Filling Characteristics for an Activated Carbon Based Adsorbed

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Filling Characteristics for an Activated Carbon Based Adsorbed Natural Gas Storage System Pradeepta K. Sahoo,† Mathew John,‡ Bharat L. Newalkar,‡ N. V. Choudhary,‡ and K. G. Ayappa*,† † ‡

Department of Chemical Engineering, Indian Institute of Science, Bangalore, India 560012 Corporate R&D Centre, Bharat Petroleum Corporation, Ltd., Greater Noida, Uttar Pradesh, India 201306 ABSTRACT: The storage capacity of an activated carbon bed is studied using a 2D transport model with constant inlet flow conditions. The predicted filling times and variation in bed pressure and temperature are in good agreement with experimental observations obtained using a 1.82 L prototype ANG storage cylinder. Storage efficiencies based on the maximum achievable V/V (volume of gas/volume of container) and filling times are used to quantify the performance of the charging process. For the high permeability beds used in the experiments, storage efficiencies are controlled by the rate of heat removal. Filling times, defined as the time at which the bed pressure reaches 3.5 MPa, range from 120 to 3.4 min for inlet flow rates of 1.0 L min1 and 30.0 L min1, respectively. The corresponding storage efficiencies, ηs, vary from 90% to 76%, respectively. Simulations with L/D ratios ranging from 0.35 to 7.8 indicate that the storage efficiencies can be improved with an increase in the L/D ratios and/or with water cooled convection. Thus for an inlet flow rate of 30.0 L min1, an ηs value of 90% can be obtained with water cooling for an L/D ratio of 7.8 and a filling time of a few minutes. In the absence of water cooling the ηs value reduces to 83% at the same L/D ratio. Our study suggests that with an appropriate choice of cylinder dimensions, solutions based on convective cooling during adsorptive storage are possible with some compromise in the storage capacity.

’ INTRODUCTION The abundant reserves of natural gas (NG), estimated to be about 24% of the total energy resource,1 has been recognized as an alternative fuel source for the transportation sector. The relatively clean-burning quality and high octane number compared to that of gasoline makes natural gas attractive for vehicular use.2,3 A lower volumetric energy density of methane (the major constituent of natural gas) at ambient conditions compared to that of conventional liquid fuels limits the driving range for vehicles, making it inconvenient for onboard storage and transportation.2,4,5 In order to enhance the storage density of NG, many gas storage systems such as compressed natural gas (CNG), liquefied natural gas (LNG), and adsorbed natural gas (ANG) have been explored worldwide. In a CNG system, natural gas is stored at a pressure of about 20 MPa. The costs associated with multistage compression at filling stations, thick walled pressure vessels, and high pressure safety issues discourage the use of CNG systems for vehiclar transport.6,7 In the case of LNG based technologies, although the energy density of 23.0 MJ L1 is comparatively higher than that of a CNG system (8.8 MJ L1),8 expensive cryogenic technology required for the LNG systems poses a major drawback. With the goal of overcoming these disadvantages associated with CNG and LNG based technologies, solutions based on ANG technologies have attracted interest over the past decade.911 In the ANG system, natural gas is stored in an adsorbed state in porous adsorbents at a moderate pressure of about 3.5 to 4 MPa. The storage target of 180 V/V (i.e., liters of gas stored per liter of storage vessel internal volume under NTP conditions) as set by the US Department of Energy for ANG has been achieved with the discovery of super activated carbons, (Maxsorb) with a thermoplastic binder.12 The highest reported storage capacities r 2011 American Chemical Society

of methane of 200 V/V in monolithic activated carbons have been reported by Wegrzyn and Gurevich.13 However, development of a technology based on these materials requires a complete assessment of the charging and discharging dynamics of the adsorbent bed with accompanying heat and mass transfer effects.14,15 There are a number of challenges associated with developing a robust and viable ANG system. While assessing novel materials in the laboratory, storage capacities are based on the small sample volumes used in equilibrium adsorption isotherm measurements. Once a suitable material has been identified, it has to be further pelletized prior to being used in an adsorbent bed. The process of pelletization involves compaction of the powder samples with a suitable binder which can reduce the adsorption capacity by about 2025%. An alternate strategy not involving binders, which has been adopted for carbons, is to directly prepare monolithic samples such as Maxsorb. This process results in high density samples with enhanced adsorption capacities that can directly be used in the adsorbent bed. The final stage of performance assessment is the adsorption and delivery characteristics of the adsorbent bed itself. At the level of the storage bed, the release of significant heat during adsorption and cooling during desorption has detrimental effects on the performance of the storage system. As a result, a smaller amount of gas is stored at the target pressure during the charging cycle and a residual Special Issue: Ananth Issue Received: February 1, 2011 Accepted: April 19, 2011 Revised: April 15, 2011 Published: April 19, 2011 13000

dx.doi.org/10.1021/ie200241x | Ind. Eng. Chem. Res. 2011, 50, 13000–13011

Industrial & Engineering Chemistry Research

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amount of stored gas is retained (i.e., about 25% to 30% of the amount stored) in the cylinder at the depletion pressure during the discharge cycle.6,7,16 Thus it is essential to manage thermal effects in order to maximize the performance of the bed and retain the operating conditions both during charging and discharging as close to the equilibrium conditions.17 In this manuscript we are concerned with assessing heat and mass transfer effects associated with the charging characteristics of activated carbon storage cylinders and use a combination of experiments and modeling to evaluate this process. Both 1D models18,19 and 2D models14,15,20,21 which incorporate hydrodynamic as well as heat and mass transfer effects for Table 1. Properties of the Adsorbent Particles (Norit RGM1) BET surface area micropore surface area

1308 m2 g1 1108 m2 g1

external and macro pore surface area

194 m2 g1

total pore volume

0.5138 cc g1

micropore volume

0.3413 cc g1

average pore diameter

8.216 Å

mean particle diameter

1.0 mm

prediction of temperature and pressure variations in the adsorbent bed have been reported in the literature. To achieve fast filling of the ANG system, all these models, with the exception of Goetz and Biloe19 have considered uncontrolled flow conditions, where the inlet pressure of the storage system remains constant with the reservoir pressure and filling is based on a Darcy law model for the porous bed. Experiments on carbon beds with constant pressure inlet (3.5-4.0 MPa) conditions show a maximum temperature rise ranging from 75-80 K.6,7,16,22,23 Simulation studies with carbon based adsorbents have shown temperatures rises, ranging from 63-80 K.14,15,20,21 From a 1D model, a temperature increase of about 30 K has been obtained by Bastos-Neto et al.18 in granular activated carbons, which is lower than the temperatures reported in other carbon based beds. The storage capacity reduces significantly with the rapid rise of bed temperature during uncontrolled flow condition due to near adiabatic filling conditions. In the 1D model by Goetz and Biloe19 using constant volumetric flow rate inlet conditions with an axial gas diffuser, a temperature rise of 4 K was observed for the high thermal conductivity sample and a rise of about 45 K was observed for the low conductivity sample. It is possible to minimize temperature gradients by enhancing the thermal conductivity of the activated carbons using thermal binders such as expanded natural graphite.19,24 In this manuscript we present a combined experimental and modeling study of the filling characteristics of carbon based adsorbents in a 1.82 L cylinder. We develop a 2D model to study the temperature and pressure distributions in the adsorbent bed as a function of filling time. To our knowledge a 2D simulation with constant volumetric inlet conditions has yet to be reported in the literature. The experiments and simulations are carried out at different inlet volumetric flow rates to understand the influence of filling rates on the filling time and storage capacity. In order to optimize the geometry of the adsorbent cylinder for a fixed mass of adsorbent, simulations were carried out at different L/D ratios with and without a water cooled jacket. Our study suggests that the filling efficiencies as high as 90% can be achieved with a suitable choice of L/D ratios and forced convection cooling.

’ EXPERIMENTAL SECTION Figure 1. Fitting of the experimental isotherm, for methane adsorption into the Norit RGM1 activated carbon at 303 K with the DubininAstakhov (DA) equation.

Adsorption Isotherms. Norit RGM1, a commercially available (Norit American Inc.) microporous activated carbon, has been used as the adsorbent for our study. It is an impregnated

Figure 2. Adsorption experimental setup of the storage system. Temperatures are measured at the center of the adsorption bed (9), and the gas is charged from the inlet at point P. A mass flow controller is used to set the inlet flow conditions. 13001

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Figure 3. Schematic diagram of the ANG storage system with dimensions: r1 = 13 mm, r2 = 53.3 mm, L1 = 30 mm, L2 = 202 mm, the radius of the inlet (ri) = 3.175 mm. T is the location of the thermocouple probe located at the center of the bed.

Table 2. Physical Properties Used in the Model specific heat of methane, Cpg

2450 J kg1 K1

specific heat of activated carbon, Cps

650 J kg1 K1

molar mass of methane, Mg

16.03 103 kg mol1

isosteric heat of adsorption,24 4H

16 kJ mol1

bed porosity, εb

0.30

total porosity, εt initial bed temperature, Ti

0.65 300 K

methane source temperature, Ts

300 K

ambient temperature, T¥

300 K

thermal conductivity of solid, λs

0.54 W m1 K1

thermal conductivity of gas, λg

0.0343 W m1 K1

methane gas viscosity, μg

1.25 105 Pa-s 500 kg m3

bulk density of adsorbent bed, Fb bulk density of low permeability bed, Fb Darcy permeability of experimental bed, K

650 kg m3 3.7 1010 m2

Darcy permeability of low permeability bed, K

1015 m2

natural convection, heat transfer coefficient, h

5.0 W m2 K1

forced convection, heat transfer coefficient, h

700 W m2 K1

2

steam activated carbon with 1 mm diameter extrudates. Properties of the Norit RGM1 activated carbon are given in Table 1. The adsorbent properties were obtained from nitrogen sorption experiments. The average pore diameter of Norit RGM1 carbon was obtained from its pore size distribution as determined by the NLDFT (Non-Local Density Functional Theory) model for CO2 adsorption at 273.15 K. Methane gas having 99.9% purity has been used in all the experiments. The high-pressure methane isotherms have been measured at 303 K using a gravimetric adsorption analyzer (GHP-FS, VTI corporation) equipped with a Cahn vacuum electrobalance (TA Instruments, USA). The sample volume is evaluated by helium displacement followed by a buoyancy correction using the PengRobinson equation of state for high pressures. Prior to the adsorption isotherm measurements, about 0.1 g of the sample is loaded into the balance and then outgassed for 10 h at 473 K under high vacuum. The sample temperature is maintained constant, and data at various pressures are collected to obtain the adsorption isotherm as shown in

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Figure 1. The sample is determined as having reached equilibrium when the sample weight changes by less than 0.005 wt % in 5 min with a maximum equilibrium time of 2 h. The pressure step is terminated if the equilibrium criterion has not been met. For temperatures up to 333 K, the sample temperature is controlled with a constant temperature bath and above 333 K with an electric furnace. Depending on the pressure range, one or two pressure transducers are used to measure the gas pressure. The gas pressure is controlled through an in-built software. Adsorption Cycle Set-up and Operation. The experimental setup for the adsorption cycle of methane is depicted in Figure 2. The heart of the experimental setup is a 1.82 L prototype ANG storage cylinder. A schematic diagram of the ANG storage system with dimensions is shown in Figure 3. The cylinder is constructed using aluminum having a total length of 232.0 mm, inner diameter of 106.6 mm, and a wall thickness of 2.5 mm. It is filled and packed densely with the adsorbent (Norit RGM1 activated carbon having average particle diameter of 1.0 mm and a bulk density of 0.5 g cc1) by automated tapping. An opening of diameter 6.35 mm is located at the top of the cylinder for charging the gas. A controlled methane flow rate during charging has been maintained by a mass flow controller (Bronkhorst type) with flows in the range of 1.0 to 30.0 L min1 at STP. A pressure gauge is provided at the inlet of the cylinder for monitoring the pressure during charging. A K-type thermocouple is provided at the center of the bed along the longitudinal axis as shown in Figure 2. Prior to running each cycle, nitrogen gas is allowed to feed into the ANG system and then evacuated with the help of a vacuum pump. This process is repeated two to three times in order to remove any gas previously adsorbed in the bed. When the temperature inside the cylinder is steady, the inlet valve of the cylinder is opened and methane gas is allowed to fill at the desired volumetric flow rate. During the charging operation, variables such as pressure, temperature, and volume of the gas are monitored. When the cylinder pressure reaches 3.5 MPa, the inlet valve is closed. The time taken by the storage system to reach 3.5 MPa is referred to as the filling time. At the end of filling, the ratio of the volume of gas stored to the internal volume of the cylinder is expressed as the filling capacity (i.e., V/V at NTP). The recorded filling capacity, pressure, and temperature profiles have been compared with the simulated results.

’ MODEL A two-dimensional axi-symmetric model is assumed for transient heat transfer analysis of the problem as shown in Figure 3. The thermo-physical properties of Norit-RGM1 carbon, methane, and other relevant data used in the simulation are shown in Table 2. While studying adsorption in packed beds, inter- and intraparticle heat and mass transfer processes must be considered.25 The model is simplified if local gassolid thermal equilibrium is established and intraparticle mass transfer resistances can be neglected. For average particle radii, Rp = 0.5 mm, and effective particle thermal conductivity of 0.2 W m1 K1, the Biot number, assuming an external heat transfer coefficient in the range of 1-5 W m2 K1, lies in the range of 0.0025-0.0125. Thus thermal gradients within the particle can be neglected. For a thermal diffusivity value of methane gas of about 106 m2 s1 the thermal diffusion time is on the order of 0.01-1.0 s for gas film thickness ranging from 0.1-1 mm. Since the experimental observation times range from a few minutes to hours, it is reasonable to assume local thermal equilibrium and use effective 13002



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thermal properties to obtain spatial temperature variations. The intraparticle diffusional time constant is estimated from De/R2p = 3.2 s1, where De = 8.0 107 m2 s1 is the effective diffusivity of methane.26 Thus intraparticle gas-phase concentration gradients can be neglected. The film diffusion resistance is also small, as the corresponding Biot number for mass transfer in packed beds is usually greater than unity.27 Intraparticle mass transfer effects have been assessed by Mota et al.,21 where mass transfer resistances were found to have a negligible effect on the pressure and temperature distributions considering De/R2p > 0.1 s1. From the above analysis, we use the following assumptions in the model: (i) Methane is assumed to be an ideal gas. (ii) All thermo-physical properties (density, specific heat capacity, and thermal conductivity) of the adsorbent material are constant in the range of temperatures and pressures under consideration. Although the variation in the temperature and pressure range for the physical properties is small, to facilitate comparison, we have used data similar to those used in other adsorbent bed simulations reported in the literature. (iii) The solid adsorbent and the gas in the adsorbed phase are in local thermal equilibrium with the surrounding gas phase. (iv) Intraparticle and film resistances to heat and mass transfer are neglected. (v) Based on available experimental data, the isosteric heat of adsorption, ΔH, is assumed to be constant. Since the adsorption conditions for methane are supercritical, the heats of adsorption have been shown to be relatively invariant with the adsorbed amount at these conditions, lying in the range of 14.2-17 kJ/mol.18 (vi) Heat transfer through the ANG cylinder wall of thickness 2.5 mm is neglected. The model consists of the following governing equations. Continuity Equation. The continuity equation for the adsorbent bed is Dðεt Fg þ Fb qÞ Dt

þ r 3 ðFg ug Þ ¼ 0

ð1Þ

where εt = εb þ (1-εb)εp is the total porosity accessible to the gas phase. The total porosity, εt, has contributions from both the macropores which make up the interparticle porosity, εb, as well as from the micropores that contribute to intraparticle porosity, εp. Fb is the density of the packed bed, q is the adsorbed gas concentration, which is defined as the mass of gas adsorbed per unit mass of adsorbent, and ug is the gas velocity. From the ideal gas law, Fg = (PMg)/(RT), where Mg is the molecular weight of gas, R is the universal gas constant, and P and T are the pressure and temperature of gas, respectively. Momentum Equation. The volume averaged NavierStokes equations for homogeneous fluid flow in isotropic porous media can be written as follows14,28 Fg Dug Fg μg þ 2 ug 3 rug ¼ rP þ μg r2 ug ug εt Dt εt K

ð2Þ

where P is pressure, K is the permeability of the bed, μg is the gas viscosity, and t is time. The permeability K is the measure of the flow conductance of the porous adsorbent and is obtained using the Kozeny-Carman equation K ¼

4ε3b Rp2 150ð1 εb Þ2

K = 3.7 1010 m2. The first two terms in eq 2 represent the unsteady and convective contributions in the momentum balance. If these terms are neglected, the equation reduces to the Brinkman equation, which further reduces to Darcy’s law if the viscous effects (μgr2ug) are neglected. The above formulation is general and includes both viscous and inertial effects.14 For gas adsorption and moderate bed porosites typically found in packed beds, the dimensionless form of eq 2 indicates that the inertial and viscous effects are small and Darcy’s law is is a good approximation.29 A few representative simulations were carried out using Darcy’s law and compared with the solutions obtained from eq 2. Energy Equation. The energy balance for the porous bed is Ceff

ð4Þ

where the effective heat capacity Ceff = (εtFg þ Fbq)Cpg þ (1εt)FsCps and the bed density Fb = (1εt)Fs, where Fs is the corresponding solid bed density in the absence of any porosity, and Cps and Cpg are specific heats of adsorbent and gas, respectively. The effective thermal conductivity of the bed is λeff = εtλg þ (1εt)λs, where λg and λs are thermal conductivities of gas and carbon, respectively. ΔH is the isosteric heat of adsorption. Adsorption Isotherm. Since the adsorption isotherm is obtained at a single temperature of 303 K, the Dubinin-Astakhov (DA) equation,30 which has been widely accepted in adsorption studies, is used to obtain the adsorbed amount at different temperatures and pressures. The Dubinin-Astakhov (DA) equation is " # A n q ¼ Fads W0 exp ð5Þ βE0 where Fads is the adsorbed gas density, W0 is the microporous volume per unit mass of adsorbent, β is the affinity coefficient related to the adsorbateadsorbent interaction, the value of which is 0.35 for methane adsorption.31 E0 is the characteristic energy of adsorption, and n is the DA exponent which is related to the pore size dispersion. Upon fitting our isotherm data of the Norit-RGM1 sample at temperature of 303 K to the DA equation (Figure 1), the estimated parameters are E0 = 25.04 kJ mol1, n = 1.8, and W0 = 3.3 104 m3 kg1. The Polany adsorption potential A = RT ln(Ps/P), where the saturated vapor pressure of the gas (Ps) is calculated using the Dubinin form as Ps = Pcr(T/Tcr)2, where Pcr =45.96 bar and Tcr = 191 K are the critical pressure and temperature of methane, respectively. The adsorbed_gas density (Fads) is expressed32 as Fads = Fhads/ 422.62 kg m3 is the density of (exp[Re(T T b)]), where Fhads = _ liquid methane at boiling point (T b = 111.2 K) and Re = 2.5 103 K1 is the mean value of the thermal expansion of liquefied gases. Initial Conditions. The following initial conditions are used. At t = 0, r,z ∈ Ω, where Ω is the domain as illustrated in Figure 4

ð3Þ

where Rp is the adsorbent particle radius. Using an average particle diameter of 1 mm, we obtain a permeability value of

DT Dq þ Fg Cpg ug 3 rT ¼ r 3 ðλeff rTÞ þ Fb ΔH Dt Dt

Pðz, rÞ ¼ Pi ¼ 0:1 MPa

ð6Þ

Tðz, rÞ ¼ Ti ¼ 300 K

ð7Þ

and q ¼ qðPi , Ti Þ

ð8Þ

where Pi and Ti are initial pressure and temperature in the adsorbent bed, respectively. 13003



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Boundary Conditions. At the opening for gas inlet at z = 0 and 0 e r e ri depicted as Γ2 in Figure 4, a constant mass flow inlet boundary condition and corresponding heat flux inlet boundary condition has been applied. The inlet condition for a constant mass flow rate, m_ in, at Γ2 is Z m_ in ¼ Fg n 3 ug dΓ2 ð9Þ Γ2

where n is the unit outward normal on the surface. The heat flux at the inlet boundary Γ2 is n 3 λeff rT ¼ Fg ug , in Cpg ðTs TÞ

ð10Þ

where Ts is the source gas temperature, and ug,in is the average gas velocity at the inlet of the cylinder. Symmetry conditions have been taken along the axis (Γ1). No slip boundary conditions are

Figure 4. 2D axi-symmetric geometry used for simulation, with the inlet of radius ri depicted as Γ2. The triangular elements used for the simulation are illustrated in the figure. A fine mesh is used at the inlet in order to accurately model the inlet flow conditions.

imposed on Γi, where i = 4,5,6,7. Convective heat flux boundary conditions are imposed on Γi where i = 4,5,6,7 as n 3 λeff rT ¼ hðT¥ TÞ

ð11Þ

where h is the convective heat transfer coefficient, and T¥ is the ambient temperature. Equations 1, 2, 4, and 5 define four variables P, T, q, and ug dependent on space and time. The coupled differential equations are solved using the COMSOL MULTIPHYSICS 3.5a software, which is based on the finite element method. While solving the continuity equation, Fb(∂q/∂t), which appears in the lefthand side of eq 1, is incorporated as a source term. Similarly FbΔH(∂q/∂t) is also incorporated as a source term for the energy balance equation (eq 4). All finite element simulations were carried out using a triangular mesh as illustrated in Figure 4 with linear basis functions. Convergence criterion based on the error norm of the unknown variables at the mesh points has been set as 106. While defining the finite element mesh a fine mesh spacing is used at the inlet. This was necessary to satisfy the constant inlet flow condition imposed during the simulation, and the optimal amount of refinement was decided after several convergence tests based on the set inlet conditions. We point out that for the flow rates considered in this study, a dimensionless analysis of the heat flux inlet boundary condition (eq 10) indicates that a Dirichlet condition (T = Ts) can also be used. Simulation using this condition did not alter the results presented here indicating that this is a good approximation. We also carried out a few simulations at inlet filling rate 1 and 30 L min1 using Darcy’s law and found that the temperature, pressure distributions, and filling times were similar to those obtained using the full momentum equation (eq 2).

Figure 5. Pressure distributions in the adsorbent bed at different times during charging of the ANG cylinder at a flow rate of 10.0 L min1. Due to the high permeability of the bed, uniform pressure distributions are observed. The color bars are in units of MPa. 13004



Figure 6. Comparison of predicted and experimental pressure increase with time in ANG cylinder during charging at fixed flow rates of (a) 1.0 L min1 and (b) 10.0 L min1 and 30.0 L min1, respectively. In all cases the model predictions are in excellent agreement with the experimental data. Filling times decrease from about 2 h for the lowest flow rates to 3.4 min at the highest flow rate.

’ RESULTS AND DISCUSSION Simulations have been carried out for charging of the 1.82 L (inner volume) ANG cylinder filled with Norit RGM1 carbons at fixed flow rates of 1.0 L min1, 10.0 L min1, and 30.0 L min1 (STP conditions). The methane source is considered to be an infinite reservoir, which is at 3.5 MPa pressure and 300 K temperature. We also carried out a few simulations for a low permeability sample with monolith bulk densities to contrast with the high permeability samples considered in this study. Unless stated otherwise all simulations correspond to the physical properties given in Table 2. Pressure and Temperature Distributions. Pressure distributions obtained from the simulations (Figure 5) at different filling times for a filling rate of 10.0 L min1 reveals a nearly uniform pressure distribution in the bed. Thus the sample rapidly equilibrates to the inlet pressure, and a pressure of 3.5 MPa is established within a few minutes of opening the inlet. The high permeability of the sample (K = 3.7 1010 m2) is the primary reason for rapid pressure equilibration in the cylinder. The pressure distributions at lower and higher filling rates of 1.0 L min1 and 30.0 L min1 also show similar uniform pressure

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distributions within the bed. These findings are consistent with pressure distributions reported from other simulations in high permeability activated carbon adsorption beds.15,18 Comparison of the inlet pressure with that obtained from the experiments is illustrated in Figure 6. The rise of pressure with time, predicted by the model is in good agreement with the experimental results for all the inlet flow rates examined. In all cases the simulated results have been compared with two independent sets of experimental results. We define the filling time (tf) as the time required for the ANG cylinder to attain 3.5 MPa pressure during the charging operation. The predicted filling times of our prototype ANG cylinder are 120 min, 10.5 min, and 3.4 min for fixed methane flow rates of 1.0 L min1, 10.0 L min1, and 30.0 L min1, respectively. Since the pressure increase as a function of time is in good agreement with the experimental data, the predicted filling times also compare well with the experimental results. Since the spatial pressure variation in the bed is negligible (less than 1/100th of an atm) the definition of the filling time based on the inlet pressure of the adsorbent bed is reasonable. The temperature profiles of the adsorbent bed for various time intervals for a slow charging rate at 1.0 L min1 and a fast charging rate at 30.0 L min1 have been depicted in Figure 7 and Figure 8, respectively. For slow filling (Figure 7) we observe the presence of temperature gradients developing due to cooling at the surface of the cylinder. These gradients were not observed at the higher filling rates where an almost uniform temperature distribution is observed throughout the adsorbent bed except in the region close to the entrance of the cylinder (Figure 8). At the entrance region, the low temperature compared to the other parts of the adsorbent bed is due to the influence of the cooler incoming gas temperature.14,15 During a slow charging process, the adsorbent bed gets enough time to exchange the heat generated due to adsorption with the surrounding environment. As a result a maximum temperature of 327 K is developed at the center of the bed after 120 min of charging at 1.0 L min1 as shown in Figure 7. However, during fast charging conditions of 30.0 L min1 the adsorbent bed does not get enough time to exchange heat with the surrounding environment, approaching a nearly adiabatic condition. As a consequence the bed temperature rises quickly as observed from the temperature distributions shown in Figure 8. Figure 9 illustrates the comparison between the model predictions and the temperatures measured at the center of the bed as illustrated in Figure 3. For the lower inlet flow rates (Figure 9a), the temperature rise as predicted by the model is in excellent agreement with the measured data. At the higher gas flow rates (Figure 9b), despite a small overprediction in the lower temperatures, the final bed temperatures are well predicted. Since the adsorbed amount is close to the equilibrium value at lower temperatures, the reasons for the overprediction most likely lie in the accuracy of the thermal properties assumed for the adsorbent bed. Thus at the higher flow rates and fast transients, the rate at which heat is removed is slightly underestimated resulting in small increases in predicted temperatures. We note that we have not attempted to fit any of the physical properties to the experimental data. It is seen that the temperature at the center of the bed increases monotonocally with time and reaches its maximum toward the end of filling. At a charging rate of 1.0 L min1, a maximum temperature increase of 27 K is obtained at the center of the bed, whereas for fast charging of 30.0 L min1, the maximum temperature increase of about 58 K is obtained. 13005



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Figure 7. Temperature distributions in the adsorbent bed at different times during charging of ANG cylinder at a flow rate of 1.0 L min1. At these low flow rates there is sufficient time for the bed to lose heat by natural convection, and cooling is observed at the cylinder boundaries. The inlet temperatures are low due to the cooler incoming gas. The color bars are in degree K.

Figure 8. Temperature distributions in the adsorbent bed at different times during charging of the ANG cylinder at a flow rate of 30.0 L min1. Due to the high inlet flow rates the system approaches adiabatic filling conditions, and heat loss from the boundaries by natural convection is minimized. The color bars are in degree K.

We note that the permeability for very compact activated carbon beds (for example monolith samples), which is typically in the range of 1013-1015 m2 (Biloe et al.33), is 35 orders of magnitude lower than the permeability of the beds investigated in this study. In order to assess the variations that arise in lower permeability beds, we also carried out a few simulations at a low permeability value of 1015 m2, keeping the other physical

properties the same. Figure 10a and b illustrates the pressure and temperature distributions for the low permeability case study at an inlet flow rate of 10.0 L min1 after 5 min. The results indicate a strong variation in the pressure distributions across the bed, in sharp contrast to the uniform pressure distributions observed for the low permeability samples (Figure 5). Thus, although an inlet pressure of 3.5 MPa is achieved, the pressure at 13006



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Figure 10. Distribution of (a) pressure and (b) temperature in the low permeability adsorbent bed after 5.0 min of charging the ANG cylinder at a flow rate of 10.0 L min1. Due to the low permeability both the pressure and temperature distributions are nonuniform, and a distinct front is seen to progress through the bed as a function of time. The color bars are in units of (a) MPa and (b) degree K.

Table 3. Adsorption Data at Controlled Flow Rates, Q Predicted by Modela Q (L min1)

Figure 9. Comparison of experimental and simulated temperature changes at the center of bed with time during charging of the ANG cylinder at fixed flow rates of (a) 1.0 L min1 and (b) 10.0 L min1 and 30.0 L min1, respectively. The simulated data are in good agreement with the experimental data. A small overprediction is observed at the highest flow rates. We note that the model does not contain any fitted parameters, with the exception of the parameters in the DA equation, used for the adsorption isotherm.

the far end of the adsorption bed is as low as 0.5 MPa. As a result of this large pressure drop, the adsorption and the corresponding temperature distributions are highly nonuniform as illustrated in Figure 10. A relatively well formed temperature front progresses through the sample as a function of time. Performance Characteristics. In order to assess the different filling conditions investigated, we compare the filling time (tf), filling capacity, storage efficiency (ηs), and maximum temperature increase (ΔTmax) in the adsorbent cylinder for different charging rates as listed in Table 3. The filling capacity (Vf) is the volume of gas in liters filled into the ANG cylinder at the end of the filling time (tf). At a given average temperature and pressure of the bed, Vf is the sum of the volume of methane that is present in the gaseous state and the volume of methane corresponding to the adsorbed state. A sample calculation for evaluating Vf is given in the Appendix. The filling capacity of the ANG cylinder is expressed in a V/V basis, which is the ratio of Vf to the volume of adsorbent bed (Vb). The V/V basis filling capacity of the ANG

a

tf (min)

ΔTmax (K)

Vf/Vb (V/V)

ηs

1.0

120.0

27.0

72.5

90%

10.0

10.5

54.0

63.4

79%

30.0

3.4

58.0

61.6

76%

uncontrolled flow

2.3

64.0

60.0

74%

See text for definitions of various quantities.

Table 4. Physical Dimensions of the ANG Cylinder for Various L/D Ratiosa

a

L (m)

D (m)

L/D

0.066

0.1866

0.35

0.107 0.202

0.1466 0.1066

0.73 1.90

0.518

0.0666

7.80

In all cases the inner cylinder volume is maintained constant at 1.82 L.

cylinder at different charging rates is presented in Table 3. The storage efficiency, ηs of the ANG container is the ratio of the storage capacity (on a V/V basis) at the end of filling to the equilibrium storage capacity as obtained from the adsorption isotherm of the material at 3.5 MPa pressure and a temperature of 298 K. The value of the equilibrium storage capacity for the Norit RGM1 activated carbon used in this study is 80.6 V/V at NTP (298 K, 1 atm). The maximum temperature increase (ΔTmax) in the storage cylinder is the difference between the maximum temperature (which occurs at the center of bed as depicted in Figure 7 and Figure 8) and the initial temperature in the bed. 13007



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Figure 11. Temperature distributions in the adsorbent beds after 3 min of charging the ANG cylinders under natural convection cooling with different L/D ratios at a inlet gas flow rate of 30.0 L min1. The temperature gradients are seen to reduce as the L/D ratios increases. In all cases the volume of the cylinder is mantained constant at 1.82 L. The color bars are in degree K.

Figure 12. Temperature distributions in the adsorbent beds after 3 min of charging the ANG cylinders coupling with cooling water jacket with different L/D ratios at a flow rate of 30.0 L min1. Temperature gradients due to cooling at the cylinder boundaries are observed. Although the maximum temperatures are similar to those observed in Figure 11, the average temperatures decrease in the water cooled system as seen in Figure 13. The color bars are in degree K.

From the data in Table 3 the highest ηs is obtained for the lowest filling rate of 1.0 L min1. However at these filling rates the long filling time of 120 min makes this system impractical

while developing solutions comparable to current gasoline filling times at stations. On the other hand a more realistic filling time of about 3.4 min at 30.0 L min1 results in a significant reduction in 13008



Figure 13. Variation of average adsorbent bed temperature with different L/D ratios of the ANG cylinders after 3 min of charging with a flow rate of 30.0 L min1. A decrease of about 11 K is observed with forced convection water cooling.

Figure 14. Variation of filling times with different L/D ratios of the ANG cylinders. The filling times are seen to increase for the forced convection system since the lower average temperatures retard the pressure build-up in the bed. Inlet flow rate of 30 L min1.

storage capacity by about 15%. The maximum temperature rise with fast filling (58 K at 30.0 L min1) is more than double that of the slow filling process (27 K at 1.0 L min1). This large temperature rise associated with the fast filling process is the main reason behind the lower storage capacity of the ANG cylinder. We also carried out one simulation to contrast the simulation with an uncontrolled flow condition where the inlet pressure is held steady at 3.5 MPa. Although this condition yields the lowest filling time of 2.3 min, the ηs is only slightly lower than the highest filling rate studied. The temperature gradients are however significantly larger for this case. For the high permeability sample which is the focus of this study, the controlling factor that limits the storage efficiency is the removal of heat from the bed. For a fixed adsorbent material, heat transfer from the bed is limited by the thermal properties of the adsorbent. Heat removal can be altered by changing the geometry of the container and/or heat exchange with the aid of a suitable coolant. In this

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Figure 15. Variation of storage efficiency, ηs with different L/D ratios of the ANG cylinders. At the largest L/D ratio, ηs is seen to increase to 90% when compared with the 83% efficiency for the natural convection system. Inlet flow rate of 30 L min1.

regard, we have investigated the influence of changing the L/D ratios of the cylinder as well as studied the performance with water cooling. These results are discussed next. Influence of L/D Ratios and Water Cooling. The thermal behavior of the adsorbent bed during charging has been simulated with different L/D ratios (Table 4) for a 1.82 L ANG cylinder. Figure 11 represents the temperature distributions in different L/D geometries of the ANG cylinder (with natural convection of air at the outer wall) during the filling step after 3 min of charging with a flow rate of 30.0 L min1. The adsorbent bed with L/D ratio of 0.35 (minimum L/D ratio considered in our study) is heated up to a maximum temperature of 358 K (ΔTmax = 58 K), whereas for an L/D ratio of 7.8 (maximum L/D ratio considered in our study) a maximum temperature of about 349 K (ΔTmax = 49 K) is observed. With an increase in the L/D ratios, the adsorbent bed temperature reduces as expected. Providing a cooling water jacket (NTP flows @ 5.0 L min1) at the outer wall of the cylinder lowers the temperature gradients as illustrated in Figure 12. The variation of average bed temperatures with L/D ratios after 3 min of charging at 30.0 L min1 is depicted in Figure 13. In a natural convection cooling system, the average bed temperature is 352 K at a low L/D ratio of 0.35 and 345 K at the larger L/D ratio of 7.8. The corresponding average bed temperatures are 341 and 334 K with the water cooled system. In the presence of the cooling water jacket, the average bed temperatures decrease by about a constant value of 11 K for all the L/D ratios. Clearly increasing the L/D ratio will lower the temperature rise in the bed; however, since the bed is charged from one end, this would also increase the filling times. Variations of filling times and storage efficiency of the ANG cylinder with L/D ratios are shown in Figure 14 and Figure 15, respectively. The filling time increases with the L/D ratios, and about a 610% increase in filling time is observed with the water cooled system when compared with the natural convection system. Since filling time is based on the time at which the bed pressure reaches 3.5 MPa, the slower rise in bed temperature in the water cooled system delays the approach of the final target bed pressure. We note that for the small cylinder volumes examined in this study, the filling time for the high inlet flow rate of 30 L min1 is the range of a few 13009


Industrial & Engineering Chemistry Research minutes over the range of L/D ratios considered. We restricted the L/D ratios of the ANG cylinder (0.35-7.80) so that the lengths and diameters lie in a practically feasible range of values as shown in Table 4. Storage efficiencies are more indicative of the performance of the adsorbent bed, and increases in the range of 610% are observed while using the water cooled system. For an ideal filling situation, a system with a low filling time with a high value of ηs is preferred. In the absence of a cooling jacket, the highest value of ηs = 90% (Table 3) is obtained for the lowest filling rate with a large filling time of 120 min. With variations in L/D we are able to obtain a similar high value of ηs at a high filling rate of 30.0 L min1 and consequently a low filling time of about 4.1 min. This is achievable only with an external forced convection water cooled system. Based on the different configurations examined in this study, the highest adsorption efficiency with filling times on the order of a few minutes is an adsorption cylinder with forced convection water cooling and an L/D = 7.8. At the same L/D ratio the ηs value reduces to 83% for convective cooling and filling times remain on the order of a few minutes. Note that similar ηs values were obtained for a smaller L/D ratio of 1.9 at a lower filling rate of 10.0 L min1 (Table 3), albeit with an increase in filling time to 10.5 min.

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convection is a moderate 7%. Thus it is possible to develop an on board storage solution based on natural convection, with some compromise in the driving distance. We are currently extending this study to analyze discharge characteristics for adsorption beds as well as beds with higher storage capacities.

’ APPENDIX Mass Balance and Calculation of Volume of Methane Filled, Vf for a Filling Rate of 30.0 L min1. A sample mass

balance calculation for a methane filling rate of 30.0 L min1 is illustrated below. Methane in the ANG cylinder is present in both gaseous and adsorbed states, whose volumes are Vg and Vads, þ Vads. The average pressure (P) and respectively. Vf = Vg _ average temperature (T ) of gas obtained from the simulation, after a filling time of 3.45 min are 3.5 _ MPa and 352 K, respectively. Corresponding to P and T the average density (Fhg) of methane in the gaseous state is PMg Fg ¼ _ ¼ 19:17 kg m3 RT The corresponding mass of methane in the gaseous state is mg ¼ εt Fg Vb ¼ 0:0226 kg

’ SUMMARY AND CONCLUSIONS We have carried out a combined experimental and simulation study to analyze the charging performance of an activated carbon adsorption bed. Simulations were carried out using a 2D time dependent transport model for adsorption to simulate conditions of constant inlet mass flow rate. The differential equations are solved using the Galerkin finite element method with a triangular mesh and linear elements. All simulations are carried out using the COMSOL MULTIPHYSICS 3.5a software. Experimental data collected at different flow rates for the pressure and temperatures compare well with the simulated values. The model in the absence of any fitted parameters is able to accurately predict filling times as well as the temperature rise in the center of the bed where experimental data were collected. For the high permeability beds used in the experiments, simulations reveal a uniform pressure distribution during the charging process. Hence for these situations the storage efficiency is controlled by the rate at which heat is removed from the bed during adsorption. For the 1.82 L cylinder, filling times, defined as the time at which the bed pressure reaches 3.5 MPa, range from 120 to 3.4 min for inlet flow rates of 1.0 L min1 and 30.0 L min1, respectively. The corresponding storage efficiencies, ηs, vary from 90% to 76%, respectively. Simulations with L/ D ratios ranging from 0.35 to 7.8 indicate that the storage efficiencies can be improved with an increase in the L/D ratios. A further increase in storage can be achieved with a water cooled jacket. Thus an ηs value of 90% can be obtained with water cooling, for an L/D ratio of 7.8 and a filling time of a few minutes. In the absence of water cooling the ηs value reduces to 83%. In conclusion we observe that the engineering solution to an effective onboard solution lies in many factors. For a given material, the final amount stored as reflected in the storage efficiency will be decided on the discharge volumes required to achieve target driving distances. Since the charging process is controlled by the rate of heat removal, our study shows that increasing the L/D ratios with external convective cooling yields the highest storage capacity. However the drop in storage capacity at the highest L/D ratios in the absence of external

where the total porosity εt = 0.65, and the adsorbent bed volume Vb = 1.82 L. The corresponding volume of gaseous state methane at STP is Vg ¼

mg 103 22:414 ¼ 31:60 L Mg

where Mg is the molecular weight of methane. _ Corresponding to P and T the density of adsorbed methane is _ _ Fads ¼ Fads exp½ Re ðT T b Þ ¼ 231:47 k gm3 _ where Fhads = 422.62 kg m3, Re = 2.5 103 K1, and T b = 111.2 K. Using this value of Fads the methane mass adsorbed per unit mass of adsorbent is given by the Dubinin-Astakhov equation as " # A n q ¼ Fads W0 exp ¼ 0:057 βE0 where A = 4.376 kJ mol1, W0 = 3.3 104 m3 kg1, β = 0.35, n = 1.8, and E0 = 25.04 kJ mol1. Mass of the adsorbed methane is mads ¼ Fb qVb ¼ 0:0518 kg where Fb = 500 kg m3. The corresponding volume of adsorbed methane at STP is Vads ¼

mads 103 22:414 ¼ 72:52 L Mg

The total volume of methane filled in the cylinder from the simulation at STP is Vf ¼ Vg þ Vads ¼ 104:12 L The volume of gas filled based on a filling rate of 30.0 L min1 after 3.45 min, Vfill = 103.5 L at STP. Thus Vfill = Vf (within 0.5%) indicating the conservation of mass for the charging process. In order to compute the V/V values reported in the manuscript, the volume of Vf is divided by the cylinder inner volume (Vb) at NTP. 13010



’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors wish to acknowledge the financial support provided by Bharat Petroleum Corporation Limited (BPCL), India. P.K.S. and K.G.A. would like to acknowledge Shobhana Narasimhan and Shreyas Bhide for several inputs during the progress of this work. ’ REFERENCES (1) Wang, L.; Gardler, H.; Gmehling, J. Model and Experimental Data Research of Natural Gas Storage for Vehicular Usage. Sep. Purif. Technol. 1997, 12, 35–41. (2) Burchell, T.; Rogers, M. Low Pressure Storage of Natural Gas for Vehicular Applications. SAE Tech. Pap. Ser. 2000, 1653–1662. (3) Talu, O. An Overview of Adsorptive Storage of Natural Gas. Presented at the 4th International Conference on Fundamentals of Adsorption, Kyoto, Japan, 1992. (4) Chang, K.; Talu, O. Behaviour and Performance of Adsorptive Natural Gas Storage Cylinders During Discharge. Appl. Therm. Eng. 1996, 16, 359–374. (5) Menon, V.; Komarneni, S. Porous Adsorbents for Vehicular Natural Gas Storage: A Review. J. Porous Mater. 1998, 5, 43–58. (6) Jasionowski, W.; Tiller, A.; Fata, J.; Arnold, J.; Gauthier, S.; Shikari, Y. Charge/Discharge Characteristics of High Capacity Methane Adsorption Storage Systems. Presented at the 1989 International Gas Research Conference, Tokyo, Japan, 1989. (7) Remick, R.; Tiller, A. Advanced Methods for Low Pressure Storage of CNG. In Proceedings of the Nonpetroleum Vehicles Fuels Symposium, 1986; pp 105119. (8) Lozano-Castello, D.; Alca~niz Mongea, J.; de la Casa-Lillob, M.; Cazorla-Amoros, D.; Linares-Solano, A. Advances in the Study of Methane Storage in Porous Carbonaceous Materials. Fuel 2002, 81, 1777–1803. (9) Firas, N.; Mat, H.; Zakaria, Z. On-board Adsorptive Natural Gas storage: Hindrances for Commercial Applications. Clean Technol. Transp. 2001, 179. (10) Komodromus, C.; Fricker, N.; Horne, D. Development of Carbon Adsorbents for Low Pressure Adsorbed Natural Gas in Natural Gas Vehicles. In Conference Proceedings of NGV-94, 1994. (11) Yang, X.; Zheng, Q.; Gu, A.; Lu, X. Experimental Studies of The Performance of Adsorbed Natural Gas Storage System During Discharge. Appl. Therm. Eng. 2005, 25, 591–601. (12) Bose, T. K.; Chahine, R.; St-Arnaud, J.-M. High Density Adsorbent and Method of Producing Same. U.S. Patent 4,999,330, 1991. (13) Wegrzyn, J.; Gurevich, M. Adsorbent Storage of Natural Gas. Appl. Energy 1996, 55, 71–83. (14) Basumatary, R.; Dutta, P.; Prasad, M.; Srinivasan, K. Thermal Modeling of Activated Carbon Based Adsorptive Natural Gas Storage System. Carbon 2005, 43, 541–549. (15) Mota, J.; Rodrigues, A.; Saatdjian, E.; Tondeur, D. Dynamics of Natural Gas Adsorption Storage Systems Employing Activated Carbon. Carbon 1997, 35, 1259–1270. (16) Sejnoha, M.; Chahine, R.; Yaici, W.; Bose, T. Adsorption Storage of Natural Gas on Activated Carbon. Presented at AIChE Annual Meeting, San Francisco, CA, 1994. (17) Bhatia, S.; Myers, A. Optimum Conditions for Adsorptive Storage. Langmuir 2006, 22, 1688–1700. (18) Bastos-Neto, M.; Torres, A.; Azevedo, D.; Cavalcante, C., Jr. A Theoretical and Experimental Study of Charge and Discharge Cycles in a Storage Vessel for Adsorbed Natural Gas. Adsorption 2005, 11, 147–157.

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(19) Goetz, V.; Biloe, S. Efficient Dynamic Charge and Discharge of an Adsorbed Natural Gas Storage System. Chem. Eng. Commun. 2005, 192, 876–896. (20) Mota, J.; Saatdjian, E.; Tondeur, D.; Rodrigues, A. A Simulation Model of a High Capacity Methane Adsorptive Storage System. Adsorption 1995, 1, 17–27. (21) Mota, J.; Rodrigues, A.; Saatdjian, E.; Tondeur, D. Charge Dynamics of aMethane Adsorption Storage System: Intraparticle Diffusional Effects. Adsorption 1997, 3, 117–125. (22) Saez, A.; Toledo, M. Thermal Effect of The Adsorption Heat on an Adsorbed Natural Gas Storage and Transportation Systems. Appl. Therm. Eng. 2009, 29, 2617–2623. (23) Vasiliev, L.; Kanonchik, L.; Mishkinis, D.; Rabetsky, M. Adsorbed Natural Gas Storage and Transportation Vessels. Int. J. Therm. Sci. 2000, 39, 1047–1055. (24) Biloe, S.; Goetz, V.; Mauran, S. Dynamic Discharge and Performance of a New Adsorbent for Natural Gas Storage. AIChE J. 2001, 47, 2819–2830. (25) Yang, R. Gas Separation by Adsorption Process; Butterworths: Boston, MA, 1987. (26) Prasetyo, I.; Do, D. Adsorption Rate of Methane and Carbon Dioxide on Activated Carbon by the Semi-batch Constant Molar Flow Rate Method. Chem. Eng. Sci. 1998, 53, 3459–3467. (27) Aris, R. Mathematical Theory of Diffusion and Reaction in Permeable Catalysts; Oxford University Press: London, U.K., 1975. (28) Ingham, D.; Pop, I. Transport Phenomena in Porous Media; Elsevier, Ltd.: London, U.K., 2005. (29) Nield, D.; Bejan, A. Convection in Porous Media; SpringerVerlag: New York, 1998. (30) Dubinin, M. M.; Astakhov, V. A. Description of Adsorption Equilibrium of Vapours on Zeolites Over Wide Ranges of Temperature and Pressure. Adv. Chem. Ser. 1971, 102, 69. (31) Stoeckli, F.; Guillot, A.; Slasli, A.; Hugi-Cleary, D. Pore Size Distributions of Active Carbons Assessed by Different Techniques. Carbon 2000, 38, 929–941. (32) Osawa, S.; Kusumi, S.; Ogino, Y. Physical Adsorption of Gases at High Pressure: An Improvement of DA Equation. J. Colloid Interface Sci. 1976, 56, 83–91. (33) Biloe, S.; Goetz, V.; Mauran, S. Characterization of Adsorbent Composite Blocks for Methane Storage. Carbon 2001, 39, 1653–1662.

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Filling Characteristics for an Activated Carbon Based Adsorbed

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