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Adsorption kinetics of propane on energetically heterogeneous activated carbon
Applied Thermal Engineering 72 (2014) 206e210
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Adsorption kinetics of propane on energetically heterogeneous activated carbon Azhar Bin Ismail a, Kyaw Thu b, Kandadai Srinivasan b, Kim Choon Ng a, b, * a b
Water Desalination and Reuse Center, 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117576 Singapore, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 December 2013 Received in revised form 3 July 2014 Accepted 8 July 2014 Available online 16 July 2014
The modeling of the adsorption isotherms and kinetics of the adsorbent þ adsorbate pair is essential in simulating the performance of a pressurized adsorption chiller. In this work, the adsorption kinetics is analyzed from data measured using a magnetic suspension balance. The Statistical Rate Theory describes the DubinineAstakhov (DA) equation and extended to obtain an expression for transient analysis. Hence both the experimental excess equilibria data and the adsorption kinetics data may then be fitted to obtain the necessary parameters to fit the curves. The results fit the data very well within 6% of the error of regression. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Adsorption Activated carbon Statistical theory
1. Introduction Interest in adsorption (AD) refrigeration has grown due to its advantages related to its direct utilization of thermal energy sources such as low grade waste heat from various industrial sources, solar hot water as well as geothermal sources. As a result, there has been a diversified approach in the study of adsorption with a goal to explore various applications of the thermal heat pump system [1,2]. In this work, the authors report the kinetics of adsorption of propane at various temperatures and pressures. They are presented as an ongoing study of utilizing alternative refrigerants as adsorbate in an AD system. Ismail et al. (2014) [3] has previously elaborated how the highly porous activated carbon Maxsorb III þ propane gas pair is favorable amongst tested pressurized adsorption pairs when low temperature-cooling is required or operated in localities where the ambient temperature is relatively high (above 40 C). This is because, as illustrated using the experimental isotherms [4], the steady state simulation suggests that the cooling capacity (SCE) of an adsorption chiller declines with an increasing ambient temperature and decreasing evaporator temperatures until it is deemed inoperable. Under these adverse conditions in arid localities, a pressurized * Corresponding author. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore. Tel.: þ65 65162214. E-mail addresses: [email protected] (A.B. Ismail), mpekyaw@nus. edu.sg (K. Thu), [email protected] (K. Srinivasan), [email protected] (K.C. Ng). http://dx.doi.org/10.1016/j.applthermaleng.2014.07.023 1359-4311/© 2014 Elsevier Ltd. All rights reserved.
adsorption chiller which utilizes propane as a refrigerant with activated carbon as the adsorbent offers a best selection amongst the tested refrigerant pairs for the utilization of low grade waste heat in continuous batch-operated cooling [3]. The properties of this adsorption pair had been acquired experimentally and its theoretical thermodynamic framework developed and presented in previous works [3,4]. The kinetics of Maxsorb III þ propane pair is first measured using a thermal-gravimetric approach by utilizing a magnetic suspension balance. The Statistical Rate Theory model of Rudzinski et al. which has previously been extended to describe the kinetics process of heterogeneous systems [5], is used to mathematically describe the adsorption rate of propane on Maxsorb III.
2. Materials and methods A magnetic suspension balance (Rubotherm) is used to measure the instantaneous uptake of the adsorbent as shown in Fig. 1. This balance measures the weight of the sample with a reproducibility of ±0.03 mg [6]. The advantages of utilizing such a suspension balance are its high accuracy as well as stability. This is because of the placement of the suspension balance outside the measuring chamber and it thus does not have any interactions with the refrigerant. This system also allows for continuous logging of data. Maxsorb III activated carbon (by Kansai Coke Company, Japan) is utilized with pure propane as the adsorbate at a purity of 99.5%. The values of derived quantities of Nitrogen is taken from Wagner (2000) [7], while that of helium from Ortiz-Vega et al. (2010) [8]
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
207
Fig. 1. Schematics diagram for the magnetic suspension balance unit (Rubotherm).
and the thermodynamic properties of pure propane from Lemmon et al. (2009) [9]. In the uptake measurements, the buoyancy effects resulted from gas density variances needs to be eliminated. The volumetric displacements of the propane gas by the container, activated carbon, and the adsorbed phase propane are taken into account. The correction related to the adsorbent container is calculated by performing blank experiments at different densities (r (P,T)) with the empty container. The buoyancy caused by the solid matrix of the activated carbon, which caused a mass reduction from the measurements, is estimated using the Archimedes' principle which is the product of the skeletal volume of the adsorbent and the gas density. Finally, the buoyancy effect exerted on the adsorbed phase is corrected to obtain the absolute adsorption uptake q (P,T). The weight, m, displayed by the balance is an addition of various contributions which summing up to the net force exerted on the sample:
m ¼ mh 1 rg r þ ms 1 rg r þ q 1 rg r s
h
a
(1)
Here, mh and rh are the mass and density of the container ms and rs are the mass and density of the activated carbon sample while rg and ra are the densities of the refrigerant at the gas and adsorbed phases at equilibrium. The blank experiments with an empty holder give the mass and density of the holder from the intercept and the slope. The graph of apparent weight against gas density is expected to be a linear decrease as shown in the following equation:
m ¼ mh
mg r rh g
(2)
The density (rg) of nitrogen gas is obtained using the equations of Span et al. [7]. Adsorption experiments using helium which is assumed to be a non-adsorbing gas since it is carried out at a high temperature of 120 C, provide the mass (ms) and density (rs) of the solid matrix of the activated carbon sample by utilizing Eq. (3):
¼ ms ms=r rg m mh 1 rg r h
s
(3)
In Eq. (3) it is assumed that helium is inert, taking up the volumes of all available pores of the carbon i.e., without being
adsorbed. Finally, the experiments of propane gas with the activated carbon provide the uptake q from Eq. (4):
¼ m mh 1 rg r ms 1 rg r ms q 1 rg r a
h
s
(4)
The value of ra is estimated using the approximation by Ozawa (1976) [10], given by Eq. (5) as follows
ra ¼ m
r*a exp½ae ðT Tb Þ
(5)
In Eq. (5), r*a is the density of the refrigerant in the liquid state at its normal boiling point Tb. ae on the other hand is its thermal expansion. The pressure dependencies of ra, r*a and ae are regarded to be small in the pressure ranges of the present work and are thus not considered. The normal boiling point of propane and its liquid density at the normal boiling point are taken from Lemmon et al. (2000) [9]. Further, the thermal expansion was assumed to be independent of the adsorbate species, and the mean value of gases (ae ¼ 2.5 103 K1) was used in the numerical calculation. The utilization of this equation accounts for the adsorbed phase volume correction has successfully been used in previous works resulting in an improved fit [11,12] with relative ease. A pressure controller ER3000 is used to set the chamber pressure, and water from the water bath enters the jacket to maintain the desired temperature. When equilibrium is reached, the valve is opened to allow the propane gas to enter the chamber, and the pressure, temperature and weight changes are logged in the data logger. 3. Supporting theory In this paper, the kinetics of propane on activated carbon Maxsorb III is described using the statistical theory. The Statistical Rate Theory assumes a Gaussian distribution for the distribution of adsorption sites and it successfully derives the well-known DubinineAstakhov (DA) equation [13] which is as follows
q kT po r ln ¼ exp qo E P
(6)
208
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
4.5000
Table 1 Mass and densities of empty cell and activated carbon.
4.4990 Empty cell Maxsorb III
Density (g/cm3)
4.4989 0.1547
8.3 2.2
4.4970 1.0
4.4960
0.9
4.4950 4.4940 0
0.002
0.004
density
0.006
0.008
(g/cm3)
Fig. 2. Blank measurements of the empty cylinder with nitrogen gas with 0.01% error bars.
+6%
0.8
Balance Uptake (g/g)
mass (g)
4.4980
Mass (g)
-6%
0.7 0.6 0.5 0.4 0.3 0.2 0.1
where k is the Boltzmann constant while E and r describes the variance and symmetry of the distribution of the adsorption sites respectively. The kinetics of a localized adsorption site is given by Ref. [14]
d q=q o dt
¼ Ka P 2
o
q=q o
0.20
0.40
0.60
0.80
1.00
CVVP Uptake (g/g) Fig. 4. Deviation plots between current equilibrium uptake and those obtained from previous work utilizing CVVP apparatus.
2 1 q=q
0.0 0.00
expε=RT Kd qexpε=RT
(7)
The average uptake for a given adsorbent surface could be mathematically expressed as
dqt dt
ε¼εc
¼
vqt dε dε ¼ cðεc Þ dt ε¼εc vε dt ε¼εc
(8)
1 0.9
Utilizing Eqs. (6)e(8), Rudzinski et al. (2001) had extended these relations to obtain the expression for the uptake rate at a given equilibrium pressure p and temperature T [15].
0.8
ε0 i r q kT h ln Kp exp RT tanh 2pKgs t ¼ exp qo E
0.6 (9)
K and εo in Eq. (9) are regarded as constant terms which relate the reference pressure po which is in this theory determined by the adsorbent þ adsorbate pair interaction properties and not just the adsorbate properties. These values are regressed from the isotherms obtained in our previous work [4]. Kgs on the other hand is
0.7
0.5 0.4 0.3 0.2 10
100
1000
1 0.9
4.65370
0.8
4.65360
0.7
mass (g)
4.65350
0.6
4.65340
0.5
4.65330
0.4
experimental 283.16K 192kPa experimental 283.16K 497kPa experimental 303.16K 193kPa experimental 303.16K 497kPa experimental 303.16K 700kPa regressed
0.3
4.65320
0.2 0
4.65310 0
0.2
0.4
0.6
0.8
200
400
600
1
density (g/cm3) Fig. 3. Buoyancy measurements of the empty cylinder with helium gas at high temperature of 120 C with 0.001% error bars.
Fig. 5. Uptake versus time for the Maxsorb III þ propane pair, for temperatures 283.16 K and 303.16 K, —— denotes the fitted curves from the regression made on the experimental results in logarithmic scale (top) with 5% error bars and normal scale (bottom).
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
related to the total number of adsorption sites, So, its individual area as, the probability of collision x, the Boltzmann constant k, molecular mass m and the equilibrium temperature T as follows [16]:
So asx Kgs ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2PmkTe
(10)
The Kgs term is the rate of exchange between the adsorbed and gaseous phase. The exact relation involves the relation of temperature on the (i) mean free path of the molecule, l, as well as (ii) the probability that a propane molecule which hits a site will actually adsorb. As the time approaches infinity, Eq. (9) reduces to the DA Eq. (6). Thus, at low pressures and concentrations, the model is not able to depict the Henry's behavior [17]. 4. Results and discussion The blank experiments conducted with propane and N2 gas with an empty cylinder as expected gave a straight line graph which is linearly decreasing as shown in Fig. 2. Similarly, the high temperature experiments at 120 C with helium which is considered inert gave the following straight line graph. From the slope and the intercept of these curves shown in Figs. 2 and 3, the values of the combined density of the empty cylinder as well as its mass are obtained. The densities as well as the mass of the activated carbon sample have also been calculated. They are presented and tabulated
0.8
209
in Table 1. The Maxsorb III density of 2.2 g/cm3 was compared to those reported in previous works [4,5,12,18] using commercial pycnometers was found to be within (9e10) % variation. The kinetics tests are carried out at 10 C, 30 C, 50 C and 70 C which are within the thermal compressor of the AD chiller operational range and at pressures up to 800 kPa to avoid condensation of the propane refrigerant gas in the capillary. It takes between 10 and 15 s for the ER3000 to stabilize the pressure within the chamber to the desired pressure, as the temperature varies minimally between 1 and 2 C due to the heats of adsorption with the effective water circulation system. With the density of the empty cylinder and the activated carbon, as well as the y-intercepts, the uptake, q may now be calculated using Eq. (3) from the weight logged by the Messpro software over the adsorption time. The equilibrium uptakes obtained from the experiments deviates within ±6% of the uptake values obtained from previous published excess adsorption data of the Maxsorb III þ Propane pair [4] utilizing a constant volume variable pressure (CVVP) apparatus as shown in Fig. 4. The deviation plot suggests that while both methods suffer from errors associated to temperature and pressure measurements (which heavily depend on the sensors used), the constant volume variable pressure method is highly dependent upon the mass determination of the gas phase before and after adsorption. This in turn heavily relies on the accuracy of the derived densities which in our case is obtained from NIST REFPROP. Furthermore, any leakage occurring in the chambers and capillary as well as unaccounted void spaces will further aggravate its accuracy. There are also uncertainties in the measured volume related to the helium expansion procedure. The instantaneous uptake was found to follow the SRTIT theory as shown in Figs. 5e7. The regressed values of E, r, εo, qo and K are
0.7 0.6
0.6 0.5
0.5
0.4
0.4
Experimental 323.17K 195.8kPa Experimental 323.03K 701.02kPa regressed
0.3 0.2 10
100
0.3 experimental 342.96.16K 701kPa experimental 343.23K 498.9kPa experimental 342.91K 194.85kPa regressed
0.2
1000 0.1 10
0.8 0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
Experimental 323.17K 195.8kPa Experimental 323.03K 701.02kPa regressed
0.3
100
experimental 342.96.16K 701kPa experimental 343.23K 498.9kPa experimental 342.91K 194.85kPa regressed
0.2
0.2
1000
0.1
0
200
400
600
800
Fig. 6. Uptake versus time for the Maxsorb III þ propane pair for 323.16 K, —— denotes the fitted curves from the regression made on the experimental results in logarithmic scale (top) with 5% error bars and normal scale (bottom).
0
100
200
300
400
500
600
700
800
Fig. 7. Uptake versus time for the Maxsorb III þ propane pair for 343 K, —— denotes the fitted curves from the regression made on the experimental results in logarithmic scale (top) with 5% error bars and normal scale (bottom).
210
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
References
Table 2 Regressed values for the Kgs term. Run
T (K)
P (kPa)
Kgs
KgsP
1 2 3 4 5 6 8 9 10 11
282.30 284.11 302.41 302.04 301.75 323.03 323.17 342.91 343.23 342.96
192 497 195 497 700 701 196 195 499 701
5.97E-06 2.57E-06 8.78E-06 2.93E-06 2.44E-06 2.38E-06 8.77E-06 8.93E-06 4.30E-06 2.64E-06
1.15E-03 1.28E-03 1.71E-03 1.45E-03 1.71E-03 1.67E-03 1.72E-03 1.74E-03 2.14E-03 1.85E-03
8331 J mol1, 1.50, 19,000 J mol1, 0.85 and 4.95 107 kPa1 respectively. These are regressed to obtain the lowest Root Mean Square Error (RMSE) between the experimental and calculated profiles of Eq. (9). The first 15 s of the adsorption process is ignored during the adsorption as the pressure has not stabilized in the initial phase of adsorption. The values of Kgs for the assorted pressures and temperatures has been tabulated and presented in Table 2. 5. Conclusion The experimental adsorption uptake data of the PropaneMaxsorb III has been collated for adsorption equilibrium temperatures of 283.2 K and 303.2 K for pressures up to 700 kPa. The data is then fitted on the basis of statistical theory to obtain the regressed values for Kgs and K. It was found that the equilibrium uptake values agree within ±6% of the values obtained from previous published data utilizing the CVVP apparatus and has good agreement with the equation obtained from SRTIT theory. These values would be used in the formulation of the modeling of an adsorption chiller that utilizes this pair for refrigeration. Acknowledgements Azhar Bin Ismail is supported by the National Research Foundation Singapore under its National Research Foundation (NRF) Environmental and Water Technologies (EWT) Ph.D. Scholarship Programme and administered by the Environment and Water Industry Programme Office (EWI).
[1] K.C. Ng, X. Wang, Y.S. Lim, B.B. Saha, A. Chakarborty, S. Koyama, A. Akisawa, T. Kashiwagi, Experimental study on performance improvement of a four-bed adsorption chiller by using heat and mass recovery, Int. J. Heat Mass Transfer 49 (2006) 3343e3348. [2] B.B. Saha, A. Chakraborty, S. Koyama, K. Srinivasan, K.C. Ng, T. Kashiwagi, P. Dutta, Thermodynamic formalism of minimum heat source temperature for driving advanced adsorption cooling device, Appl. Phys. Lett. 91 (2007) 111902. [3] A.B. Ismail, A. Li, K. Thu, K.C. Ng, W. Chun, Pressurized adsorption cooling cycles driven by solar/waste heat, Appl. Therm. Eng. 67 (2014) 106e113. [4] W.S. Loh, A.B. Ismail, B. Xi, K.C. Ng, W.G. Chun, Adsorption isotherms and isosteric enthalpy of adsorption for assorted refrigerants on activated carbons, J. Chem. Eng. Data 57 (2012) 2766e2773. [5] A.B. Ismail, A. Li, K. Thu, K. Ng, W. Chun, On the thermodynamics of refrigerant þ heterogeneous solid surfaces adsorption, Langmuir 29 (2013) 14494e14502. [6] K. Yoshida, T. Yamaguchi, S. Kittaka, M. Bellissent-Funel, P. Fouquet, Neutron spin echo measurements of monolayer and capillary condensed water in MCM-41 at low temperatures, J. Phys. Condens. Matter 24 (2012) 064101. [7] R. Span, E.W. Lemmon, R. Jacobsen, W. Wagner, A reference quality equation of state for nitrogen, Int. J. Thermophys. 19 (1998) 1121e1132. [8] D.O. Ortiz Vega, A New Wide Range Equation of State for Helium-4 (Doctoral dissertation), Texas A & M University, 2013. Available electronically from: http://hdl.handle.net/1969.1/151301. [9] E.W. Lemmon, M.O. McLinden, W. Wagner, Thermodynamic properties of propane. III. A reference equation of state for temperatures from the melting line to 650 K and pressures up to 1000 MPa, J. Chem. Eng. Data 54 (2009) 3141e3180. [10] S. Ozawa, S. Kusumi, Y. Ogino, Physical adsorption of gases at high pressure. IV. An improvement of the DubinineAstakhov adsorption equation, J. Colloid Interface Sci. 56 (1976) 83e91. [11] K.A. Rahman, A. Chakraborty, B.B. Saha, K.C. Ng, On thermodynamics of methane þ carbonaceous materials adsorption, Int. J. Heat Mass Transfer 55 (2012) 565e573. [12] K.A. Rahman, W.S. Loh, H. Yanagi, A. Chakraborty, B.B. Saha, W.G. Chun, K.C. Ng, Experimental adsorption isotherm of methane onto activated carbon at sub-and supercritical temperatures, J. Chem. Eng. Data 55 (2010) 4961e4967. [13] S. Chen, R. Yang, Theoretical basis for the potential theory adsorption isotherms. The DubinineRadushkevich and DubinineAstakhov equations, Langmuir 10 (1994) 4244e4249. [14] W.A. Steele, G. Zgrablich, W. Rudzinski, Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, Elsevier, 1996. [15] W. Rudzinski, T. Panczyk, Kinetics of gas adsorption in activated carbons, studied by applying the statistical rate theory of interfacial transport, J. Phys. Chem. B 105 (2001) 6858e6866. [16] W. Rudzinski, D.H. Everett, Adsorption of Gases on Heterogeneous Surfaces, Academic Press, 1991. [17] A. Chakraborty, B.B. Saha, K.C. Ng, S. Koyama, K. Srinivasan, Theoretical insight of physical adsorption for a single component adsorbent þ adsorbate system: II. The Henry region, Langmuir 25 (2009) 7359e7367. [18] W.S. Loh, K.A. Rahman, A. Chakraborty, B.B. Saha, Y.S. Choo, B.C. Khoo, K.C. Ng, Improved isotherm data for adsorption of methane on activated carbons, J. Chem. Eng. Data 55 (2010) 2840e2847.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Adsorption kinetics of propane on energetically heterogeneous activated carbon Azhar Bin Ismail a, Kyaw Thu b, Kandadai Srinivasan b, Kim Choon Ng a, b, * a b
Water Desalination and Reuse Center, 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117576 Singapore, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 December 2013 Received in revised form 3 July 2014 Accepted 8 July 2014 Available online 16 July 2014
The modeling of the adsorption isotherms and kinetics of the adsorbent þ adsorbate pair is essential in simulating the performance of a pressurized adsorption chiller. In this work, the adsorption kinetics is analyzed from data measured using a magnetic suspension balance. The Statistical Rate Theory describes the DubinineAstakhov (DA) equation and extended to obtain an expression for transient analysis. Hence both the experimental excess equilibria data and the adsorption kinetics data may then be fitted to obtain the necessary parameters to fit the curves. The results fit the data very well within 6% of the error of regression. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Adsorption Activated carbon Statistical theory
1. Introduction Interest in adsorption (AD) refrigeration has grown due to its advantages related to its direct utilization of thermal energy sources such as low grade waste heat from various industrial sources, solar hot water as well as geothermal sources. As a result, there has been a diversified approach in the study of adsorption with a goal to explore various applications of the thermal heat pump system [1,2]. In this work, the authors report the kinetics of adsorption of propane at various temperatures and pressures. They are presented as an ongoing study of utilizing alternative refrigerants as adsorbate in an AD system. Ismail et al. (2014) [3] has previously elaborated how the highly porous activated carbon Maxsorb III þ propane gas pair is favorable amongst tested pressurized adsorption pairs when low temperature-cooling is required or operated in localities where the ambient temperature is relatively high (above 40 C). This is because, as illustrated using the experimental isotherms [4], the steady state simulation suggests that the cooling capacity (SCE) of an adsorption chiller declines with an increasing ambient temperature and decreasing evaporator temperatures until it is deemed inoperable. Under these adverse conditions in arid localities, a pressurized * Corresponding author. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore. Tel.: þ65 65162214. E-mail addresses: [email protected] (A.B. Ismail), mpekyaw@nus. edu.sg (K. Thu), [email protected] (K. Srinivasan), [email protected] (K.C. Ng). http://dx.doi.org/10.1016/j.applthermaleng.2014.07.023 1359-4311/© 2014 Elsevier Ltd. All rights reserved.
adsorption chiller which utilizes propane as a refrigerant with activated carbon as the adsorbent offers a best selection amongst the tested refrigerant pairs for the utilization of low grade waste heat in continuous batch-operated cooling [3]. The properties of this adsorption pair had been acquired experimentally and its theoretical thermodynamic framework developed and presented in previous works [3,4]. The kinetics of Maxsorb III þ propane pair is first measured using a thermal-gravimetric approach by utilizing a magnetic suspension balance. The Statistical Rate Theory model of Rudzinski et al. which has previously been extended to describe the kinetics process of heterogeneous systems [5], is used to mathematically describe the adsorption rate of propane on Maxsorb III.
2. Materials and methods A magnetic suspension balance (Rubotherm) is used to measure the instantaneous uptake of the adsorbent as shown in Fig. 1. This balance measures the weight of the sample with a reproducibility of ±0.03 mg [6]. The advantages of utilizing such a suspension balance are its high accuracy as well as stability. This is because of the placement of the suspension balance outside the measuring chamber and it thus does not have any interactions with the refrigerant. This system also allows for continuous logging of data. Maxsorb III activated carbon (by Kansai Coke Company, Japan) is utilized with pure propane as the adsorbate at a purity of 99.5%. The values of derived quantities of Nitrogen is taken from Wagner (2000) [7], while that of helium from Ortiz-Vega et al. (2010) [8]
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
207
Fig. 1. Schematics diagram for the magnetic suspension balance unit (Rubotherm).
and the thermodynamic properties of pure propane from Lemmon et al. (2009) [9]. In the uptake measurements, the buoyancy effects resulted from gas density variances needs to be eliminated. The volumetric displacements of the propane gas by the container, activated carbon, and the adsorbed phase propane are taken into account. The correction related to the adsorbent container is calculated by performing blank experiments at different densities (r (P,T)) with the empty container. The buoyancy caused by the solid matrix of the activated carbon, which caused a mass reduction from the measurements, is estimated using the Archimedes' principle which is the product of the skeletal volume of the adsorbent and the gas density. Finally, the buoyancy effect exerted on the adsorbed phase is corrected to obtain the absolute adsorption uptake q (P,T). The weight, m, displayed by the balance is an addition of various contributions which summing up to the net force exerted on the sample:
m ¼ mh 1 rg r þ ms 1 rg r þ q 1 rg r s
h
a
(1)
Here, mh and rh are the mass and density of the container ms and rs are the mass and density of the activated carbon sample while rg and ra are the densities of the refrigerant at the gas and adsorbed phases at equilibrium. The blank experiments with an empty holder give the mass and density of the holder from the intercept and the slope. The graph of apparent weight against gas density is expected to be a linear decrease as shown in the following equation:
m ¼ mh
mg r rh g
(2)
The density (rg) of nitrogen gas is obtained using the equations of Span et al. [7]. Adsorption experiments using helium which is assumed to be a non-adsorbing gas since it is carried out at a high temperature of 120 C, provide the mass (ms) and density (rs) of the solid matrix of the activated carbon sample by utilizing Eq. (3):
¼ ms ms=r rg m mh 1 rg r h
s
(3)
In Eq. (3) it is assumed that helium is inert, taking up the volumes of all available pores of the carbon i.e., without being
adsorbed. Finally, the experiments of propane gas with the activated carbon provide the uptake q from Eq. (4):
¼ m mh 1 rg r ms 1 rg r ms q 1 rg r a
h
s
(4)
The value of ra is estimated using the approximation by Ozawa (1976) [10], given by Eq. (5) as follows
ra ¼ m
r*a exp½ae ðT Tb Þ
(5)
In Eq. (5), r*a is the density of the refrigerant in the liquid state at its normal boiling point Tb. ae on the other hand is its thermal expansion. The pressure dependencies of ra, r*a and ae are regarded to be small in the pressure ranges of the present work and are thus not considered. The normal boiling point of propane and its liquid density at the normal boiling point are taken from Lemmon et al. (2000) [9]. Further, the thermal expansion was assumed to be independent of the adsorbate species, and the mean value of gases (ae ¼ 2.5 103 K1) was used in the numerical calculation. The utilization of this equation accounts for the adsorbed phase volume correction has successfully been used in previous works resulting in an improved fit [11,12] with relative ease. A pressure controller ER3000 is used to set the chamber pressure, and water from the water bath enters the jacket to maintain the desired temperature. When equilibrium is reached, the valve is opened to allow the propane gas to enter the chamber, and the pressure, temperature and weight changes are logged in the data logger. 3. Supporting theory In this paper, the kinetics of propane on activated carbon Maxsorb III is described using the statistical theory. The Statistical Rate Theory assumes a Gaussian distribution for the distribution of adsorption sites and it successfully derives the well-known DubinineAstakhov (DA) equation [13] which is as follows
q kT po r ln ¼ exp qo E P
(6)
208
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
4.5000
Table 1 Mass and densities of empty cell and activated carbon.
4.4990 Empty cell Maxsorb III
Density (g/cm3)
4.4989 0.1547
8.3 2.2
4.4970 1.0
4.4960
0.9
4.4950 4.4940 0
0.002
0.004
density
0.006
0.008
(g/cm3)
Fig. 2. Blank measurements of the empty cylinder with nitrogen gas with 0.01% error bars.
+6%
0.8
Balance Uptake (g/g)
mass (g)
4.4980
Mass (g)
-6%
0.7 0.6 0.5 0.4 0.3 0.2 0.1
where k is the Boltzmann constant while E and r describes the variance and symmetry of the distribution of the adsorption sites respectively. The kinetics of a localized adsorption site is given by Ref. [14]
d q=q o dt
¼ Ka P 2
o
q=q o
0.20
0.40
0.60
0.80
1.00
CVVP Uptake (g/g) Fig. 4. Deviation plots between current equilibrium uptake and those obtained from previous work utilizing CVVP apparatus.
2 1 q=q
0.0 0.00
expε=RT Kd qexpε=RT
(7)
The average uptake for a given adsorbent surface could be mathematically expressed as
dqt dt
ε¼εc
¼
vqt dε dε ¼ cðεc Þ dt ε¼εc vε dt ε¼εc
(8)
1 0.9
Utilizing Eqs. (6)e(8), Rudzinski et al. (2001) had extended these relations to obtain the expression for the uptake rate at a given equilibrium pressure p and temperature T [15].
0.8
ε0 i r q kT h ln Kp exp RT tanh 2pKgs t ¼ exp qo E
0.6 (9)
K and εo in Eq. (9) are regarded as constant terms which relate the reference pressure po which is in this theory determined by the adsorbent þ adsorbate pair interaction properties and not just the adsorbate properties. These values are regressed from the isotherms obtained in our previous work [4]. Kgs on the other hand is
0.7
0.5 0.4 0.3 0.2 10
100
1000
1 0.9
4.65370
0.8
4.65360
0.7
mass (g)
4.65350
0.6
4.65340
0.5
4.65330
0.4
experimental 283.16K 192kPa experimental 283.16K 497kPa experimental 303.16K 193kPa experimental 303.16K 497kPa experimental 303.16K 700kPa regressed
0.3
4.65320
0.2 0
4.65310 0
0.2
0.4
0.6
0.8
200
400
600
1
density (g/cm3) Fig. 3. Buoyancy measurements of the empty cylinder with helium gas at high temperature of 120 C with 0.001% error bars.
Fig. 5. Uptake versus time for the Maxsorb III þ propane pair, for temperatures 283.16 K and 303.16 K, —— denotes the fitted curves from the regression made on the experimental results in logarithmic scale (top) with 5% error bars and normal scale (bottom).
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
related to the total number of adsorption sites, So, its individual area as, the probability of collision x, the Boltzmann constant k, molecular mass m and the equilibrium temperature T as follows [16]:
So asx Kgs ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2PmkTe
(10)
The Kgs term is the rate of exchange between the adsorbed and gaseous phase. The exact relation involves the relation of temperature on the (i) mean free path of the molecule, l, as well as (ii) the probability that a propane molecule which hits a site will actually adsorb. As the time approaches infinity, Eq. (9) reduces to the DA Eq. (6). Thus, at low pressures and concentrations, the model is not able to depict the Henry's behavior [17]. 4. Results and discussion The blank experiments conducted with propane and N2 gas with an empty cylinder as expected gave a straight line graph which is linearly decreasing as shown in Fig. 2. Similarly, the high temperature experiments at 120 C with helium which is considered inert gave the following straight line graph. From the slope and the intercept of these curves shown in Figs. 2 and 3, the values of the combined density of the empty cylinder as well as its mass are obtained. The densities as well as the mass of the activated carbon sample have also been calculated. They are presented and tabulated
0.8
209
in Table 1. The Maxsorb III density of 2.2 g/cm3 was compared to those reported in previous works [4,5,12,18] using commercial pycnometers was found to be within (9e10) % variation. The kinetics tests are carried out at 10 C, 30 C, 50 C and 70 C which are within the thermal compressor of the AD chiller operational range and at pressures up to 800 kPa to avoid condensation of the propane refrigerant gas in the capillary. It takes between 10 and 15 s for the ER3000 to stabilize the pressure within the chamber to the desired pressure, as the temperature varies minimally between 1 and 2 C due to the heats of adsorption with the effective water circulation system. With the density of the empty cylinder and the activated carbon, as well as the y-intercepts, the uptake, q may now be calculated using Eq. (3) from the weight logged by the Messpro software over the adsorption time. The equilibrium uptakes obtained from the experiments deviates within ±6% of the uptake values obtained from previous published excess adsorption data of the Maxsorb III þ Propane pair [4] utilizing a constant volume variable pressure (CVVP) apparatus as shown in Fig. 4. The deviation plot suggests that while both methods suffer from errors associated to temperature and pressure measurements (which heavily depend on the sensors used), the constant volume variable pressure method is highly dependent upon the mass determination of the gas phase before and after adsorption. This in turn heavily relies on the accuracy of the derived densities which in our case is obtained from NIST REFPROP. Furthermore, any leakage occurring in the chambers and capillary as well as unaccounted void spaces will further aggravate its accuracy. There are also uncertainties in the measured volume related to the helium expansion procedure. The instantaneous uptake was found to follow the SRTIT theory as shown in Figs. 5e7. The regressed values of E, r, εo, qo and K are
0.7 0.6
0.6 0.5
0.5
0.4
0.4
Experimental 323.17K 195.8kPa Experimental 323.03K 701.02kPa regressed
0.3 0.2 10
100
0.3 experimental 342.96.16K 701kPa experimental 343.23K 498.9kPa experimental 342.91K 194.85kPa regressed
0.2
1000 0.1 10
0.8 0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
Experimental 323.17K 195.8kPa Experimental 323.03K 701.02kPa regressed
0.3
100
experimental 342.96.16K 701kPa experimental 343.23K 498.9kPa experimental 342.91K 194.85kPa regressed
0.2
0.2
1000
0.1
0
200
400
600
800
Fig. 6. Uptake versus time for the Maxsorb III þ propane pair for 323.16 K, —— denotes the fitted curves from the regression made on the experimental results in logarithmic scale (top) with 5% error bars and normal scale (bottom).
0
100
200
300
400
500
600
700
800
Fig. 7. Uptake versus time for the Maxsorb III þ propane pair for 343 K, —— denotes the fitted curves from the regression made on the experimental results in logarithmic scale (top) with 5% error bars and normal scale (bottom).
210
A.B. Ismail et al. / Applied Thermal Engineering 72 (2014) 206e210
References
Table 2 Regressed values for the Kgs term. Run
T (K)
P (kPa)
Kgs
KgsP
1 2 3 4 5 6 8 9 10 11
282.30 284.11 302.41 302.04 301.75 323.03 323.17 342.91 343.23 342.96
192 497 195 497 700 701 196 195 499 701
5.97E-06 2.57E-06 8.78E-06 2.93E-06 2.44E-06 2.38E-06 8.77E-06 8.93E-06 4.30E-06 2.64E-06
1.15E-03 1.28E-03 1.71E-03 1.45E-03 1.71E-03 1.67E-03 1.72E-03 1.74E-03 2.14E-03 1.85E-03
8331 J mol1, 1.50, 19,000 J mol1, 0.85 and 4.95 107 kPa1 respectively. These are regressed to obtain the lowest Root Mean Square Error (RMSE) between the experimental and calculated profiles of Eq. (9). The first 15 s of the adsorption process is ignored during the adsorption as the pressure has not stabilized in the initial phase of adsorption. The values of Kgs for the assorted pressures and temperatures has been tabulated and presented in Table 2. 5. Conclusion The experimental adsorption uptake data of the PropaneMaxsorb III has been collated for adsorption equilibrium temperatures of 283.2 K and 303.2 K for pressures up to 700 kPa. The data is then fitted on the basis of statistical theory to obtain the regressed values for Kgs and K. It was found that the equilibrium uptake values agree within ±6% of the values obtained from previous published data utilizing the CVVP apparatus and has good agreement with the equation obtained from SRTIT theory. These values would be used in the formulation of the modeling of an adsorption chiller that utilizes this pair for refrigeration. Acknowledgements Azhar Bin Ismail is supported by the National Research Foundation Singapore under its National Research Foundation (NRF) Environmental and Water Technologies (EWT) Ph.D. Scholarship Programme and administered by the Environment and Water Industry Programme Office (EWI).
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