Thermodynamic Simulations of Isobaric Hydrate ... - ACS Publications

Energy & Fuels 2009, 23, 849–856

849

Thermodynamic Simulations of Isobaric Hydrate-Forming Operations for Natural Gas Storage Hiroyuki Ogawa, Naotaka Imura, Tatsuya Miyoshi, Ryo Ohmura, and Yasuhiko H. Mori* Department of Mechanical Engineering, Keio UniVersity, Yokohama 223-8522, Japan ReceiVed September 21, 2008. ReVised Manuscript ReceiVed December 1, 2008

This study is concerned with clathrate hydrate formation from natural gas for its storage and/or transport. During each hydrate-forming operation using an isobaric reactor into which a feed gas (i.e., natural gas with a fixed composition) is continuously supplied, the composition of the gas phase inside the reactor should continuously change as the result of preferential uptake of some species from the gas phase into the hydrate, which should, in turn, affect the subsequent hydrate formation. In a previous paper (Tsuji, H.; Kobayashi, T.; Okano, Y.; Ohmura, R.; Yasuoka, K.; Mori, Y. H. Energy Fuels 2005, 19, 1587-1597), we reported a computational scheme of thermodynamic simulations of such operations and its application to the hydrate formation from a methane + ethane + propane mixture. In the present study, we have extended the scheme to be applicable to a gas mixture composed of an arbitrary number of species and have applied it to methanebased gas mixtures simulating natural gas that may contain traces of hydrocarbons heavier than propane. Our major concern is the effects of such trace components in the feed gas during each long-term hydrate-forming operation. The vapor of some heavy hydrocarbons may accumulate in the gas phase inside the reactor, possibly leading to either the onset of its condensation or a structural transition of the hydrate being formed inside the reactor, which may pose a problem regarding the quality control of the hydrate products. The possibility of the occurrence of such a phase change or hydrate-structural transition is discussed on the basis of thermodynamic simulations.

Introduction Natural gas is a methane-based mixture that generally includes various chemical species, mainly hydrocarbons, such as ethane, propane, and to much lesser proportions, heavier homologues, such as butane and pentane. Non-hydrocarbons, such as nitrogen, carbon dioxide, hydrogen sulfide, and helium, may also be included. Some of these components are known to form clathrate hydrates by themselves or with the help of methane, the primary component of natural gas. Such compositional complexity of natural gas should be carefully taken into account in the process design for hydrate production from natural gas for the purpose of natural-gas storage and/or transport. As in the majority of chemical or material processing operations, it should be more efficient and economical to use continuous operations of equipment for forming the hydrates, with a minimum of interruptions or shutdowns. This means that a hydrate-forming reactor incorporated in the equipment should be operated under an isobaric condition, which could be maintained by a continuous supply of a feed gas (i.e., natural gas with a fixed composition) and a continuous outflow of the hydrate product. It should be noted, however, that such continuous operations with accurate control of the pressure and temperature inside the reactor cannot necessarily be steady operations. During each operation, the composition of the gas phase inside the reactor should continuously change as the result of the preferential uptake of some species from the gas phase into the hydrate, which should, in turn, affect the subsequent hydrate formation. Thus, the multiphase system inside the reactor is generally in an unsteady state at each instant during * To whom correspondence should be addressed. Telephone: +81-45566-1522. Fax: +81-45-566-1495. E-mail: [email protected].

the transient process asymptotically approaching a steady state, at which the chemical composition of the feed gas and that of the guest molecules contained in the hydrate being formed should coincide with each other.1 For the purpose of the process design for industrial hydrate production, we need to know how the system conditions (the gas-phase composition, the guestmolecule composition in the hydrate formed, and the phaseequilibrium temperature at each instant) vary during each operation toward a steady state. Recently, Kobayashi et al.2 experimentally investigated how the gas-phase composition inside a hydrate-forming reactor changes with time, while a gas mixture of methane, ethane, and propane in a 90:7:3 molar ratio is continuously supplied to the reactor to compensate for the gas consumption by hydrate formation, thereby maintaining the pressure inside the reactor at a constant level. Because of a technical problem in their experimental system, however, the duration of each hydrateforming experimental run was limited to about 180 min, in which gas molecules in the amount corresponding to only ∼80% of those initially filling the reactor had been consumed by the hydrate formation. Thus, the results of their study are insufficient as a basis for predicting the evolution of an industrial hydrateforming operation that may continue for weeks, until the total amount of natural gas consumed in the reactor has increased to more than 100 times the amount that the reactor instantaneously holds. If the natural gas in use contains a trace of heavy (1) Mori, Y. H. Recent advances in hydrate-based technologies for natural gas storage-A review. J. Chem. Ind. Eng. (China) 2003, 54 (Supplement). 1-17. (2) Kobayashi, T.; Imura, N.; Ohmura, R.; Mori, Y. H. Clathrate hydrate formation by water spraying in a methane + ethane + propane gas mixture: Search for the rate-controlling mechanism of hydrate formation in the presence of methylcyclohexane. Energy Fuels 2007, 21, 545–553.

10.1021/ef800799q CCC: $40.75  2009 American Chemical Society Published on Web 01/12/2009

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Figure 1. Model of a reactor in use of a continuous hydrate-forming operation.

hydrocarbon species (e.g., isopentane), which may be taken into neither structure-II (sII) nor structure-I (sI) hydrates, the species will be concentrated in the gas phase inside the reactor through such a long-term hydrate-forming operation as mentioned above. A monotonic increase in the fraction of the species in the gas phase should continue until the species undergoes condensation, generating an oily liquid phase, or a structure-H (sH) hydrate starts to form, incorporating molecules of the heavy hydrocarbon species into its 51268 cages. The condensation would necessitate an additional phase-separation process to prevent the condensate from being mixed with the hydrate product. The formation of a sH hydrate would also disturb the uniformity in quality of the hydrate product. Thus, it is necessary for us to have some practical means of predicting at which stage during each hydrateforming operation, such a condensation or sH hydrate formation occurs and how it affects the quality (i.e., the guest-molecule composition) of the hydrate product. We expect that thermodynamics-based simulations will be an effective tool for predicting the evolution of each long-term hydrate-forming operation, possibly including the occurrence of the condensation of some feed-gas component or the structural transition of the hydrate instantaneously formed. The general concept and framework of such simulations are described in detail in our previous paper.3 In that paper, we reported a computational scheme for thermodynamic simulations of hydrate formation from a gas mixture and demonstrated how the scheme predicts the variations in the gas-phase composition and phase-equilibrium temperature during each process of hydrate formation from a methane + ethane + propane mixture. In the present study, we have extended the scheme to enable its application to a gas mixture composed of an arbitrary number of species, including some hydrocarbons heavier than propane. The extended scheme is applied to two natural-gas models each consisting of seven components, including heavy hydrocarbons up to isopentane. The possibility of the occurrence of isopentane condensation or sH hydrate formation and its possible effect on the quality of the hydrate product are our concerns. Description of the Simulation Scheme Modeling and Assumptions. The concept of our thermodynamic modeling of hydrate-forming operations in this study is essentially the same as that previously contrived to perform the simulations of isobaric, continuous, or semibatch hydrate-forming operations.3 For simplicity, continuous operations are exclusively considered in this study. As schematically illustrated in Figure 1, we assume a reactor into which a feed gas (a mixture of seven gaseous hydrateforming substances) and water are continuously supplied, while a (3) Tsuji, H.; Kobayashi, T.; Okano, Y.; Ohmura, R.; Yasuoka, K.; Mori, Y. H. Thermodynamic simulations of isobaric hydrate-forming operations: Formulation of computational scheme and its applications to hydrate formation from a methane + ethane + propane mixture. Energy Fuels 2005, 19, 1587–1597.

Ogawa et al. hydrate formed there is instantaneously removed from the reactor in the form of a slurry (i.e., a mixture of hydrate crystals and an aqueous solution containing dissolved gases). The hydrate slurry is then separated into a dry hydrate product and the aqueous solution in a separator (or a separator plus a hydrate pelletizer,4,5 wherein the hydrate slurry pre-dewatered in the separator is to be squeezed). The aqueous solution is recirculated into the reactor. The rates of the feed gas and fresh water flowing into the reactor are controlled such that the total mole number of the feed-gas components and that of water instantaneously confined in the reactor are held constant, respectively. The pressure inside the reactor is held constant at a prescribed level. The assumption of the instantaneous discharge of the formed hydrate from the reactor may need some annotation. If the hydrates formed at the as-yet unsteady stages during a continuous hydrateforming operation remain inside the reactor for some duration, they may subsequently interact with the gas phase in the reactor, thereby restructuring themselves and affecting the subsequent compositional evolution of the gas phase. Presumably, the rate of such a hydratecrystal restructuring is sufficiently low, and hence, the abovementioned effects of the remaining hydrates are insignificant. To better define our model for simulations, however, we introduce the assumption of the null residence time of the formed hydrates inside the reactor and exclude any possibility of their effects on the subsequent gas-phase evolution. The entirety of the contents of the reactor is assumed to be an open thermodynamic system, in which only an infinitesimal amount of a hydrate always coexists with the gas and liquid phases. This system is evolved through a quasistatic irreVersible process6 because of the in- and outflow of substances depending upon the hydrate formation inside it, while maintaining itself in a nearequilibrium state at each instant. The quasistatic irreversible process covering the entire hydrate-forming operation is regarded as a series of discrete equilibrium states, with each only slightly deviating from its neighboring states. The transition from one equilibrium state to the next occurs as a result of a slight change in the composition of the gas phase, which is in turn caused by the in- and outflow of substances in sufficiently small amounts compared to their total amounts held inside the system. Each equilibrium state may be specified with the aid of an appropriate phase-equilibrium calculation program (abbreviated as PECP hereafter) applicable to hydrateforming systems. In specifying each equilibrium state, we make it a condition that only a hydrate of a particular structure (sI, sII, or sH) with which the highest equilibrium temperature corresponding to the prescribed system pressure is predicted by the PECP should actually form. Phase-Equilibrium Calculation Programs. In this study, we tested three commercially available PECPs, CSMHYD,7 HWHydrate,8 and CSMGem,9 for their applicability to our simulations dealing with seven-component natural gas models. Although CSMHYD was successfully used in our previous simulation studies dealing with hydrate formation from binary or ternary mixtures of (4) Iwasaki, T.; Katoh, Y.; Nagamori, S.; Takahashi, S.; Oya, N. Continuous natural gas hydrate pellet production (NGHP) by process development unit (PDU). Presented at the 5th International Conference on Gas Hydrates, Trondheim, Norway, June 13-16, 2005; paper 4003, pp 1107-1115. (5) Takahashi, M.; Moriya, H.; Katoh, Y.; Iwasaki, T. Development of natural gas hydrate (NGH) pellet production system by bench scale unit for transportation and storage of NGH pellet. Presented at the 6th International Conference on Gas Hydrates, Vancouver, Canada, July 610, 2008; paper P-166 (5566). (6) Kestin, J. A Course in Thermodynamics; Xerox College Publishing: Waltham, MA, 1966; Section 4.6. (7) CSMHYD, a phase-equilibrium calculation program package accompanying the following book: Sloan, E. D., Jr. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Decker, Inc.: New York, 1998. (8) HWHydrateGUI (version 1.1), a phase-equilibrium calculation program developed at the Centre for Gas Hydrate Research, Heriot-Watt University, Edinburgh, U.K., 2005. (9) CSMGem, a phase-equilibrium calculation program package accompanying the following book: Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2007.

Simulations of Hydrate-Forming Operations

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Figure 2. Conceptual illustration of the “serial equilibrium states” model for a continuous hydrate-forming operation. Each rectangular box denotes the multiphase hydrate-forming system confined in a reactor. The horizontal arrows indicate the stepwise evolution of the state of the system, while the vertical arrows indicate the flows of substances to or from the system relevant to the transition of the system from the ith to (i + 1)th equilibrium states.

methane, ethane, and propane,3,10 we noticed that this program fails to function when isopentane, the heaviest hydrocarbon component in the above natural gas models, is so concentrated in the gas phase as to approach its vapor-liquid equilibrium condition. Such failure was not found with HWHydrate and CSMGem. Thus, we selected these two PECPs for alternative use in our simulations, expecting that we can crosscheck the results of simulations based on either PECP by those based on the other PECP. Algorithm for Simulations. According to the “serial equilibrium states” model described above, we assume each hydrate-forming operation to be composed of a series of the equilibrium states (numbered 0, 1, 2,..., i,...) established by turns in the system, the entirety of the contents of the reactor consisting of the feed-gascomponent substances (numbered 0, 1, 2,..., j,..., m) and water. Figure 2 shows a conceptual illustration of the evolution of the system for the transition from one equilibrium state (say the ith state) to the next [the (i + 1)th state]. It is assumed that we know the number of molecules of each substance confined in the system, i.e., Nj,i for each feed-gas component substance and Nw for water, when the system is subjected to the equilibration toward the ith equilibrium state under a prescribed pressure p. (Note that ∑jNj,i and Nw are invariable with i and should be prescribed for each hydrate-forming operation to be simulated.) Once Nj,i, Nw, and p are specified,11 we can predict, based on a gas/liquid flash calculation using a PECP, the mole-based proportion between the gas and liquid phases as well as the chemical composition of each phase when these fluid phases are in equilibrium with a hydrate in each of the three crystallographic structures (sI, sII, and sH). The equilibrium temperature Teq,i corresponding to each hydrate structure is also predicted. Here, we employ the predictions relevant to the hydrate structure giving the highest equilibrium temperature. The compositions of each phase may be expressed in terms of the mole fraction of each feed-gas component substance defined as m

xj,gas,i ≡ Nj,gas,i /

∑N

j,gas,i

(1)

j,liq,i

(2)

j)1

for the gas phase and

for the liquid phase, where Nj,gas,i denotes the number of molecules of substance j in the gas phase and Nj,liq,i denotes that in the liquid phase. From the above quantities given by the flash calculation, we can readily determine Nj,gas,i and Nj,liq,i as well as the number of water molecules in the gas phase, Nw,gas,i, and that in the liquid phase, Nw,liq,i. At the same time, we can predict, using the PECP, the guest-molecule composition of the hydrate that would be in equilibrium with the gas and liquid phases specified above. The guest-molecule composition of this hydrate may be specified in terms of the mole fraction of each substance defined as m

xj,hyd,i ≡ Nj,hyd,i /

∑N

j,hyd,i

(3)

j)1

where Nj,hyd,i is the number of guest molecules of substance j in this hydrate. We then assume that this hydrate is formed, consuming a minute fraction δ of the total number of the feed-gas-originated molecules in the gas phase. That is, the number of molecules of substance j fixed in the hydrate and hence lost from the gas phase is given by m

Nj,hyd,i ) xj,hyd,i δ

∑N

j,gas,i

(4)

j)1

For convenience in rearranging the contents of the system to be ready for the flash calculation for the next equilibrium state, we assume that the hydrate thus formed, the residual aqueous phase, and the water vapor in the gas phase are entirely removed from the system, leaving only a water-free gas mixture inside the system. This means that the molecules counted by Nj,liq,i, Nw,liq,i, Nw,gas,i, Nj,hyd,i, and Nw,hyd,i are all taken out of the system, where Nw,hyd,i denotes the number of water molecules contained in the hydrate. It should be noted, however, that Nj,liq,i is then fed back into the system (see Figure 2) to count the recirculation of the feed-gasoriginated substances dissolved in the aqueous solution, which is once discharged from the reactor (see Figure 1). The system is then

m

xj,liq,i ≡ Nj,liq,i /

∑N j)1

(10) Kobayashi, T.; Mori, Y. H. Thermodynamic simulations of hydrate formation from gas mixtures in batch operations. Energy ConVers. 2007, 48, 242–250.

(11) HWHydrate does not allow us to directly specify the system pressure p in performing each phase-equilibrium calculation. The system pressure is determined as the result of each phase-equilibrium calculation corresponding to a given temperature T. Thus, an iterative calculation procedure is required to make the calculated system pressure agree with the prescribed system pressure p and to determine the equilibrium state corresponding to the prescribed pressure p.


Ogawa et al.

charged with the feed gas in the amount of ∑jNj,in,i and fresh water in the amount of Nw. ∑jNj,in,i is adjusted to be equal to ∑jNj,hyd,i, the net loss of the feed-gas-originated molecules from the system due to the discharge of the hydrate. The amount of each substance contained in the above supply of the feed gas is simply given by m

Nj,in,i ) xj,feed

∑N

j,in,i

(5)

j)1

where xj,feed,i denotes the mole fraction of substance j in the feed gas. As for water, the loss of Nw,liq,i and, although much less in the amount, Nw,gas,i from the system may appear to be inconsistent with the reactor model illustrated in Figure 1, in which the water inside the reactor is never flushed away but is lost only partially through the formation and discharge of the hydrate. This apparent inconsistency is merely due to the algorithmic convenience in using the PECP. In the system-operational practice, we should regard Nw, the nominal amount of the fresh-water supply (Figure 2), to be the sum of Nw,liq,i, Nw,gas,i, and the amount of the actual supply of fresh water to the system, Nw,in,i, which should be equal to Nw,hyd,i. As the result of the mixing of the residual gases (∑jNj,gas,i) with the feed gas newly supplied (∑jNj,in,i), the number of molecules of each feed-gas-originated substance in the system is changed to Nj,i+1 () Nj,gas,i + Nj,in,i) as indicated in Figure 2. Again, a flash calculation is applied to the system at this stage to determine the next equilibrium state. For simulating the evolution of each hydrate-forming operation, we need to start the calculation procedure outlined above by specifying Nj,0 (Nj,i at i ) 0), the initial amount of each feed-gas component inside the system, with which the first flash calculation is to be made to determine the first equilibrium state. The value of Nj,0 is simply given as follows: m

Nj,0 ) xj,feed

∑N

j,i

(6)

j)1

where ∑jNj,i is, as already noted, an invariable that we can arbitrarily prescribe in relation to the other invariable, Nw. In practice, we can define the scale of the hydrate-forming system as desired by arbitrarily adjusting ∑jNj,i and Nw. It should be noted that the variation of any intensive quantity characterizing each equilibrium state (e.g., xj,gas,i, the hydrate structure, xj,hyd,i, or Teq,i) with an increasing i is not dependent upon the scale of the system but the fraction of water in the system defined as

Xw )

Nw m

Nw +

∑N

(7)

j,i

j)1

as well as the system pressure p and the feed-gas composition. The specification of these three parameters is described in the next subsection. In the above description of the simulation algorithm, we have omitted, for the sake of simplicity, the explanation of how we can cope with the possible formation of a hydrocarbon-rich liquid phase. Once isopentane, the heaviest hydrocarbon component of the feed gas, condenses inside the system as the result of its partial pressure in the gas phase increasing to the saturation pressure, there should appear a hydrophobic liquid phase composed not only of the isopentane condensate but also of the other feed-gas components and water physically dissolved into the condensate. The mole-based proportion of this liquid phase in the system as well as its composition is given by the flash calculation at each equilibrium state. We assume that this liquid phase is discharged, together with the hydrate product, from the system and is not recirculated to the system. It turns out from this assumption that, if the flash calculation for the ith equilibrium state predicts the formation of a hydrophobic liquid phase, ∑jNj,in,i needs to be adjusted to the sum of ∑jNj,hyd,i

Table 1. Compositions of Two Natural-Gas Models Alternatively Used as the “Feed Gas” in the Simulations mole fraction xj,feed × 100 component

gas model A

gas model B

j ) 1 methane 2 ethane 3 propane 4 isobutane (methylpropane) 5 butane 6 isopentane (2-methylbutane) 7 nitrogen

88.89 7.00 3.00 0.50 0.50 0.10 0.01

88.97 7.00 3.00 0.50 0.50 0.02 0.01

and the loss of the feed-gas-originated molecules due to the discharge of the liquid phase. Specification of Feed-Gas Composition, Operational Conditions, and Practice of Simulations. Concerning the feed gas, we have prepared two natural-gas models as specified in Table 1. Either model assumes a mixture of seven substances: six hydrocarbon components plus a trace of nitrogen. The two models are different from each other only in the fraction of isopentane, the heaviest hydrocarbon component. The system pressure p is set at 5.5 MPa, following the operation plan for the 5 ton/day hydrateforming plant, which was recently constructed at Yanai, Yamaguchi prefecture, Japan, in a joint project of Mitsui Engineering and Shipbuilding Co., Ltd. and Chugoku Electric Power Co., Inc.12 and will be put into test operations during the first quarter of the year 2009. The mole fraction of water in the system, Xw, may significantly vary in real hydrate-forming operations, depending upon the geometrical and functional design of the reactors used and the operational conditions, such as the system pressure p. The mole fraction Xw is typically as high as 0.90-0.99 in the case of using a vessel-type reactor that holds an aqueous-liquid pool, into which a feed gas is bubbled (see, for example, refs 4, 5, and 12) or from which the liquid is continuously drained out to be cooled in an external heat exchanger and then injected into the gas phase above the pool in the reactor (e.g., ref 2). If the aqueous phase occupies 60% of the entire volume of a reactor in which the pressure and temperature are controlled at 5.5 MPa and 277 K, respectively,12 it turns out that Xw ≈ 0.97. (Note that, if the reactor is equipped with a liquid- or gas-circulation loop, its internal volume should be counted in the “entire volume” of the reactor.) Thus, we have prescribed Xw to be 0.97 in the simulations demonstrated below. The numerical precision of the simulations should increase with a decrease in δ, the parameter relevant to the advancement of stepwise calculations in each simulation (eq 4), at the cost of an increase in the computation time required for completing each simulation. As a reasonable compromise between the numerical precision and the computation time, we set δ to 0.01. This means that feed-gas-originated molecules equal in amount to those instantaneously filling the gas phase inside the reactor are taken into the hydrate product during each process covering 100 successive equilibrium states, say, from the initial equilibrium state (i ) 0) to the 100th equilibrium state (i ) 100).

Results of Simulations The results of the simulations using HWHydrate8 for determining each equilibrium state are summarized in the two sets of diagrams, a and b, in Figure 3. Each of them graphically shows how the gas-phase composition, the structural composi(12) Watanabe, S.; Takahashi, S.; Mizubayashi, H.; Murata, S.; Murakami, H. A demonstration project of NGH land transportation system. Presented at the 6th International Conference on Gas Hydrates, Vancouver, Canada, July 6-10, 2008; paper 4-B3 (5442). In this paper, the pressure to be imposed in the process from hydrate formation to hydrate pelletizing is indicated to be 5.5 MPa (gauge). However, this is in error. The pressure actually expected in the above process is 5.4 MPa (gauge) or 5.5 MPa (absolute). This correction is based on a private communication (an e-mail on Aug 18, 2008) from S. Watanabe (the corresponding author of the above paper) to Y. H. Mori.



Figure 3. Results of simulations using HWHydrate. The results of each simulation are displayed in the form of simultaneous variations of the gas-phase composition, the structural composition of formed hydrates, the guest-molecule composition in these hydrates, and the equilibrium temperature with the count of the phase-equilibrium calculations (i.e., the serial number i of the equilibrium states), during a continuous operation for forming hydrates from either of the two gas mixtures specified in Table 1 at a constant pressure 5.5 MPa. (a) Simulation incorporating naturalgas model A as the feed gas and (b) simulation incorporating natural-gas model B as the feed gas.

tion of formed hydrates, the guest-molecule composition in these hydrates, and the equilibrium temperature simultaneously vary with the count of the phase-equilibrium calculations, i.e., the serial number i of the equilibrium states, during a continuous operation for forming hydrates from either of the two gas mixtures specified in Table 1. Here, the gas-phase composition

is represented by xj,gas,i, the mole fraction of each feed-gas component substance at each equilibrium state. To characterize the hydrate product at each stage in the operation, however, we observe the aggregate of the hydrates formed in 50 successive equilibrium states [say, from the (i - 50)th state to the ith state], instead of each equilibrium state (say, the ith state).


Ogawa et al.

This is because the simulation predicts exclusive formation of a hydrate with a particular crystallographic structure (sI, sII, or sH) at each equilibrium state, and hence, the guest-molecule composition as quantified by xj,hyd,i should exhibit an excessively large factitious fluctuation from state to state. The three “structure fraction” values plotted at count i on the abscissa indicate the fractions of sI, sII, and sH hydrates, respectively, in the aggregate of the hydrates formed at 50 successive equilibrium states from the (i - 50)th state to the ith state. The “mole fraction in hydrate” index, jxj,hyd,i, indicates the mole fraction of each feed-gas-component substance fixed in the above-mentioned aggregate of hydrates, i.e., i

jxj,hyd,i )

∑

Nj,hyd,k

k)i-50 i m

∑ ∑N

(8)

j,hyd,k

k)i-50 j)1

Comparing the two sets of diagrams, a and b in Figure 3, we find an apparent similarity in the gross behavior of the evolution of gas- or hydrate-phase composition between the two simulations incorporating the different natural-gas models specified in Table 1. In fact, except for the variations in methane and isopentane fractions in the gas phase, we find that the variations in composition of the gas and hydrate phases with count i of the phase-equilibrium calculations in the two simulations are quite similar not only qualitatively but also quantitatively. Concerning the accumulation of isopentane in the gas phase and its consequence (the decrease in methane fraction in the gas phase and the formation of sH hydrates), the evolution with natural-gas model A is accelerated in comparison to that with model B, by nearly 5 times, being almost in proportion to the ratio of the isopentane concentration in model A to that in model B. Now, we closely inspect of the results of the two simulations. Either simulation extends to the asymptotic stages in which the system no longer undergoes appreciable change (except for periodical fluctuation) in both gas and hydrate phases with an increasing i. The entire i range covered by the simulation may be divided into three characteristic regimes as follows: (i) the first regime ranging up to i ≈ 75, in which the gas-phase composition undergoes a sharp change; (ii) the second regime ranging up to i ≈ 1850 with model gas A or up to i ≈ 8600 with model gas B, in which the system is free from any appreciable change except for the monotonic decrease and increase in methane and isopentane fractions, respectively, in the gas phase; and (iii) the third regime beyond i ≈ 1850 with model gas A or i ≈ 8600 with model gas B, in which the system is held in a practically steady state despite periodic fluctuation in isopentane fraction in the gas phase. The characteristics of each of these regimes are discussed below in some detail. The first regime begins with the exclusive formation of sII hydrates. Because of the preferential uptake of ethane and propane into the sII hydrates, the fraction of methane in the gas phase sharply increases, which in turn should promote the formation of sI hydrates. Because the transition from the first to the second regime is caused by the increase in the methane fraction and, at the same time, the simultaneous decreases in the fractions of sII-forming substances (propane, isobutene, and butane) in the gas phase, the duration of the first regime is hardly dependent upon the fraction of isopentane in the feed gas and hence is almost the same for the two simulations. In either simulation, the first regime extends until gas molecules in the

amount nearly corresponding to three-quarters of those initially filling the system have been consumed by hydrate formation. The second regime is characterized by a monotonic increase in the fraction of isopentane in the gas phase, which is compensated by a decrease in the methane fraction in the same phase. The fractions of ethane and propane remain almost constant. Both sII and sI hydrates are formed in almost a constant ratio of 0.68:0.32 throughout this regime. Consequently, the chemical composition of the entire hydrate product is held constant. In this respect, the second regime is very suitable for producing hydrate products of uniform quality. Because this regime ends as the result of the increase in the mole fraction of isopentane in the gas phase to about 0.02, its duration is different between the two simulations. In general, the duration of this regime should be inversely proportional to the mole fraction of isopentane in the feed gas. Both simulations indicate that the accumulation of isopentane in the gas phase results in the formation of sH hydrates, instead of the condensation of isopentane. What we call the third regime here is the period that starts with the inception of sH hydrate formation. Once an sH hydrate is formed, consuming methane and isopentane, the fractions of these substances (particularly the fraction of isopentane) in the gas phase drops so that an sII or sI hydrate is apt to be formed subsequently. Thus, it turns out that hydrates of three different structures periodically form at individual intervals, thereby generating the saw-toothed change in mole fraction of isopentane in the gas phase. The pitch of this change coincides with the interval of the sH hydrate formation. For the purpose of crosschecking the simulations demonstrated above, we have repeated the simulation with model gas A, incorporating CSMGem9 instead of HWHydrate8 into our simulation algorithm. The results of this simulation are shown in Figure 4, which should be compared to Figure 3a, which shows the results of the corresponding simulation using HWHydrate. Comparing these figures, we can readily recognize some significant differences between the two simulations using different PECPs, particularly in the evolution of (a) the isopentane fraction in the gas phase and (b) the structure of the hydrate to be formed. The simulation using CSMGem predicts that sII hydrates are exclusively formed throughout the operation, encaging even isopentane molecules into their 51264 cages. As the result of such isopentane uptake into the sII hydrates being formed, the fraction of isopentane in the gas phase is no longer increased monotonically but is held almost constant once i, the count of serial equilibrium states, exceeds 111. It should be noted that, because of the exclusive formation of sII hydrates, the composition-averaging procedure formulated in eq 8 is not necessary in this simulation. Thus, the hydrate-phase composition parameters used in Figure 4 are not jxj,hyd,i but xj,hyd,i. According to this simulation, the entire process of hydrateforming operation may be divided into two regimes: the first regime ranging up to i ≈ 135, in which some of the gas- and hydrate-phase parameters, xj,gas,i and xj,hyd,i, undergo appreciable changes, and the second regime beyond the border at i ≈ 135, in which all of the phase-characterizing parameters are practically held constant. Small peaks in xj,hyd,i for ethane and butane in the first regime (at i ≈ 28) are presumably ascribable to the exhaustion of propane and, although to a much lesser extent, isobutane in the gas phase at earlier stages. Because the molecules of ethane and heavier hydrocarbon homologues in the gas phase may be competitively encaged into the 51264 cages of the sII hydrates, the exhaustion of propane and isobutane in the gas phase should promote the uptake of ethane and butane



into the hydrates, thereby leading to the peaks in xj,hyd,i relevant to them. Note that the first stage defined here is ∼1.8 times longer than that defined in the simulations using HWHydrate (cf. parts a and b of Figure 3). Discussion and Remarks The discrepancy between the simulations using HWHydrate (Figure 3) and that using CSMGem (Figure 4) is primarily caused by the difference between these two PECPs in the capability of isopentane inclusion into the sII hydrates formed in the presence of the other lighter hydrocarbon homologues from methane to butane. HWHydrate rigorously excludes the possibility of isopentane inclusion in the sII hydrates. This is not the case with CSMGem. CSMGem allows for the inclusion, although only to minute fractions, of isopentane in the sII hydrates. The occupancy of the 51264 cages in the sII hydrates with isopentane molecules predicted by CSMGem is only ∼0.06% in the second regime, in which the system is in a nearly steady state. That is, even such a minute inclusion of isopentane in the formed hydrates is capable of preventing the isopentane fraction in the gas phase from monotonically increasing, thereby eliminating the risk of the generation of an isopentane-rich hydrophobic liquid phase or the structural transition of the hydrate product. Now, we encounter a fundamental problem regarding the phase equilibrium in the mixed-hydrate-forming system of our interest: are isopentane molecules actually encaged in the 51264 cages of the sII hydrates to be formed in this system? Unfortunately, no definite answer to this question is available at present. Recently, Luzi et al.13 reported on the basis of their 13C nuclear magnetic resonance (NMR) and powder X-ray diffraction measurements that the hydrate formed from a ternary methane + neopentane + isopentane guest mixture was in structure II, while the hydrate formed from a methane + isopentane mixture was exclusively in structure H. They also presumed, with the aid of ab initio calculations, that isopentane molecules take the gauche conformation in the 51264 cages of structure II, leading to a hypothetical conclusion that isopentane can be incorporated into sII hydrates when it is accompanied by another higher hydrocarbon, such as neopentane, with a slightly smaller molecular size. If this is the case, does butane or isobutane included in our model gases (Table 1) play, similar to neopentane, a role of aiding isopentane inclusion into sII hydrates? At present, no definite evidence is available that either supports or denies the above possibility. Thus, we cannot judge if the results shown in Figure 4 are more realistic compared to those shown in Figure 3. To have a clearer insight into this issue, we need more experimental information about the fundamentals of mixed hydrate formation. Despite the as-yet unsolved issue discussed above, we can still derive some important implications for the aspect of engineering practice, which are summarized below. The evolution of the hydrate-forming system and the hydrate product as illustrated in Figure 4 may appear to be more favorable (or easier to handle in practical operations) than that illustrated in Figure 3, because of the almost steady-state process lasting throughout the second regime, which may be extended unlimitedly. The hydrate products to be obtained throughout the second regime (13) Luzi, M.; Schicks, J. M.; Naumann, R.; Erzinger, J.; Udachin, K.; Moudrakowski, I.; Ripmeester, J. A.; Ludwig, R. Investigations on the influence of guest molecule characteristics and the presence of multicomponent gas mixtures on gas hydrate properties. Presented at the 6th International Conference on Gas Hydrates, Vancouver, Canada, July 610, 2008; paper P-146 (5633).

Figure 4. Results of a simulation using CSMGem. The hydrate-forming operation addressed here is completely the same as that demonstrated in Figure 3a, i.e., a continuous operation for forming hydrates from natural-gas model A at a constant pressure of 5.5 MPa.

must be composed exclusively of sII crystals with uniform guestmolecule composition. Obviously, this is an ideal situation from the viewpoint of the quality control of the hydrate products. In contrast, the evolution of the system and the product as illustrated in parts a or b of Figure 3 is rather complicated. The products collected in the second regime, which is relatively long but inevitably limited, are mixtures of the sI and sII hydrates,


while those in the third regime, which may continue unlimitedly, are mixtures of the sI, sII, and sH hydrates. It should be noted, however, that, despite such variations in crystallographic structure in the hydrate products, the gross guest-molecule composition indicated by the index jxj,hyd,i is held nearly constant throughout the second and third regimes. This fact means that the quality of the hydrate product (as measured by the calorific value of the gas mixture available by its dissociation) instantaneously obtained will hardly change with the progress of the operation except for the relatively short first regime, even if the actual behavior of the system-state evolution is better approximated by Figure 3 rather than Figure 4. The occurrence of isopentane condensation leading to the formation of a hydrophobic liquid phase is not predicted by any of the simulations demonstrated above. The simulations using HWHydrate predict that sH hydrate formation will start ahead of the isopentane condensation that should otherwise occur. The simulation using CSMGem predicts that neither the sH hydrate formation nor the isopentane condensation will occur. Obviously, the absence of such a hydrophobic condensate phase throughout each hydrate-forming operation is favorable for simplifying the equipment design of the natural-gas hydrate facilities. However, it seems premature to exclude any possibility of such a condensate-phase formation in practical hydrateforming operations from natural gas. In general, the thermodynamic condition for sH hydrate formation and that for isopentane condensation at a given system pressure are rather close. The preference for sH hydrate formation to isopentane condensation predicted in our simulations using HWHydrate should be accepted carefully. The preference may be in part dependent upon the PECP used (HWHydrate in this case). Even if the preference for sH hydrate formation to isopentane condensation is thermodynamically correct, we cannot necessarily ensure the preferential occurrence of sH hydrate formation rather than isopentane condensation. Dependent upon the stochastic nature of nucleation of an sH hydrate and that of isopentane condensation, the condensation might occur ahead of the sH hydrate formation. It is reasonably conservative in equipment design to allow for the isopentane condensation at least before this issue is experimentally examined. Acknowledgment. We thank Dr. Judith M. Schicks (GeoForschungsZentrum Potsdam, Potsdam, Germany) and Prof. E. Dendy Sloan, Jr. (Colorado School of Mines, Golden, CO) for their valuable comments on the possibility of isopentane inclusion into sII hydrates. This study was supported by the Industrial Technology Research Grant Program (Grant 05A45004) from the New Energy and Industrial Technology Development Organization (NEDO) of

Ogawa et al. Japan in the fiscal year of 2007. Also, the study has been supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (Grant 20246040).

Nomenclature i ) count of serial equilibrium states of the hydrate-forming system of interest j ) index number for feed-gas-component substances () 1 to m) m ) number of feed-gas-component substances Nj,i ) total number of molecules of substance j in the hydrateforming system at the ith equilibrium state Nj,gas,i ) number of molecules of substance j in the gas phase at the ith equilibrium state Nj,hyd,i ) number of molecules of substance j in the hydrate discharged from the system during its transition from the ith to the (i + 1)th equilibrium states Nj,in,i ) number of molecules of substance j supplied to the system during its transition from the ith to the (i + 1)th equilibrium states Nj,liq,i ) number of molecules of substance j in the aqueous phase at the ith equilibrium state Nw ) total number of water molecules in the hydrate-forming system Nw,gas,i ) number of water molecules in the gas phase at the ith equilibrium state Nw,hyd,i ) number of water molecules discharged from the system during its transition from the ith to the (i + 1)th equilibrium states Nw,in,i ) number of water molecules newly supplied to the system during its transition from the ith to the (i + 1)th equilibrium states () Nw - Nw,liq,i - Nw,gas,i) Nw,liq,i ) number of water molecules in the aqueous phase at the ith equilibrium state p ) system pressure Teq,i ) equilibrium temperature in the system at the ith equilibrium state Xw ) mole fraction of water in the system xj,feed ) mole fraction of substance j in the feed gas xj,gas,i ) mole fraction of substance j in the gas phase at the ith equilibrium state xj,hyd,i ) mole fraction of substance j in the entirety of guest molecules encaged in the hydrate discharged from the system during its transition from the ith to the (i + 1)th equilibrium states xj,liq,i ) mole fraction of substance j in the aqueous phase at the ith equilibrium state jxj,hyd,i ) mole fraction of substance j in the entirety of guest molecules encaged in the hydrates that have been discharged from the system during the last 50 state-to-state transitions preceding the (i + 1)th equilibrium state EF800799Q

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