simulator and numerical algorithms are discussed,and relevant examples are shown.

Introduction

Natural-gas hydrate in the reservoir is continuously attracting theattention of more researchers around the world, and the reason isits importance from different aspects, ranging from a potentialenergy resource to environmental threat. Hydrate can occur insediments below the oceanic floor or in the permafrost, whereverthe thermodynamic conditions are suitable and water and guestmolecules are available. Investigations show that there are hugeresources of natural-gas hydrate in the Earth, which because ofthe high volumetric concentration of methane gas per hydrate vol-ume is considered as a substantial energy resource. Besides, meth-ane (CH4) combustion releases less CO2 per unit energy releasecompared with both coal and oil, which means a cleaner fuel froman environmental point of view. On the other hand, CH4 can bemore than 20 times more aggressive than CO2 in trapping the heatin the atmosphere, and its leakage from sediments affects the ma-rine life and the climate substantially. Another attractive aspect ofsediment gas hydrates is the potential of storing CO2 in the formof CO2 hydrate. Disposal of the CO2 below the seabed is consid-ered as one of the most promising and safe options for storage ofCO2 (Koide et al. 1997; Zatsepina and Pooladi-Darvish 2011).

There are several scenarios for CH4 production from natural-gas-hydrate reservoirs. Depressurization is the one of these meth-ods in which the hydrate stability condition is disturbed by pres-sure reduction according to the water/gas/hydrate equilibriumcurve, resulting in hydrate dissociation and release of CH4. It hasbeen investigated by many research groups through both simula-tion and experimental studies. Thermal stimulation is anothermethod, based on moving out from the stability region by temper-ature increase. The third method is to use inhibitors such as meth-anol or brine to shift the equilibrium curve and dissociate hydrate.The final method is injection of CO2 into CH4-hydrate reservoirs.CO2 hydrate is more stable than CH4 hydrate. Therefore CO2-hydrate formation will provide the necessary heat to dissociateCH4 hydrate, and it can be considered both as a natural-gas-pro-duction method and a CO2-sequestration process (Graue et al.2008). In this method, the two primary mechanisms for CO2 toconvert in-situ CH4 hydrate are (1) solid-state conversions and (2)new CO2 hydrate being formed from free liquid water in thepores. Both of these mechanisms have been proved theoreticallyas well as experimentally (Kvamme et al. 2007; In press). Mecha-nism (1) can hardly be viewed as any of the three classicalmechanisms mentioned previously because the enthalpy change islimited and it is dominated by entropy changes. Therefore, it isconsidered as an independent method.

Regarding the second mechanism, direct conversion of CH4hydrate to a mixed hydrate (in which some CH4 remains in smallcavities and CO2 dominates filling of the large cavities) is a slowprocess. According to publications on molecular studies of thisprocess, as well as advanced kinetic modeling of the process(PFT), this mechanism is restricted by solid-phase mass transportwith diffusivity coefficients on the order of 1016 m2/s (Buaneset al. 2006; Svandal et al. 2006a, b; Tegze et al. 2006a, b; Buaneset al. 2009; Kvamme et al. 2006a, b; 2007; 2009; Svandal andKvamme 2009).

Creation of new hydrate from free water surrounding thehydrate is typically also mass-transport limited (as we have shownthrough several publications), but liquid-state transport with diffu-sivity coefficients is on the order of 108 m2/s. Heat transport inwater/hydrate systems is roughly two orders of magnitude faster.Practically, this implies that dissociation of CH4 hydrate causedby released heat from new CO2-hydrate formation is liquid-state-transport limited, and several orders of magnitude faster than thedirect solid state conversion (Kvamme et al. In press). Duringmore than 2 decades, many researchers have tried to study CH4production from hydrate reservoirs, and more recently storage ofCO2 in the form of hydrates in the sediments through modelingand simulation techniques. The progress has been considerable,but there are still many uncertainties involved in these phenom-ena. A review of the past studies of hydrate with the approach ofmodeling and simulation is presented in this section. The purposehere is mainly to recognize major tools developed for studyinghydrate in the reservoir, specifically in the form of simulators, andto distinguish some of their differences, specifically with respectto the thermodynamic approach used in these tools.

Holder and Angert (1982) considered a system of stratifiedhydrate and gas surrounded by impermeable layers from bottomand top to build a 3D model for studying the hydrate-dissociationeffect on gas production caused by depressurization. Severalassumptions were made to simplify the calculations. They consid-ered the dissociation to happen only at the interface betweenhydrate and gas phase, and only conduction was considered to

CopyrightVC 2014 Society of Petroleum Engineers

This paper (SPE 167259) was revised for publication from paper IPTC 14609, first presentedat the International Petroleum Technology Conference, International Petroleum TechnologyConference, Bangkok, Thailand, 1517 November 2011. Original manuscript received forreview 21 October 2011. Revised manuscript received for review 21 August 2013. Paperpeer approved 27 August 2013.

J167259 DOI: 10.2118/167259-PA Date: 9-April-14 Stage: Page: 215 Total Pages: 12

ID: jaganm Time: 15:00 I Path: S:/3B2/J###/Vol00000/130088/APPFile/SA-J###130088

April 2014 SPE Journal 215

find temperature distribution in the gas phase. They concludedthat hydrate can contribute significantly in gas production fromsuch reservoirs (Holder and Angert 1982).

Burshears et al. (1986) developed a two-phase, 3D numericalmodel to study gas production from a system of hydrate formationand dissociation in the reservoir. Their model consisted of waterand any mixture of CH4, ethane, and propane. They considered ra-dial flow and equilibrium conditions in the gas/hydrate interface.Water flow was present in their model, but only heat conductionwas considered (Burshears et al. 1986).

Yousif et al. (1991) developed a 1D model to simulate isother-mal depressurization of hydrate in Berea sandstone samples. Themodel considered three phases of water, gas, and hydrate and usedthe kinetics model of Kim et al. for dissociation of hydrate (Kimet al. 1987; Yousif et al. 1991). It also considered the water flowcaused by hydrate dissociation, which according to experimentaland numerical results was considerable. The variations in porosityand permeability of the gas phase were taken into account. Finally,they validated their model with experimental data.

Xu and Ruppel (1999) developed an analytical formulation tosolve the coupled momentum, mass, and energy equations for thegas-hydrate system, consisting of two components (water andCH4 gas) and three phases (gas hydrate, free gas, water and dis-solved CH4). They made several assumptions, such as ignoringcapillary effects and ignoring kinetics of the phase transitionbetween hydrate and aqueous phase (Xu and Ruppel 1999).

Swinkels and Drenth (2000) used an in-house 3D thermal res-ervoir simulator and modified the pressure/volume/temperature(PVT) tool to study hydrate-production scenarios as well as heatflow and compaction in the reservoir and hydrate cap. They repre-sented the reservoir fluid by a gaseous, a hydrate, and an aqueousphase. Their system consisted of three components including twohydrocarbons and a water component. Heat was considered as anextra component for all phases internally in the simulator. Joule-Thomson cooling effect was also considered automatically (Swin-kels and Drenth 2000).

Davie and Buffet (2001) proposed a numerical model for cal-culation of gas-hydrate volume and distribution in marine sedi-ments. They considered the organic material from sedimentationas the main source of carbon supply to the hydrate stable region.The rate of sedimentation, the quantity and quality of organic ma-terial, and biological productivity were considered as key parame-ters in this model. Hydrate formation and dissociation werecontrolled by thermodynamic conditions and driving force fromequilibrium concentration. A first-order model with a large rateconstant was used to account for the reaction rate. They comparedtheir results with observations from the practical field. Theirmodel was dependent on the available data of sedimentation rateand organic content (Davie and Buffet 2001).

Goel et al. (2001) developed a single-phase-flow model to pre-dict the performance of an in-situ gas hydrate. The gas-with-drawal rate was assumed to be constant, and the reservoir wasassumed to be infinite. It used an nth-order kinetics rate coupledwith gas flow in the porous media (Goel et al. 2001).

Moridis (2003) introduced a new module for the TOUGH2simulator named EOSHYDR2. TOUGH2 is a 3D, multicompo-nent, multiphase-flow simulator for subsurface purposes (Law-rence Berkeley National Laboratory 2013). EOSHYDR2 isdesigned to model hydrate behavior in both sediments and labora-tory conditions. It is able to consider up to four phases of gas, liq-uid, ice, and hydrate and up to nine components of water, CH4hydrate, CH4 as native and from hydrate dissociation, a secondnative and dissociated hydrocarbon, salt, water-soluble inhibitors,and heat as a pseudocomponent. It includes both equilibrium andkinetic models for hydrate formation and dissociation. It uses thehydrate reaction model of Kim et al. (1987) for kinetic studies.Moridis studied four test cases of CH4 production and concludedthat both depressurization and thermal stimulation can a producesubstantial amount of hydrate; he suggested that the combinationof both can be desirable. He has used just the equilibriumapproach because of a lack of enough suitable data necessary for

the parameters of the kinetic model, although he mentioned thatslower processes such as depressurization follow kinetic dissocia-tion (Moridis 2003).

Hong et al. (2003) presented a 2D cylindrical model to studygas production from hydrate reservoirs. They used both analyticaland numerical approaches. The numerical model considered theequations for gas and water two-phase flow, and for conductiveand convective heat flow, and treated hydrate decompositionkinetically by use of the Kim et al. (1987) model. In the analyticalapproach they did not consider the fluid flow. They studied theeffect of the hydrate zone on the gas production from the gas layerand also the importance of the intrinsic kinetics of hydrate decom-position with respect to equilibrium assumptions. They concludedthat the kinetic equation was affected only when it was consideredfive orders of magnitude lower than the values found by Kimet al. (1987) in a PVT cell (Hong et al. 2003; Hong and Pooladi-Darvish 2005).

Xu (2004) has modeled dynamic gas-hydrate systems consid-ering two main elements. The first element provides a model toaccount for dynamic phase transitions of marine gas hydrates byconsidering the effects of fluid pressure, temperature, and salinitychanges on hydrate stability, solubility, and fluid densities andenthalpies. This allows describing coexistence of three phaseshydrate, gas, and liquid solution at equilibrium. The model con-sists of three components (water, gas, and salt) and four phases(free gas, liquid solution, gas hydrate, and solid halite). He con-sidered thermodynamic equilibrium for and among individualphases. The second element of the model consists of the numeri-cal tool to solve for fluid-flow and -transport equations in porousmedia. It considers four components and up to five phases. He hasstudied the response of the model to the pressure-drop and tem-perature-rise scenarios at the seafloor (Xu 2004).

Ahmadi et al. (2004) developed a 1D model to study CH4 pro-duction from hydrate dissociation in a confined reservoir by useof a depressurization method. They considered heat of dissocia-tion and conduction and convection in both gas and hydrate phase.They considered equilibrium conditions at the dissociation frontand neglected water flow in the reservoir and the Joule-Thomsoncooling effect (Ahmadi et al. 2004).

Sun and Mohanty (2006) developed a 3D simulator by use ofthe Kim et al. (1987) kinetic model to study formation and disso-ciation of hydrate in porous media. They considered four compo-nents (hydrate, CH4, water, and salt) and five phases (hydrate,gas, aqueous, ice, and salt precipitate). Water freezing and icemelting are considered, assuming equilibrium phase transitions.Mass transport including fluid flow and molecular diffusion, plusheat transport including conduction and convection, is solved im-plicitly (Sun and Mohanty 2006).

Phirani and Mohanty (2010) upgraded the simulator to accountfor CO2 as a new component and CO2 hydrate as a new phase.The purpose was to study CO2 flooding of CH4-hydrate-bearingsediments. They used the model of Kim et al. (1987) for kineticsof dissociation and constant rates for hydrate formation (Phiraniand Mohanty 2010).

Uddin et al. (2006) developed a general kinetic model ofhydrate formation and decomposition on the basis of the Kimet al. (1987) model to study CO2 sequestration in CH4-hydratereservoirs along with CH4 production. The model consisted offive components: water in aqueous phase, CH4 and CO2 in gasphase, and CO2 hydrate and CH4 hydrate in solid phase. The gas-hydrate model was coupled with a compositional thermal reser-voir simulator (STARS; Computer Modelling Group 2013) tostudy dynamics of hydrate formation and decomposition in thereservoir. It was concluded that the effect of kinetic rate constanton hydrate decomposition was significant in the case where it waslowered a few orders of magnitude. Reservoir permeability alsohas a great impact on the decomposition rate (Uddin et al. 2006).

Nazridoust and Ahmadi (2007) developed a computationalhydrate module for ANSYS FLUENT (2013) code. It providesthe possibility to study hydrate dissociation for complex 3D geo-metries. They used the kinetics rate of dissociation proposed by



216 April 2014 SPE Journal

Kim et al. (1987), and they included the heat of reaction, effectsof water and gas permeabilities, and effective porosity with possi-bility of variation with time. They found that the production pro-cess was sensitive with respect to temperature, pressure, and corepermeability. They also compared their results with experimentaldata (Nazridoust and Ahmadi 2007).

Liu et al. (2008) developed a 1D model to study hydrate disso-ciation by depressurization in porous media. They used a movingfront to separate the hydrate zone from the gas zone. They consid-ered conductive and convective heat transfer and mass transfer ingas and hydrate zones and energy balance at moving front. Theyconsidered equilibrium at the front and concluded that theassumption of stationary water phase results in overprediction ofdissociation-front location and underprediction of gas productionin the well. They also found that reservoir permeability and wellpressure can highly affect the production rate (Liu et al. 2008).

Gamwo and Liu (2010) have presented a detailed theoreticaldescription of the open-source reservoir hydrate simulator Hydra-teResSym (NETL 2013) developed previously by LawrenceBerkeley National Laboratory. They have also applied it to a sys-tem of three components (CH4, water, and hydrate) and fourphases (aqueous, gas, hydrate, and ice). Darcys law is used formultiphase flow of mass in porous media, and local thermal equi-librium is considered in the code. It considers both kinetic andequilibrium approaches by use of the Kim et al. (1987) scheme asthe kinetic model of hydrate dissociation. The studied model hasbeen validated by use of the TOUGH-HYDRATE simulator (Law-rence Berkeley National Laboratory 2013). They concludedthat HydrateResSim is a suitable freeware, open-source code forsimulating CH4-hydrate behavior in the reservoir. They foundthat the equilibrium approach usually overpredicts the hydrate disso-ciation compared with the kinetic approach (Gamwo and Liu 2010).

From the presented literature review, it is clear that thehydrate-dissociation process in the reservoir is mostly treated asan equilibrium reaction, and in fewer cases as kinetics. The major-ity of kinetic approaches are modeled after the kinetic model ofKim et al. (1987), developed according to laboratory experiments:

dnHdt

kdAsfe f : 1

In this paper, a different approach according to the nonequili-brium nature of hydrate phase transitions in the reservoir will bepresented. In spite of some recommendations by previousresearchers who consider the equilibrium assumption as a suitablesimplification for hydrate modeling in certain conditions, the ki-netic approach is used in this study, as explained in the Theorysection. On the basis of this approach, a new reservoir hydratesimulator will be introduced that is developed on a former reac-tive-transport reservoir simulator: RCB (Saaltink et al. 2004). Themodule is designed so that it can easily work according to thenonequilibrium thermodynamic package that is being developedin this group. The ultimate goal is to develop the simulator for thefollowing main purposes:

1. Hydrate production (depressurization, thermal stimulation,CO2/CH4 exchange).

2. Hydrate formation during aquifer storage of CO2 in reser-voirs with cold zones.

3. Dissociation of natural-gas hydrates caused by contact withundersaturated groundwater through fractures and channels.

4. Dynamics of new hydrate formation from groundwater andupcoming natural gas from sources below through fracturesystems.

5. Combination of Points 3 and 4 that leads to situations of netfluxes of natural gas to ecosystems outside (water, air).

At this stage, kinetic models of hydrate formation and dissoci-ation from phase-field simulations are used to examine the per-formance of the module through example cases.

Theory

When a clathrate hydrate comes into contact with an aqueous so-lution containing its own guest molecules (CH4 or CO2), the num-

ber of the degrees of freedom available to the new system of threephases (aqueous, gas, hydrate) will be decreased compared withthe two-phase system (aqueous, gas) because of the Gibbs phaserule:

F N p 2; 2

where F is the degree of freedom, N the number of components,and p the number of phases. From a fundamental point of view inthermodynamics, a phase is unique if density, composition, andstructure are different from other coexisting phases. In the ulti-mate limit of this, hydrate can never fill pore space more thanthermodynamics permits. Every mineral imposes specific structur-ing of surrounding water molecules related to the partial chargesof the mineral surface, which will never be compatible with par-tial charges on structured water molecules in the hydrate surface(Svandal et al. 2006a, b; Kvamme et al. 2009; Kvamme and Kuz-netsova 2010; Kvamme et al. 2012; Van Cuong et al. 2012a, b). Itis similar for the hydrate, in which the fairly rigid distribution ofpartial charges on oxygen and hydrogen will have a structuringimpact on surrounding fluids. The absolute minimum number ofphases for a system of one hydrate former and water is three,which gives one degree of freedom, and the system cannot reachequilibrium. Practically, there will always also be fluid phase(s) inthe system because of the fact that hydrates in nature are open sys-tems. No hydrate reservoir reaches infinity in any direction. Thereis a bottom line at which hydrate is in contact with fluids and/orclay at a temperature for given depth where hydrate cannot be sta-ble. In the horizontal directions, the hydrate reservoir may enterfracture systems that bring the hydrate in contact with ground-water that dissociates hydrate and/or other boundaries where frac-ture systems bring fresh hydrocarbon feed into the hydrate zones.In summary, this implies that all hydrate reservoirs are open sys-tems. Natural hydrate resources are not even close to 100% inhydrate saturation, according to estimates published for differentparts of the world (Collett 2009; Wanga et al. 2013; Xiao et al.2013). Full thermodynamic equilibrium is therefore impossiblefor hydrates in a reservoir. The situation does not change if thereare more hydrate formers in the system. According to the first andsecond laws of thermodynamics, the most-stable hydrate willform first and result in a range of different hydrates with graduallyincreasing free energies proportional to depletion of the besthydrate formers. These hydrates have different compositions andare by definition different phases. Furthermore, there is no directmechanism to make these hydrates uniform because the most-sta-ble hydrates cannot rearrange to less-stable hydrates without con-tradicting the first and second laws. So in summary, there is nopossibility for reaching true thermodynamic equilibrium. Theimplementation of kinetic models for the different competingphase transitions in the reservoir is in its initial phase, so at thisstage it is not possible to quantitatively evaluate the impact ofnonequilibrium thermodynamics compared with the very oversim-plified 2D pressure vs. temperature equilibrium evaluation. Oneexample that is not captured in that approach is the dissociation ofhydrate toward undersaturated groundwater, which can be quitesignificant for the initial stages of production in reservoirs withouta gas cap. Solid surfaces are efficient nucleation sites for hydrateformation, so reformation of hydrate can be facilitated by the min-eral surfaces. But there are many other examples. The bottom lineis that hydrates in porous media are complex systems that areunique for every distinct reservoir, and there are no real caseswith sufficient monitoring for comparison purposes. For this rea-son, we should strive toward making the physical description asgood as possible. The contribution from this work is a proposedmethodology to incorporate appropriate thermodynamics of themultiphase system of hydrate/water/gas/minerals.

A comparison between a two-phase system and a three-phasesystem is made here for further clarification of the nonequilibriumconcept. For a two-phase system comprising two components,water and gas, there will be two degrees of freedom, whereas in athree-phase system with hydrate as an additional phase, there willbe only one degree of freedom. As a result, when both

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temperature and pressure are specified, as is the case in reservoirconditions, the system is overdetermined and may be unable toreach three-phase equilibrium. The system will, however, alwaystend toward the minimum free energy, and when the hydrate isinside its pressure/temperature stability region, this means that itsfree energy is lower than that of the aqueous solution (Svandalet al. 2006a). In case of hydrate formation and dissociation in thereservoir, the system will be even more complex because hydratecan form from, or dissociate toward, phases with different freeenergies, which will produce different phases. Consequently,degree of freedom will decrease further and there will be no equi-librium condition, and competing phase-transition reactions ofhydrate formation, dissociation, and reformation among differentphases will rule the system. The main factor in such a system istherefore the minimum free energy of the system and kinetics ofcompeting reactions. Looking at hydrate in porous media, threephases (gas, aqueous, and hydrate) are evident. The total inde-pendent thermodynamic variables in this system are temperature,pressure, and compositions of all coexisting phases. Locally, tem-perature and pressure are fixed (given by flow) in every point ofthe reservoir. From Gibbs phase rule (which is the conservationof mass under constraints of equilibrium), only two phases can beat equilibrium for water and one hydrate former. For water andtwo hydrate formers, the most-favorable hydrates are formed firstand a distribution of hydrate compositions will be formed, whichmay be slow in reorganization, if possible at all. Furthermore, ifthe system is not at equilibrium,that also implies that chemicalpotentials of hydrate formers in different phases are not uniform(equal). From statistical mechanics (the van der WaalsPlatteeuwtheory), this implies different free energies for different hydratesthat are formed (hydrate from liquid water and gas hydrate for-mer, hydrate formed from adsorbed hydrate former on mineralsurfaces, and so on). Even a hydrate film formed on a water/

hydrate interface will not be uniform because in a very short timethe hydrate film will be so slow in transport that further growthwill happen from the solution on one side and from gas on theother side.

According to Fig. 1, main phase-transition scenarios caused byhydrate dissociation and reformation for a system of water andone hydrate former can be summarized as

Hydrate dissociation toward free bulk gas free bulkliquid water original hydrate left (DG1)

Hydrate dissociation caused by sublimation (little water ingas phase) (DG2)

Hydrate dissociation toward liquid water caused by unsatu-rated CH4 in water (DG3)

Hydrate reformation from free bulk gas free bulk liq-uid water (DG4)

Hydrate reformation on gas/water interface (DG5) Hydrate reformation from dissolved CH4 in aqueous solution

(DG6) Hydrate reformation from water and CH4 adsorbed on min-

eral surfaces (DG7)where

DGi xH;iw lH;iw lpw xH;iCH4lH;iCH4 lpCH4

: 3

In Eq. 3, H represents hydrate phase; i represents any of theseven phase-transition scenarios; p represents liquid, gas, andadsorbed phases; x is composition; and l is chemical potential.

It should be noted that hydrate is not uniform and there can bemany hydrate phases with different compositions, depending onwhich phase the hydrate formers come from and which phase thewater comes from. For example, if a hydrate phase is formedslightly outside of a mineral, the hydrate surface itself is anadsorption side with specific properties as such. To analyze this

. . . . . . . .

Hydrate PhaseTransitions

ReformationFrom:

DissociationTowards:

CH4 in the gas+

Water in liquid

Dissolved CH4+

Water in liquid

Dissolved CH4+

Water in liquid

CH4 in the gas+

Water vapor

CH4 in the gas+

Water vapor

Water and CH4adsorbed on mineral

surfaces

CH4 in the gas+

Water in liquid

Fig. 1Possible hydrate phase-transition scenarios in porous media.




system all impossible (DG > 0) and unlikely (jDGje) cases mustbe disregarded. Taking into account the mass-transport-limitedcases, all realistic phase-transition scenarios will be determined.

The purpose of this study is to develop a hydrate reservoir sim-ulator that has the possibility to consider the free-energy changesof all phase-transition scenarios and take into account the effectof the realistic ones on the flow and the properties of the porousmedia through advanced kinetic models.

Kinetic Model

The results from phase-field simulations (Baig 2009) have beenmodified to be used in the kinetic model. Phase-field simulationsare modeled after the minimization of Gibbs free energy on theconstraint of heat and mass transport. Extensive research has beenongoing in the same group on application of PFT in prediction ofhydrate-formation and -dissociation kinetics, which is still in pro-gress (Svandal et al. 2006a, b; Svandal 2006; Tegze et al. 2006a,b; Baig 2009; Kivela et al. 2012; Qasim et al. 2011). In this study,the simulation results of such studies have been extrapolated andused as the constant rate of the kinetic model in the numerical tool.

Numerical Tool

For reservoirs where hydrate may form in some regions, hydrateformation involves roughly 10 vol% increase of water. In parallelto this, there are chemical reactions that can for example supplyextra CO2 through dissolution of carbonates in regions of low pH,and also regions of high pH where transported ions may precipitateand even extract CO2 from water and hydrate. The formed hydratewill not be in equilibrium because of Gibbs phase rule, as men-tioned previously. Neither will it attach to the mineral surfacesbecause of incompatibilities of hydrogen bonds in hydrate andinteractions with atomic partial charges on the mineral surfaces.For this reason, there is a need for a logistic system that can handlecompeting processes of formation and dissociation. A reactive-transport simulator can handle that. Implicit geomechanics areneeded to handle competing phase transitions that are very rapid(seconds) and are dynamically coupled to geochemical reactionsthat can be fairly fast (hours to days). For this purpose RCB, a re-active-transport reservoir simulator, is used in this study andextended with hydrate phase transitions as pseudoreactions.RCB is capable of realistic modeling of the reaction rates for min-eral dissolution and precipitation, at least to the level of availableexperimental kinetic data. In contrast to some oil and gas simula-tors, the simulator has flow description ranging from diffusion toadvection and dispersion (Saaltink et al. 1997, 2004) and as such isable to handle flow in all regions of the reservoir, including thelow-permeability regimes of hydrate-filled regions.

The equations for the system are highly nonlinear and aresolved numerically. The numerical approach can be viewed as di-vided into two parts: spatial and temporal discretizations. Thefinite-element method is used for the spatial discretization, while

finite differences are used for the temporal discretization. TheNewtonRaphson method is adopted for the iterative scheme(Saaltink et al. 1997, 2004).

A brief overview of independent variables, constitutive equa-tions, and equilibrium restrictions are given in Tables 1 through3, respectively. More details can be found in Appendix A of thisstudy, and in the mentioned references.

The Independent Variables. The governing equations for noni-sothermal multiphase flow of liquid and gas through porousdeformable saline media have been established. Variables andcorresponding equations are tabulated in Table 1.

Constitutive Equations and Equilibrium Restrictions. Asso-ciated with this formulation is a set of necessary constitutive andequilibrium laws. Tables 2 and 3 present a summary of the consti-tutive laws and equilibrium restrictions that should be incorpo-rated in the general formulation. The dependent variables that arecomputed by use of each law are also included.

RCB is a coupling of a reactive transport code, Retraso, with acode for simulation of multiphase flow of material and heat, Code-Bright. CodeBright contains an implicit algorithm for solution ofmaterial-flow, heat-flow, and geomechanical-model equations (Oli-vella et al. 1994, 1996, 1997). The Retraso extension of CodeBrightinvolves an explicit algorithm for updating the geochemistry (Saal-tink et al. 1997, 2004), as shown in Fig. 2. This new coupled toolRCB is capable of handling both saturated and unsaturated flow, aswell as heat transport and reactive transport in both liquid and gas. Itis a user-friendly code for flow, heat, geomechanics, and geochemis-try calculations. It offers the possibility of computing only the cho-sen unknowns of the users interest, such as hydromechanical,hydrochemical/mechanical, hydrothermal, hydrothermal/chemical/mechanical, thermomechanical, and so forth.

It can handle problems in one, two, and three dimensions (Oli-vella et al. 1994, 1996, 1997; Saaltink et al. 1997). An importantadvantage of RCB is the implicit evaluation of geomechanical dy-namics. According to Fig. 2, flow, heat, and geomechanics aresolved initially in the CodeBright module through the NewtonRaphson iteration, and then the flow properties are updatedaccording to the effects of reactive transport on porosity and salin-ity in a separate NewtonRaphson procedure but for the sametimestep (Saaltink et al. 1997). This makes it possible to study theimplications of fast kinetic reactions, such as hydrate formation ordissociation, more realistically.

Modifications in RCB. The Retraso part of the code has a built-in, state-of-the-art geochemical solver, as well as the capabilitiesof treating aqueous complexation (including redox reactions) andadsorption. The density of CO2 plumes that accumulate undertraps of low-permeability shale or soft clay depend on depth andlocal temperature in each unique storage scenario. The differencebetween that density and the density of the groundwater results ina buoyancy force for penetration of CO2 into the caprock. Andeven if the solubility of water into CO2 is small, dissolution ofwater into CO2 may also lead to the drying out of clay. Mineralreactions between CO2 and shale minerals are additional effectsthat eventually may lead to embrittlement. Linear geomechanics

TABLE 2CONSTITUTIVE EQUATIONS

Constitutive Equation Variable Name

Darcys law Liquid and gas advective flux

Ficks law Vapor and gas nonadvective flux

Fouriers law Conductive heat flux

Retention curve Liquid-phase degree of saturation

Mechanical constitutive model Stress tensor

Phase density Liquid density

Gas law Gas density

TABLE 3EQUILIBRIUM RESTRICTIONS

Equilibrium Restrictions Variable Name

Henrys law Air-dissolved mass fraction

Psychometric law Vapor mass fraction

TABLE 1EQUATIONS AND INDEPENDENT VARIABLES

Equation Variable Name

Equilibrium of stresses Displacements

Balance of liquid mass Liquid pressure

Balance of gas mass Gas pressure

Balance of internal energy Temperature




may not be appropriate for these effects. Clay is expected to ex-hibit elastic nonlinear contributions to the geomechanical proper-ties. Different types of nonlinear models are already implementedin the CodeBright part of the code, and the structure of the codemakes it easy to implement new models derived from theory and/or experiments. The current version of RCB has been extendedfrom ideal gas into handling of CO2 according to the SoaveRedlichKwong equation of state (EOS) (Kvamme and Liu2008b). This EOS is used for density calculations and for fugac-ities of the CO2 phase as needed in the calculation of dissolutionof the CO2 into the groundwater (Hellevang and Kvamme 2007;Kvamme and Liu 2008a, b). The equations for the system arehighly nonlinear and are solved numerically (Saaltink et al. 1997,2004). The NewtonRaphson method used in the original RCBalso has been modified to improve the convergence of the numeri-cal solution while increasing the range of working pressure in thesystem (Kvamme and Liu 2008b).

The following modifications are additional in this study. Toaccount for nonequilibrium thermodynamics of hydrate and todetermine the kinetic rates of different competing scenarios ineach node and each timestep according to the temperature, pres-sure, and composition of the system, CO2 and CH4 hydrates areadded into the simulator as pseudomineral components with a con-stant kinetic rate for hydrate formation and dissociation. Hydrateformation and dissociation can be observed directly through poros-ity changes in the specific areas of the porous media. Porosityreduction indicates hydrate formation, and porosity increase indi-cates hydrate dissociation. Temperature, pressure, and CO2/CH4concentrations in all possible phases are three factors that influ-ence hydrate formation or dissociation. The kinetic rate used inthis study is calculated from extrapolated results of PFT simula-tions by Baig (2009). In the next stage, it will be replaced by a

thermodynamic code, which is already in the final stages, toaccount for all different competing reactions. In the mixed hydratesystem, the two resulting phases from CO2/CH4 splits will havesignificant free-energy benefit differences in terms of hydrate for-mation, and it is therefore also not implemented yet. However, thefundamental kinetic modeling of these processes is being con-ducted for later implementation.

Hydrate reaction is considered on the basis of Eq. 4. Theenergy balance for the gas phase is modified from ideal gas (id) toreal gas (gas) according to Eq. 5 by use of the SoaveRedlich-Kwong EOS to calculate fugacity coefficient and derivatives:

8CH4

CO2

46 H2O $ Hydrate; 4

H Hid;gas RT2 dlnUdT

: 5

The energy balance for solid phase is also modified accordingto the hydrate reaction enthalpy of Table 4. The enthalpy of CH4hydrates, CO2 hydrates, and mixed hydrates are readily availablefrom Kvamme and Tanaka (1995) through simple classical ther-modynamic relationships between free energy and enthalpy. Notein particular that empty hydrate water chemical potential isavailable and has been verified through other separate studies toreproduce experimental equilibrium curves without adjustable pa-rameters; similar circumstances hold for liquid water (or ice)entering the hydrate reaction in Eq. 4. Furthermore, Eq. 5 com-plements the enthalpy from the gas(es) entering the hydrate.Released heat by hydrate formation or consumed heat by hydratedissociation is therefore trivially available and incorporated. Thereaction heat will appear as a source or sink term in the heat-flow equation, and the enthalpy that follows the mass transport istrivially incorporated into the heat flux equation. The heat that dis-tributes to (or consumes) surroundings by conduction (only a sim-plified conduction model is implemented so far) is so far simplifiedthrough an average heat conductivity on the basis of all surroundingphases. At present, this has not been a major focus but it is on theagenda for a follow-up project. As such, the heat transport may beinterpreted with some caution, although the incorporated descrip-tion seems to be on the same level as other hydrate simulators.Heat transport in a dynamically flowing system undergoing solid/fluid phase transitions is very complex. We therefore plan to usePFT with implicit hydrodynamics to conduct pore-scale modelingof hydrate phase transitions under different flow regions and differ-ent impacts of mineral surfaces. Strategies for this have alreadybeen discussed by Kvamme et al. (2013, In press).

Model Description

A system of CO2 injection into the aquifer presented in Fig. 3 isselected for evaluating the simulator. It consists of a 2D model of3001000 m at the depth of 100 m. The pressure gradient in thereservoir is 1 MPa/100 m, and the temperature gradient is 3.6C/100 m. The model is discretized into 1,500 elements with dimen-sions of 1020 m. CO2 is injected at constant pressure of 4 MPaat the specified location on Fig. 3. The equation proposed by Phir-ani and Mohanty (2010) is used to describe CO2 hydrate equilib-rium conditions in the model. Choice of conditions is intentionalto allow hydrate formation in certain areas of the system, as

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

Independent Variables(Temperature, Gas Pressure, Liquid

Pressure, Deformation)

Dependent Variables(Flux of Liquid, Flux of Gas, Hydraulic

Saturation, Porosity...)

Newton RaphsonIteration

Converged

Newton RaphsonIteration

Converged

Copy Relative Variables forRetraso

Update Flow Properties Affected byReactive Transport, Including Porosity and

Salinity

No

No

Go To the NextTime Step

Yes

Code

Brig

ht(F

low, H

eat, G

eome

chan

ics)

Ret

raso

(Rea

ctive

Tran

sport

Mod

ule)

Yes

Fig. 2RCB solves the integrated equations sequentially inone timestep.

PTop = 1 MPa, TTop = 273.35K

PBottom = 4 MPa, TBottom = 284.15K

1000 m

Injection well400 m

100 m

yxz

Fig. 3Details of the simulation model.




presented in Fig. 4. Tables 4 through 6 present the informationregarding available species in different phases, initial and bound-ary conditions, and material properties, respectively. The systemis closed laterally by mechanical boundary conditions.

Results and Discussion

The simulation results processed by RCB are visualized by use ofGiD visual window (GiD, International Center for NumericalMethods in Engineering, Technical University of Catalonia, Bar-celona, Spain; more information is available at http://gid.cimne.upc.es/). Fig. 4 presents the suitable thermodynamic conditionsfor CO2-hydrate formation according to initial conditions of thereservoir. Figs. 5 through 10 show gas pressure, porosity changes,temperature profile, liquid- and gas-phase fluxes, and liquid satura-tion, respectively, after 1, 100, 500 and 1,000 days. Porositychanges caused by the hydrate-formation process start after 54days and below the original possible zone of Fig. 4, and extend toregions above this zone. This can be explained by the pressure pro-file presented in Fig. 5. According to pressure increase in andabove the injection zone, thermodynamic conditions for hydrateformation are achieved outside the initial region.

The exothermic enthalpy of hydrate formation appears as tem-perature increase near Day 500, as demonstrated in Fig. 7. Itaffects the hydration process. According to Fig. 6, the porosity inthe area where temperature increase is noticeable has decreasedless than that in the upper area.

Both liquid- and gas-phase flux figures show the effect of po-rosity change on the flow. This is more obvious in Fig. 9, wheresome scattered pattern of flow is found after 500 days in theregion where hydrate formation has happened. The impact of dif-ferent phase transitions on the local permeability calls for devel-opment of new permeability correlations as well as new strategiesfor efficient CO2 injection.

It should be mentioned that geomechanics have not been afocus for this paper, but received more attention in the form of aneffective-stress profile in other publications on hydrates from thesame simulator (Kvamme et al. 2011).

TABLE 4AQUIFER, ROCK, AND HYDRATE PROPERTIES

Youngs modulus (GPa) 0.5

Poissons ratio 0.25

Zero-stress porosity 0.1

Zero-stress permeability (m2) 1.01013Van Genuchtens gas-entry pressure

(at zero stress) (kPa)

196

Van Genuchtens exponent 0.457

Thermal conductivity of dry

medium [W/(mK)]0.5

Thermal conductivity of saturated

medium [W/(mK)]3.1

Solid-phase density (kg/m3) 2163

Rock specific heat [J/(kgK)] 874CO2-hydrate molecular weight (g/mol) 147.5

CO2-hydrate density (kg/m3) 1100

CO2-hydrate specific heat [J/(kgK)] 1,376CO2-hydrate reaction enthalpy (J/mol) 51,858

CO2-hydrate kinetic formation rate constant

(mol/Pam2s)1.4411012

Hydrate stable region170 m

290 m

Fig. 4Thermodynamically suitable area for CO2-hydrate for-mation, according to initial conditions of the reservoir.

TABLE 5CHEMICAL SPECIES IN THE MEDIA

Phase Species

Aqueous H2O, HCO3, OH, H, CO2 (aq), CO3

2

Gas CO2(g)

TABLE 6INITIAL AND BOUNDARY CONDITIONS

Pressure at the top (MPa) 1.0

Pressure at the bottom (MPa) 4.0

Temperature at the top (K) 273.35

Temperature at the bottom (K) 284.15

Initial mean stress at the top (MPa) 2.33

Initial mean stress at the bottom (MPa) 8.76

CO2-injection pressure (MPa) 4.0

Pres.

4.00033.66693.33363.00022.66682.33352.00011.6667

1.33341

y

xz

Fig. 5Gas pressure (MPa) after 1, 100, 500, and 1,000 days.

Porosity0.10.0999220.0998440.0997670.0996890.0996110.0995330.0994560.0993780.0993

y

xz

Fig. 6Porosity after 1, 100, 500, and 1,000 days.




Conclusion

A new hydrate simulator is developed on the basis of the availablereactive-transport code of RCB. It consists of a system of threephases including solid phase (mineral), liquid phase (water and dis-solved gas), and gas phase (CO2 and water vapor). Three compo-nents (water, CO2, and heat) are considered in the balance

equations. Hydrate is defined as a pseudomineral, meaning thatalthough it is considered as part of the solid phase, regarding theenergy balance it is considered independently for both internalenergy and reaction enthalpy. At this stage, heat-transport proper-ties of hydrate are not considered as different from solid phase. Thekinetic approach is used in this study, and the kinetic rates obtainedfrom PFT simulations are used. Because of the nonequilibrium na-ture of hydrate in the reservoir, the ultimate purpose is to study thedynamics of hydrate in the reservoir by considering all possiblephase-transition scenarios. The reactive-transport module in thissimulator along with the hydrate definition in the system as a pseu-domineral gives this opportunity to reach this goal by coupling thecode with a nonequilibrium thermodynamic module.

The main purpose of this paper has been to discuss the generalconcept, not to demonstrate all features that will be opened up byit. One example that will be implemented next is the reaction ofhydrate with pure water (or, groundwater with some salinity),which results in dissociation of hydrates caused by undersaturatedwater. This will contribute substantially to dissociation of hydratein initial stagesmaybe even more than pressure reduction atthese stages in reservoirs without underlying gas phase. Otherexamples are refreezing of hydrate caused by cooling, which canbe very complex and can consist of significant hydrate formationfrom several phases (heterogeneous hydrate nucleation fromadsorbed hydrate former on mineral surfaces are favorable, as arehydrate formation from aqueous solution and from water/hydrate-former interface). These different phase transitions have funda-mentally different kinetic rates. Hydrate formation from solutionis mainly mass-transport controlled and characterized by a Ficks-type law. Interface formation is complex because of competitions

Temperature17.79815.84313.88711.9329.97678.02136.0664.11072.15530.2

y

xz

Fig. 7Temperature (C) after 1, 100, 500, and 1,000 days.

|Liq Ph. Flux|5e074.4446e073.8891e073.3337e072.7782e072.2228e071.6673e071.1119e075.5644e081e10

|Liq Ph. Flux|5e084.4456e083.8911e083.3367e082.7822e082.2278e081.6733e081.1189e085.6444e091e10

y

xz

y

xz

Fig. 8Liquid-phase flux (m/s) after 1, 100, 500, and 1,000 days (for better illustration, the color range for the two top figures is dif-ferent from that of the two bottom ones).




of different cores when the interface closes in by the hydrate.Hydrate formation from adsorbed hydrate-former is very fast innucleating and might produce many active nuclei for rapidgrowth. None of these features are possible in existing hydratecodes, and they are not currently implemented in RCBbut workis in progress.

Nomenclature

aPmki catalytic effectAs surface area, L2, m2b vector of body force per unit volume, ML2T2,

Nm3C concentration, NL3, molm3

Ea,m activation energy, ML2T2N1, Jmol1Ei internal energy per unit mass in solid (is), liquid

(il), and gas (ig) phase, L2T2, Jkg1f fugacity, ML1T2, Pafa supply term for gas component a, ML3T1,

kgm3s1fe fugacity, ML1T2, PafQ internal/external energy supply, ML1T3, Jm3s1fW external supply of water, ML3T1, gm3s1F degree of freedom in phase ruleg gravity acceleration, LT2, ms2G molar Gibbes free energy, ML2T2N1, kgm2s2mol1H molar enthalpy, ML2T2N1, kgm2s2mol1

H(id,gas) molar enthalpy of ideal gas, ML2T2N1,kgm2s2mol1

ic conduction energy flux, MT3, Jm2s1jEi advective energy flux in solid (is), liquid (il) and

gas (ig) phase, MT3, Jm2s1j0ag mass flux of gas component a in gas phase, ML2T1,

kgm2s1j0al mass flux of gas component a in liquid phase,

ML2T1, kgm2s1jwg mass flux of water in gas phase, ML2T1, kgm2s1jwl mass flux of water in liquid phase, ML2T1,

kgm2s1js flux of solid, ML2T1, kgm2s1kd kinetic rate constant, NM1TL1, molPa1m2s1kmk experimental rate constant, NL2T1, molm2s1kra relative permeabilityK equilibrium constantn shape factor

nH number of hydrate moles, N, moleN number of components in phase rule

Pf partial pressure of the fth species in the gas phase,ML1T2, Pa

P pressure, ML1T2, Paqa advective flux of volumetric flow in liquid (al) and

gas (ag) phase, LT1, ms1rm mineral dissolution rate, NL3T1, molm3s1R gas constant, ML2T2N1I1, gm2s2m11K11Sg gas saturationSl liquid saturationt time, T, sT temperature, I, Ku solid displacement, L, mxw composition of waterc activity coefficienthag mass of gas component per unit volume in gas phase,

ML3, kgm3hal mass of gas component per unit volume in liquid

phase, ML3, kgm3hwg mass of water per unit volume of gas in gas phase,

ML3, kgm3hwl mass of water per unit volume of liquid in liquid phase,

ML3, kgm3hs mass of solid per unit volume of solid, ML3, kgm3l chemical potential, ML2T2N1, kgm2s2mol1la viscosity of liquid (al) and gas (ag) phase,

ML1T1, Pasv stoichiometric coefficient

nm factor to determine mineral precipitation (l) or disso-lution (l)

p number of phases in phase ruleqi density in solid (is), liquid (il), and gas (ig)

phase, ML33, kgm3r stress, ML1T2, Pa

rm reactive surface, L1, m2m3/ porosityU fugacity coefficientXm ratio of the ion-activity product for the real concentra-

tions to the corresponding equilibrium constant

Acknowledgments

We acknowledge the grant and support from Research Council ofNorway through the following projects: SSC-Ramore, Subsurfacestorage of CO2Risk assessment, monitoring and remediation,project No. 178008/I30; FME-SUCCESS, project No. 804831; andPETROMAKS, CO2 injection for extra production, ResearchCouncil of Norway, project No. 801445.

|Gas Ph. Flux|5.396e054.7964e054.1969e053.5973e052.9978e052.3982e051.7987e051.1991e055.9956e060

y

xz

Fig. 9Gas-phase flux (m/s) after 1, 100, 500, and 1,000 days.

Liq. Sat.10.919110.838210.757320.676420.595530.514630.433740.352840.27195

y

xz

Fig. 10Liquid saturation after 1, 100, 500, and 1,000 days.




References

Ahmadi, G., Ji, C. and Smith, D.H. 2004. Numerical Solution for Natural

Gas Production from Methane Hydrate Dissociation. J. Pet. Sci. Eng.

41 (4): 269285. http://dx.doi.org/10.1016/j.profnurs.2003.09.004.

ANSYS FLUENT. 2013. http://www.ansys.com/Products/Simulation+

Technology/Fluid+Dynamics/Fluid+Dynamics+Products/ANSYS+Fluent

(accessed November 24, 2013).

Baig, K. 2009. Phase Field Theory Modeling of CH4 and CO2 Fluxes from

Exposed Natural Gas Hydrate Reserviors. MS thesis, University of

Bergen, Bergen, Norway (October 2009).

Buanes, T., Kvamme, B. and Svandal, A. 2006. Computer Simulation of

CO2 Hydrate Growth. J. Cryst. Growth 287 (2): 491494. http://dx.doi.org/10.1016/j.jcrysgro.2005.11.074.

Buanes, T., Kvamme, B. and Svandal, A. 2009. Two Approaches for Mod-

elling Hydrate Growth. J. Math. Chem. 46 (3): 811819. http://

dx.doi.org/10.1007/s10910-009-9551-3.

Burshears, M., OBrien, T.J. and Malone, R.D. 1986. A Multi-Phase, Multi-

Dimensional, Variable Composition Simulation of Gas Production From a

Conventional Gas Reservoir in Contact With Hydrates. Paper SPE 15246

presented at the SPE Unconventional Gas Technology Symposium, Louis-

ville, Kentucky, 1821 May. http://dx.doi.org/10.2118/15246-MS.

Collett, T. 2009. The Promise of Methane Hydrates. Oral testimony given

before the US Department of the Interior, Subcommittee on Energy

and Mineral Resources, Oversight Hearing on Unconventional Fuels,

Part II: The Promise of Methane Hydrates, Washington, DC, 30 July.

Computer Modelling Group. 2013. STARS - Advanced Processes & Ther-

mal Reservoir Simulator. http://www.cmgl.ca/software/soft-stars

(accessed November 24, 2013).

Davie, M.K. and Buffett, B.A. 2001. A Numerical Model for the Forma-

tion of Gas Hydrate Below the Seafloor. J. Geophys. Res. 106 (B1):497514. http://dx.doi.org/10.1029/2000JB900363.

Gamwo, I.K. and Liu, Y. 2010. Mathematical Modeling and Numerical

Simulation of Methane Production in a Hydrate Reservoir. Ind. Eng.Chem. Res. 49 (11): 52315245. http://dx.doi.org/10.1021/ie901452v.

Goel, N., Wiggins, M. and Shah, S. 2001. Analytical Modeling of Gas Re-

covery from In Situ Hydrates Dissociation. J. Pet. Sci. Eng. 29 (2):

115127. http://dx.doi.org/10.1016/S0920-4105(01)00094-8.

Graue, A., Kvamme, B., Baldwin, B., et al. 2008. MRI Visualization of

Spontaneous Methane Production From Hydrates in Sandstone Core

Plugs When Exposed to CO2. SPE J. 13 (2): 146152. http://

dx.doi.org/10.2118/118851-PA.

Hellevang, H. and Kvamme, B. 2007. An Explicit and Efficient Algorithm

to Solve Kinetically Constrained CO2-Water-Rock Interactions. Proc.,

3rd WSEAS International Conference on Mathematical Biology and

Ecology, Gold Coast, Queensland, Australia, 1719 January.

Holder, G. and Angert, P. 1982. Simulation of Gas Production From a

Reservoir Containing Both Gas Hydrates and Free Natural Gas. Paper

SPE 11105 presented at the SPE Annual Technical Conference and

Exhibition, New Orleans, Louisiana, 2629 September. http://

dx.doi.org/10.2118/11105-MS.

Hong, H. and Pooladi-Darvish, M. 2005. Simulation of Depressurization

for Gas Production From Gas Hydrate Reservoirs. J. Cdn. Pet. Tech.

44 (11): 3946. http://dx.doi.org/10.2118/05-11-03.

Hong, H., Pooladi-Darvish, M. and Bishnoi, P.R. 2003. Analytical Model-

ing of Gas Production from Hydrates in Porous Media. J. Cdn. Pet.

Tech. 42 (11): 4556. http://dx.doi.org/10.2118/03-11-05.

Kim, H.C., Bishnoi, P.R., Heidemann, R.A., et al. 1987. Kinetics of Meth-

ane Hydrate Decomposition. Chem. Eng. Sci. 42 (7): 16451653.

http://dx.doi.org/10.1016/0009-2509(87)80169-0.

Kivela, P.-H., Baig, K., Qasim, M., and Kvamme, B. 2012. Phase field

theory modeling of methane fluxes from exposed natural gas hydrate

reservoirs. AIP Conference Proceedings 1504: 351363. http://dx.doi.org/10.1063/1.4771728.

Koide, H., Takahashi, M., Shindo, Y., et al. K. 1997. Hydrate Formation

in Sediments in the Sub-Seabed Disposal of CO2. Energy 22 (23):

279283. http://dx.doi.org/10.1016/S0360-5442(96)00122-3.

Kvamme, B., and Kuznetsova, T. 2010. Investigation into Stability and

Interfacial Properties of CO2 Hydrate-Aqueous Fluid System. Math.

Comput. Model. 51 (34): 156159. http://dx.doi.org/10.1016/j.mcm

.2009.08.007.

Kvamme, B. and Liu, S. 2008a. Reactive Transport of CO2 in Saline Aqui-

fers with Implicit Geomechanical Analysis. Proc., International Confer-

ence on Greenhouse Gas Control Technologies, Washington, DC.

Kvamme, B. and Liu, S. 2008b. Simulating Long Term Reactive Transport

of CO2 in Saline Aquifers with Improved Code RetrasoCodeBright.

Oral presentation given at the 12th International Conference of Inter-

national Association for Computer Methods and Advances in Geome-

chanics, Goa, India, 16 October.

Kvamme, B. and Tanaka, H. 1995. Thermodynamic Stability of Hydrates

for Ethane, Ethylene, and Carbon Dioxide. J. Phys. Chem. 99 (18):71147119. http://dx.doi.org/10.1021/j100018a052.

Kvamme, B., Buanes, T. and Kuznetsova, T. 2006a. Kinetics of Hydrate

Growth on the CO2/Aqueous Solution Interface. WSEAS Trans. HeatMass Transfer 1 (5): 612617.

Kvamme, B., Graue, A., Buanes, T., et al. 2009. Effects of Solid Surfaces

on Hydrate Kinetics and Stability. Geol. Soc. London Special Publica-tion 319: 131144. http://dx.doi.org/10.1144/SP319.11.

Kvamme, B, Graue, A., Kuznetsova, T., et al. 2006b. Exploitation of Nat-

ural Gas Hydrate Reservoirs Combined with Long-Term Storage of

CO2. WSEAS Trans. Environ. Dev. 2 (6): 699710.

Kvamme, B., Graue, A., Kuznetsova, T., et al. 2007. Storage of CO2 in

Natural Gas Hydrate Reservoirs and the Effect of Hydrate as an Extra

Sealing in Cold Aquifers. Int. J. Greenh. Gas Con. 1 (2): 236246.

http://dx.doi.org/10.1016/S1750-5836(06)00002-8.

Kvamme, B., Jemai, K., Chejara, A., et al. 2011. Simulation of Geome-

chanical Effects of CO2 Injection in Cold Aquifers with Possibility of

Hydrate Formation. Proc., 7th International Conference on Gas

Hydrates, Edinburgh, Scotland, United Kingdom, July 1721.

Kvamme, B., Kuznetsova, T., Kivel, P.-K., et al. 2013. Can Hydrate

Form in Carbon Dioxide from Dissolved Water? Phys. Chem. Chem.Phys. (in press; published online 28 November 2012). http://

dx.doi.org/10.1039/C2CP43061D.

Kvamme, B., Kuznetsova, T. and Kivel, P-H. 2012. Adsorption of Water

and Carbon Dioxide on Hematite and Consequences for Possible

Hydrate Formation. Phys. Chem. Chem. Phys. 14 (13): 44104424.http://dx.doi.org/10.1039/C2CP23810A.

Kvamme, B., Kuznetsova, T. and Uppstad, D. 2009. Modeling Excess Sur-

face Energy in Dry and Wetted Calcite Systems. J. Math. Chem. 46(3): 756762. http://dx.doi.org/10.1007/s10910-009-9548-y.

Kvamme, B., Qasim, M., Baig, K., Kivel, P.-H., Bauman, J. In press.

Hydrate Phase Transition Kinetics from Phase Field Theory With

Implicit Hydrodynamics and Heat Transport. International Journal of

Greenhouse Gas Control (submitted August 21, 2013).

Lawrence Berkeley National Laboratory. 2013. TOUGH. http://esd.lbl.-

gov/research/projects/tough/ (accessed November 24, 2013).

Liu, Y., Strumendo, M. and Arastoopour, H. 2008. Simulation of Methane Pro-

duction from Hydrates by Depressurization and Thermal Stimulation. Ind.Eng. Chem. Res. 48 (5): 24512464. http://dx.doi.org/10.1021/ie8005275.

Moridis, G.J. 2003. Numerical Studies of Gas Production from Methane

Hydrates. SPE J. 8 (4): 359370. http://dx.doi.org/10.2118/87330-PA.

Nazridoust, K. and Ahmadi, G. 2007. Computational Modeling of Meth-

ane Hydrate Dissociation in a Sandstone Core. Chem. Eng. Sci. 62(22): 61556177. http://dx.doi.org/10.1016/j.ces.2007.06.038.

National Energy Technology Laboratory (NETL). 2013. HydrateResSim.

http://www.netl.doe.gov/technologies/oil-gas/FutureSupply/Methane-

Hydrates/rd-program/ToughFX/ToughFx.html#HydrateResSim.

Olivella, S., Gens, A. and Carrera, J. 1997. CodeBright Users Guide. Uni-

versitat Politecnica de Catalunya and Instituto de Ciencias de la Tierra,

Barcelona, Spain.

Olivella, S., Gens, A., Carrera, J., et al. 1996. Numerical Formulation for a

Simulator (CODE_BRIGHT) for the Coupled Analysis of Saline

Media. Eng. Computation 13 (7): 87112. http://dx.doi.org/10.1108/

02644409610151575.

Olivella, S., Carrera, J., Gens, A., et al. 1994. Nonisothermal Multiphase

Flow of Brine and Gas through Saline Media. Transport Porous Med.

15 (3): 271293. http://dx.doi.org/10.1007/BF00613282.

Phirani, J. and Mohanty, K. 2010. Kinetic Simulation of CO2 Flooding of

Methane Hydrates. Paper SPE 134178 presented at SPE Annual Tech-

nical Conference and Exhibition, Florence, Italy, 1922 September.

http://dx.doi.org/10.2118/134178-MS.




Qasim, M., Kvamme, B. and Baig, K. 2011. Phase Field Theory

Modeling of CH4/CO2 Gas Hydrates in Gravity Fields. Int. J. Geol. 5(2): 4852.

Saaltink, M., Batlle, M. and Ayora, C. 2004. RETRASO, a Code for Mod-

eling Reactive Transport in Saturated and Unsaturated Porous Media.

Geologica Acta 2 (3): 235251.Saaltink, M., Benet, I. and Ayora, C. 1997. RETRASO, a FORTRAN

Code for Solving 2D Reactive Transport of Solutes, Users Guide.

Barcelona, Spain: Universitat Politecnica de Catalunya and Instituto

de Ciencias de la Tierra.

Sun, X. and Mohanty, K.K. 2006. Kinetic Simulation of Methane Hydrate

Formation and Dissociation in Porous Media. Chem. Eng. Sci. 61 (11):34763495. http://dx.doi.org/10.1016/j.ces.2005.12.017.

Svandal, A. 2006. Modeling Hydrate Phase Transitions Using Mean-Field

Approaches. PhD dissertation, University of Bergen, Bergen, Norway

(February 2006).

Svandal, A. and Kvamme, B. 2009. Modeling the Dissociation of Carbon

Dioxide and Methane Hydrate using the Phase Field Theory. J. Math.

Chem. 46 (3): 763769. http://dx.doi.org/10.1007/s10910-009-9545-1.Svandal, A., Kuznetsova, T. and Kvamme, B. 2006a. Thermodynamic Proper-

ties and Phase Transitions in the H2O/CO2/CH4 System.Fluid Phase Equi-libr. 246 (12): 177184. http://dx.doi.org/10.1016/j.fluid.2006.06.003.

Svandal, A., Kvamme, B., Granasy, L., et al. 2006b. The Phase-Field

Theory Applied to CO2 and CH4 Hydrate. J. Cryst. Growth 287 (2):486490. http://dx.doi.org/10.1016/j.jcrysgro.2005.11.071.

Swinkels, W. and Drenth, R.J.J. 2000. Reservoir-Simulation Model of Pro-

duction from Gas-Hydrate Accumulations. SPE Res Eval & Eng 3 (6):559566. http://dx.doi.org/10.2118/68213-PA.

Tegze, G., Granasy, L. and Kvamme, B. 2006a. Phase Field Modeling of

the Conversion of Methane Hydrate into Carbon Dioxide Hydrate.

WSEAS Trans. Biol. Biomed. 3 (7): 532537.

Tegze, G., Pusztai, T., Toth, G., et al. 2006b. Multiscale Approach to CO2Hydrate Formation in Aqueous Solution: Phase Field Theory and Mo-

lecular Dynamics. Nucleation and Growth. J. Chem. Phys. 124 (23):47104721. http://link.aip.org/link/doi/10.1063/1.2207138.

Uddin, M., Coombe, D., Law, D., and Gunter, W. 2006. Numerical Studies of

Gas-Hydrates Formation and Decomposition in a Geological Reservoir.

Presented at the SPE Gas Technology Symposium, Calgary, Alberta, Can-

ada, 1517 May. SPE-100460-MS. http://dx.doi.org/10.2118/100460-MS.

Van Cuong, P., Kvamme, B., Kuznetsova, T., et al. 2012a. Adsorption of

Water and CO2 on Calcite and Clathrate Hydrate: The Effect of Short-

Range Forces and Temperature. Int. J. Energy Environ. 6 (3): 301309.Van Cuong, P., Kvamme, B., Kuznetsova, T., et al. 2012b. Molecular

Dynamics Study of Calcite and Temperature Effect on CO2 Transport and

Adsorption Stability in Geological Formations. Mol. Phys. 110 (1112):10971106. http://dx.doi.org/10.1080/00268976.2012.679629.

Wanga, X., Sainb, K., Satyavanib, N., et al. 2013. Gas Hydrates Saturation

Using Geostatistical Inversion in a Fractured Reservoir in the Krishna-

Godavari Basin, Offshore Eastern India. Mar. Petrol. Geol. 45:

224235. http://dx.doi.org/10.1016/j.marpetgeo.2013.04.024.

Xiao, K., Zou, C., Xiang, B., et al. 2013. Acoustic Velocity Log Numeri-

cal Simulation and Saturation Estimation of Gas Hydrate Reservoir in

Shenhu Area, South China Sea. The Scientific World J. 2013 (2013):113. http://dx.doi.org/10.1155/2013/101459.

Xu, W. 2004. Modeling Dynamic Marine Gas Hydrate Systems. Am. Min-eral. 89 (89): 12711279.

Xu, W. and Ruppel, C. 1999. Predicting the Occurrence, Distribution, and Evo-

lution of Methane Gas Hydrate in Porous Marine Sediments. J. Geophys.Res. 104 (B3): 50815095. http://dx.doi.org/10.1029/1998JB900092.

Yousif, M.H., Abass, H.H., Selim, M.S., et al. 1991. Experimental and Theo-

retical Investigation of Methane-Gas-Hydrate Dissociation in Porous

Media. SPE Res Eng 6 (1): 6976. http://dx.doi.org/10.2118/18320-PA.

Zatsepina, O.Y. and Pooladi-Darvish, M. 2011. Storage of CO2 Hydrate in

Shallow Gas Reservoirs: Pre- and Post-Injection Periods. Greenh. Gas.

Sci. Tech. 1 (3): 223236. http://dx.doi.org/10.1002/ghg.23.

Appendix A

Governing Equations in RCB. The mass balance of solid is

@

@ths1 / r js 0; A-1

where hs is the mass of solid per unit volume of solid, js is theflux of solid, and / is porosity. From Eq. A-1, an expression forporosity variation is obtained as

Ds/Dt

1hs

1 /DshsDt

1 /r du

dt; A-2

where u is solid displacements.The mass balance of water is

@

@thwl Sl/ hwg Sg/ r jwal jwag f w; A-3

where hwl and hwg are mass of water per unit volume of liquid in

the liquid phase and mass of water per unit volume of gas inthe gas phase, respectively; Sl and Sg are degree of saturation ofliquid and gas phases (i.e., fraction of pore volume occupied byeach phase), respectively; jwl and j

wg are mass flux of water in liq-

uid and gas phase, respectively; and f w is the external supply ofwater that also includes water from hydrate.

The mass balance of gas is

@

@thal Sl/ hagSg/ r j0al j0ag f a; A-4

where hal and hagare mass of gas component (CH4, CO2,..) per unit

volume in liquid and gas phase, respectively; j0al and j0ag are mass

flux of gas component a in liquid and gas phase relative to thesolid phase, respectively; and f a is a supply term that, similar towater phase, also considers hydrate formers from hydrate phase.

Momentum Balance of the Medium. The momentum balancereduces to the equilibrium of stresses if the inertial terms areneglected:

r r b 0; A-5where r is the stress tensor and b is the vector of body force.

The Internal-Energy Balance of the Medium. The equation forinternal-energy balance for the porous medium is established bytaking into account the internal energy in each phase (Es, El, Eg):

@

@tEsqs1 / ElqlSl/ EgqgSg/ r ic jEs jEl jEg f Q; A-6

where ic is energy flux caused by conduction through the porousmedium; the other fluxes (jEs; jEl; jEg) are advective fluxes ofenergy caused by mass motions; and f Q is an internal/externalenergy supply.

Constitutive Equations and Equilibrium Laws. The set of nec-essary constitutive and equilibrium laws as mentioned in Tables 2and 3, respectively, associates the previously discussed balances.Some of the most important of these laws are described here.

Generalized Darcys law is used to compute the advective fluxq of the a phase (a l for liquid, a g for gas). It is expressed as:

qa KkralarPa qag;

A-7where K is the tensor of intrinsic permeability, kra is the relativepermeability of the phase, la is the phases dynamic viscosity(Pas), and g is the gravity vector (ms2).

Van Genuchtens retention curve expressing saturation as afunction of liquid or gas pressure is given by

S 1 Pg PlP0

11 n

8

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