Ind. Eng. Chem. Fundam. 1983, 22, 504-505
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Simple Experimental Method for Flnding the Kinetics of Gas-Solid Reactions An experimental method is developed for evaluating the kinetic constants of gas-solid reactions in which small batches of solids are added to a fluidiied bed of inert solids while the reactant gas concentration leaving the reactor is monitored. This method requires but rile equipment, is easily and quickly run, uses only small amounts of solids, and gives the rate constants directly.
Consider the problem of evaluating the kinetic constant k, for the reaction of solid particles containing reactant B, with gas containing reactant A, or A(g) + bB(s) products (1)
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which reacts by the shrinking core model (SCM), reaction control (Levenspiel, 1972), or
where S is the surface area of unreacted core and CIA is the mean concentration of gas encountered by the reacting particles. Zheng et al. (1982) presented a paper in which the following technique was described: a fluidized bed reactor filled with inert solids and fluidized with reactant gas at CAo was preheated to the desired operating temperature. Then at time to a weighed batch of reactant solid, W, was added to the reactor and the exit concentration of reactant gas CA was monitored until reaction was complete. An idealized plot of the exit concentration of reactant gas vs. time is shown in Figure 1. This experimental technique can be used to find the rate constant k, for the gas-solid reaction. Consider the simplest case of isothermal operations in which there is no change in the volumetric flow rate of gas due to reaction; i.e., one mole of gas is produced for each mole of reactant gas consumed. Since the moles of gaseous reactant entering and leaving the reactor per unit time are given respectively by uCAo and uCA,a material balance over the whole reactor gives (3)
Combining eq 2 and 3 gives the following relationship which is true at any instant U ( c ~ 0- CA) = k,CAS
(4)
For reactant gas in mixed flow C A = CA, while for plug flow C A = (CAO - CA)/h (CAo/CA). Since the values of CAO, CA, CA, and u would all be known, it is only necessary to determine the values of S in order to evaluate k,. Determination of S For spherical particles all of the same size, R, the total surface area of unreacted cores at any time is given by S = m4ar,2
(5)
where n is the number of particles within the reactor, given by n = 3 W/4aR3p, (6)
and MB is the molecular weight of B. Thus substituting eq 2 and 6 into 7 gives
Returning to eq 3 we have on integration
The integral of eq 9 corresponds to the shaded area of Figure 1 and may be evaluated graphically from the experimental data. This is all the information needed to calculate k,. Thus, choose t, evaluate NA from the area of Figure 1, insert into eq 8 to find ro and then insert rc into eq 5 to give S . Equation 4 then gives k,. One can accomplish all these substitutions to end up with the following equation k, =
uRps(CA0 - c.4)
(10)
Remarks 1. The particular attractiveness of this experimental technique is that it requires simple equipment, it is easily and quickly run, it uses only small batches of solids, and it obtains the kinetics under actual reactor conditions with its mass transfer resistances, etc. 2. Since reaction occurs in the fluidized bed, a close to uniform temperature prevails even though the reaction may be highly exothermic or highly endothermic. Thus one avoids, as much as or even more than any other method, the problems of nonisothermal behavior. 3. The main drawback of this method is that it may be difficult to determine with confidence the mean gas concentration within the reactor. 4. The paper shows how to evaluate k, for the simplest case of spherical particles of unchanging size, SCM/reaction control. Various extensions can be considered. (a) If the particle shrinks or expands with the same kinetics the analysis remains unchanged. Thus one can apply this method directly to solids which completely disappear on reaction, such as occurs in the combustion of carbon particles, or A(g) + B(s) gaseous products. (b) For other regular shaped particles simply modify eq 5 , 6, and 7 accordingly. The rest of the analysis remains unchanged. Thus, for example, for long cylindrical particles the final equation becomes
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The moles of solid which have reacted away up to any time is given by (7)
where xB is the weight fraction of reactant B in the solid 0196-4313/83/1022-0504$01.50/0
where R is now the cylinder radius. (c) Where the number of moles of product gas does not equal the number of moles of reactant gas, or aA(g) + 0 1983 American Chemical Society
Ind. Eng. Chem. Fundam. 1083, 22, 505-506 hserF, ,
I
t
reactant solid introduced here
h V
CA
I
I I
Solids are all reacted
I I
I
I
I
to
t time-
Figure 1. Exit concentration of reactant gas vs. time following the addition of a batch of reactant solid. Integratingthe shaded region allows one to determine the amount of reactant consumed until time
t.
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bB(s) rR(g) + sS(s), with an expansion factor (see Levenspiel, 1972), eq 10 is modified to give
CA
# 0
(d) For other kinetics follow a similar procedure. Thus, for example, a plot of
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Nomenclature A = gaseous reactant b = stoichiometric coefficient B = solid reactant CA = concentration of A leaving reactor, mol/m3 CAo = concentration of A entering reactor, mol/m3 C A = mean concentration of A within the reactor at any instant, mol/m3 k, = reaction rate constant, defined by eq 2, m/s MB = molecular weight of B, kg/mol n = number of reactant particles added to reactor NA = moles of A NB = moles of B re = radius of unreacted core, m R = radius of reactant particles, m S = total surface area of unreacted cores of n reactant particles in reactor, m2 t = time, s to = time when solid reactant is added, s u = volumetric flow rate of reactor feed, m3/s W = weight of solid reactant added to reactor, kg XB = weight fraction of B in reactant particles Greek Letters t A = expansion factor ps mass
density of reactant particle, kg/m3 Literature Cited Levenspiel, 0. “Chemical Reaction Engineering”, 2nd ed.;Wiley: New York, 1972. Zheng, J.; Yates, J. 0.: Rowe, P. N. Chem. Eng. Scl. 1982, 37, 167.
should give a straight line thought the origin with a slope of De, the kinetic constant for the SCM/ash diffusion control. For models other than the SCM, analysis is more involved because the rate forms are more complex.
Chemical Engineering Department Oregon State University Corvallis, Oregon 97331
George F. Davis Octave Levenspiel*
Received for review September 29, 1982 Accepted June 6, 1983
An Experfmental Technique for Determining Solubilities of Complex Liquid Mixtures in Dense Gases A flow method has been developed for measuring soiubiiities of heavy complex mixtures in compressed gases to 100 bar and 600 K. Quantitative analysis of the effluent gas is not required: therefore, this method Is suitable for liquid mixtures containing many unidentified components. Further, the method is suitable for gaseous mixtures containing a subcritical component such as water.
For high-pressure process design (e.g., supercritical-fluid extraction), it is often necessary to know the solubility of a heavy-component mixture in a compressed gas. Experimental methods for measuring such solubilities have been reported by numerous authors, including, for example, Diepen and Scheffer (1948), Rigby and Prausnitz (1968), Czurbryt et al. (1970), Simnick et al. (1977), Kaul and Prausnitz (1978), McHugh and Paulaitis (1980), Kurnik and Reid (1982), and Johnston and Eckert (1981). These methods require gravimetric measurements or chemical analysis (usually by gas-liquid chromatography) for the heavy component. Since nearly all experimental work in this area has been confined to systems wherein all components (usually only two) are clearly identified, chemical analysis is straightforward. However, if the heavy liquid is a mixture of many unidentified components (e.g., a narrow-boiling fraction from a heavy-fuel source), such analysis may be difficult, perhaps impossible. For such mixtures, gravimetric analysis is also not useful because, when volatility is low, an excessive amount of time is required to complete one run. Therefore, we have developed 0196-4313/83/1022-0505$01.50/0
an experimental solubility method which can be completed in a reasonable time frame and does not require quantitative chemical analysis. Experimental methods which replace precise, quantitative, chemical analysis with gravimetric measurement are essentially restricted to noncondensable gases; they are not useful for gas mixtures containing a subcritical gas as, for example, water vapor. Our technique, however, has been used to measure the solubility of a heavy fraction in a compressed methane/water mixture. This capability is important because water is often present in processing heavy fossil fuels. We use a flow method wherein a weighed amount of fraction is totally vaporized by a measured amount of gas. Figure 1 shows the total-vaporization method. The packed-bed equilibrium cell contains a known amount (typically 0.3 g) of heavy narrrow-boiling fraction. Gas at high pressure flows slowly through the equilibrium cell. After expansion to ambient pressure, the saturated gas flows to a wet test meter which measures the amount of gas passed through the equilibrium cell. 0 1983 American Chemlcai Society
