Thermodynamic Simulations of Hydrate-Based Removal of Carbon

Article pubs.acs.org/IECR

Thermodynamic Simulations of Hydrate-Based Removal of Carbon Dioxide and Hydrogen Sulfide from Low-Quality Natural Gas Satoru Akatsu, Shuhei Tomita, Yasuhiko H. Mori, and Ryo Ohmura* Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan ABSTRACT: This paper aims at presenting a computational scheme to thermodynamically simulate a continuous multistage operation for separating, by forming clathrate hydrates, carbon dioxide (CO2) and hydrogen sulfide (H2S) from a low-quality natural gas and at showing the stage-to-stage changes in the gas-phase composition, the crystallographic structure and composition of the formed hydrate, and the gas/aqueous-liquid/hydrate equilibrium temperature (the higher temperature limit for hydrate formation). The paper first describes the fundamental concept and algorithm of the computational scheme and then applies the scheme to the processing of a specific natural gas modeled as a CH4 + C2H6 + C3H8 + N2 + H2S + CO2 mixture. It is demonstrated that the optimum number of stages should be determined by finding a compromise between the improving removal of CO2 and H2S and increasing losses of combustible substances, particularly C2H6 and C3H8, from the residual gas with an increasing number of stages.

1. INTRODUCTION Natural gas is generally considered to be the cleanest fossil fuel, producing less carbon dioxide (CO2) and other pollutants per unit quantity of energy released by its combustion compared to coal or oil. Natural gas currently accounts for about 23% of the world energy supply,1 and this proportion will likely further increase in the future with the world increasing demand for a cleaner energy supply. Inevitably, more attention is being given to low-quality reserves in small gas fields where conventional gas production/processing technology may not be economically feasible. The natural gas from such small gas fields, specifically those located in Southeast Asia, contains CO2 and hydrogen sulfide (H2S) at significant fractions (up to the order of 10%). In order to improve the quality of such natural gas to be eligible for commercial use, the fractions of CO2 and H2S must be significantly reduced. Such precombustion capture of CO2, a greenhouse gas, and H2S, a highly toxic and metalcorrosive chemical, from natural gas at the locations of individual gas fields can also effectively decrease the risk of their emission into the environment during the succeeding gas transport, storage, distribution, and combustion processes. Because natural gas emerges from the ground at a pressure of 5−25 MPa and both CO2 and H2S are known to form clathrate hydrates (abbreviated hydrates) at lower pressures than the hydrocarbon components of natural gas,2 we can expect that the gas-separation technology utilizing hydrate formation can be effective for removing CO2 and H2S from natural gas. The idea of utilizing hydrate formation as a means of separating gases goes back to the 1930s.3 Numerous studies based on this idea have already been reported, focusing on specific engineering issues such as the separation of CO2, H2S, hydrofluorocarbons, or hydrochlorofluorocarbons from flue gas, syngas, biogas, or various waste gases (see, for example, the literature surveys by Sloan and Koh3 and Rufford et al.4). The issue about natural-gas processing, i.e., the removal of contaminants (typically CO2, H2S, and N2) from well gas streams by hydrate formation, has received less attention and only been studied by a limited number of research groups.5−8 © 2013 American Chemical Society

However, all of these studies substituted binary CH4 + CO2 or CH4 + N2 gases for the multicomponent raw natural gas in their hydrate-forming experiments or separation-process analyses. This is an oversimplification for the purpose of revealing how the chemical composition of the natural gas, and hence its quality as a fuel (as measured by its caloric value), should change during the separation process. Moreover, except for the study by Dabrowski et al.9 that dealt with an equimolar CH4 + CO2 mixture as a model biogas, the compositional progress of separation during a realistic multistage operation has not been investigated. In order to obtain a processed natural gas with the desired quality, the hydrate-based separation process inevitably needs a multistage operation. Moreover, this multistage operation should desirably be a continuous operation, instead of a batch-type one, to make it sufficiently efficient and economical. During such an operation, the hydrate-forming reactor at each stage is held at a constant pressure, while receiving a gas mixture supplied from the adjacent upstream-side reactor, discharging a formed hydrate as an intermediate product, and discharging the residual gas to be delivered to the reactor at the next downstream-side stage. Because of the preferential uptake of CO2 and H2S into the hydrate, their fractions in the gas mixture outflowing from the reactor must be decreased from those in the gas mixture supplied to this reactor. For designing such a multistage separation system for practical use, we need to predict how the chemical composition of the gas mixture changes from stage to stage. Because the composition of raw natural gas significantly varies from source to source, i.e., from gas field to gas field or even from well to well in the same gas field,10,11 it is desirable that we have some computational scheme readily applicable to any raw-gas compositions to Received: Revised: Accepted: Published: 15165

June 26, 2013 September 10, 2013 September 13, 2013 September 13, 2013 dx.doi.org/10.1021/ie402010p | Ind. Eng. Chem. Res. 2013, 52, 15165−15176

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of the (k − 1)th stage. The constituents of this gas mixture are partially removed from the gas phase into the aqueous phase as well as the hydrate being formed inside the reactor. The hydrate taking the form of a slurry (i.e., a hydrate + aqueous liquid mixture) is continuously drained out of the reactor and pumped to the decomposer. For simplicity, it is assumed that, inside the decomposer, this hydrate slurry is completely separated into pure liquid water and a water-free gas mixture containing CO2 and H2S at higher fractions than those in the gas mixture supplied from the reactor of the (k − 1)th stage. (This assumption may be reasonable, as long as the decomposer is held at a sufficiently lower pressure than that inside the reactor, thereby substantially degassing the aqueous liquid phase inside the decomposer.) The liquid water free from any feed-gas-originated substance (such as CO2 or H2S) is pumped back from the decomposer to the reactor. The gas mixture discharged from the decomposer is separated from the main gas-processing line and may be supplied to a separate gastreatment facility, which is beyond the scope of this simulation study. The residue of the gas mixture inside the reactor, in which the fractions of CO2 and H2S are decreased, is supplied to that of the (k + 1)th stage. It should be noted that the feedgas supply to the reactor of the first stage is the only material inflow into the entire cascade system and that the discharge of gas mixtures from the reactor of the last stage and from the decomposers of all of the stages is the outflow from the system. Both are in balance regarding any constituent species of the feed gas because the system includes no chemical reaction. Water is simply recirculated within the reactor + decomposer assembly of each stage. Thus, the entire system is free from any inflow or outflow of water throughout the gas-processing operation. Our main concern is to predict the compositional evolution of the gas mixture flowing through the reactors in the multistage cascade system during the transient process of its operation toward a steady state of the system. To enable this, we need to calculate the compositional evolution in individual reactors, taking the stage-to-stage flow of each feed-gasconstituent species into account. To perform this calculation, we take the same line that we took in our previous simulation studies about continuous or semibatch single-stage hydrateforming operations.12,14 That is, we assume each reactor to be an open thermodynamic system, in which only an infinitesimal amount of a hydrate always coexists in equilibrium with the gas and liquid phases. This system is evolved through a quasistatic irreversible process15 due to the inflow and outflow of substances (the feed-gas-constituent substances and water circulating through the reactor−decomposer loop) depending upon the hydrate formation inside it. This process is regarded as a series of discrete equilibrium states, with each only slightly deviating from its former state. The transition from one equilibrium state to the next results from the inflow and outflow of substances in sufficiently small amounts compared to their total amounts held inside the system. Each equilibrium state can be specified utilizing an appropriate phase-equilibrium calculation program (abbreviated as PECP) applicable to hydrate-forming systems. In the present study, we used CSMGem, a commercially available PECP, for this purpose.16 2.2. Algorithm for Simulation. On the basis of the “serial equilibrium states” concept described above, we assume the evolution process for the reactor of each of the multistages (numbered 1, 2, ..., k, ...) in a cascade to be composed of a series of equilibrium states (numbered 0, 1, 2, ..., i, ...) established by

provide the predictions of stage-to-stage changes in the gasphase composition. In this paper, we first present such a computational scheme for a thermodynamics-based simulation of a continuous multistage gas-separating operation. This computational scheme has been constructed on the basis of the scheme that we previously developed for the purpose of simulating the compositional changes in the gas phase inside a hydrate-forming reactor and also in the hydrate product during a continuous or batch-type single-stage hydrate-forming operation from a natural gas with a specific composition.12−14 We then apply this scheme to a hypothetical operation of processing a six-component model of low-quality natural gases to reveal the stage-to-stage evolutions in the gas-phase composition, the crystallographic structure and composition of the hydrate product, and the gas/aqueous-liquid/hydrate equilibrium temperature (the higher temperature limit for hydrate formation).

2. DESCRIPTION OF THE SIMULATION SCHEME 2.1. Modeling and Assumptions. Figure 1 schematically illustrates the material flowchart for the continuous multistage

Figure 1. Material flowchart for a hydrate-based multistage gasprocessing operation.

gas-processing operation that we consider in this study. The stages in the cascade are numbered as 1, 2, ..., k, ... along the major gas-flow line. For graphic simplicity, Figure 1 shows only three successive stages centered by an arbitrary stage, the kth stage. Each stage is equipped with a hydrate-forming reactor and a hydrate decomposer connected to each other. The reactor of each stage is initially charged with a specified quantity of liquid water. The residual space in the reactor is filled with the feed gas, i.e., a water-free raw natural gas of a specified chemical composition, at a prescribed pressure p, which exceeds the three-phase (gas/liquid/hydrate) equilibrium pressure, peq, corresponding to the system temperature T. It is assumed that the gas-processing operation starts by simultaneous hydrate nucleation in the reactors of all stages. Once the operation starts, the reactor of the first stage continuously receives the feed gas to compensate for the loss of the gas due to hydrate formation inside it, thereby maintaining the inside pressure unchanged from its initial level, and to deliver the residual gas to the reactor of the second stage. This gas is consecutively delivered to the reactors of the later stages, with its quantity and composition being changed from stage to stage. More details of the material flows from stage to stage and also inside each stage are described below, focusing on the three successive stages illustrated in Figure 1. The reactor of the kth stage continuously receives a gas mixture from the reactor 15166

dx.doi.org/10.1021/ie402010p | Ind. Eng. Chem. Res. 2013, 52, 15165−15176


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Figure 2. Conceptual illustration of the “serial equilibrium states” model for a hydrate-based multistage gas-processing operation. Each rectangular box with double outlines denotes the multiphase hydrate-forming system confined in the reactor installed in the kth stage, one of the stages aligned in a cascade. 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 one equilibrium state, for example, the ith state, to the next. m

turns in the system, i.e., all of the contents of the reactor consisting of the feed-gas-constituent substances (numbered 0, 1, 2, ..., j, ..., m) and water. Figure 2 illustrates the algorithm for calculating the evolution of the system; more specifically, the calculation procedure for the transition from one arbitrary equilibrium state, the ith state, to the next, the (i + 1)th state. We should note here that ∑jNj,i,k, the total number of molecules of the feed-gas-constituent substances in the system, and Nw, the total number of water molecules in the system, are invariable with i and k, while Nj,i,k, the number of molecules of each feed-gas-component substance, is variable with i and k. The three invariables relevant to the multistage operation of present interest, i.e., ∑jNj,i,k, Nw, and the system pressure p, need to be prescribed before starting the simulation. As illustrated in Figure 2, the calculation procedure for the stateto-state transition of the system consists of two serial steps, i and ii, which are detailed below in order. Step i begins by specifying Nj,i,k such that we obtain complete information about the chemical composition of the system consisting of the ∑jNj,i,k + Nw molecules. The actual procedure to determine Nj,i,k is given later, after both of the two steps are described. The system is then subjected to a gas/liquid flash calculation using a PECP (CSMGem16 in this study) to determine the ith equilibrium state. This calculation indicates the compositions of the gas and liquid phases inside the system in terms of the mole fraction of each feed-gas-constituent substance defined as

xj ,liq, i , k = Nj ,liq, i , k /∑ Nj ,liq, i , k

for the liquid phase, where Nj,gas,i,k denotes the number of molecules of substance j in the gas phase and Nj,liq,i,k denotes that in the liquid phase. Also determined by this calculation is the distribution of Nw, the number of water molecules, between the gas and liquid phases. On the basis of these data, we can readily determine Nj,gas,i,k and Nj,liq,i,k as well as the number of water molecules in the gas phase, Nw,gas,i,k, and that in the liquid phase, Nw,liq,i,k. In addition, the above phase-equilibrium calculation indicates the crystallographic type of hydrate with which the system can be equilibrated at the highest temperature, Teq, and the guest-molecule composition in this hydrate, which may be specified in terms of the mole fraction of each substance defined as m

xj ,hyd, i , k = Nj ,hyd, i , k /∑ Nj ,hyd, i , k (3)

j=1

where Nj,hyd,i,k is the number of guest molecules of substance j in the hydrate. At step ii, we assume that the hydrate characterized above is formed, consuming a minute fraction δhyd,i,k of the total number of the feed-gas-originated molecules in the gas phase. The number of molecules of substance j in the formed hydrate is given by m

Nj ,hyd, i , k = xj ,hyd, i , kδ hyd, i , k ∑ Nj ,gas, i , k

m

j=1

xj ,gas, i , k = Nj ,gas, i , k /∑ Nj ,gas, i , k j=1

(2)

j=1

(4)

This hydrate is entirely removed from the system and supplied to the decomposer of the kth stage. Along with the hydrate, a minute fraction δliq,i,k of the liquid phase is removed to the

(1)

for the gas phase and 15167



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formed hydrate, and Nw,liq,i,k + Nw,gas,i,k − Nw,hyd,i,k, the residual water molecules contained in the liquid and gas phases, from the system and by newly adding Nw to the system (see Figure 2). As a result of the partial exchange of its contents during step ii, the system has replaced its composition with a new one. The number of molecules of the feed-gas-constituent substance j in the current system is given by

decomposer. The number of molecules of substance j contained in this outflow of the liquid is given by m

Nj ,liq,out, i , k = xj ,liq, i , kδ liq, i , k ∑ Nj ,liq, i , k (5)

j=1

After removal of the hydrate from the system, i.e., removal of the feed-gas-originated molecules given by eq 4 from the gas phase in the system, a minute fraction δgas,i,k of the feed-gasoriginated molecules is removed from the residue of the gas phase to the reactor of the (k + 1)th stage. The number of molecules of substance j contained in this outflow of the gas mixture is given by

Nj , i + 1, k = Nj , i , k − Nj ,hyd, i , k − Nj ,liq,out, i , k − Nj ,gas,out, i , k + Nj ,in, i , k

This system is subjected to step i in the next round of the serial two-step calculation procedure to determine the (i + 1)th equilibrium state. In order to start up the simulation of each natural-gasprocessing operation based on the above-described algorithm, we need to specify Nj,i,k at the initial equilibrium state (i = 0). This quantity is simply given as follows:

Nj ,gas,out, i , k = δgas, i , k(Nj ,gas, i , k − Nj ,hyd, i , k) m

= δgas, i , k(xj ,gas, i , k ∑ Nj ,gas, i , k − xj ,hyd, i , kδ hyd, i , k j=1 m

∑ Nj ,gas,i ,k)

m

(6)

j=1

Nj , i = 0, k = xj ,feed ∑ Nj , i , k

Therefore, the feed-gas-originated molecules counted by ∑jNj,hyd,i,k, ∑jNj,liq,out,i,k, and ΣjNj,gas,out,i,k are lost from the system during step ii. On the other hand, the system is charged with the gas mixture in the amount of ∑ j N j , i n , i , k (=∑jNj,gas,out,i,k−1), supplied from the reactor of the (k − 1)th stage. To ensure the invariability of ∑jNj,i,k with i, the inflow and outflow of the feed-gas-originated molecules must be in balance, i.e., the following molecule (or mole) balance relation must be satisfied: m

m

m

j=1

where xj,feed is a constant specific for the given feed gas and ∑jNj,i,k is also a constant that we can, in principle, arbitrarily prescribe. Once Nj,i=0,k is determined, we can sequentially determine the values of Nj,i,k in the later equilibrium states by using eq 10. As for the prescription of the two invariables, ∑jNj,i,k and Nw, concerning the reactor capacity, we should note that the compositional evolution of the system with an increase in i is not dependent on their individual magnitudes but on the ratio of ∑jNj,i,k to Nw or the fraction of water in the system, Xw, defined as follows:

m

j=1

j=1

(7)

Xw =

For the first stage (k = 1), ∑jNj,in,i,k is simply calculated by eq 7 once we arbitrarily prescribe δhyd,i,k; this is explained in subsection 2.4. This value of ∑jNj,in,i,k=1 is then used to calculate Nj,in,i,k=1 for each feed-gas-constituent substance as follows: m

(8)

where xj,feed denotes the mole fraction of substance j in the feed gas. For any later stage (k ≥ 2), Nj,in,i,k is obtained as the number of molecules of substance j contained in the gaseous outflow from the adjacent upstream-side stage; that is, m

Nj ,in, i , k = Nj ,gas,out, i , k − 1 = xj ,gas, i , k − 1 ∑ Nj ,gas,out, i , k − 1 j=1

Nw m Nw + ∑ j = 1 Nj , i , k

(12)

That is, it is not always necessary to make ∑jNj,i,k and Nw coincide with the actual number of feed-gas-originated molecules and that of water molecules, respectively, contained in each reactor during the real gas-processing operation that is to be simulated. The operational parameters with which equality between the simulation and real operation is required are ∑jNj,in,i,k=1/Nw or Xw in addition to the system pressure p and the feed-gas composition xj,feed. 2.3. Split Fractions. In order to quantify the recovery of each feed-gas-constituent substance in the gas discharged from the reactor of each stage, we introduce the split fractions (abbreviated S.Fr.) defined as follows:

Nj ,in, i , k = 1 = xj ,feed ∑ Nj ,in, i , k = 1 j=1

(11)

j=1

∑ Nj ,in,i ,k = ∑ Nj ,hyd,i ,k + ∑ Nj ,liq,out,i ,k + ∑ Nj ,gas,out, i , k j=1

(10)

(9)

(S.Fr.)j , k =

In order to satisfy eq 7, we need to appropriately adjust the three δ parameters, i.e., δhyd,i,k, δliq,i,k, and δgas,i,k. The scheme that we used for specifying these parameters is described in subsection 2.4. As illustrated in Figure 1, our simulation model assumes that the water molecules once removed from the system to the decomposer because of discharge of a hydrate slurry are totally fed back to the system, thereby maintaining Nw, the total number of water molecules in the system, constant. During the actual calculation process, the above water recycling is realized by removing Nw,hyd,i,k, the water molecules contained in the

Nj ,gas,out, k Nj ,in, k

, (S.Fr.)combust, k =

Ncombust,gas,out, k Ncombust,in, k (13)

where Nj,in,k and Nj,gas,out,k denote the asymptotic values of Nj,in,i,k and Nj,gas,out,i,k, respectively, when the gas-processing operation has sufficiently approached the steady state in which the chemical composition of the gas discharged from the reactor of each stage no longer changes with i, and Ncombust,in,k and Ncombust,gas,out,k denote ∑jNj,in,i,k and ∑jNj,gas,out,k, respectively, for the combustible species (such as light hydrocarbons) among the m constituents of the feed gas. Either of these gas-side split fractions may be viewed as the complement of the hydrate-side 15168



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split fraction that Linga et al.17 first proposed for assessing the recovery of CO2 by hydrate formation from a CO2 + H2 mixture. In addition to such split fractions for each stage, we define the split fractions for the multistage unit (MSU) composed of k stages in a cascade, as follows: (S.Fr.)MSU j,k

=

Nj ,gas,out, k Nj ,in, k = 1

,

MSU (S.Fr.)combust, k

=

feed-gas-originated substances lost from the former reactor by the hydrate-slurry discharge; that is δgas, i , k = ςgas/hydδ hyd, i , k

where the proportionality constant ςgas/hyd is, similar to ςliq/hyd in eq 16, invariable with i or k. Using ςliq/hyd and ςgas/hyd, eq 15 can be rewritten as follows:

Ncombust,gas,out, k Ncombust,in, k = 1

m

(14)

j=1

constituent

mole fraction xfeed × 100

CH4 C2H6 C3H8 N2 H2S CO2

70 6 2 2 10 10

+ ςliq/hyd ∑ Nj ,liq, i , k} j=1

m

3. RESULTS AND DISCUSSION The results of each simulation run are obtained in the form of simultaneous changes in the composition of the gas mixture discharged from the reactor (xj,gas,out,i,k), the structure of the formed hydrates, the guest-molecule composition in these hydrates (xj,hyd,i,k), the composition of the feed-gas-constituent substances dissolved in the aqueous liquid phase contained in the reactor (xj,liq,i,k), and the equilibrium temperature Teq,i,k at each stage (k = 1, 2, ..., m) with the serial number i of the hypothetical equilibrium states. This number i may be replaced by some physical quantity that quantitatively indicates the progress of the gas-processing operation. Following our previous study of single-stage semibatch operations for forming hydrates from a synthetic natural gas,18 we use ngas,out/ngas,0 as the index of the progress of the operation, where ngas,out denotes the moles of feed-gas-constituent substances that have been discharged from the reactor of each stage to that of the next stage since the onset of the operation, while ngas,0 denotes the moles of feed-gas-constituent substances instantaneously contained in each reactor. In practice, we can calculate ngas,out/ngas,0 corresponding to consecutive equilibrium states, from the zeroth to ith states, for each of the multiple stages in a cascade, using the following relationship:

m

∑ Nj ,in,i ,k = δ hyd,i ,k ∑ Nj ,gas,i ,k + δ liq,i ,k ∑ Nj ,liq,i ,k j=1

j=1

j=1 m

+ δgas, i , k(1 − δ hyd, i , k) ∑ Nj ,gas, i , k j=1

(15)

The liquid-to-hydrate ratio in the hydrate slurry transferred from each reactor to the coupled decomposer needs to be controlled such that the slurry has a sufficient fluidity and, during its flow to the decomposer, does not cause any flowplugging problems due to the growth and/or aggregation of the suspended hydrate particles. Thus, we assume that the liquidto-hydrate ratio in the hydrate slurry is adjusted at an adequate level, which is invariable with i or k. That is, we assume that δliq,i,k has a linear relationship with δhyd,i,k as follows: δ liq, i , k = ςliq/hydδ hyd, i , k

(18)

In the present simulation, we prescribed ςliq/hyd and ςgas/hyd to be 5.75 and 3.08, respectively. The former value of ςliq/hyd corresponds to the mass fraction of the hydrate crystals in the hydrate slurry discharged from each reactor, being around 0.03. (According to the rheological study of tetra-n-butylammonium bromide hydrate slurries by Darbouret et al.,19 this hydrate fraction is low enough to eliminate the yield shear stress from the slurry and make it behave as a Newtonian fluid.) The latter value of ςgas/hyd was empirically selected such that the gas-phase composition exhibits a desirable stage-to-stage change. For the calculation about the first stage (k = 1), we can arbitrarily determine δhyd,i,k because ∑jNj,in,i,k=1, the quantity of the lefthand side of eq 18, is not prescribed. For the later stages (k ≥ 2), Nj,in,i,k or ∑jNj,in,i,k is given as the result of the calculation of Nj,gas,out,i,k or ∑jNj,gas,out,i,k for the adjacent former stage (see eq 9); hence, δhyd,i,k must be adjusted such that it satisfies the number-of-molecules conservation equation (eq 18). The numerical precision of the simulations should increase with a decrease in δhyd,i,k=1 at the cost of an increase in the total computation time of each simulation. On the basis of our experience from the previous simulation studies,12,14 we set δhyd,i,k=1 to 0.01. The number of stages in a cascade may be arbitrarily selected. We set it at 5 for the present simulation.

mole fraction of water in the multiphase system in each reactor, Xw, is prescribed to 0.97. This fraction corresponds to the phase-split condition in which, when p = 5.0 MPa, ∼60% of the inside volume of a gas-bubbling-type reactor is occupied by the aqueous phase, while the rest is occupied by the gas phase. When p = 2.5 MPa, the volume fraction of the aqueous phase is lowered to ∼38%. The procedure that we used to specify δhyd,i,k, δliq,i,k, and δgas,i,k is described below. For clarifying this description, we rewrite eq 7 using eqs 4−6 as follows: m

j=1 m

Table 1. Composition of the Feed Gas, a Hypothetical LowQuality Natural Gas, Assumed in This Simulation Study j

m

∑ Nj ,in,i ,k = δ hyd, i , k{[1 + ςgas/hyd(1 − δ hyd, i , k)] ∑ Nj ,gas, i ,k

where Nj,in,k=1 and Ncombust,in,k=1 denote Nj,in,k and Ncombust,in,k, respectively, for the first stage, i.e., the quantities of substance j and the combustibles, respectively, contained in the feed gas supplied to the first stage of the MSU. 2.4. Specification of Feed-Gas Composition, Operational Conditions, and Practice of Simulation. The chemical composition of the feed gas, a hypothetical lowquality natural gas, that we assumed in this study is specified in Table 1. The system pressure p is set at 5.0 or 2.5 MPa. The

1 2 3 4 5 6

(17)

(16)

where ςliq/hyd denotes a proportionality constant invariable with i or k. We also assume δgas,i,k to be proportional to δhyd,i,k such that the quantity of the gas discharged from each reactor to the neighboring reactor is nearly proportional to the quantity of the 15169



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Figure 3. continued

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Figure 3. Summarized results of a simulation of a five-stage gas-processing operation under a constant system pressure: (a) 5.0 MPa; (b) 2.5 MPa. The results are displayed in the form of simultaneous variations in the chemical compositions (given in mole fractions) of the processed gas (first and second rows), the guest molecules of formed hydrates (third row), and the feed-gas constituents dissolved in the aqueous liquid (fourth row); the fractions of sI and sII crystals in the formed hydrates (fifth row); and the equilibrium temperature corresponding to the system pressure (sixth row), with an increase in the normalized amount of processed gas, ngas,out/ngas,0, for each of the five stages (k = 1−5).

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Table 2. Composition of the Processed Gas (Specified in Terms of the Mole Fraction of Each Feed-Gas-Constituent Substance) and the Split Fraction for Each Substance or Entire Combustibles in the Processed Gas at Each of the Five Successive Stages (k = 1−5) or the MSU Composed of k Stages (from First to kth Stages) in the Asymptotic Regime of a Gas-Processing Operation [the System Pressure p Is (a) 5.0 MPa and (b) 2.5 MPa]

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ngas,out /ngas,0 =

m

Article

m

∑ ∑ Nj ,gas,out,i′ ,k /∑ Nj , i ,k

i ′= 0 j = 1

j=1

two system pressures, p = 5.0 and 2.5 MPa, we do not separately discuss the results for these two pressures. That is, unless otherwise noted, every description given below is relevant to the results for both pressures. Before going into the core of the results shown in the xj,gas,out,k versus ngas,out/ngas,0 diagrams, we should note that the initial value of xj,gas,out,k, i.e., its value at ngas,out/ngas,0 → 0, for each of the feed-gas-constituent substances may be deviating from xj,feed, the mole fraction of the same substance in the fresh feed gas (cf. Table 1). This is ascribed to the preferential dissolution of some of those substances (such as H2S and CO2) into the liquid phase and, to a lesser extent, the preferential uptake of some (C2H6, C3H8, and H2S) into the hydrate. Hence, the deviation from xj,feed is dependent on Xw, which is fixed at 0.97 in the present simulation. Except for N2, xj,gas,out,k undergoes a sharp change only in the ngas,out/ngas,0 range up to ∼2, beyond which xj,gas,out,k changes no more than gradually and asymptotically approaches a constant value. As expected, the fractions of H2S and CO2 (xj=5,gas,out,k and xj=6,gas,out,k) monotonically decrease with increasing ngas,out/ ngas,0 at each of the five stages from k = 1 to 5. This fact is simply ascribable to the preferential uptake of H2S and CO2 molecules into the hydrates and the liquid phase inside the reactor of each stage. It is also noted that, as demonstrated in Table 2, the asymptotic values of these fractions significantly decrease from stage to stage, indicating the suitability of the hydrate-based multistage operations for removing H2S and CO2 from the feed gas. (It should be noted that the asymptotic values of the H2S fraction at the third or even later stages are calculated to be on the order of 0.01 mol % or less, which are presumably too low to be properly evaluated by CSMGem16 used in this simulation or by any other PECPs currently available.) On the other hand, the similar stage-to-stage decreases in the C2H6 and C3H8 fractions (xj=2,gas,out,k and xj=3,gas,out,k) are unfavorable facts that indicate significant losses of C2H6 and C3H8, valuable combustible constituents of the feed gas, from the gas-processing line. We should note that these losses lead to not only a decrease in (S.Fr.)combust,k, the split fraction of the combustibles preserved in the gas discharged from the reactor of each stage (Table 2), but also a decrease in the calorific value of the gas. As a consequence of the preferential uptake of H2S, CO2, C2H6, and C3H8 into the hydrates and liquid phase, the fraction of CH4 (xj=1,gas,out,k) monotonically increases with increasing ngas,out/ngas,0 at least up to ∼1.5 at every stage, and its asymptotic value exhibits a stepwise increase over the first three stages (k = 1−3). At each of the third to fifth stages in the case of p = 5.0 MPa, however, the CH4 fraction takes a downward turn before ngas,out/ngas,0 exceeds 1.5. Also, the asymptotic value of the CH4 fraction peaks at the third stage then tends to decrease from stage to stage. Such a downward turn in the CH4 fraction with an increase in ngas,out/ngas,0 of k is ascribable to the coexistence of CH4 and N2 in the gas phase; that is, CH4 is preferentially consumed by hydrate formation and dissolved in the liquid phase, compared to N2, thereby making the residual gas inside each reactor leaner with CH4 and richer with N2. As far as the CH4-to-N2 proportion in the processed gas is concerned, we may conclude that the number of stages in a cascade should be limited to 3. The most prominent difference in the xj,gas,out,k versus ngas,out/ ngas,0 relationships between the two system pressures, p = 5.0 and 2.5 MPa, is observed in the CO2 fraction. The asymptotic values at the first three stages (k ≥ 3) of this fraction for p = 2.5

(19)

The evolution in xj,gas,out,i,k, xj,hyd,i,k, xj,liq,i,k, the hydrate structure, and Teq,i,k with ngas,out/ngas,0 for each of the five successive stages (k = 1 − m) is shown in each of the two diagram arrays, (a) for p = 5.0 MPa and (b) for p = 2.5 MPa, in Figure 3. Note that the subscript i is omitted from the notations of the physical quantities plotted in Figure 3 and referred to in the following discussion; this is not only for the visual simplicity, but also for the reason that these quantities are related to ngas,out/ngas,0, instead of the serial number i, in Figure 3 and the relevant discussion. In diagram array (b) in Figure 3, we observe that every graphical plot for the fourth and fifth stages (k = 4 and 5) is interrupted in an early ngas,out/ngas,0 range. This is due to the decrease in Teq,k, the equilibrium temperature corresponding to the system pressure of 2.5 MPa, at the fourth stage to 272.9 K, the temperature at and below which water ice should form. (Note that this critical temperature is lower than the normal water-freezing point, 273.15 K, because of dissolution of CO2, H2S, and other feed-gas constituent substances in the aqueous phase.) Our simulation algorithm in the present form does not work when CSMGem,16 the PECP incorporated in it, predicts a gas + ice + hydrate equilibrium, instead of a gas + liquid + hydrate equilibrium. Because we do not expect gas-separation operations under an ice-forming conditions, we have devoted no technical effort for extending our simulation to a temperature range below the freezing point. A few comments may be necessary about the quantity termed “structure fraction”, i.e., the quantity plotted in the diagrams aligned on the fifth row in each diagram array, (a) or (b), in Figure 3, and also on the evaluation of the relevant quantity, xj̅ ,hyd,k. The phase-equilibrium calculation using a PECP (CSMGem 16 in this study) to determine each equilibrium state predicts the hydrate structure with which the equilibrium temperature Teq,k should be the highest. The algorithm of the present simulation assumes the exclusive formation of this hydrate structure, which can be either structure I (sI) or structure II (sII) as far as the chemical species contained in each reactor are limited to the six feed-gas constituents listed in Table 1 plus water. Consequently, the simulation may predict that these two structures sequentially alternate as the equilibrium state is renewed one after another. What we call the “structure fraction” is the fraction that either sI or sII occurs in the entire hydrates that have formed in the last 10 consecutive equilibrium states, i.e., those from the (i − 10)th to the ith states (see the Appendix). Accordingly, we substitute for xj,hyd,i,k, defined by eq 3, the following quantity xj̅ ,hyd,i,k, which corresponds to the mean of the individual xj,hyd,i,k values for the last 10 equilibrium states: i

xj̅ ,hyd, i , k =

∑i ′= i − 10 Nj ,hyd, i′, k i

m

∑i ′= i − 10 ∑ j = 1 Nj ,hyd, i′, k

(20)

This quantity is written as xj̅ ,hyd,k by omitting the subscript i in Figure 3 and the following discussion because of the reason described above. The xj,gas,out,k versus ngas,out/ngas,0 diagrams on the top two rows in each of the two diagram arrays, (a) and (b), in Figure 3 are of our primary concern in this study. Because the general xj,gas,out,k versus ngas,out/ngas,0 behavior is almost the same for the 15173



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MPa are higher than those for p = 5.0 by 19, 39, and 71%, respectively. This fact is mainly ascribable to a decrease in the quantity of CO2 dissolved in the aqueous phase with a decrease in the system pressure, which, in turn, increases the quantity of the residual CO2 in the gas phase. The evolution of xj,gas,out,k described above is dependent on that of xj,liq,k and, to a greater extent, that of xj,hyd,k, which, in turn, depends on that of the “structure fraction” plotted in the diagrams in the fifth row in Figure 3. We find there a systematic stage-to-stage change in the “structure fraction” versus ngas,out/ ngas,0 relationship. In the first stage, only sII hydrates form throughout the entire ngas,out/ngas,0 range (≤9) covered by the present simulation. This is ascribed to the C3H8 fraction in the gas phase inside the reactor being held at 0.02 or above in the first stage. In the second stage, the exclusive sII-forming regime is limited to a ngas,out/ngas,0 range up to ∼1.9 (p = 5.0 MPa) or ∼1.1 (p = 2.5 MPa), beyond which the sII and sI hydrates alternately form (see the Appendix). The transition from the sII-forming regime to the sII/sI-forming regime occurs when the C3H8 fraction in the gas phase decreases to the order of 10−5 as a result of preferential C3H8 consumption by the sII hydrate formation. Accordingly, the exclusive sII-forming regime becomes narrower in the third and later stages. In the third stage, a ngas,out/ngas,0 range beyond ∼1.6 (p = 5.0 MPa) or ∼1.5 (p = 2.5 MPa) is covered by an exclusive sI-forming regime. The exclusive sI-forming regime extends forward in the later stages. The equilibrium temperature, Teq,k, monotonically decreases with increasing ngas,out/ngas,0 at any stage. It should be noted here that the extent of the drop in Teq,k from its initial value of ∼292 K to its asymptotic value significantly increases from stage to stage, i.e., from ∼7 K in the first stage to ∼12 K in the fifth stage in the case of p = 5.0 MPa. The system subcooling defined as the difference between Teq,k and Tk, the system temperature maintained in the reactor of each stage, is considered to be the driving force for hydrate formation. Hence, it seems to be necessary in a real gas-processing operation to control Tk at each stage such that all of the stages have nearly the same degree of system subcooling. Such control of the system subcooling will cause the ratio of the rate of hydrate formation to the rate of gas supply at each stage to not significantly vary from stage to stage, thereby providing nearly even split fractions, (S.Fr.)j,k, for all of the stages. If Tk needs to be decreased to an ice-forming temperature in order to maintain the system subcooling at an appropriate magnitude, we must devise a special reactor/decomposer design that possibly overcomes the risk of a system-operation failure due to ice agglomeration inside the reactor and/or flow plugging in the reactor-to-decomposer conduit. In general, it is recommended to adjust the system pressure p such that an appropriate degree of the system subcooling can be maintained throughout the stages in a cascade without decreasing Tk to an ice-forming temperature. The simulation-based estimates of the split fractions defined by eqs 13 and 14 are provided in Table 2. Here we note that (S.Fr.)j,k, the split fraction for each substance in each of the five stages in a cascade (k = 1−5), does not significantly change from stage to stage, whereas it is significantly different from substance to substance at each stage. The relatively low values of (S.Fr.)j,k for H2S and CO2 again indicate that these sour-gas substances are effectively removed from the gas phase by hydrate formation. In the case of p = 5.0 MPa, for example, the (S.Fr.)j,k values for CH4 are higher than 0.7 throughout the five

stages, whereas those for C2H6 and C3H8 are as low as 0.36− 0.49 and 0.08−0.16, respectively. Because of the predominance of CH4 in the class of combustible constituents of the gas phase at each stage, (S.Fr.)combust,k is held at a higher level nearly equal to that of (S.Fr.)j,k for CH4. From the viewpoint of engineering practice, however, the magnitudes of (S.Fr.)MSU for the three j,k combustible substances or that of (S.Fr.)MSU combust,k may be of primary concern. Both (S.Fr.)MSU and (S.Fr.)MSU j,k combust,k sharply decrease with an increase in k, the number of stages included in the MSU. Thus, the number of stages should be limited to the minimum, as far as the xj,gas,out,k values of H2S and CO2 are reduced to allowable levels.

4. CONCLUDING REMARKS We have presented a computational scheme for the thermodynamic simulations of hydrate-based multistage gasprocessing operations and its application to a typical operation for removing CO2 and H2S from a model low-quality natural gas and increasing its potential as a fuel gas. The scheme enables one to predict the simultaneous changes in the chemical composition of the processed gas, the structure and guest-molecule composition of the formed hydrate, the composition of the aqueous liquid coexisting with the gas and hydrate phases, and the three-phase (gas/liquid/hydrate) equilibrium temperature corresponding to a given system pressure at each of the stages in a cascade during each gasprocessing operation. Our simulation for a five-stage operation for processing a six-component (CH4 + C2H6 + C3H8 + N2 + H2S + CO2) model natural gas reveals an efficient multistage effect for reducing the CO2 and H2S fractions in the processed gas. On the other hand, an increase in the number of stages in a cascade yields an increasing loss of the combustible substances (CH4, C2H6, and C3H8) from, and also an increasing N2 fraction in, the processed gas. Thus, the optimum number of stages should be determined by finding a good compromise between the advantages and disadvantages of increasing stages. On the basis of the results of our simulation, we recommend the use of a hydrate-based three-stage operation on the condition that it can be combined, if necessary, with some other gas-separation techniques to further decrease the H2S fraction in the processed gas and to effectively remove N2 concentrated in the processed gas due to the hydrate-based operation.

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APPENDIX. NOTE ON THE “STRUCTURE FRACTIONS” According to the Gibbs phase rule, hydrates in two different structures, st I and st II, may coexist in a CH4 + C2H6 + C3H8 + N2 + H2S + CO2 + H2O system under a given pressure. However, the present simulation scheme incorporating a PECP (CSMGem) allows hydrate formation only in one structure at every equilibrium state. If the fraction of C3H8, an sII-forming species, in the gas phase is maintained in a moderately low range (around the order of 10−5) during each continuous hydrate-forming process, the above algorithmic restriction in the simulation scheme possibly leads to the prediction of a sequentially alternate formation of the sI and sII hydrates with an increase in the serial “equilibrium state” number i. This is because, once an sII hydrate forms in an equilibrium state, say the ith state, preferentially consuming C3H8 in the gas phase, an sI hydrate free from C3H8 molecules may form in the next (i + 1)th equilibrium state. sI hydrate formation in the (i+ 1)th equilibrium state results in a full or partial recovery of the C3H8 15174



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ngas,0 = moles of the feed-gas-constituent substances instantaneously contained in each reactor p = system pressure, Pa S.Fr. = split fraction T = temperature, K x = mole fraction of each species in each phase (gas, liquid, or hydrate) X = mole fraction of each species in each reactor

fraction in the gas phase, thereby rendering sII hydrate formation in the (i + 2)th equilibrium state, and so forth. In order to quantify the evolution in the proportions of sII and sI hydrates, respectively, to the entire hydrates formed in each reactor, we determined the fractions of sII and sI hydrates for each package of hydrates formed in 10 consecutive equilibrium states, for example, from the (i − 10)th to the ith states, and assigned the obtained fraction values to the ith state. The evolution of the structure fractions obtained in this way for the second stage (k = 2) is, as observed in both parts a and b in Figure 3, apparently different from those for the other stages in that neither the fraction of sII nor the fraction of sI tends to approach a single steady-state value with an increase in ngas,out/ ngas,0. In the case of higher system pressure (p = 5.0 MPa), the fraction of sII alternately takes two values, 0.80 and 0.70, while the fraction of sI alternately takes two complementary values, 0.20 and 0.30, in the ngas,out/ngas,0 range exceeding ∼3. It should be noted that such oscillatory changes in the sII and sI fractions are computational artifacts depending on the “size” of the hydrate package mentioned above. For example, if we double the number of consecutive equilibrium states to be packaged for obtaining each pair of sII- and sI-fraction data, the sII and sI fractions should take single values0.75 and 0.25, respectivelyin the ngas,out/ngas,0 range above ∼3. In the case of lower system pressure (p = 2.5 MPa), sII takes the fraction of 0.40 and, at a lower frequency, the fraction of 0.30, while sI takes the higher fractions of 0.60 and, at a lower frequency, 0.70. This “dual fraction” pattern remains unchanged if ngas,out/ngas,0 exceeds ∼3. Thus, we can reasonably claim that, whether the system pressure p is 5.0 or 2.5 MPa, the gas/liquid/hydrate system inside the reactor of the second stage (k = 2) closely approaches a steady state as ngas,out/ngas,0 increases to ∼3.

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Greek Symbols

δ = fraction of the gas, liquid, or hydrate removed from the relevant phase in each reactor ζ = proportionality constant relating the δ values for two different phases Subscripts

combust = combustibles (the sum of CH4, C2H6, and C3H8 molecules) eq = equilibrium state feed = feed gas gas = gas mixture hyd = hydrate in = number of molecules supplied to each reactor liq = aqueous liquid out = number of molecules discharged from each reactor w = water Superscript

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REFERENCES

(1) Economides, M. J.; Wood, D. A. The State of Natural Gas. J. Nat. Gas. Sci. Eng. 2009, 1, 1−13. (2) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008; section 6.3. (3) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008; section 1.2.7. (4) Rufford, T. E.; Smart, S.; Watson, G. C. Y.; Graham, B. F.; Boxall, J.; Diniz da Costa, J. C.; May, E. F. The Removal of CO2 and N2 from Natural Gas: a Review of Conventional and Emerging Process Technologies. J. Petrol. Sci. Eng. 2012, 94/95, 123−154. (5) Happel, J.; Hnatow, M. A.; Meyer, H. The Study of Separation of Nitrogen from Methane by Hydrate Formation Using a Novel Apparatus. Ann. N.Y. Acad. Sci. 1994, 715, 412−424. (6) Golombok, M.; Ineke, E.; Luzardo, J. C. R.; He, Y. Y.; Zitha, P. Resolving CO2 and Methane Hydrate Formation Kinetics. Environ. Chem. Lett. 2009, 7, 325−330. (7) Van Denderen, M.; Ineke, E.; Golombok, M. CO2 Removal from Contaminated Natural Gas Mixtures by Hydrate Formation. Ind. Eng. Chem. Res. 2009, 48, 5802−5807. (8) Ricaurte, M.; Torré, J. P.; Broseta, D.; Diaz, J.; Dicharry, C.; Renaud, X. CO2 Removal from a CO2−CH4 Gas Mixture by Hydrate Formation: Evaluation of Additives and Operating Conditions. Proceedings of the 7th International Conference on Gas Hydrates, Edinburgh, U.K., July 17−21, 2011; Paper 616. (9) Dabrowski, N.; Windmeier, C.; Oellrich, L. R. Purification of Natural Gases with High CO2 Content Using Gas Hydrates. Energy Fuels 2009, 23, 5603−5610. (10) Baker, R. W.; Lokhandwala, K. Natural Gas Processing with Membranes: an Overview. Ind. Eng. Chem. Res. 2008, 47, 2109−2121. (11) Liu, Q.; Jin, Z.; Hu, A.; Bi, C. Origin of Marine Sour Natural Gas and Gas-Filling Model for the Wolongne Gas Field. J. Asian Earth Sci. 2012, 58, 24−37. (12) 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

AUTHOR INFORMATION

Corresponding Author

*Tel.: +81 45 566 1813. Fax: +81 45 566 1495. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported, in part, by a Keirin-racing-based research-promotion fund from the JKA Foundation. A part of this study was performed as a joint research by Mitsui Engineering & Shipbuilding Co., Ltd. (MES), and Keio University. The authors are indebted to M. Miyagawa, S. Sakurai, and M. Takahashi of MES for their encouragement.

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MSU = multistage unit composed of k stages (from the first to kth stages)

NOMENCLATURE

i = ordinal indicating the serial number of the current phaseequilibrium calculation j = ordinal indicating the serial number of a given species as a constituent of the feed gas k = ordinal indicating the serial number of a given stage in a multistage gas-processing system m = total number of species composing the feed gas N = number of molecules contained in each phase (gas, liquid, or hydrate) or each reactor ngas,out = moles of the feed-gas-constituent substances that have been discharged from each reactor to the one of the next stage 15175



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Application to Hydrate Formation from a Methane + Ethane + Propane Mixture. Energy Fuels 2005, 19, 1587−1597. (13) Kobayashi, T.; Mori, Y. H. Thermodynamic Simulations of Hydrate Formation from Gas Mixtures in Batch Operations. Energ. Convers. Manage. 2007, 48, 242−250. (14) Ogawa, H.; Imura, N.; Miyoshi, T.; Ohmura, R.; Mori, Y. H. Thermodynamic Simulations of Isobaric Hydrate-Forming Operations for Natural Gas Storage. Energy Fuels 2009, 23, 849−856; Erratum. ibid. 25, 1333. (15) Kestin, J. A. Course in Thermodynamics; Xerox College Publishing: Waltham, MA, 1966. (16) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008; appendix A and a CDROM supplement. (17) Linga, P.; Kumar, R.; Englezos, P. The Clathrate Hydrate Process for Post and Pre-Combustion Capture of Carbon Dioxide. J. Hazard. Mater. 2007, 149, 625−629. (18) Kondo, W.; Ogawa, H.; Ohmura, R.; Mori, Y. H. Clathrate Hydrate Formation from a Hydrocarbon Gas Mixture: Evolution of Gas-Phase Composition in a Hydrate-Forming Reactor. Energy Fuels 2010, 24, 6375−6383. (19) Darbouret, M.; Cournil, M.; Herri, J.-M. Rheological study of TBAB hydrate slurries as secondary two-phase refrigerants. Int. J. Refrig. 2005, 28, 663−671.

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Thermodynamic Simulations of Hydrate-Based Removal of Carbon

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