Optimal design of an activated carbon for an adsorbed natural gas storage system

Carbon 40 (2002) 1295–1308

Optimal design of an activated carbon for an adsorbed natural gas storage system S. Biloe´ a , V. Goetz a , *, A. Guillot b a

´ ´ ´ ´ , Site Carnot, Rambla de la thermodynamique, des Materiaux et Procedes IMP-CNRS UPR 8521, Institut de science et genie 66100 Perpignan, France b Universite´ de Perpignan, 52 avenue de villeneuve, 66860 Perpignan, France Received 12 June 2001; accepted 20 October 2001

Abstract The Dubinin–Astakhov equation was used to determine the influence of the microporous characteristics of activated carbon on the performances of both charge and discharge of an ANG system. From the dynamic performance criterion as a function of total microporous volume (Wo ), average micropore width (Lo ), and micropore size dispersion (n), it is possible to identify the optimal activated carbon for methane storage under dynamic conditions by way of the heat and mass transfer limitations. This study shows that the activated carbon must be conductive (with an average micropore width of 1.5 nm) for the charge step only, permeable and sufficiently conductive for the discharge process (with an average micropore width of 2.5 nm). The well-known Maxsorb activated carbon shows the better performance. This theoretical investigation has been validated by experimental results.  2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Activated carbon; C. Adsorption; D. Gas storage; D. Textures

1. Introduction Microporous materials are widely used as adsorbents for various applications [1,2]: gas separation and purification, catalysis support, gas storage. The use of adsorbent materials for storing natural gas is another application attempting to make natural gas vehicles (NGVs) competitive with current vehicles using conventional fuels. Adsorbed natural gas (ANG) uses adsorbents, such as activated carbons (ACs), to store natural gas at moderate pressures, 3.5 MPa, compared to the required high-pressures (20 MPa) for current compressed natural gas (CNG) technology [3]. Before carrying on with the discussion, some definitions and variables have to be defined in this work. 1. Firstly, we denote by Q s (T, P), the stored natural gas capacity at pressure P and temperature T. It is ex-

*Corresponding author. Tel.: 133-4-6855-6855; fax: 133-46855-6869. ´ goetz@univE-mail addresses: [email protected] (S. Biloe), perp.fr (V. Goetz), [email protected] (A. Guillot).

pressed as the stored volume of natural gas per unit of adsorbent volume, measured under standard conditions (STP): P50.101 MPa and T5273 K. 2. Secondly, we define by Q st , the total stored natural gas capacity at charge pressure (Pc 53.5 MPa) and room temperature (T o 5298.15 K): Q st 5 Q s (T o , Pc )

(1)

3. Thirdly, we define by Q av , the available natural gas capacity for the charge and the discharge process of an ANG system. It is expressed as the total stored gas capacity minus the stored gas capacity at depletion pressure (Pd 50.1 MPa): Q av 5 Q s (T o , Pc ) 2 Q s (T o , Pd ).

(2)

Several authors traditionally report it as the isothermal delivered methane capacity. 4. Under real working conditions (or dynamic conditions), the charge step as well as the discharge step is normally performed at constant flow rate. Any finite flow rate of adsorption and desorption is accompanied by heat and mass transfer limitations as described later. These

0008-6223 / 02 / $ – see front matter  2002 Elsevier Science Ltd. All rights reserved. PII: S0008-6223( 01 )00287-1

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Nomenclature A Polaniy’s adsorption potential, J mol 21 Eo characteristic energy of adsorption, J mol 21 fva volumetric fraction of methane in adsorbed phase, – fvg volumetric fraction of methane in the gas phase, – fvc volumetric fraction of graphite, – k permeability, m 2 Lo average micropore width, nm Lom optimal average micropore width, nm Mg molecular mass of the gas, kg mol 21 n DA exponent, – P pressure, Pa Pd depletion pressure, Pa Pc charge pressure, Pa Pcr critical pressure, Pa Po saturated vapour pressure, Pa Q av available methane capacity, V V 21 Q ds stored methane capacity under dynamic conditions, V V 21 Q dd delivered methane capacity under dynamic conditions, V V 21 Qs stored methane capacity, V V 21 Q st total stored methane capacity, V V 21 q adsorbed amount, kg kg 21 R ideal gas constant, J mol 21 K 21 Se external surface area, m 2 g 21 t thickness of the layer adsorbed on the external surface area, m T temperature, K T cr critical temperature, K To room temperature, K Vmg molar volume in standard conditions, m 3 mol 21 Vt total adsorbed volume, m 3 g 21 w1 mass ratio of ENG, – W adsorbed volume, m 3 kg 21 Wo total microporous volume, m 3 kg 21 Z compressibility factor, – a factor, – b affinity coefficient, – DP pressure drop, MPa DT thermal gradient, K l thermal conductivity, W m 21 K 21 h efficiency, – ra packing density of activated carbon bed, kg m 23 rads adsorbed gas density, kg m 23 rc graphite density, kg m 23 rg gas phase density, kg m 23 rmax maximal density of activated carbon bed, kg m 23

limitations reduce the available natural gas capacity. So we define by Q ds and Q dd , the stored and the delivered methane capacity under dynamic conditions. For the ANG process, the most important parameter is the delivered natural gas capacity of the adsorbent. To be a commercially viable system, a 150 V V 21 delivered methane capacity is necessary [4], i.e. volume of methane delivered per volume of adsorbent used. Nevertheless, several problems affect ANG technology. The first one is the amount of gas that is retained at depletion pressure when discharging an ANG vessel. The available methane

capacity, assuming isothermal conditions and no mass transfer limitation, is therefore different by 10–15% compared with the total stored gas capacity (Fig. 1a). The capacity loss depends mainly on the shape of the isotherm as described later. Secondly, since the adsorption (resp. desorption) is an exothermic process (resp. endothermic), an increase in temperature (resp. decrease) results in less stored methane capacity (resp. delivered methane capacity) under dynamic conditions (Fig. 1a and b). The thermal effects closely depend on the heat transfer properties of the adsorbent bed as well as the heat external exchange at vessel wall.

S. Biloe´ et al. / Carbon 40 (2002) 1295 – 1308

Fig. 1. Impact of heat and mass transfer limitations on the delivered (a) and stored (b) methane capacity, respectively, for the special case of an activated carbon packed bed (Maxsorb, ra 5500 kg m 23 ).

Previous studies have shown that the total stored methane capacity is reduced by 35% when charging a storage vessel under adiabatic conditions. The corresponding temperature drop reached 708C [5]. In addition, the rate of fill and discharge are major factors influencing the exothermic and endothermic effects [5–8]. Thirdly, the required high packing densities of adsorbent beds create mass transfer limitation, that limit in the same way Q ds and Q dd [8,9]. Consequently, the performances and hence the viability of an ANG system depend closely on the microporous

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characteristics of the adsorbent as well as the heat and mass transfer properties. The choice of a suitable adsorbent is an active area of scientific research. This search is based broadly on experimental adsorption isotherms and theoretical investigations. Adsorption isotherm measurements have already been carried out to investigate the feasibility of microporous adsorbents for methane storage [10–17]. The most successful adsorbent is to date the well-known activated carbon (AC) designed as Maxsorb. The total stored methane capacity is 101 V V 21 and 172 V V 21 in powder form and in monolith form (with thermoplastic binder), respectively [18]. The packing density of the AC bed is 300 and 700 kg m 23 , respectively. More recently, Baker et al. [14] have produced a highly microporous wood-based AC by a two-step chemical activation (H 3 PO 4 , KOH). The available methane capacity (Q av ) reached 153 V V 21 . The total stored capacity was similar to Maxsorb: 173 V V 21 . The characterization of microporous carbons by simulation or theoretical methods can provide tools to screen beforehand suitable adsorbents for methane storage. Grand canonical ensemble Monte Carlo (GCEMC) molecular simulations and non-local density functional theory (DFT) were used for example to predict the adsorption of methane in a slit-shaped pores model and to identify the optimal micropore structure [19–26]. Matranga et al. [20] have shown that, for an optimal pore size, the available methane capacity measured over an operating cycle (3.4– 0.14 MPa) and under specific conditions (P50.1 MPa, T5288 K) was close to 195 and 137 V V 21 for a monolithic carbon and a pelletized carbon, respectively. All these studies provided insights into adsorbents that could be favourable for methane storage. Nevertheless, the current definition of the idealized microporous adsorbent is free from heat and mass transfer limitations. For the issue of the related problems to ANG storage systems, several scales have to be considered to define the optimal AC: the scale of the AC itself that plays a specific role in adsorption properties, and the packing scale that is concerned by the thermal and mass transfer properties. For example, one can expect an AC bed having a low conductivity ( l 50.1 W m 21 K 21 ), and an adsorption isotherm that increases very steeply at low pressures, to present stored and delivered gas capacities under dynamic conditions, largely lower than that available, making its use inappropriate for an ANG system. In this paper, we explore, using the well-known Dubinin–Astakhov (DA) equation, the variation of the performances during both the charge and the discharge process according to the microporous characteristics of the AC and the heat and mass transfer limitations. It was realized by introducing an average pressure and an average temperature drop in the DA equation, respectively. These are derived from heat and mass transfer properties of the AC bed as well as the geometric configuration of the vessel and the heat exchange conditions at the reactor wall.

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This paper is an extension of a previous study that dealed with cold production by sorption solid using activated carbon and CO 2 [27].

critical gas is transformed in quasi vapor. It is then possible, as suggested by Dubinin [30] to use the following phenomenological estimate of Po for a supercritical gas:

2. Methodology

T Po 5 Pcr ] T cr

S D

2.1. Constitutive equations The well-known Dubinin–Astakhov equation was used to calculate adsorbed amounts of methane. The DA equation is expressed as follows: W 5 Wo exp

F S DG A 2 ] b Eo

n

(3)

where W and Wo are the adsorbed volume at the relative pressure Po /P and the total adsorbed volume of the micropores, respectively; Eo is a characteristic energy of adsorption; b is an affinity coefficient related to the adsorbent–adsorbate interaction; and n is the DA exponent related to the pore size dispersion. A is the Polanyi’s adsorption potential defined as:

S D

Po A 5 RT ln ] P

(4)

where Po is the saturated vapour pressure. The adsorbed amount of gas is then expressed as follows: q(T, P) 5 Wo rads (T ) exp

F S DG A 2 ] b Eo

n

(5)

where rads (T ) is the adsorbed gas density at temperature T. The DA equation makes it possible to estimate the amount of gas adsorbed in a wide range of pressure and temperature from a small number of isotherms. Its use is particularly interesting for the studies of processes of gas cycling because one can deduce from Eq. (3), the isosteres, and thus connect the coefficients of performance of the processes to the microporous characteristics of the adsorbent [28]. It results from Polanyi’s theory, for a same adsorbent, the equation can be applied to a large variety of vapor, each one being characterized by the affinity coefficient b. The data of different vapors can be fitted to a single curve. One can estimate from that curve the amount adsorbed by a vapor knowing its b coefficient. The use of the DA equation is in principle limited by its starting assumptions: (1) it is limited to the process of micropore filling and cannot account for the adsorption on the external surface area. (2) It deals with vapor and does not describe the process of micropore filling by a supercritical gas. In that state, the concept of saturated vapor pressure Po does not exist. However, there are some indications that supercritical fluid can be physisorbed in the micropores under high pressures of adsorbate. As advanced by Kaneko [29], the strong adsorbent–adsorbate interaction induces an enhanced adsorbate–adsorbate interaction and the super-

2

.

(6)

So, in this paper, the pseudo-saturated vapour pressure is expressed according to Dubinin’s expression. In addition, the adsorbed gas density is expressed according to Osawa’s expression [31]. Due to the non-ideality of methane, fugacities are used instead of pressures. The affinity coefficient b, related to adsorbate–adsorbent interaction, is close to 0.35 for methane [32]. The Dubinin–Stoeckli (DS) relation [33] is used to correlate the characteristic energy Eo (kJ mol 21 ) and the average width of the slit-shaped micropore Lo (nm): 10.8 Lo 5 ]]]. Eo 2 11.4

(7)

The average micropore width is defined by the vertical distance from the surface of a carbon atom in one plane to the surface of a carbon atom in the next plane. The variation of Lo is chosen as 0.5,Lo (nm),2.5 according to the validity of the previous relation. The stored capacity of methane at pressure P and temperature T, expressed as volume of methane under standard conditions per unit adsorbent volume, depends on both the stored amount of methane in adsorbed phase and in gas phase, respectively, according to: Vmg Q s (T, P) 5 ] f fva (T, P)rads (T ) 1 fvg (T, P)rg (T, P) g . Mg

(8)

The gas phase density is expressed according to the following relation: Mg P rg (T, P) 5 ]]] Z(T, P)RT

(9)

where Z(T, P) is the compressibility factor. The volumetric fraction of methane in adsorbed phase and the volumetric fraction of methane in the gas phase are given by:

ra fva (T, P) 5 q(T, P)]] rads (T )

(10)

fvg (T, P) 5 1 2 fva (T, P) 2 fvc

(11)

where fvc is the volumetric fraction of carbon, expressed as: ra fvc 5 ] (12) rc where rc and ra are the carbon density ( rc 52250 kg m 23 ) and the packing density of the AC bed. We define the density of a perfect monolith as the maximal theoretical density of an AC bed by eliminating the void spaces

S. Biloe´ et al. / Carbon 40 (2002) 1295 – 1308

between activated carbon particles. It can be expressed by the following relationship:

rc rmax (Wo ) 5 ]]]. rcWo 1 1

(13)

Therefore, the packing density of the AC bed can be correlated to the density of a perfect monolith rmax (Wo ), by way of a factor a, according to:

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available for natural gas storage: 150 V V 21 delivered methane capacity. This simple representation could easily give tools to identify the most promising existing ACs by way of its microporous properties.

2.2. Performance criterion

The factor a is related to the implementation of the AC bed. It takes place in the range of 0–1. The lower limit value of a 50 represents a vessel filled by CNG, without microporous materials. On the other hand, the upper limit of a 51 corresponds to an ANG vessel filled by a perfect monolith. Fig. 2 shows for example the available methane capacity (Q av ) in a CNG-filled vessel and in an ANG-filled vessel with two ACs: a carbon molecular sieve (CMS) and a super-adsorbent (Maxsorb), respectively. Two implementations were chosen according to a 51 and a 50.5. As a result, whichever a, there is a pressure at which the available methane capacity for CNG vessel is the same as that for ANG vessel for the particular case of CMS (point A). If one operates at this level of pressure, there’s no advantage to using ANG storage technology. A carbon molecular sieve (CMS) is efficient under lower pressure (P,3 MPa), but its available methane capacity is more and more limited as the pressure increases (P.4 MPa). On the other hand, a super-adsorbent is quite efficient. Nevertheless, its implementation must be optimal (a 51) to be

As described previously, the performances of ANG systems closely depend on the heat and mass transfer properties of the adsorbent. At the same time, the performances depend on the external heat transfer exchange (at reactor wall) as well as the geometric vessel (diameter, length . . . ). Fig. 3 shows the thermodynamic path of an AC bed in the Clausius–Clapeyron diagram for both the charge and the discharge process. The thermodynamic path depends on the microporous characteristics of the adsorbent (Wo , Lo , n) by way of the isosteres. The straight lines represent the isosteric network, derived from the DA equation. Each line corresponds to an isostere where the adsorbed amount is constant. Let us illustrate the particular case of the discharge process at constant flow rate. The same reasoning can be easily transposable for the charge step. In the beginning, the ANG vessel is at room temperature (T o ) and at charge pressure (Pc ). The ANG storage vessel is then submitted to a finite flow rate of desorption up to the point B. At this point, the constant discharge flow rate cannot be ensured any more according to the heat and mass transfer limitations. The corresponding delivered methane capacity is Q dd . Afterwards, the temperature increases and the pressure recovers down to depletion pressure: the ANG storage vessel is then

Fig. 2. Available methane capacity in a CNG-filled vessel (—) and in an ANG vessel filled with a CMS (s, n) and a superadsorbent (d, m), respectively.

Fig. 3. Thermodynamic path of activated carbon bed in the Clausius–Clapeyron representation during the charge and the discharge process.

ra 5 armax (Wo ).

(14)

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situated at the point C. The corresponding delivered methane capacity is Q av . In this paper, these heat and mass transfer limitations are gathered according to a pressure drop DP, and a temperature drop DT, respectively. So we define two criteria on dynamic discharge step Q dd , and dynamic charge Q ds step, taking into account the heat and mass transfer limitations. The delivered methane capacity under dynamic conditions is given by the stored capacity of methane at charge pressure and room temperature minus the stored capacity of methane at pressure Pd 1DP and temperature T o 2DT (Fig. 3): Q dd 5 Q s (T o , Pc ) 2 Q s (To 2 DT, Pd 1 DP).

(15)

In the same way, the stored methane capacity under dynamic conditions (at finite charge flow rate) is given by the stored capacity of methane at pressure Pc 2DP and temperature T o 1DT minus the stored capacity of methane at depletion pressure (Pd ) and room temperature (Fig. 3): Q ds 5 Q s (T o 1 DT, Pc 2 DP) 2 Q s (T o , Pd ).

(16)

For a given (DT, DP), the optimal AC in terms of microporous volume, average micropore width and pore size dispersion, is determined by resolving the above equations: ≠Q ]50 ≠Wo ≠Q ]50 ≠Lo ≠Q ]50 ≠n

The constitutive Eqs. (1)–(18) allow us to identify the optimal AC during both the charge and the discharge step of an ANG system under dynamic conditions by way of DP and DT.

3.1. Static regime First of all, we have considered that there is no heat and mass transfer limitation during the two-step process (DP5 0, DT50). According to the previous definitions (Eqs. (15) and (16)), the delivered and the stored methane capacity are the available methane capacity (Fig. 1). In addition, we have considered a perfect monolith (a 51). This allows us to evaluate the ideal AC without consideration of AC bed implementation. Fig. 4 shows, for a fixed value of the total microporous volume (Wo 51.0 cm 3 g 21 ), the available methane capacity as a function of both the average micropore width (Lo ) and the dispersion of the PSD (n). For a given value of Lo , an increase of n leads to an increase of the available methane capacity with respect to ≠Q / ≠n . 0. When n increases, the isosteric network (Fig. 3) is more closed up. For the same range of thermodynamic conditions (Pc 2Pd ), one sweeps away a greater number of isosteres, increasing then the available methane capacity. For each value of n, and independently of Wo , the available methane capacity passes through a maximum (represented by symbols s) with respect to ≠Q / ≠Lo 5 0 (Fig. 4). This maximum moves to larger value of Lo when

(17)

3. Results and discussion For this study, the charge pressure, the depletion pressure and the room temperature are fixed to 3.5 MPa, 0.1 MPa and 298.15 K, respectively. The maximum range of variation of the microporous characteristics in the DA equation (Wo , Lo , n) is: 0.1 , Wo (cm 3 g 21 ) , 1.4 0.5 , Lo (nm) , 2.5 1,n,2

(18)

Activated carbons are microporous materials with variable pore size distributions (PSDs). Therefore, these ranges are representative of most AC findings in the literature, from carbon molecular sieve to super-adsorbent fields. Elaboration of AC with high microporous potential leads to an increase of the average micropore width as well as the dispersion of the PSD [34]. However, relations between Eo , Wo and n are still lacking. Then, the microporous properties are supposed, in first approximation, independent of each other.

Fig. 4. Available methane capacity versus the average micropore width for different pore size dispersions (constant step of 0.2) under static regime (DP50, DT50).

S. Biloe´ et al. / Carbon 40 (2002) 1295 – 1308

n decreases. The more n decreases, the more the PSD is widened. Therefore, there’s quite a longer influence of a given value of Lo , and the isosteres are less sensitive to the variation of Lo . For example, the available methane capacity is about 120 V V 21 for whatever Lo , and for n51. The influence of Wo on the delivered methane capacity is shown in Fig. 5. For each n, the value of Lo has been taken equal to that calculated previously, maximising Q av . The value of Q av increases relatively steeply in the lower Wo and rises to an asymptotic value as Wo increases. This phenomenon is attributed to the closed dependence of the available methane capacity, expressed in terms of V V 21 , on the perfect monolith density of the AC that is related to Wo . As Wo increases, rmax decreases (Eq. (13)). Nevertheless, the available methane capacity increases with increasing Wo , showing the necessity of using highly microporous AC for methane storage. From Fig. 5, it is interesting to note that numerous AC (represented by symbols d), having very different microporous characteristics, are able to reach the performance target of 150 V V 21 . Nevertheless, we have assumed a perfect monolith. In practice, the factor a lies between 0.5 and 0.8 [5,8]. Consequently, for the special case of static charge and discharge processes, the optimal AC, in monolith form, will be the more homogeneous (n→2) with an average micropore width in the range of 1–2.5 nm, and a maximum total microporous volume. For Wo 51 cm 3 g 21 , Lo 51.6 nm and n52, the delivered methane capacity is

Fig. 5. Available methane capacity versus the microporous volume for different pore size dispersions under static regime (DP5 0, DT50).

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close to 208 V V 21 . This value can be considered as the upper limit that could be reached.

3.2. Dynamic regime Previous experimental studies and simulations on both charge and discharge dynamics of a methane adsorption storage system [5–8] have reported that a temperature drop of about 70–808C is observed. On the other hand, the knowledge of the mass transfer limitation is still lacking. The majority of the authors have assumed uniform pressure within the storage system. However, a recent study [8] has shown that, for an adsorbent composite block (ACB) made from expanded natural graphite (ENG) and Maxsorb AC, and for high discharge flow rates, the average volumetric pressure drop has reached 0.3 MPa. The packing density was 450 kg m 23 , with an apparent density of the AC in the block of 330 kg m 23 . The corresponding a, as described previously, is then equal to 0.5. The requirement of higher packing densities could lead to a greater mass transfer limitation. In addition Cook et al. [9,35] have reported that for monolithic adsorbents with high packing density ( ra .0.5 g cm 23 ), a pressure drop of up to 0.7 MPa was reached. Consequently, the values of DP and DT are chosen over a fixed range of 0–808C and 0–1 MPa, respectively. For a given value of a, the heat and mass transfer limitations can vary over a large range. This fact depends on both the microporous characteristics of the AC and the implementation of the AC bed: in monolith form or in pellet form for example. So in this work, the factor a was chosen arbitrarily equal to 0.7. For whichever DP and DT, the AC must have a homogeneous PSD (with narrow microporosity) and the microporous volume as high as possible (≠Q / ≠n . 0 and ≠Q / ≠Wo . 0). Under dynamic conditions, an increase of both n and Wo leads to an increase of the delivered and the stored methane capacity, respectively. The AC is then considered homogeneous (n52) and the total microporous volume has been taken arbitrarily equal to 1 cm 3 g 21 . In the following step, we investigate the evolution of the stored and the delivered methane capacities under dynamic conditions as a function of Lo only.

3.2.1. Charge process The stored methane capacities under dynamic conditions are shown in Fig. 6a and b as a function of the average micropore width, by considering successively heat transfer limitation only (0,DT ,808C, DP50) and mass transfer limitation only (0,DP,1 MPa, DT50). As shown by Fig. 6a and b, the stored methane capacity is very sensitive to heat transfer limitation contrary to the mass transfer limitation. As DT increases from 0 to 808C, the loss reaches 50%, reducing the stored methane capacity from 153 to 76 V V 21 for Lo 52.5 nm. This loss is in the same magnitude of that obtained from previous experimen-

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from the isosteric network or the shape of the adsorption isotherm of the AC. Indeed, at low pressures, a gradually increasing methane uptake is observed. As the pressure reaches the charge pressure, the methane uptake may level off and a plateau is observed (isotherm in flat shape), the mass transfer limitation has no longer influence then. This phenomenon remains true for larger Lo , but with a more pronounced difference. Near the charge pressure, the isosteric network is more close up. Consequently, the stored methane capacity is very sensitive to the level of temperature (Fig. 3). This phenomenon is more pronounced as Lo decreases, because the isosteric network is more and more closed up. As one can see for a given DT, changes in average micropore width from 1.0 to 0.5 nm could have very large detrimental effects on the stored methane capacity. The resolution of Eq. (16) leads to determine the optimal average micropore width (Lom ) for each DT, DP and n. As the heat transfer limitation becomes high, Lom increases from 1.0 to 1.6 nm. Similarly, as the mass transfer limitation becomes high, Lom increases from 1.36 to 1.6 nm. It is clear from Fig. 6a and b that the highest stored methane capacity is in the micropores with an average slit micropore of 1.5 nm whatever the heat transfer limitation or the mass transfer limitation, otherwise the detrimental effects are more important. Additionally, for the charge step, the heat transfer is considerably more limited than the mass transfer whatever the microporous characteristics of the AC used. This is the more important observation.

Fig. 6. Impact of the heat transfer limitation (a) and the mass transfer limitation (b) on the stored methane capacity for various average micropore widths. The symbols (s) denote the optimal average micropore width.

tal and simulated results derived from Jasionowski et al. and Mota et al., respectively [5,7]. On the other hand, the stored methane capacity is not too sensitive to the mass transfer limitation whatever the average micropore width. If the pressure drop continually increases from 0 to 1 MPa, then the stored methane capacity decreases very slowly. The maximum loss is about 18% for Lo 52.5 nm. The corresponding stored methane capacity is then reduced from 153 to 129 V V 21 . These quantitative features of the influence of the type of limitation can be understood either

3.2.2. Discharge process Similarly, Fig. 7a and b show the delivered methane capacities as a function of the average micropore width by considering heat and mass transfer limitation, respectively. Contrary to the charge process, the delivered methane capacity is very sensitive to mass transfer limitation. Indeed, increasing DP from 0 to 1 MPa, leads to a large decrease of the delivered methane capacity (from 153 to 82 V V 21 , Lo 52.5 nm). The corresponding loss reaches 46.5%, compared with 18% for the charge step. As described previously, as the pressure decreases from the charge pressure to lower pressures, the shape of the isotherm is more and more steep. For a given Lo , there is then a large influence of a DP on the delivered methane capacity. As Lo decreases, the adsorption isotherm is more and more steep under low pressure, reducing dramatically the performances. In the same way, when heat transfer limitation takes place and for Lo .1.0 nm, the loss is lower than that observed during the charge step, from 28 to 42% (Lo 52.5 nm). Nevertheless, the delivered methane capacity does not exceed 110 V V 21 for the highest DT. Similarly to the charge step, there is a large influence, for a given DT or DP, of the average micropore width. Small changes in Lo in the region of low limitation could

S. Biloe´ et al. / Carbon 40 (2002) 1295 – 1308

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have very large effects on the ability of the AC to release the necessary amount of methane. For Lo 50.8 nm and DP50.3 MPa, the loss is close to 32%, compared to 15% for Lo 52.5 nm. The decrease of Lo involves decrease of the slope of the isosteres (isosteric heat of adsorption) as well as the space between them, for an equal adsorbed amount. This induces more detrimental effects on the performances. The resolution of ≠Q / ≠Lo 5 0 allows us to determine the optimal average micropore width (Lom ) for each DT, DP and n. As the limitation increases, Lom increases from 1.6 to 2.5 nm whatever the specific limitation. As shown by Fig. 6a and b, for DT .408C and DP.0.3 MPa, an AC with an average micropore width of 2.5 nm is the best available one. Consequently, the optimal AC must have an average micropore width of 2.5 nm for the discharge step. The most important observation is the detrimental effect of the mass transfer limitation on the performances rather than the heat transfer limitation. This fact was never before emphasized. On the contrary, in the study of Jasionowski et al. [5], the authors conclude that the loss in performances was due to the poor conductivity of the AC bed only. Nevertheless, we think that the AC bed used, with a packing density of 0.45 g cm 23 (corresponding a 50.7), must lead to large mass transfer limitation.

3.3. Commercially available activated carbon

Fig. 7. Impact of the heat transfer limitation (a) and the mass transfer limitation (b) on the delivered methane capacity for various average micropore widths. The symbols (s) denote the optimal average micropore width.

As described previously, elaboration steps of ACs lead mostly to non-ideal microporous characteristics. The development of the microporosity is generally accompanied with an increase of the dispersion of the PSD. Table 1 provides some relevant microporous characteristics on three current activated carbons: a molecular sieve (CMS), an activated fiber KF-1500 and the well-known Maxsorb. The different microporous characteristics are derived from the best-fitted curve (DA equation) on the CH 4 adsorption isotherm for three levels of temperatures (253, 273 and 298 K) and for a range of pressure of 0.1–3.5 MPa. In addition, the micropore volume Wo and the external surface area Se can be determined by the method of comparison of isotherms. It consists of comparison of the experimental adsorption data with a reference isotherm determined under the same conditions on a non-porous material. The

Table 1 Microporous characteristics of some activated carbons AC

Standard DA analysis

Maxsorb KF-1500 CMS

21

Comparison plots

Wo (cm g )

Eo (kJ mol )

n (–)

Wo (cm 3 g 21 ) CH 4 (253 K)

Wo (cm 3 g 21 ) CO 2 (273 K)

1.088 0.601 0.303

16.15 20.44 26.30

1.4 1.58 1.875

0.875 0.588 0.3

1.35 0.6 0.3

3

21

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great majority of published work has involved the analysis of low temperature nitrogen adsorption isotherms in the form of the well-known as -plot developed by Sing [36– 38], and refined by Kaneko [39]. Other adsorbates have been used as internal reference. For example, Carrott et al. [40,41] have suggested the use of benzene and dichloromethane at 298 K. Recently Guillot and Stoeckli [42] have shown that the adsorption of CO 2 on Vulcan-3G at 273 K up to 3.2 MPa can be used as a reference isotherm. The application to well-characterized activated carbons leads to results in good agreement with determinations based on nitrogen and benzene. In addition, adsorption of CH 4 on the same carbon black at 253 K up to 6.8 MPa has been determined. The corresponding comparison plots are shown in Fig. 8. The results of the characterization for the three activated carbons by CO 2 and CH 4 comparison plots are given in Table 1. If the estimated values of the total micropore volume Wo by both determinations are in good agreement for CMS and KF-1500, on the other hand, there is a discrepancy for the Maxsorb values. One finds a Wo of 1.35 cm 3 g 21 for CO 2 , and 0.875 cm 3 g 21 for CH 4 only. It is well known that the pore size distribution of strong activated carbon is generally broad and extends to the limit of the definition of micropores (2 to 2.5 nm). That is confirmed for the Maxsorb by the PSD proposed by Quirke et al. [43]. As methane is in supercritical state, one can suppose that it condenses less in the broadest micropores. On this assumption, the microporous network seen by the methane molecule would be thus more restricted than that seen by the CO 2 or nitrogen molecule. Table 1 shows that, except for the Maxsorb, the values of Wo adopted to fit the

experimental methane isotherms are higher than those given by the method of comparison. As described previously, the DA equation is limited to the process of micropore filling and cannot account for the adsorption on the external surface area. In that case, the experimental adsorption isotherm consists of two terms: Vt 5 Wo 1 Se t

(19)

where t is the thickness of the layer adsorbed on Se . Following this relation, if the value of the external surface area is significant, the last part of the isotherm accounts for the surface adsorption, beyond relative pressures of 0.4. In that case, the Wo value adopted to fit the experimental isotherms includes the term of surface and the parameters of the DA equation are not strictly characteristics of the microporosity. The available methane capacity, the stored and the delivered methane capacity have been evaluated from the microporous characteristics derived from the best-fitted curve on the experimental adsorption isotherm, according to a 50 K heat transfer limitation only. In addition, we have considered a perfect monolith (a 51). As shown in Table 2, Maxsorb AC is the best available one with a 21 stored methane capacity of 113.8 V V and a delivered 21 methane capacity of 142.6 V V , respectively. It corresponds to a loss of 35% and 18% compared to the available methane capacity. On the other hand, the delivered methane capacity represents 75% and 64% only of the available methane capacity for the KF-1500 activated fiber and the CMS, respectively. This result depends closely on the shape of the adsorption isotherm as described previously.

3.4. Experimental investigation In this section, an attempt has been made to validate the previous theoretical study. For this purpose, several experiments on both dynamic methane charges and discharges have been carried out with a 2-l ANG vessel. The objective was to investigate, for a given geometric configuration of an ANG vessel, the dynamic of both the charge and the discharge step of the ACBs. In order to minimize the influence of the limitations derived from heat exchange at reactor wall as well as mass transfer limitations in the ACB, the vessel wall is maintained at a fixed temperature by using an annular space wrapping around the vessel, Table 2 Performances of some activated carbon

Fig. 8. Comparison plots for CH 4 at 253 K on carbons CMS (n), KF-1500 (s) and Maxsorb (h).

AC

Q av (V V 21 )

Q ds (V V 21 )

Q dd (V V 21 )

Maxsorb KF1500 CMS

174.4 149.4 103.0

113.8 103.8 74.4

142.6 111.8 65.8

S. Biloe´ et al. / Carbon 40 (2002) 1295 – 1308

where water can flow axially by forced convection; and a gas diffuser is inserted into the center of the vessel. The adsorbent composite blocks used are made from ENG and Maxsorb with variable mass ratio of ENG, w 1 (Table 3). Expanded natural graphite was used as a high conductive medium for the enhancement of the heat transfer. Maxsorb activated carbon was used for its highly microporous volume [28,44,45]. The procedure of in-situ consolidation in the ANG vessel has been reported elsewhere [8]. Table 3 collects the heat and mass transfer properties of the ACBs used. During the charge step, a constant volumetric flow rate of methane was applied via an upstream mass flow meter. The adsorption step was terminated when the equilibrium was reached at charge pressure (Pc 53.5 MPa) and room temperature (T o 5298.15 K). For the desorption step, the ANG vessel was connected to a downstream mass flow meter. The experimental procedure was terminated when the vessel was at depletion pressure (Pd 50.1 MPa) and room temperature. The total stored and the available methane volumes were determined by way of two mass flow controllers and a gravimetric balance. To test the validity of the previous theoretical study, the ANG vessel was charged and discharged with a constant volumetric flow rate in the range of 1 to 10 l STP min 21 . These induce various thermal gradients. Thermal gradients have been measured by way of four thermocouples distributed radially throughout the vessel with a spacing of 1.1 cm [8]. The average volumetric temperature drop was evaluated by means of each thermocouple on each elementary volume Vi , according to:

O O

T iVi i DT 5uT o 2 T mu 5 T o 2 ]] . Vi

*

i

*

(20)

Contrary to the earlier study, the performances have been evaluated according to a dynamic efficiency h, defined as follows for the charge step (hc ) and the discharge step (hd ), respectively: Q ds hc 5 ] Q av

(21)

Q dd hd 5 ]. Q av

(22)

Fig. 9 shows, for the charge step, the dynamic efficiency as a function of the average volumetric thermal drop for Table 3 Heat and mass properties of adsorbent composite blocks made from ENG and Maxsorb activated carbon No.

w 1 (%)

k (m 2 )310 12

l (W m 21 K 21 )

ACB-1 ACB-2

1 26.5

2.4 0.01

0.375 7.3

1305

Fig. 9. Charge efficiency as a function of thermal gradients for ACB-1 (s) and ACB-2 (d). Line (—) indicates DA equation.

ACB-1 and ACB-2, respectively. The efficiency, which was calculated from the DA equation, including the microporous properties of Maxsorb, was represented by comparison. The major result is a very good agreement between the efficiency that was calculated from the DA equation and the experimental one. This first result validates then the previous study. An additional major result is the enhancement of the heat transfer by conduction in the ACB-2. The efficiency leads in the range of 0.95–1. The average volumetric temperature drop is then less than 5 K. The charge process using ENG is under quasiisothermal conditions. On the other hand, average volumetric temperature drop in the ACB-1 can reach 35 K for 21 the largest charge flow rate (7.5 l STP min ). The corresponding efficiency is about 0.8, reducing the available 21 methane capacity from 100 to 80 V V . Clearly, for the charge step, the heat transfer properties are the key factor to the success of an ANG storage system. Fig. 10 shows as confirmation, the average volumetric temperature drop occurring when charging the vessel at an infinite flow rate. The average volumetric temperature drop reaches about 70–80 K without ENG. The filling time is then increased by a factor 10. Consequently, the use of ENG as high conductive medium is a key factor to limit the thermal effects during the charge step and to reduce the filling time of the ANG vessel. Additionally, to further test the validity of the previous study, the dynamic efficiency on ACB-1 for both the charge and the discharge step are gathered in Fig. 11 and compared with the efficiency which was calculated from the DA equation. As shown by Fig. 11, a very good accuracy was observed between theoretical and experimen-

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showing the necessity of using a highly conductive medium for the charge step.

4. Conclusion

Fig. 10. Average volumetric temperature drop as function of time for ACB-1 (—) and ACB-2 (- - -) at infinite charge flow rate.

tal results for both the charge and the discharge process. One can see that the heat transfer limitation is more limited for the charge step than the discharge step. The efficiency decreases as the average temperature drop increases,

Fig. 11. Efficiency as a function of thermal gradients for ACB-1 during both charge (m) and discharge (.) process. Lines indicate DA equation for the charge step (- - -) and the discharge step (—), respectively.

Adsorbed natural gas technology is an attractive alternative to reduce high pressures required for current compressed natural gas. Activated carbons are recognised to be very suitable adsorbents for methane storage due to their high microporous potentials. The performances of an ANG vessel closely depend on both the microporous properties of the adsorbents and the global heat and mass transfer properties. An ideal microporous material must ensure a rapid charge process and deliver a sufficient methane capacity, which is close to 150 V V 21 . The current methods to give insights into adsorbents that are ideal for the ANG system are based either on experimental adsorption isotherms or molecular simulations. Nevertheless, these methods are free from the heat and mass transfer limitations that occurred systematically when charging and discharging an ANG vessel. In this paper, we have implicitly introduced these limitations in the DA equation by way of a DP and a DT. This study has shown how the microporous properties of the activated carbon as well as its heat and mass transfer properties and its implementation can reduce dramatically the performances of the ANG system and so its viability. From the Dubinin relations, this study has shown that the activated carbon must have a highly microporous potential (Wo ), a very narrow microporosity (n52) and an average micropore width of 1.5 nm and 2.5 nm for the charge and the discharge step, respectively. As a result, the ideal AC should have an average micropore width of 2.0 nm for the ANG system. Maxsorb was the best available commercial AC, with an average micropore width of 2.2 nm. This explains why it is so often used for ANG storage systems. For a geometric configuration of the ANG vessel and specific heat exchange conditions, the AC must be highly conductive for the charge step, and highly permeable as well as sufficiently conductive for the discharge step. Theoretical investigation was validated from experimental results on a 2-l ANG vessel. Such investigations can reduce considerably the work of identifying the most promising existing microporous materials, giving new perspectives for the preparation of microporous materials for an ANG storage system. The future objective will be to validate this study for AC with various microporous properties in order to illustrate the influence of the average micropore width as well as the total microporous volume and the PSD.

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