Reaction of Hydrogen Chloride Gas with Sodium Carbonate and Its

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Reaction of Hydrogen Chloride Gas with Sodium Carbonate and Its Deep Removal in a Fixed-Bed Reactor Miloslav Hartman,*,† Karel Svoboda,† Michael Pohořelý,†,‡ Michal Šyc,† Siarhei Skoblia,§ and Po-Chuang Chen∥ Institute of Chemical Process Fundamentals of the ASČ R, v.v.i. Rozvojová 135, 165 02 Prague 6, Czech Republic Department of the Power Engineering and §Department of Gas, Coke, and Air Protection, Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republic ∥ Institute of Nuclear Energy Research, Wenhua Road, No. 1000, Jiaan Village, Longtan Township, Taoyuan County 32546, Taiwan, R.O.C. † ‡

ABSTRACT: The chloridization rates of sodium hydrogen carbonate calcines were determined using both a differential fixedbed reactor and an integral fixed-bed, flow-through reactor at ambient pressure and a temperature of 500 °C. In the course of the reaction with hydrogen chloride gas, monoclinic or hexagonal Na2CO3 was transformed into cubic NaCl. The expansion of the volume of the solid phase, because of the reaction, was described by means of a simple structural model. The reacted solids remained quite porous (∼29%), having decreased from an initial porosity of 45%. Up to advanced stages of the reaction, the ratedecaying behavior of the chloridization reaction can be approximated by first-order kinetics as a function of either the solids conversion or the elapsed time of reaction. The reaction between hydrogen chloride gas and the Na2CO3-based sorbents is rapid, and a high degree of sorbent utilization can be attained. The unsteady-state sorption of hydrogen chloride gas in a column packed with reactant solids can be described by a pair of partial differential equations, and their analytical, closed-form solution is presented in terms of three dimensionless variables. Unsteady-state experimental runs were carried out in a small integral fixedbed reactor (14-mm i.d.) with spherical alumina particles having an average diameter of 1.5 mm, impregnated with NaHCO3 and packed to a depth of 6.5 cm. The effective reaction rate constants inferred from the experimental breakthrough curves in accordance with the model were found to be in reasonable agreement with those determined from the experiments executed in the differential mode of reaction. The presented, tractable expressions can readily serve as a rational basis for the conceptual design and effective operation of packed-bed reactors for the deep removal of hydrogen chloride gas from hot producer gas.

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INTRODUCTION Biomass is viewed as a promising, at least partial replacement for traditional fossil fuels. In addition to direct combustion, it can also be transformed by gasification into fuel (producer) gas (syngas) and utilized in more advanced technologies such as fuel cells, liquid fuels, and gas turbines.1−4 However, stringent requirements for the purity of the produced fuel gas necessitate efficient cleaning methods.5,6 In a reducing environment, chlorine species in biomass (fuel) are converted into hydrogen chloride, which is a strongly acidic, highly corrosive, and toxic colorless gas. Moreover, it often acts as a catalyst poison and also has harmful effects on the performance of zinc-based desulfurization sorbents. It is known that long-term contact with HCl and other halides can be harmful to both the electrodes and electrolytes in fuel cells. A tolerance limit of hydrogen chloride in producer gas is generally acknowledged as low as 1 ppmv, which is, for instance, 2 orders of magnitude less than the commonly accepted level for hydrogen sulfide.5,7 Molten carbonate fuel cells (MCFCs) appear to be quite attractive for direct electricity production: they can employ fuel gas very effectively and at relatively low cost. As MCFCs are operated at high temperature (600−700 °C), an essential cleanup step(s) should also work at such temperatures and ensure low residual concentrations of all unwanted contaminants. Efficient gas cleaning at high temperature is also required in processes © 2014 American Chemical Society

employing the promising integrated gasification combined cycle (IGCC). Abundant, inexpensive natural limestone or lime or hydrated lime are used for the removal of HCl from flue gas at elevated temperature.8−12 However, this method does not make it possible to attain the above-mentioned stringent limit for hydrogen chloride required for MCFC applications (1 ppmv). As discovered quite recently,12 a certain quantity of newly formed CaCl2 evaporates at high temperature, which further worsens the overall separation performance of calcium-based sorbents. In stark contrast to commercial, dense soda ash (Solvay soda), sodium carbonate is very highly reactive when it is prepared by the thermal decomposition of sodium hydrogen carbonate13,14 (sodium bicarbonate) or sodium carbonate hydrates15,16 under appropriate conditions. Such well-controlled decompositions produce a highly porous sodium carbonate (also called active soda) that reacts, for example, very rapidly with sulfur dioxide17−20 and also with nitrogen dioxide19 in waste or flue gas. Mocek et al.21 were probably among the first researchers to test HCl sorption on active sodium carbonate. They21 used an integral fixed-bed reactor operated with nitrogen as the carrier Received: Revised: Accepted: Published: 19145

September 3, 2014 November 12, 2014 November 17, 2014 December 1, 2014 dx.doi.org/10.1021/ie503480k | Ind. Eng. Chem. Res. 2014, 53, 19145−19158

Industrial & Engineering Chemistry Research

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gas at 150 °C. They found that the active modification of sodium carbonate exhibits a reactivity to hydrogen chloride that is orders of magnitude higher than that of the inactive form. The reactivity of the solid was found to vary with the method of its preparation, but a possible catalytic effect of water vapor on the rate of reaction was not proved. In an effort to solve problems with acid gases, Dvirka et al.22 considered direct once-through injection of powdered sodium hydrogen carbonate into the flue gas duct work of combustion systems. Primarily on a theoretical basis (activated complex reaction theory), the authors estimated that the rate at which hydrogen chloride gas reacts with sodium carbonate is very favorable. However, our previous experience23 clearly indicates that any transport-line reactor is capable of removing a large portion of gas reactant only at large recirculation ratios of the solid sorbent. Also, adequate temperature profiles in the duct work are an additional prerequisite. Using very fine particles of sodium hydrogen carbonate (10− 160 μm), Fellows and Pilat24 measured the separation of hydrogen chloride in a 2.5-cm-i.d. fixed-bed reactor at elevated temperature. The determined HCl separation efficiencies increased strongly with increasing temperature and decreased quite rapidly with sorbent loading. In light of our recent experimental measurements,14 it appears that a significant portion of the parent NaHCO3 remained undecomposed and reacted directly with HCl at lower temperatures. In an effort to support the economic feasibility of dry sorption of HCl, Gupta et al.25 tested pellets and granules made from nahcolite, which is a relatively inexpensive, white, monoclinic mineral consisting of natural sodium hydrogen carbonate. Their economic estimates25 indicated that the cost of HCl removal by nahcolite sorbents would be sufficiently low for practical use. With the aim of increasing the overall performance (i.e., the reactivity and the capacity of sodium-based sorbents), Nunokawa et al.26 tested sodium−aluminum composites prepared from sodium carbonate solution, alumina sol (Al2O3 sol), and activated alumina (γAl2O3). X-ray diffraction analyses identified the sodium in the tested mixed sorbents in the form of sodium aluminate (NaAlO2). The reactivity of sorbents containing sodium aluminate at 400 °C was found to be higher than that of sodium carbonate itself. Unfortunately, the authors26 did not present any more detailed information about the method of preparation of the sodium carbonate they used in their comparison. Using a small-scale fixed-bed reactor, Duo et al.27 confirmed that calcium carbonate is not an efficient sorbent for hydrogen chloride in fuel gas. In their work, the performance of Na-based sorbents was found to be influenced considerably by temperature and slightly by sorbent particle size. The authors27 proposed a mathematical model to describe the gas−solid reactions in fixed beds that is embodied in a set of nonlinear partial differential equations. The optimum combination of reaction rate constant, product-layer diffusion coefficient, and effective particle porosity were deduced from the measured breakthrough curves. A similar approach to HCl sorption was taken by Verdone and De Filippis:28 They also incorporated the particle grain (sub)model into a general fixed-bed reactor model. In the explored system, more or less pure solid particles (cs ≈ 10−2 g-atom of Na/cm3) react quite rapidly with a very lean gas phase (cg ≈ 10−9 mol of HCl/cm3). The combination of the considerable rapidity of the reaction in the dilute gas phase and the very large sorption capacity of the solids is the principal cause of the high stiffness of the model equations in the physicochemical sense.29

The present work is a sequel to a previous study of ours14 on the thermal decomposition of sodium hydrogen carbonate and the textural properties of (re)active sodium carbonate. This article explores the kinetics of the reaction between hydrogen chloride gas and solid sodium carbonate originating from the hydrogen carbonate. The main objective of the current work is to develop a tractable model of unsteady-state sorption of HCl gas in a fixed-bed reactor, which is closely related to the experimental reality but does not require sophisticated numerical procedures and analyses. The effort is aimed at the essential knowledge necessary for the deep removal of hydrogen chloride gas from producer gas at elevated temperature.

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PHYSICOCHEMICAL PRINCIPLES Reaction Equilibria. The sorption of HCl on Na2CO3 takes place as follows Na 2CO3(s) + 2HCl(g) = 2NaCl(s) + H 2O(g) + CO2 (g)

(1)

Neutralization/chloridization reaction 1 is considerably exothermic, with ΔH°(298.15 K) = −142.179 kJ/(mol of Na2CO3) as estimated from Barin’s thermodynamic data.30 The effect of temperature on the standard enthalpy of reaction 1 can be described by −ΔH °(T ) = 0.01757T + 135.6

(2)

for T ∈ (298, 1000) K. The overall sorption reaction with sodium bicarbonate, given by NaHCO3(s) + HCl(g) = NaCl(s) + H 2O(g) + CO2 (g) (3)

is slightly exothermic, with a standard enthalpy of reaction as small as ΔH°(298 K) = −2.66 kJ/(mol of NaHCO3). As can be seen, reaction 1 is accompanied by an increase in the number of moles of the solid phase [i.e., Δns = 1 mol/(mol of Na2CO30}, whereas the number of moles in the gas phase remains constant (i.e., Δng = 0). This implies that equimolar counterdiffusion of the species occurs in the gas phase. This fact is important in solving the problem of mass transfer between reacted particles and a moving gas stream. Thermodynamic constraints imposed on reaction 1 were also deduced from Barin’s compiled thermochemical data30 and are expressed in the form log K =

7084.4 − 2.1134 log T + 8.2111 T

(4)

where K = Kp =

pH O pCO 2

pHCl 2

2

(5)

As is evident from eq 5, the equilibrium constant, K, is dimensionless and does not depend on pressure. Having minimized the total Gibbs free energy of the system under the mass balance constraints, Verdone and De Filippis28,31 computed the equilibrium constants of reaction 1 for temperatures of 200 and 600 °C as large as 1.7 × 1018 and 2.5 × 1010, respectively. The corresponding predictions of our proposed eq 4 for the same temperatures are fairly close to these values, at 3.4 × 1017 and 1.3 × 1010, respectively. The concentration of hydrogen chloride in the reaction system at equilibrium is then given as 19146

dx.doi.org/10.1021/ie503480k | Ind. Eng. Chem. Res. 2014, 53, 19145−19158


yHCl

⎛ yH O yCO2 ⎞0.5 =⎜ 2 ⎟ ⎝ K ⎠

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cubic NaCl with the face-centered lattice.14−16 This process is accompanied by expansion of the volume of the solid phase. Because the reacted particle commonly retains its original gross external volume, the pore volume and surface area of the solid are reduced because of reaction. The expansion factor, defined as the stoichiometric ratio of the molar volume of sodium chloride to the molar volume of sodium carbonate, is significant and amounts to 1.287. Thus, it appears that a relevant layer of solid reaction product (NaCl) forming on the active solid surface (Na2CO3) can grow considerably as reaction 1 proceeds. Nevertheless, Table 1 indicates that such growth is not as

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Table 1. Changes of the Volume of the Solid Phase and Changes in Its Mass Accompanying the Reactions of Hydrogen Chloride Gas with Solid Sodium (Hydrogen) Carbonate and Calcium Carbonate reaction Na2CO3 + 2HCl = 2NaCl + H2O + CO2 NaHCO3 + HCl = NaCl + H2O + CO2 2NaHCO3 = Na2CO3 + H2O + CO2 CaCO3 + 2HCl = CaCl2 + H2O + CO2 Na2CO3 + SO2 = Na2SO3 + CO2

Figure 1. Equilibrium concentrations of hydrogen chloride, yHCl, in contact with sodium carbonate (curve 1), potassium carbonate (curve 2), and calcium carbonate (calcite) (curve 3) computed from eqs 4−8 for yH2OyCO2 = 0.01.

solid volume expansion/ reduction coefficient,a f

relative solid mass change

1.2873

1.1028

0.7053

0.6957

0.5479

0.6308

1.3977

1.1089

1.1454

1.1892

a

Expansion/reduction coefficient introduced as the stoichiometric ratio of the molar volume of solid product to the molar volume of reactant.

progressive as, for example, in the case of the HCl sorption on calcium carbonate. Table 1 compares the expansion factors and relative mass changes of several reactions that are related to Na2CO3 or HCl. The true densities of the respective pure compounds, used for the molar volume calculations, were taken from the standard handbooks.32,33 These values lead to the following molar volumes: VNa2CO3 = 41.843 cm3/mol, VNaCl = 26.932 cm3/mol, VNaHCO3 = 38.185 cm3/mol, VCaCO3 (calcite) = 36.932 cm3/mol, and VCaCl2 = 51.620 cm3/mol. The data in Table 1 suggest that the effective sorbent/solid reactant should be porous whether prepared from NaHCO314 or, for example, from sodium carbonate hydrates.15,16 Evidently, the pore volume is gradually filled with the reaction product as the reaction progresses. Nevertheless, the reduction/expansion coefficient for the NaHCO3-derived sorbent (0.7053) indicates that the reacted particle remains quite porous (e = 0.2947), even though it is completely converted to NaCl. It is also worth noting that both Na2CO3 and CaCO3 exhibit quite significant expansion coefficients of 1.2873 and 1.3977, respectively. The relative mass gains of the two reactants are not much different. Transfer of the Gaseous Reactant from the Bulk of the Flowing Gas to the External Surface of the Reacting Particle. This individual physicochemical step can play a significant role in determining the overall rate of reaction 1. In principle, it is possible to compute the mass-transfer rate by solving the appropriate fluid-flow and diffusion equations.34,35 However, a more pragmatic approach based on experimentally determined mass-transfer coefficients is employed here. It is believed that several simplifying assumptions, such as a spherical reacting particle with uniform symmetrical conditions in its interior, a pseudosteady state, and no or negligible bulk flow due

Predictions of eqs 4−6 are visualized in Figure 1 for yH2OyCO2 = 0.01. As can be seen in this figure, the limiting value, most often required to be as low as yHCl = 10−6, is still obtained at approximately 883 K (610 °C). Gupta et al.25 reported the equilibrium concentration of HCl for 900 K (627 °C) as yHCl = 1.5 × 10−6. This value is in good agreement with the prediction obtained using proposed eqs 4−6, namely, yHCl(900 K) = 1.2 × 10−6. For the sake of comparison, similar predictive relationships were also developed to estimate the equilibrium constants for the analogous reactions between hydrogen chloride gas and potassium carbonate and hexagonal calcium carbonate (calcite). Specifically, for the reaction of HCl(g) with K2CO3(s) [ΔH°(298 K) = −173.89 kJ/(mol of K2CO3)], we obtained 8803.0 log K = − 1.7525 log T + 7.3169 (7) T and, for the reaction of HCl(g) with CaCO3, calcite [ΔH°(298 K) = −39.58 kJ/(mol of CaCO3)], we obtained 1943.6 − 0.79897 log T + 4.5210 (8) T As is apparent from Figure 1, the equilibrium concentrations of HCl over K2CO3 are an order of magnitude smaller than those over Na2CO3 at the same temperature. However, it is also evident that inexpensive CaCO3 sorbents cannot reach the stringent limit for hydrogen chloride (yHCl = 10−6) even at room temperature. Volume Changes of the Solid Phase. A structural transformation takes place during reaction 1: the monoclinic, base-centered Na2CO3 (stable below 483 °C) or its hexagonal form (stable above 487 °C) is converted into the crystalline, log K =

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to diffusion or pressure gradient, are reasonable. Because the reaction system comprises a lean gas and dense, round, and isometric solids with well-defined chemistry (reaction 1), these simplifications appear to be quite plausible. Then, the balance of the reacting gaseous component makes it possible to express the relative concentration at the solid surface, yp/y, as yp d p 1 ρs dX for yp /y ∈ ⟨0, 1⟩ =1− y 6 hd ρg y dτ (9)

By breaking down these equations, it can be shown that the masstransfer coefficient, hd, increases markedly with the superficial gas velocity, U, and with the gas-phase diffusion coefficient, D, and decreases with increasing particle diameter, dp

where dX/dτ is the overall rate of reaction and hd is the masstransfer coefficient. In the past, gas-phase mass-transfer rates were measured quite often: the relevant experiments involved, for example, the evaporation of drops or the sublimation of solids into gaseous streams. The measured data were mostly correlated in terms of dimensionless groups, such as the Sherwood, Reynolds, and Schmidt numbers. It should be noted that this interpretation is in accordance with the rigorous solution of the convective diffusion equations, as well as with the results of dimensional analysis for forced convection. Predictions of the triad of well-established correlations (i.e., Froessling36 and Ranz and Marshall,37,38 Petrovic and Thodos,39 and Dwivedi and Upadhyay40) are compared in Figure 2. As can

hd ≈ U 0.28−U 0.59

(12)

hd ≈ D2/3

(13)

hd ≈ d p−0.41−d p−0.72

(14)

The effects of the Reynolds number and the rate of reaction on the relative concentrations of reactants at the solid surface are illustrated in Figure 3. It should be stressed that the values of the

Figure 3. Dependence of the relative concentration of reacting gas at the surface of sorbent on the Reynolds number for a single particle. Predictions of eqs 9−11 for e = 1, dp = 0.0565 cm, t = 450 °C, ρs = 0.02385 mol/cm3, and ρg = 1.685 × 10−5 mol/cm3: curve 1, (1/y)(dX/ dτ) = 0.2 s−1;20 curve 2, (1/y)(dX/dτ) = 0.1 s−1.

reaction-rate term, (1/y)(dX/dτ), were selected more or less arbitrarily. For example, the higher value, 0.2 s−1, corresponds to the high initial rate of sorption of sulfur dioxide by a very reactive cryptocrystalline limestone at 850 °C.20 The computed curves in Figure 3 show that the concentrations at the solid surface can be fairly lower than those in the bulk of the gas stream. Thus, at least in the early stages of reaction, the resistance to mass transfer in the gas phase surrounding the reacting particle should also be taken into consideration. Also, the mass-transfer effect cannot be overlooked at very low gas flow rates even at more advanced stages of sorption. At low pressures (below 1−1.5 MPa), the diffusion coefficient in binary gaseous systems varies only very slightly with the composition, increases considerably with the temperature, and is inversely proportional to the pressure. Our experience indicates that the method of Fuller, Schettler, and Giddings (FSG), based on the Stefan−Maxwell hard-sphere model and carefully evaluated, additive atomic diffusion volumes,42,43 provides reliable estimates of gas-phase diffusivities. The FSG procedure was employed to predict the constant, aAB, in eq 15

Figure 2. Comparison of gas−particle mass-transfer correlations: curve 1, Froessling/Ranz and Marshall relationship;36−38 curve 2, Petrovic− Thodos equation;39 curve 3, Dwivedi−Upadhyay correlation,40 expressed by eqs 10 and 11. The predictions are related to single particles with a Schmidt number equal to unity (Sc = 1).

be seen, the three correlations are in fair agreement. Dwivedi and Upadhyay40 also developed a regression equation for gas−solid systems on the basis of a large volume of experimental data measured by different authors with various systems in a broad Reynolds number range. That is why this well-substantiated correlation was selected for use in this work ejd =

0.765 0.365 + 0.386 0.820 Re Re

where jd is the Chilton−Colburn factor for mass transfer jd =

h Sh = d Sc 2/3 U ReSc1/3

(10) 41

DAB = aABT1.75

(11) 19148

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experiment (about 2.5 m/s). Very small changes in the gas composition (to approximate differential conditions) were realized by using small samples (about 15 mg) of precalcined sodium carbonate particles. Larger samples were used for a porosity study in which the rate of reaction was not determined. Stainless steel, quartz glass, and polytetrafluoroethylene (PTFE) were employed as HCl-resistant materials in the experimental setup. Samples exposed to the producer gas in the reactor were analyzed for chloride by first being dissolved in deionized water. The amount of chloride was then determined by ion chromatography. Conversions were calculated from both the chloride content in the reacted particles and the relative mass gain of the loaded solids. Results of these procedures were in good agreement. Pore volumes/porosities of the samples were determined by helium and mercury displacement using AccuPyc 1330 and AutoPore III instruments, respectively (Micromeritics Instrument Corp.). Pore size distributions were determined by measuring the volume of mercury penetrating the pore volume as pressure was increased to 690 MPa (105 psi). The Brunauer− Emmett−Teller (BET) surface area was measured with an ASAP 2050 instrument. The hydrogen chloride separation efficiency of the sorbent was determined by means of an integral fixed-bed reactor (14.03-mm i.d.) The reactor was made of quartz glass, so it could be operated safely at temperatures up to 800 °C. The reactor vessel was composed of two parts and was placed in an electrically heated furnace. Measured and controlled amounts of gaseous components were thoroughly mixed and heated before being fed into the reactor. The simulated producer gas passed through the sorbent bed from top to bottom. Both the exiting gas and the inlet stream were analyzed for HCl by ion chromatography upon absorbing in deionized water. The temperature in the reactor was monitored by three thermocouples located along the height of the bed. The apparatus was operated at ambient pressure. The volume of the bed was 10 cm3, and it had a porosity of ebed = 0.5276 and a depth of 6.462 cm. The mean diameter of solids amounted to 1.496 mm, and alumina particles impregnated with NaHCO3 contained 1.009× 10−3 g-atom of Na/cm3 of particles. For comparison, the stoichiometric value is as large as 0.026188 g-atom of Na/cm3 of porous Na2CO3. The superficial gas velocity based on the empty cross-sectional area of the bed (1.547 cm2) was in the range from 9.39 to 25.60 cm/s based on a temperature of 500 °C and atmospheric pressure (101.325 kPa). Unsteady-state sorption experiments were mostly conducted at 500 °C with respect to practical gasifier exit temperatures. This temperature is near practical operating temperatures in gasification processes and well below the melting point of sodium chloride32 (800.7 °C). For conditions of 500 °C and yH2OyCO2 = 0.01, eqs 4 and 6 predict an equilibrium concentration of hydrogen chloride gas as low as 0.232 ppm. First, the reactor and the sampling lines were purged with nitrogen gas. The weighted volume of sorbent particles (10 cm3) was placed within the cold reactor vessel, and the setup was heated to the desired temperature and allowed to remain at this temperature for 1 h to steady all temperature profiles. Then, the model gas mixture was admitted into the reactor vessel. At the end of the sorption run, the system was purged with nitrogen and allowed to cool. The loaded sorbent was removed from the reactor and subjected to further examinations.

for the pertinent systems with hydrogen chloride. The values of aAB computed for a standard pressure of 101.325 kPa are presented in Table 2. Unfortunately, no experimental data on the Table 2. Coefficient aAB in the Relationship DAB = aABT1.75 for the Prediction of Gas-Phase Diffusivities in Binary Mixtures of HCl(g) Deduced from the Fuller−Schettler−Giddings Correlation43 and Diffusivity, DAB, at 450 °C for a Standard Pressure of 101.325 kPa complementary component

aAB [×106 cm2/(K1.75·s)]

diffusivity, DAB, at 450 °C (cm2/s)

CO2 CO N2 CH4 H2O(g) H2

6.7122 8.4792 8.6299 9.2830 11.016 32.765

0.6769 0.8551 0.8703 0.9361 1.1109 3.3042

diffusion of hydrogen chloride were found in the literature. The diffusivity predicted for the system CO−CO2 at 273.2 K as high as 0.1358 cm2/s agrees very well with the experimental value of 0.1390 cm2/s.44 Similar agreement between prediction (0.6881 cm2/s) and experiment (0.7260 cm2/s) was confirmed for the system H2−CH4 at 298.2 K.44 The results given in Table 2 can also be used as data for predicting multicomponent diffusion rates.45−47 When plotted, the values of aAB and DAB show an approximately linear increase with increasing formula mass raised to the power of −0.5.

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EXPERIMENTAL SECTION Materials. Sodium hydrogen carbonate, whose thermal decomposition was explored in a recent work of ours,14 was employed as a parent material for preparing sodium carbonate. The precursor obtained from commercial sources (AR grade) with a purity of 99.6% contained less than 0.001 wt % chloride and 0.01 wt % sulfate. Its weight loss upon ignition at 500 °C was determined to be 36.77 wt %. Sodium carbonate for the experimental work was prepared by the calcination of hydrogen carbonate at a temperature of 180 °C in a muffle furnace under a slow flow of nitrogen as the sweep gas. The decomposed particles were carefully sieved, and narrow fractions 0.25−0.32 mm (d̅p = 0.285 mm), 0.50−0.63 mm (d̅p = 0.565 mm), and 1.00−1.25 mm (d̅p = 1.12 mm) were maintained in airtight containers (stored in a desiccator) and investigated in this work. The irregular shape of the particles was not altered by the calcination process. A model producer gas was prepared by metering and thorough blending of the individual components with the aid of mass flow controllers (Bronkhorst High-Tech). The composition of the gas entering the reactor unit was 15% CO2, 10% H2O(g) and 100−700 ppmv HCl, with the remainder consisting of N2. The concentration of HCl vapor in the gas was determined by absorption in deionized water contained in a series of impingers and ion chromatography analysis (Dionex ICS 1000 or Dionex ICS 5000 instrument) for the chloride anions thereby formed. This method is capable of determining sub-part-per-million (by volume) levels of HCl vapor in the gas. Check analyses were carried out by AgNO3 titration. Apparatus. The reaction between Na2CO3 and HCl was explored under ambient pressure and at constant temperature using a differential reactor with the thin, fixed bed of solid described earlier.48 To eliminate or minimize mass-transfer interference, a high flow rate of gas was employed in each 19149



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RESULTS AND DISCUSSION Structural Characteristics of the Solids. Microscopic examinations showed that the parent monoclinic sodium hydrogen carbonate was composed of larger dense micrograins 0.1−0.01 mm in size. The solids were made porous by calcination to Na2CO3 with a mean grain diameter as small as 3 × 10−4 mm, a BET surface area of 7.9 m2/g, a medium pore diameter of 200 nm, and a pore volume of 0.325 cm3/g. It is of interest to note that sodium carbonate formed at a calcination lower temperature (∼200 °C) remained monoclinic (the same as the parent hydrogen carbonate) and exhibited some sharp filaments on the grain surface. However, only the hexagonal form of sodium carbonate is stable at temperatures above 480−490 °C. Porosities of the Reacted Particles. An effort was made to investigate how the volume of the solid phase was changed by chloridization reaction 1. On the basis of the mass and volume balances, the following relationship can be written between the porosity of the reacted particle, ex, and the progress of reaction 1 designated by X ⎡ ⎛ 2V ⎞ ⎤ ex = 1 − (1 − ec)⎢1 + yNa CO ⎜⎜ NaCl − 1⎟⎟X ⎥ 2 3 V ⎢⎣ ⎝ Na 2CO3 ⎠ ⎥⎦ (16)

was achieved. As can be seen, reaction 1 was accompanied by a noticeable expansion of the solid phase. Nevertheless, the porous structure of the solid developed by calcining nonporous sodium hydrogen carbonate was comfortably capable of accommodating all of the sodium chloride that could be formed by the reaction: The initial porosity of fresh sodium carbonate, ec = 0.4521 (X = 0) was significantly reduced upon complete conversion; nonetheless, it still remained appreciable at ex = 0.2947 (X = 1). Equation 16 can be rewritten in the somewhat more generalized form e in − ex = y(f − 1)X 1 − e in (17) where the symbol f designates the expansion/reduction factor of the solid phase, depending on the particular case under consideration. For the sake of comparison, eq 17 is visualized in Figure 5 for the sulfation and sulfidation reactions of porous

where ec is the fractional porosity of a completely calcined particle prior to chloridization.14 Implicitly, in eq 16, it is assumed that the reacted particle retains its original gross external volume, sodium chloride is the exclusive reaction product, and the conditions are uniform throughout the interior of the particle. With the above-presented molar volumes of the species involved in reacting, eq 16 predicts how the porosity of the reacted particle depends on the pore volume resulting from calcination and on the progress of sorption. In Figure 4 are plotted the results of the chloridization experiments reported here, along with the predictions of eq 16. The straight line in this figure represents the porosities calculated for yNa2CO3 = 0.996. In these calculations, it was assumed that the parent NaHCO3 was completely converted into Na2CO3 and that the porosity of the fresh sorbent was ec = 0.4521. As shown in Figure 4, rather good agreement between theory and experiment

Figure 5. Comparison of the porosity functions of reacted solid, (ein − ex)/(1 − ein), over the course of several important separation reactions, X, predicted by eq 17 for pure reactants (y = 1): line 1, 2NaHCO3 = Na2CO3 + H2O(g) + CO2, f = 0.5479; line 2, this work, reaction 1, f = 1.287; line 3, CaO + H2S = CaS + H2O(g), f = 1.659; line 4: CaO + SO2 + 1/2O2 = CaSO4, f = 2.739.

calcium oxide48,49 and for the thermal decomposition of sodium hydrogen carbonate14 as well. The effect of each of these reactions on the change in porosity can be quantitatively described in terms of the derivative obtained from eq 17 as follows dex = −(1 − e in)y(f − 1) (18) dX For the sulfation and sulfidation of porous lime (CaO), the derivative in eq 18 is as large as −0.7908 and −0.2996, respectively (for y = 1). In the case of chloridization reaction 1, the derivative in eq 18 amounts to only −0.1574, which clearly suggests that diffusional resistances are less likely to develop within a chloridized particle than in sulfated solids during the course of sorption. It should be noted that low conversions of calcium oxide to calcium sulfate are commonplace in dry limestone-based processes for sulfur dioxide removal from flue gas. Equation 18 also reflects that an extensive porous structure develops during the calcination of sodium hydrogen carbonate: (dec/dXc) = 0.4521 for ein = 0 and y = 0.996.

Figure 4. Fractional porosity of chloridized particles, ex, for initially porous particles of Na2CO3 (ein = ec = 0.4521) as a function of the fractional conversion to NaCl, X (yNa2CO3 = 0.996). Data points are the results of experiments; the straight solid line represents the predictions of eq 16. 19150



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Reaction Rate. Experimental results measured at 500 °C by means of the differential reactor indicate that the chloridization reaction is quite rapid in its initial stage. As the exposure time continued and the conversion increased, however, the rate of reaction decreased. Nevertheless, high conversions of sodium carbonate to sodium chloride could be reached. This is in contrast, for example, to the sulfation of calcium oxide, in which only lower conversions are attained.49 As mentioned above, the volume and diffusional resistance of the accumulating product of the reaction within the chloridized particle are presumably much less than those within the sulfated calcium oxide. The inhibiting effect of the progress of chloridization on the rate of reaction manifests itself in the characteristic moderately concave shape of the conversion versus time curves. Moreover, the attained conversion decreases mildly with increasing particle size. Nevertheless, when the unreacted fraction of sorbent, 1 − X, was plotted logarithmically against the time of reaction

or X = 1 − exp( −kpyHCl τ )

(21)

It should be noted that the physicochemical meaning of the product kpyHCl is the initial rate of reaction kpyHCl =

⎛ dX ⎞ ⎜ ⎟ ⎝ dτ ⎠ 0

for τ → 0, X → 0 (22)

The measured data plotted according to eq 20 are presented in Figure 6 for three particle sizes. As can be seen, all of the data fit the corresponding straight lines fairly well. The deviations from a straight line dependence do not exceed a few percent. The effective rate constants, k, were computed from the slopes of the straight lines shown in Figure 6, which were evaluated from the measured data by a least-squares procedure with the regression parameters R2 = 0.961, 0.989, and 0.984. Their values, given in Table 3, decline with increasing particle size from 6.02 × 10−3 to Table 3. Effective Reaction Rate Constants and Initial Rates of Chloridization of Sodium Carbonate at 500°Ca particle size, d̅p (mm)

effective reaction rate constant, k [(kPa·s) ]

initial rate of reaction, dX/dτ (s−1)

0.285 0.565 1.120

6.017 × 10−3 3.910 × 10−3 2.310 × 10−3

1.829 × 10−4 1.189 × 10−4 7.022 × 10−5

−1

a

On the basis of experiments conducted at ambient pressure with gas containing 0.03 vol % HCl. Solid reactant was formed by the thermal decomposition of NaHCO3 at 180 °C.

2.31 × 10−3 (kPa·s)−1. The corresponding initial rates of reaction are in the range from 1.83 × 10−4 to 7.02 × 10−5 s−1. The decrease in the value of the reaction rate constant with increasing particle size can be approximated by the regression relationship log k = − 0.69497 log d p − 2.5995

in which dp is given in millimeters and the coefficients were determined by a least-squares method with a regression term R2 as large as 0.978. Predictions according to eq 23 are compared to experimental values in Figure 7. Kinetics experiments were also performed with additional concentrations of hydrogen chloride in the gas phase (0.02 and 0.06 vol % HCl). Treatment of the initial rates of reaction deduced from the experiments confirmed that the exponent of the HCl concentration, yHCl, in eq 19 is essentially equal to unity. The above-presented correlation reflects the rate-decaying behavior of chloridization with its progress. From the standpoint of modeling,50 it might also be convenient to express the reaction rate as a function of time instead of conversion

Figure 6. Influence of average particle size, d̅p, on the course of chloridization of sodium carbonate, X(τ). Conditions: temperature, 500 °C; concentration of HCl, 0.03 vol %; solid reactant, calcine formed from NaHCO3 by decomposition at 180 °C. Line 1, d̅p = 0.285 mm; line 2, d̅p = 0.565 mm; line 3, d̅p = 1.12 mm.

(exposure) (Figure 6), an approximately linear correlation was obtained, suggesting a first-order rate of reaction dX = kpyHCl (1 − X ) dτ

(19)

where dX/dτ is the rate of conversion of sodium carbonate to sodium chloride and k is the effective, first-order reaction rate constant under invariant operating conditions of interest. The meanings of the remaining variables are explained in the Nomenclature section. This approach is also supported by the plausible assumption that the reaction is not a pure surface phenomenon. Upon rearrangement and integration of eq 19 with a variable upper limit, eqs 20and 21 were obtained to describe the progress of chloridization over the course of time ln(1 − X ) = −kpyHCl τ

for X ≠ 1

(23)

dX = kpyHCl exp( − kpyHCl τ ) dτ

(24)

The correlations presented here have the usual limitations, and they should be employed with due care beyond the scope of our experimental work. Sorption Reaction in a Packed Bed of Solids. A mathematical description of an integral fixed-bed reactor in which the dechloridization reaction takes place is treated here using the following simplifying, yet plausible assumptions:

(20) 19151



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the packed bed, as well as the time-varying separation efficiency. The solution is facilitated when a change of variables is made and eqs 25 and 26 are recast into dimensionless form. Following an approach similar to that of Du Domaine et al.,53,54 Baasel and Stevens55 found the analytical and closed-form solution for the first-order kinetics that was modified in this work as follows yout yin

=

em(1 − τrel) 1 + em(1 − τrel) − em

(29)

and Xout = 1 −

1 − X0 1 + em(1 − τrel) − em

(30)

or Xout = 1 − (1 − X 0) Figure 7. Effect of average particle size, d̅p, on the effective reaction rate constant, k. The experimental conditions are the same as those in Figure 6; the values of k are given in (kPa·s)−1; the values of d̅p are given in mm. The solid line shows the predictions of eq 23 with R2 = 0.978.

∂yHCl ∂z

=

(1 − e)ρs ρg

(31)

m = −kp

(1 − e)ρs Uρg

z = −kpyin τstech

(33)

or kpyHCl (1 − X )

∂X = kpyHCl (1 − X ) ∂τ

m = −kp

(25)

1 − e ρs τg̅ e ρg

(34)

where the symbol τstech reflects the sorption capacity of bed (26)

τstech =

with the boundary and initial conditions

(1 − e)ρs Uρg yin

z=

(1 − e)ρs eρg yin

τg̅

and τg̅ is the mean residence time of gas in the bed e τg̅ = z U

(27)

and

X(z , 0) = X 0

em(τrel − 1)

It is shown later that the quantity m acquires inherently negative values, that is, m < 0. Quick calculations indicate that the term em becomes much less than unity, that is, em ≪ 1, for, say, |m| > 10, and can be neglected in eqs 29−32. As can be seen, the relative concentration of the reacting gaseous species at the bed outlet, yout/yin, is a function of the dimensionless/relative time elapsed since the beginning of sorption, τrel = τ/τstech, and the dimensionless “reactivity and/or reaction capacity” (or the sorption power) of the bed expressed as m. The dimensionless operating variable τrel can also be conceived as a measure/degree of bed loading. The latter independent quantity m is defined by

and

yHCl (0, τ ) = (yHCl )in

yin

It is apparent that no separation reaction occurs (i.e., yout/yin = 1 and Xout = X0) when m = 0. In the case of τrel = 1, for example, eq 29 simplifies considerably to yout 1 for τrel = 1 and m < ln 2 = yin 2 − em (32)

(1) The gas exhibits plug flow while passing through the vertical bed at a constant rate. (2) Conditions in the radial direction are uniform. (3) Equilibrium constraints do not occur, and the ideal gas law can be applied. (4) The system is operated under ambient and invariant pressure and at constant temperature. (5) Mass transfer from the bulk of the gas to the reacted particle does not affect the rate of reaction. (6) Sorption reaction 1 is of first order with respect to both reactants, and its rate is given by eq 19. (7) The pseudosteady-state approximation is sufficiently accurate for application to this reaction system.51,52 Mass balance equations for hydrogen chloride gas can be written for a differential element of the packed-bed reactor. Under the preceding assumptions, the rate of removal from gas and the rate of accumulation in solids can be equated to the rate of reaction −U

yout

(28)

(35)

(36)

In light of eq 33, the parameter m can also be viewed as a distance parameter. The quantity (1 − yout/yin) represents the fractional conversion of the gaseous component, that is, the fraction of the component removed/separated from the gas. In addition to allowing the rational design of separation reactors, the analytical solution summarized above also makes it possible to quite easily evaluate kinetics data collected under integral conditions for firstorder reactions. It should be noted that, in contrast to the method of Baasel and Stevens,55 the effective reaction rate constant, k,

Equations 27 and 28 state that the composition of entering gas is invariant with respect to time and that the initial conversion of sorbent is the same throughout the bed. As is evident, the whole process of unsteady-state sorption in the packed bed of sorbent is described here by a pair of partial differential equations (eqs 25 and 26) with the appropriate boundary and initial conditions (eqs 27 and 28). Solutions to these equations provide transient concentration profiles within 19152



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occurs in this work exclusively in the parameter m introduced by eqs 33 and 34. This fact facilitates its determination from the experimental data. The relations among the quantities yout/yin, τ/ τstech, and m are visualized in Figure 8 as the performance graphs of packed-bed reactors. As can be seen, the sigmoidal shapes of the computed breakthrough curves become clearly recognizable for |m| > 2.

Figure 9. Linearized dependence of the outlet concentration, Y = (yout/ yin)/(1 − yout/yin), on the elapsed relative time of sorption, 1 − τ/τstech, for different reaction parameters, m. Computations according to eq 38. Figure 8. Dependence of the relative outlet concentration, yout/yin, on the elapsed relative time of sorption, τrel = τ/τstech, for different reaction parameters, m. Computations according to eq 29.

em +

yout /yin 1 − yout /yin

for yout /yin < 1

(37)

eq 29 can be rewritten in linear form as ln Y = m(1 − τrel) − ln(1 − e m)

for m < 0

(38)

where the slope and intercept of the resulting straight line are evident and from which m and k can be obtained on the basis of the measured breakthrough curves. Equation 38 is illustrated with some of the computed results in Figure 9. When we set the intercept, q, as q = −ln(1 − e m)

for m ∈ ⟨−10, 0⟩

(39)

we obtain a simple relation for m m = ln(1 − e−q)

for q > 0

k = 1.595 × 10−4U + 5.018 × 10−4

(40)

For e ≪ 1, eq 38 reduces and provides m

m=

ln Y 1 − τrel

for |m| > 10 and τrel ≠ 1

for Y > 0

(42)

can be employed in the search for m. As follows from the preceding paragraphs, the effective reaction rate constant, k, is contained exclusively in the reaction parameter m. Its determination from the transient experimental runs poses no problem nor difficulty. However, it should be considered as an empirical coefficient of the reaction in the reactor model rather than an intrinsic chemical term. Experimental results obtained at three superficial gas velocities, namely, U = 9.39, 17.07, and 25.61 cm/s, are plotted in Figure 10. Their treatment led to reaction parameters, m, of −4.15, −3.82, and −3.52, respectively. The corresponding values of the effective reaction rate constant, k, were then found to be 1.97 × 10−3, 3.30 × 10−3, and 4.55 × 10−3 (kPa·s)−1, respectively. In light of the entirely different operating methods employed, these values can hardly be unequivocally compared to those already listed in Table 3. Nevertheless, as can be seen, the ranges of the two groups of reaction rate constants do not differ radically and partially overlap each other. Chiefly for the purpose of facilitating possible interpolation or cautious extrapolation, the following simple regression relationship is proposed for the reaction rate constant k

Upon introduction of the new dependent variable, Y, defined as the ratio of the unremoved fraction to the removed fraction of the gas component Y=

e m(1 − τrel) −1=0 Y

(43)

and/or k = 8.024 × 10−4Re + 5.018 × 10−4 (41)

(44)

for U ∈ ⟨9.4, 25.6 cm/s⟩. As shown in Figure 11, the line representing eq 43 fits the data fairly well, with a regression parameter of R2 = 0.996. Calculations indicate that the experimentally determined values of k differ from the predictions of eq 43 by a few percent. The favorable influence of the increasing gas velocity, U, on the effective

This equation proved to be quite useful for making initial guesses of m in iterative solutions of the pertinent nonlinear algebraic equations by interval-halving in this work. If there is any wish or need to avoid the logarithms occurring in eq 38, the alternative form 19153



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basic system and operating variables on the removal of hydrogen chloride from gas. Reported experimental measurements of the sorption performances of various types of sodium carbonates are quite few. For example, Gupta et al.25 found that nahcolite (natural NaHCO3) is a superior sorbent in comparison with other Nabased carbonate minerals. However, the sorption tests of Nunokawa et al.26 revealed that Na-based sorbents containing also sodium aluminate (NaAlO2) are more reactive than those composed only of sodium carbonate. X-ray diffraction analyses identified the presence of NaAlO2 in the explored γ-alumina particles that were impregnated with NaHCO3. This is probably the reason for the somewhat lower values of k inferred from the experiments of Gupta et al.25 with nahcolite free from sodium aluminate, the results of which are also included in Figure 11. In addition to the effluent concentration of the gaseous reactant at the reactor outlet, the conversion of sorbent particles within the bed is also a matter of considerable importance. The conversion profiles along the bed depth change with elapsed time and can be predicted by the appropriate use of eq 30 or 31. However, the overall conversion of the whole bed is of interest as well and is always needed for practical purposes. The overall conversion of the bed is defined as the ratio of the reacted amount of sorbent in the whole bed to the amount of fresh sorbent originally present in the whole bed before the start of sorption. Defined in this way, the overall conversion of bed, Xoa, can be determined from the mass balance over the whole bed as follows

Figure 10. Kinetics plot of data from the breakthrough curves determined for different superficial gas velocities , U, at 500 °C (gas density, ρg = 1.576 × 10−5 mol/cm3; solid density, ρs = 1.009 × 10−3 gatom of Na/cm3; average particle size, d̅p = 1.496 mm; bed depth, z = 6.462 cm; bed voidage, e = 0.5276). Line 1: U = 9.390 cm/s, Re = 1.867, τg̅ =0.3631 s, yin = 240.1 ppm, τstech = 24.09 h, m = −4.151, k = 1.968 × 10−3 (kPa·s)−1, R2 = 0.9926. Line 2: U = 17.07 cm/s, Re = 3.394, τg̅ = 0.1997 s, yin = 240.8 ppm, τstech = 13.21 h, m= −3.824, k = 3.296 × 10−3 (kPa·s)−1, R2 = 0.9885. Line 3: U = 25.61 cm/s, Re = 5.092, τg̅ =0.1331 s, yin = 240.3 ppm, τstech = 8.823 h, m = −3.518, k = 4.548 × 10−3 (kPa·s)−1, R2 = 0.9864.

Xoa =

∫0

⎛ y ⎞ ⎜⎜1 − out ⎟⎟ dτrel yin ⎠ ⎝

τrel

(45)

Upon substitution from eq 29 and subsequent integration, we obtain Xoa = τrel +

1 ln[1 + em(1 − τrel) − em] m

(46)

for m ≠ 0 and (em − em(1−τrel)) < 1 and Xoa = 1 +

1 ln(2 − e m) m

(47)

for τrel = 1. It can easily be shown that the estimates of eq 46 converge to those of eq 47 when τrel is nearing unity from either side. As is evident in Figure 8, the value of Xoa is represented geometrically by the area between the (yout/yin) versus τrel curve and the parallel to the τrel axis with an ordinate of unity. A single experimental result for the overall bed conversion was measured and is given in Figure 12 along with the values predicted by eq 46. As can be seen, this experimental data point is in good agreement with the predicted value. It should also be noted that integral eqs 45 and 46 make it possible to describe the overall separation performance of the bed as the dimensionless time derivative of the conversion of the whole bed

Figure 11. Effective reaction rate constants, k, deduced from the experimental data plotted in Figure 10 for different superficial velocities, U: (○) values determined from the results collected in this work with γalumina impregnated with NaHCO3; (Δ,□) values inferred from the breakthrough curves measured by Gupta et al.25 with nahcolite (natural NaHCO3) under similar conditions. The solid line shows the values predicted by eq 43; R2 = 0.9898.

∂Xoa 1 = m (1 − τ rel) ∂τrel 1+e /(1 − em)

reaction rate constant, k, indicates a minor but noticeable role of mass transfer in the overall process of the fixed-bed separation. It should be borne in mind, however, that the mathematical description of sorption employed here is based on a number of simplifying assumptions. Such an approach leads to easily tractable eqs 29−31, which clearly predict the influence of the

(48)

for m ≠ 0. A decrease in the dimensionless overall rate of reaction during the course of operation as predicted by eq 48 is visualized in 19154



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Figure 14. Dimensional overall rate of sorption in the whole bed, ∂Xoa/ ∂τ, defined by eqs 48 and 49, as a function of the overall fractional conversion of bed, Xoa. The solid line shows the predictions of eq 49 for the conditions given in the captions of Figures 10 and 12. (○) Prediction of kinetic eq 19 for k = 3.91 × 10−3 (kPa·s)−1, p = 101.325 kPa, yH̅ Cl = (yinyout)0.5 = 4.90 × 10−5, t = 500 °C, and X = 0.2343. (□) Prediction of the kinetic equation describing the rate of sulfation of calcium oxide in flue gas20,49 at t = 850 °C, d̅p = 0.565 mm, ySO2 = 4.9 × 10−5, and X = 0.2343.

Figure 12. Overall fractional conversion of the bed, Xoa, defined by eq 45, as a function of elapsed relative time of sorption, τrel. The solid line shows the predictions of eq 46 for τstech = 24.09 h and m = −4.151. The operating conditions are presented in the caption of Figure 10. The experimental data point (○) was obtained from chemical analysis of the loaded bed when the sorption run was terminated at τrel = 0.956.

Figure 13. As is apparent, the normalized rate of sorption can easily be converted into its dimensional form ∂Xoa 1 ∂Xoa = ∂τ τstech ∂τrel

for τstech ≠ 0

of eqs 48 and 49. The second reference point presented in Figure 14 (□), represents the rate of sulfation of calcium oxide at 850 °C in an oxidizing environment under the corresponding conditions.20,49 Also with regard to different temperatures, the sorption of SO2 on CaO in flue gas at 850 °C appears to be slower than that of HCl gas on Na2CO3 in fuel gas at 500 °C. Practical beds are usually operated at higher gas flow rates, work with particles of larger size, and have temperature profiles that are not often uniform. Nevertheless, the presented results outline the specific conditions for the efficient removal of hydrogen chloride from very dilute producer gas by utilizing a gas−solid reaction in a fixed-bed reactor. The presented findings also indicate that the reaction kinetics and the operating conditions are factors of major importance in any situation.

(49)

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CONCLUSIONS The stringent limiting level of HCl usually allowed for cleaned producer gas from biomass, as low as 1 ppmv, is still met at 610 °C. Also, it appears that the presence of hydrogen sulfide in gas does not alter the affinity of HCl toward Na2CO3. An extensive pore structure develops during the calcination of sodium hydrogen carbonate, which is a common precursor of Na2CO3-based sorbents. During chloridization, the monoclinic or hexagonal Na2CO3 is converted into cubic NaCl. This transformation reaction is accompanied by expansion of the volume of the solid phase. Nevertheless, the expansion factor, which amounts to 1.287, allows all of the reaction product to be accommodated in the pore volume developed by calcination. The porosity of a completely reacted particle should remain as large as 29% after having started decreasing from an initial value of 45%. The mass-transfer coefficient between moving gas and single particles should increase with increasing diffusivity (∼ D2/3) and linear gas velocity (∼ U0.3−U0.6) and decrease with increasing particle diameter (∼ dp−0.4−dp−0.7). The reaction of hydrogen chloride gas with sodium carbonate originated from sodium hydrogen carbonate takes place quite

Figure 13. Dimensionless overall rate of sorption in the whole bed, ∂Xoa/∂τrel, introduced by eq 48, as a function of elapsed relative time of sorption, τrel. The solid line shows the predictions of eq 48 for the conditions presented in the captions of Figures 10 and 12.

Figure 14 illustrates how the actual overall rate of sorption decreases with the progress of the fractional overall conversion of the sorbent bed. An attempt was made to compare, at least very approximately, the predictions of eqs 48 and 49 with the estimates of kinetic equations inferred from the data measured under differential conditions of reaction. For k = 3.910 × 10−3 (kPa·s)−1 from Table 3, X = Xoa = 0.2343, and yH̅ Cl = (yinyout)0.5 = 4.90 × 10−5 from an integral bed situation, eq 19 predicts for (∂X/∂τ) a value of 1.48 × 10−5 (s−1), also included in Figure 14. As can be seen, this estimate does not lie far from the predictions 19155



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rapidly at elevated temperature. As the chloridization of NaHCO3 calcines proceeds, both the pore volume of the particles and the rate of reaction decrease. Nonetheless, high conversions to sodium chloride can be achieved under practical conditions. The fixed-bed results obtained with a differential fixed-bed reactor at 500 °C showed that the course of chloridization can be approximated up to high conversions by first-order kinetics in the conversion of solids and in the partial pressure of the gas reactant. The data also showed that the reaction rate slightly increased when the particle size was reduced. The presented description of reaction kinetics reflects the rate-decaying behavior of chloridization either with the conversion of solids or with the elapsed time of reaction. Experimental measurements under ambient pressure with a gas containing 0.03 vol % HCl provided initial rates of chloridization, (∂X/∂τ)in, for NaHCO3 calcines in the range between 7.0 × 10−5 and 1.8 × 10−4 s−1. The corresponding effective reaction rate constants varied from 2.3 × 10−3 to 6.0 × 10−3 (kPa·s)−1. On the basis of a few plausible assumptions, the unsteady-state sorption of hydrogen chloride gas in an integral fixed bed of particulate Na2CO3-based sorbent was described by a pair of simultaneous partial differential equations. Their analytical solution is presented in a tractable explicit form for first-order kinetics of the reaction initially explored under differential reaction conditions. The general solution describes the bed performance in terms of three dimensionless quantities: the relative concentration of reactants, the dimensionless reaction/ distance parameter including the effective reaction rate constant, and the elapsed relative time of reaction/sorption. The sigmoidal breakthrough curves can easily be linearized. The final integral equations can conveniently be employed to either evaluate the kinetics of reaction from experimental breakthrough curves or rationally design larger separation units. The experimental runs at 500 °C on an integral fixed-bed reactor with 1.5-mm alumina particles impregnated with NaHCO3 provided effective reaction rate constants in the range from 2.0 × 10−3 (kPa·s)−1 at U = 9.4 cm/s to 4.5 × 10−3 (kPa·s)−1 at U = 25.6 cm/s. Not only the local reaction rates but also the overall rate of sorption in a given packed-bed reactor can readily be estimated by means of the proposed model as a physicochemical quantity of major importance. Because high conversions of sorbent can be achieved and the spent sorbent is a usable commodity, deep HCl removal from producer gas with the aid of Na2CO3-based sorbents seems to be a promising process.

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NOMENCLATURE

Symbols

aAB = coefficient in eq 15, cm2/(K1.75·s) dp = particle diameter, cm d̅p = average particle diameter, cm D = molecular diffusivity in gas, cm2/s DAB = molecular diffusivity in binary gas mixtures, cm2/s e = fractional porosity/void fraction ec = fractional porosity of a calcined particle ein = initial fractional porosity of a particle ex = fractional porosity of a chloride-loaded particle, given by eq 16 f = relative increase or decrease in the solid volume caused by chemical reaction hd = mass-transfer coefficient, cm/s k = effective reaction rate constant, (kPa·s)−1 K = equilibrium constant of chemical reaction m = dimensionless reaction/distance parameter, given by eqs 33 and 34 Mi = molar (formula) mass of component i, g/mol p = total pressure in the main stream, kPa pi = partial pressure of component i, kPa R2 = regression parameter t = Celsius temperature, °C T = thermodynamic temperature, K U = superficial gas velocity, cm/s Vi = molar volume of component i, cm3/mol X = fractional conversion of solid reactant Xoa = overall fractional conversion of solids in the whole bed, given by eqs 45 and 46 Y = relative gas concentration, given by eq 37 yHCl = HCl concentration in the gas phase, mole fraction yi = mass fraction of solid reactant i yin = inlet gas concentration, mole fraction yout = outlet gas concentration, mole fraction z = distance through the bed from the inlet, cm Dimensionless Groups

jd = Chilton−Colburn factor for mass transfer = Sh/(ReSc1/3) = hdSc2/3/U Re = Reynolds number = Udpρf/μf Sc = Schmidt number = μf/(ρfD) Sh = Sherwood number = (hddp)/D

AUTHOR INFORMATION

Greek Letters

Corresponding Author

*Tel. +420 220 390 254. Fax: +420 220 661. E-mail: hartman@ icpf.cas.cz.

ΔH° = standard heat of reaction 1, kJ/(mol of Na2CO3) Δn = change in the number of moles due to chemical reaction, mol/(mol of Na2CO3) μf = fluid (gas) viscosity, g/(cm·s) ρf = fluid (gas) density at ambient pressure (101.325 kPa), g/ cm3 ρg = molar gas density at ambient pressure = 0.012187/T, mol/cm3 ρs = molar solid density, mol/cm3 τ = exposure time, s τg̅ = mean residence time of gas in the bed, given by eq 36, s τrel = relative time of sorption = τ/τstech τstech = time needed to introduce into the bed the amount of gas reactant stoichiometrically just equivalent to the amount of solid reactant present in the bed, given by eq 35, s

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors appreciate the financial support of the Grant Agency of the Czech Republic (GAČ R) and the National Science Council of Taiwan (NSC) for bilateral Grant Projects No. 1409692J (GAČ R) and No. 102WBS0300011 (NSC). The research was also supported by the specific university fund of MŠMT Č R (No. 20/2014). We express our sincere gratitude to Mrs. Eva Fišerová for her patient assistance with the manuscript and also thank Mr. Vı ́t Šuster for experimental aid. 19156



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Reaction of Hydrogen Chloride Gas with Sodium Carbonate and Its

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