Ind. Eng. Chem. Process Des. Dev. 1085, 2 4 , 57-62
57
Temperature-Swing Separation of Hydrogen-Methane Mixture M. C. Tsal, S. S. Wang, R. T. Yang,' and N. J. Desal Department of Chemical Engineering, State University of New York at Buffalo, Amherst, New York 14260
Particles of a coal char (from Montana lignite) were used in a fixed bed for cyclic separation of a mixture of hydrogen and methane. The column was operated in the temperature cycling mode between 25 and 250 OC at a total pressure ranging from 21 to 34 atm. The methane concentration was enriched from 50% to over 90%, which was the goal of separation for production of high-Btu gas. It has been shown that the coal char is a s effective as a commercial activated carbon being used as the sorbent. The experimental data showed that pore diffusion is important in separation. A simplified porediffusion model was developed which gave satisfactory bredictions of the performance of temperatwe-swing separation. In the simplified model a parabolic intraparticle concentration profile was assumed and the computation was further simplified by using a particle volume-averaging technique.
Introduction Pore-diffusion resistance has been neglected in modeling temperature, pressure swing, and other cyclic separation processes (e.g., Hill et al., 1982). In predicting breakthrough in fixed-bed adsorbers, however, pore diffusion has been considered by many authors (e.g., Liaw et al., 1979). In our recent work (Tsai et al., 1983),it was shown that pore diffusion is important in cyclic separation, and a model was developed to predict the performance of such processes. The separation of hydrogen from methane and other light hydrocarbon has been commercially practiced in petroleum refining and other industries, mostly using cryogenic processes by which a high separation factor is achieved. The separation of hydrogen and methane is also an important step in advanced coal gasification and liquefaction processes. In these processes, however, the goal is to enrich methane to 90% concentration which will be a promising process from the veiwpoint of reducing the energy requirement. In our previous work, activated carbon was used as the sorbent. In this work, we have demonstrated that coal char, which is substantially lower in cost than activated carbon, is as effective as activated carbon. Furthermore, the pore-diffusion model proposed in the previous work has been substantially simplified and the simplified model has been shown to be satisfactory in predicting the performance of the cyclic separation process. The simplifications were made by using a parabolic intraparticle concentration profile and by adopting a volume-averaging technique for the particles. Simplified Pore-Diffusion Model The following assumptions and simplifications are made: (1)The ideal gas law applies. (The compressibility factor for the gas mixture was calculated to be 0.99 under our experimental condition of 34 atm and 25 "C). (2) The axial pressure gradient across the bed is neglected. (3) Plug flow condition holds; i.e., longitudinal dispersion along the bed is neglected. (4)Inside the pores, instantaneous equilibrium exists between the gas phase and the adsorbed phase. (5) The adsorption isotherm for CHI from a single gas is used. The adsorption of H2from the mixture is neglected. (6) The temperature is assumed to vary uniformly in the bed; i.e., temperature is equilibrated instantaneously between gas and solid. Mass balances for both components CH4(A)and H2(B) in the packed-bed column a t system pressure, P, and temperature, T, are given by acA + auCA f-- s = 0 at az 0196-4305/85/1124-0057$01.50/0
and
acB
aucB -0 az
CY-+--
at
Converting to mole fraction, yA, and rearranging, we obtain (3)
We further assume that the bed is composed of spherical particles of uniform radius, a, and that the net molar flux of H2is zero. The quantity S is the total molar flux of CHI, Nh, through the exterior surfaces of the particles in a unit volume of bed
Mass balance of CHI in the pores of a spherical particle a t axial location z is given by ~CA* +p at
e-
1a + --(r2Nh) rzar
=0
(5)
By introducing the following particle volume average quantities, as used previously for predicting a breakthrough curve by Sheth and Dranoff (1973)
q = & S a q r 2 dr a3
0
the above eq 5 becomes
(7)
or
ayA*l
d9A -=+--at ae 1 -De y A s ar
rEa
P~RT~Q (8) E P at
In order to simplify the equation further, we assume a 0 1984 Amerlcan Chemical Society
58
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985
parabolic concentration profile as first used by Liaw et al. (1979) yA*
= KO
+ K2r2
(9)
KO = yAs - K2a2
Therefore e
P at
(10)
and l5PB s =-pP
P YAs - QA a 2 R T 1- y A s
De
(11)
The quantity q is a function of temperature, total pressure, and mole fraction, that is
Table I. Physical Properties of Montana Lignite Char and Activated Carbon char act. carbon bulk density, g/cm3 0.8 0.44 particle density, g/cm3 1.3 0.85 true solid density, g/cm3 2.0 2.2 interparticle void fraction 0.38 0.48 intraparticle void fraction 0.35 0.61
The above simplification approach can be easily used for Freundlich, linear, or other types of isotherms. Adsorption Isotherms. The adsorption isotherms of CHI on Montana lignite char were measured manometrically with a static apparatus a t temperatures ranging from 22 to 207 OC and pressures up to lo00 psi (Saunders and Yang, 1984). The char was prepared by carbonizing a coal sample at 800 OC in N2. The data were fitted to the Langmuir isotherm and can be represented by the following equations
v, = 8.70 x 1037492
Equation 10 becomes
B = 4.71 X
In obtaining this equation, P has been considered constant as we now consider a temperature-cyclic process. The values of (aq/ar),, and (&j/dyA)T can be determined, if the function in eq 12 is known. The general Langmuir isotherm is used here for eq 12, with the linear isotherm as a special case. Moreover, the Langmuir isotherm has been found to be valid for adsorption of CHI on carbons. (14)
V, = k,Tk4
(14a)
:)
(14b)
B = k2 exp(
where kl, k,, k3, and k4 are constants. Although the exact expression for (r is
v,
-
sLa a3
1+ B y A *
exp(
;:ET:)
X
14.7 (19b)
where V is the volume adsorbed in cm3 (STP) per gram of char a t pressure p (in atm) and temperature T (in K), and V , is the volume corresponding to monolayer coverage. The constant B is related to the net enthalpy, AH, of adsorption according to the Langmuir theory. Compared with a commercial activated carbon, the enthalpy on coal char (AH= 3.59 kcal/mol) is slightly higher than that on activated carbon (AH = 3.44 kcal/mol). Method of Solution. The computational procedure based on the proposed model is summarized as follows. Eauation 13 was first integrated bv a fourth-order medictor-corrector method (C&nahan et al., 1969) to ob'tain the value of j j A a t a new time step. The initial conditions in the particle are a t t = 0, z > 0, j j A = 0.5. With j j A having been calculated a t a new time step, the quantity S was computed using eq 11. Equation 3 was then solved by a simple numerical integration by use of the known value of S and a proper boundary condition, e.g., a fixed velocity u a t the exit end of the bed. Finally, eq 4 was solved by the Crank-Nicolson method, with the following boundary conditions. In the packed bed
t = 0, z > 0
r2 d r (15)
(19a)
t > 0, z = L
YA
= y i n (= 0.5)
ayA/az =
o
we found that q can be approximated without significant error by
This method was found to be both stable and convergent for a wide range of parameter values investigated. With the simplified method, the computation time was reduced by about 90% from that required for our previous porediffusion model (Tsai et al., 1983).
Consequently, the following simplified results are obtained
Experimental Section The separation of hydrogen-methane was studied in a continuous-flow system with a packed-bed sorption column being operated in a temperature-swing mode. The sorbent was char from Montana lignite. The char was obtained by carbonizing Montana Rosebud lignite a t 800 "C in a flow of nitrogen. The physical properties of the char are listed in Table I, along with the properties of activated
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985 59
I
Figure 1. Schematic of apparatus for temperature swing separation: (1) premixed feed gas; (2) regulator; (3) constant-temperature bath (4) fluidized-bedsand bath; (5) pressure gage; (6) adsorption column; (7) temperature readout; (8) back-pressurevalve; (9)gas chromatograph; (10) rotameter; (11) pump; (12) thermocouple well; (13) three-way valve.
carbon (designated PCB from Calgon Corp.) for comparison. A schematic diagram of the apparatus is shown in Figure 1. The flow system was designed to give a breakthrough time of the order of 30 min. The inlet gas mixture of CH4/Hz (volume ratio 5050) was a custom-made, premixed gas supplied by Linde Division of Union Carbide Corp. A water bath was used for precooling the inlet gas during the cooling half-cycle. A fluidized-bed sand bath (Tecam, SBS-2) was used to preheat the inlet gas during the heating period. The sorption volume with inside diameter 4.6 cm and height 60 cm was packed with 600 to 640 g of char particles (or about 800 cm3). The temperature of the bed was monitored with a thermocouple inserted into the bed about 10 cm below the bed surface; it was displayed on a digital readout. The system pressure was monitored with a pressure gage inserted above the bed surface. The pressure was controlled with a back-pressure valve downstream (below the bed). The effluent flow rate was controlled at a desired steady rate by adjusting the back-pressure valve and a needle valve. Besides preheating and precooling the feed gas mixture, additional heating of the column was provided by a heating tape surrounding the column. An insulation jacket was used during the heating cycle. During the cooling cycle, the insulation was taken off and four blowers were used to accelerate cooling of the column. The CH4 content in the effluent stream was analyzed with a gas chromatograph (Gow-Mac, with thermal conductivity detector and a Porapak Q column) a t time intervals of about 5 min. The experimental procedure was the same as that described in our previous work. Briefly, the bed was degassed and subsequently pressurized with a continuous feed. The cooling and heating half cycles were started when the effluent concentration approached that of the feed.
Results and Discussion The specific adsorption capacity, i.e., amount of CHI adsorbed per unit weight of sorbent, for activated carbon is approximately twice that for Montana lignite (ML) char. The bulk volume a t the same particle size is, however, substantially higher for ML char, as seen in Table I. As a result, the equilibrium driving force for separation using a packed-bed is about the same for these two sorbents. The performance of separation using coal char was measured with the following operating variables: total pressure, product flow rate, desorption temperature, and particle size. Compared with activated carbon as the sorbent, under similar conditions, coal char gave similar or better separation results. With a 5050 H2/CH4mixture feed, 9010 or better products were routinely obtained with coal char. Results of a typical run are shown in Figure 2. The operating conditions are listed in Table 11. The predicted
50
0
100
TIME, MIN.
Figure 2. Effluent concentration for temperature-swingseparation using coal char as the bed material. Experimental data for this and all other figures, except where otherwise noted, are listed in Table I 1 (A) temperature histories, experimental (solid line) and those used in model (dashed line); (Band C) effluent concentrations for heating and cooling half cycles, experimental (0) and theoretical (solid line).
90 W
J 0
u
f 0
70
sa
I
I
I
10 TIME, min.
Figure 3. Comparison of effluent concentration for experimental data ( O ) ,simplified model (solid line), and the model of Tsai et al. (dashed line). Table 11. Major Parameters Used in Experiments and Modeling heating cooling half-cycle half-cycle packed-bed length, cm 40.0 40.0 initial temperature, K 298 473 298 final temperature, K 473 system pressure, atm 27 27 heating or cooling rate, K/min -7.5 3.5 inlet concentration of CHI, yh 0.50 0.50 product flow rate, cm3 (STP)/min 400 400 particle size, cm 0.02 0.02 effective diffusivity at beginning of 2.1 x 104 2.6 X lo4 half cycles, cm2/min (or cm2/s) (3.5 x 10-8) (4.33 x 10-8)
results from the model described above are also shown in Figure 2 and compare favorably with the experimental data. The predicted results using the simplified model were also compared with those using the previous porediffusion model (Tsai et al., 1983). As mentioned, the two
80
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985
r----T
sa
x
t
0
Li
fi 0
70
it
Io
sa
ea
0 TIME,M*U
Dl8TANCE IN BED-
Figure 4. Comparison of concentration profiles in bed at t = 10 mix simplified model (solid curve) and model by Tsai et al. (dashed curve).
Figure 6. Effect of total pressure on effluent concentration with char particle sizes 20/100 U.S.mesh. The solid lines are model predictions and the experimental data are at 34 atm (A) (curve 1); 27 atm (0) (curve 2); and 21 atm (0)(curve 3).
sa
I*
0
TIME,MIN.
a
40
SO
TIME,MIN,
Figure 7. Effect of product flow rate on separation at a total pressure of 27 atm. The solid lines are theoretical, and experimental data are at 400 cm3 (NTP)/min (0) (curve 1) and 600 cm3 (NTP)/ min (A)(curve 2).
a
o +r
a
O c
r
a
O +r
Figure 6. Concentration histories midpoint in bed and in pores: (A) volume-averaged mole fraction calculated from the present simplified model; (B) intraparticle concentration profiles calculated without assuming a parabolic profile.
models differ in the two assumptions used in the present one: the parabolic intraparticle concentration profile and the use of the particle volume-average technique. Predictions from the two models are compared in Figures 3-5 for CHI concentration in the effluent, in the bed, and in the particle, respectively. In both models, the increased discrepancies between predicted and experimental data in the later stages of the half-cycles are caused mainly by the accumulated truncation errors of the numerical formula. Although the predictions from the two models are rather close as seen in Figures 3-5, the slightly higher CHI concentration (during heating half-cycle) predicted by the simplified model is probably caused by the steep concentration gradient a t the surface of the particle by assuming a parabolic profile, which results in a high flux. Nonetheless, as shown in Figure 5, the intraparticle concentration profiles do resemble a parabolic function-these profiles were calculated without making the assumption of parabolic profiles in the model. Effecb of various operating parameters on the performance of temperature-swing separation have also been
examined experimentally and the results compared with predictions by the mathematical model. The parameters investigated were total pressure, flow rate, desorption temperature, and particle size. The following discussion is limited to the heating half-cycle; the results for the cooling half-cycle were similar to those for the heating half-cycle and will not be discussed here. Effect of Total Pressure. Separation results for three total pressures are shown in Figure 6. As predicted by the model, a lower total pressure favors better separation. This effect cannot be predicted by the equilibrium model, in which equilibrium between the adsorbed in the inner surface of the particle and the bulk stream is assumed. At a higher totalpressure, the equilibrium adsorption is higher and the contact time is longer (since the product flow rate is fixed); both would result in a better separation based on the equilibrium models. However, pore diffusion is slower at a higher total pressure. The net result of the two opposing factors can be predicted only by the pore-diffusion model, as seen in Figure 6. Effect of Product Flow Rate. The effect of flow rate on separation is shown in Figure 7 along with model predictions. A longer contact time obviously favors better separation, at the cost of a lower throughput. Effects of bed height and bed volume can be predicted similarly to that of flow rate. Effect of Temperature Change. In some experiments, heating rate was increased from 3.5 OC/min to 4.5 OC/min and the desorption temperature was also varied to study the effect of temperature changes. The results are shown in Figure 8 together with theoretical predictions. It is seen
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985
so 0
20
60 TIME,MIN.
Figure 8. Effect of temperature changes on separation with adsorption temperature = 25 O C , desorption temperature at 200 O C , and heating rate = 3.5 "C/min (0) (curve 1);desorption temperature at 250 O C and heating rate = 4.5 OC/min (A)(curve 2). Solid curves are theoretical.
Y
0
I
w
1
I
60
I
61
alignment of the planar regions in coal upon carbonization. The values of De calculated in this work are within the same range as directly measured by Walker and co-workers (1978). Pressure-Swing Adsorption. Temperature swing is not used commercially for gas bulk separation-meaning that the adsorbate concentration is approximately 10 wt % or more. Pressure-swing adsorption (PSA) is a promising process for such separation (Keller, 1983). This study is a test of the pore-diffusion model by using the experimentally simple temperature-swing adsorption cycle. The experimental results do show the importance of porediffusion resistance in the separation process and thus provide support for the pore-diffusion model. This study is, however, by no means a complete one. For example, only one cycle is compared with the model. Several cycles may be needed for reaching a steady-state operation. Empirically, the number of cycles required to reach steady state is lower for longer cycles; e.g., for PSA separation of 5050 CH,/H2 involving 5 steps, about 10 cycles are needed for a cycle time of 7 min, and 5 cycles are adequate for a cycle time of 15-20 min (Yang and Doong, 1984). For the long temperature-swing cycle described here, it is likely that steady-state behavior is approached during the first cycle. Based on the pore-diffusion model, a more complete model has been formulated which includes a heat balance equation and the adsorption of all components in the gas mixture (by using the loading ratio correlation). This model has been used successfully to describe PSA bulk separation of H2/CH4involving five steps in each cycle (Yang and Doong, 1984).
80
TIME,MIN.
Figure 9. Effect of particle size on separation: 20/100 mesh (0) (curve 1) and 100/200 mesh (A) (curve 2). The solid curves are
theoretical.
Acknowledgment We appreciate the support of the Department of Energy under Contract No. DE-AC21-80MC14386.
that the plateau concentration of CH4 in the effluent is not influenced as much as predicted. Effect of Particle Size. The experiments were limited to two size fractions of the coal char sample: 20-100 and 100-200 U.S.mesh. The experimental and predicted results are shown in Figure 9. As predicted, the effect of particle size was not readily detected because the sizes were too close to each other. Effective Pore Diffusivity i n Coal Char. In the pore-diffusion model, effective pore diffusivity is the only fitting parameter which is determined by fitting the separation results with the model. Although effective diffusivity in porous materials may range from F'.6(for Knudsen diffusion) to F.7(for molecular diffusion), the temperature dependence of most of the reported effective pore diffusivities is nearly linear. In our model, pore diffusivity is assumed to be proportional to T and 1/P. The results in Table I1 show that the pore diffusivity has a value of 3.5 X lo4 cm2/s a t the start of the heating half-cycle and 4.33 X lo4 cmz/s a t the start of the cooling half-cycle for a total pressure of 27 atm. The diffusivity is thus increased by a factor of 1.26, which is approximately in the Knudsen diffusion regime, since the temperatures are 25 and 200 OC at the beginnings of the two half-cycles. The values of De are, however, about five orders of magnitude lower than that for molecular diffusion. These low values can be expected from the intensive studies on diffusion in coals and chars. Diffusion in most chars is actually slower than in their parent coals because of the molecular sieve nature of char (Walker and Mahajan, 1978) and because of the increase in size and the degree of
Nomenclature a = average radius of sorbent particle, cm b = a constant related to the net enthalpy, AH, of adsorption according to Langmuir theory B = dimensionless parameter in the Langmuir isotherm C = concentration in bulk flow, mol/L De = effective diffusivity, cm2/min or cm2/s ki, Ki= constants N , = molar flux in radial direction, mol/cm2 s p = pressure of adsorbate, atm P = total pressure, atm q = number of mole of sorbate adsorbed per gram of solid r = radial distance, cm R = gas constant S = overall rate of sorption per unit volume of bed, mol/min L of bed t = time, min or s T = solid or bed temperature, K u = superficial velocity, cm/min V = volume adsorbed per gram of sorbent, cm3 (STP)/g V , = volume adsorbed corresponding to monolayer coverage, mol/g yi = mole fraction of species i z = axial distance along the bed, cm Greek Letters a = interparticle void fraction = intraparticle void fraction pB = bed density, g/cm3 pp = particle density, g/cm3 Subscripts A = CHI B = H2
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 62-65
62
Superscripts - = volume-average quantities * = in the pores
S = at the surface
Registry No. CHI, 74-82-8; Hz, 1333-74-0.
Literature Cited Carnahan, B.; Luther, H. A,; Wilkes, J. 0. "Applied Numerical Methods"; Wiley: New York, 1969; Chapter 6. Hill, F. B.; Wong, Y. W.; Chan, Y. N. I . AIChE J . 1982, 28, 1. Keller, G.E.. I1 ACS Symp. Ser. 1983, No. 223, 145-170.
Liaw, C. H.: Wang, J. S. P.; Greenkorn. R. A,; Chao, K. C. AIChE J. 1070, 25, 376. Saunders, J. T.; Yang, R. T. Fuel 1984, in press. Sheth, A. C.; Dranoff, J. S. Chem. Eng. Prog. Symp. Ser. No. 134, 1073, 69,76. Tsai, M. C.; Wang, S. S.; Yang, R. T. AIChE J . 1083, 29,966. Walker, P. L., Jr.; Mahajan, 0. P. I n "Analytical Methods for Coal and Coal Products", Karr, C., Jr., Ed.; Academic Press: New York, 1978, Vol. I, Chapter 5. Yang, R. T.; Doong, S.J., Annual Meeting of the Amerlcan Institute of Chemical Engineers, San Francisco, CA. Nov 1984; AIChE; New York.
Received f o r review September 13, 1982 Revised manuscript received July 18, 1983 Accepted April 10, 1984
Kinetics of the Hydrolysis of Methyl Salicylate by Sodium Hydroxide W. David Brucef and Joseph J. Perona' Department of Chemical, Metallurgical, and Polymer Engineering, The University of Tennessee, Knoxville, Tennessee 37996
A stirred cell containing two nondispersed immiscible liquids was used to study the alkaline hydrolysis of methyl salicylate by aqueous sodium hydroxide. A computer program was developed in which the aqueous layer was modeled a s a semibatch reactor. Computer-generated concentration vs. time data for sodium hydroxide were compared with experimental data to yield values for mass transfer coefflcient and reaction rate coefficient. Several important physicochemical properties were measured. Reaction rate coefficients for the second-order hydrolysis reaction are 100, 350, and 1000 cm3 mol-' s-' at 30, 61, and 80 O C , respectively. The Arrhenius activation energy for the reaction in this temperature range is 9.58 kcal mol-'. The solubility of methyl salicylate in water and mass transfer coefficient values were determined over the temperature range.
Introduction The present study was motivated by the need for a technique for measurement of interfacial contact area in a direct contact boiler. In the boiler, two immiscible liquids flow countercurrently in a vertical column, and one of the phases undergoes vaporization. This type of heat exchanger is of interest for geothermal energy applications in which hot geothermal brine vaporizes isobutane in a secondary fluid power cycle. Measurement of interfacial contact area is necessary for direct comparison of the direct contact boiler with conventional heat exchangers. Danckwerts (1970) discusses the use of a chemical reaction to measure interfacial area. The principle was first utilized to study gas-liquid reactions, but it was later extended by Nanda and Sharma (1966) as a tool for studying liquidliquid contacting in a spray tower. A second motivation for this study is that an alternate technique is needed for the measurement of reaction rate coefficients in aqueous systems for which one of the reactants is nearly insoluble in water. For kinetic studies of the alkaline hydrolysis of a compound having low water solubility, a solvent such as methanol is generally added to enhance the solubility of the organic compound; however, the presence of the solvent often affects the reaction rate (Tinsley, 1979). In certain environmental applications the need to determine the hydrolysis rates of organic compounds, such as pesticides, in natural waters, is very important because hydrolysis is often the dominant route of degradation of anthropogenic chemicals in the environment. For example, 2-4-D is a widely used herbicide that may be formulated as an ester (e.g., as the 2-butoxyethylester or as the methyl W.D.B. is presently on the engineering faculty of Memphis
State University. 0196-4305/85/1124-0062$01.50/0
ester). These compounds have very low water solubility. In the pH range of 5 to 9, which is typical of natural waters, hydrolysis is an important breakdown process for the compounds, and is the dominant breakdown (or removal) process a t a pH of 9 (Tinsley, 1979). In the case of compounds having low water solubility, the solubility of the organic compound often determines the effective concentration of the compound in water and can limit or affect the rate of degradation of the compound. Therefore, it is important to consider not only the rate of chemical reaction but also the rate of mass transfer, as is done in the technique proposed in the present work. Background Alkaline hydrolysis of methyl salicylate has been studied previously by Goldschmidt and Scholz (1907) and Pal et al. (1974). Goldschmidt and Scholz indicate that the true reaction rate coefficient for the second order, bimolecular reaction between aqueous sodium hydroxide (0.05 to 0.2 N solutions) and methyl salicylate is between 100 and 110 cm3mol-' s-l at 25 "C. Goldschmidt and Scholtz also found that the solubility of methyl salicylate in water is so low a t 25 "C that 0.005 N solutions could barely be obtained. Consequently, their experiments were conducted in such a way that weighed amounts of the ester were inserted via tubes into sodium hydroxide solutions of known concentration. Samples of the aqueous phase were removed and were analyzed by titration. One apparent oversight of the technique of Goldschmidt and Scholz is that the resistance due to mass transfer of methyl salicylate into the aqueous phase was neglected. Depending on the relative rates of chemical reaction and mass transfer, either may be controlling. In the other study (Palet al., 1974), a spectrophotometric technique was used. In agreement with Goldschmidt and Scholz, those workers indicate that the overall 0 1984 American Chemical
Society
