# Modeling of Infra-Particle C-CO2 Reaction An Application of the Random Pore Model.

код для вставкиСкачатьDev.Chem. Eng. Mineral Process., 7(5/6), pp.525-536, 1999. Modeling of Intra-Particle C-CO, Reaction: An Application of the Random Pore Model G.S. Liu, A.G. Tate, H.R. Rezaei, A.C. Beath and T.F. Wall Cooperative Research Centrefor Black Coal Utilization, Department of Chemical Engineering, The University of Newcastle, Callaghan, New South Wales 2308, Australia The Random Pore Model developed by Bhatia et al. was applied to intra-particle gasijication reactivity of carbon with carbon dioxide in present contribution. Instead of the conventional n-th order equation, the Langmuir-Hinshelwood equation, which treats reaction to be an adrorption and desorption two-step reaction, was employed as an expressionfor the carbon and carbon dioxide surface reaction in the model. A balance between gas dirffusion and consumptionfor each position in the particle was established as derived in the Thiele analysis. Numerical calculations were carried out to solve the integrated equations. The results show that a big difference of reaction rate is exhibited between using the n-th order rate expression and the LangmuirHinshelwood (L-H) equation. The results also show the distributions of C02 partial pressure, surface area, reaction rate and carbon conversion within the particle during the gasification. The overall conversions at diferent structure parameters, which are correspondent to initialporosity of 0.05, 0.2 and 0.4, are also presented in the paper. A small deviation of the effectivenessfactors obtained between using the Langmuir-Hinshelwood and the n-th order equation is indicated with the carbon burn-off between 045%. Introduction The Random Pore Model has been developed by Bhatia and Perlmutter [ 1-31 in order to account for the relationship between the surface area S and the carbon burn-off X 525 G.S.Liu et al. during the char gasification. It is assumed that the char gasification reaction with carbon dioxide is reaction-rate controlled. The critical point of the random pore model is the consideration of a transformation of pore cylinders fkom non-overlapped type to overlapped one during the reaction. The relationship between the surface area S and the carbon conversion X is shown below [ 11: A Langmuir-Hinshelwood rate expression has been applied to the gasfication reaction over the last several decades [4-51. The reaction is mechanistically considered as an adsorption-desorption two-step reaction, and the product gas, CO, has inhibiting effect on the reaction, which is not shown in the n-th order equation, . . 1.e. 1.e. R, = kc .p"co: . Therefore, the intrinsic reaction rate O<g/cmZ.s)is dependent on both partial pressures of the reactant gas CO, and the product gas COYwhich is expressed as follows: In the consideration of the relationship between the partial pressure and the reaction rate, the Langmuir-Hinshelwood expression doesn't use the uncertain pressure order n, as indicated in the n-th order equation. Recent studies[4,5] show that the Langmuir-Hinshelwood expression allows a good understanding of the char gasification, especially for high pressure conditions. In the present contribution, the random pore model was applied to the C-CO, intra-particle gasification, along with the Langmuir-Hinshelwood expression. The comparison of the distributions of CO, and CO concentration within the particle is presented. The reaction rate and the surface area with bum-off are also calculated. The objective of this work is to apply the random pore model, incorparated with the Langmuir-Hinshelwoodreaction kinetic, to the char gasification with CO, and steam. 526 Modeling of intra-particle C-carbon dioxide reaction Model Considering the isothermal chemical reaction of the char particle with carbon dioxide, the reaction occurs on the surface of the pores contained in the particle. The purpose of the model is to establish a mass balance of the reactant gas between diffusion and consumption due to reaction. After the integration of equation (1) and (2), the reaction rate, defined as carbon conversion rate &dt (11s)) is composed of the intrinsic reaction rate ki and the surface area S where the carbon conversion X,C 0 2partial pressure pcq and the surface area S are a function of position x and residence time t. Following the correlation of partial pressure of CO and C 0 2 within the particle presented by Roberts ef al. [6], let w = 1+ k,(Pco,s + P c o ~ , s ~ c /oDco) , , and further let K , = k, I w and K, = (k, - k3flC02/ D,) I w , the reaction rate ki is then transformed into which is solely dependent on C 0 2 partial pressure. To establish a mass balance equation, a modified Thiele modulus is defined as where S, Vpare the surface area (cm2/g)and the particle volume (cm’/g) respectively. The effective diffusion coefficient Dco~,which is determined by porous matrix rather 527 G.S.Liu et al. than gas properties, is dependent on the bulk diffusivity and the Knudsen diffusivity as well as the pore structure. An alternative for DCo2calculation is given elsewhere [7]. The COz gas balance equilibrium at each position within the particle is then formulated as Boundary conditions for the above differential equation are described as: dPco, I a!x = dPco ldr = 0 at x = 0 (at centre) and Pco, = Pco2s , Pco = Pco,s at x = R, (on exposed surface). Then the analytical solution of the equation (6) is obtained K,(Pco, - Pco, ,o ) - In (7) This gives out the reactant gas C02gradient distribution within the char particle. Initial condition for equation (7) is: X=O at t=O. Once the local burn off is obtained from equation (3), the surface area can be calculated using equation (1). Results and discussion Numerical simulation has been performed to solve the equation (7) to determine the COz partial pressure distribution. Runga-Kutta method was used to solve equation (3) to obtain the local conversion at each residence time. The reaction rate coefficients are cited from Blackwood et al. [4], which are: kl=5.52x1O9exp(-3l7680/RT) g/g.atm.s, k2=0.3 l/atm, and k3=14 llatm. Considering pulverized coal char gasification system, following parameters are used in the calculations: D c o ~ D c ~ 0 . 1 c m 2 / Dp-0.Olcm; s; Tp-1500K;So=100m2/g; @=0.5; pp=l .45g/cm3; Ps,c02‘0.8 atm; and P s , c ~ 0 . 2atm. 528 Modeling of intra-particle C-carbon dioxide reaction In the following sections the calculation results are presented for the understanding of the reaction behavior within the particle. 0.90 0.16 -*, 0.80 $ 0.70 g- 0.60 0.14 -P -C02: n-th - - - - C02: L-H g 0.50 u) =. 0.10 2 ;0.08 co: L-H I 0.40 e 0.12 = 0 ; .- 2 0.30 0.10 0.00 0.02 0.00 0.0 0.2 0.4 0.6 0.8 Radial pcsition. x/Ro 1.0 n-lh ---- Rate: L-H 0.04 - 0.20 d -Rate: 0.06 K L 0.0 02 0.4 0.6 08 1.0 Radial position. XlRO (4 (b) Figure 1. Predicted distributions of (a) CO2 and CO relative partial pressure and (b) the calculated reaction rates within the particle using L-Hand n-th order equation, respectively (Tp=1700K) 1.0 r 7 1 0.014 0.8 0.012 X .$ .__----- 1 c&.OS. 0.6 -Rate: --8 t n-a ---- RaWL-H 0.002 I 8 ~49.5 2 Q4.2yb4.5 9 3 c@.4,*=20 0.4 0.2 I 0.0 y 0.0 02 0.6 Radial posilion. nR0 0.4 0.8 1.0 0.0 20 4.0 6.0 8.0 10.0 Tim. s Figure 2. Distributions of calculated Figure 3. Overall conversion vs. reaction rates using L-Hand n-th order residence time with different particle equation, respectively (T,=lSOOK) structure parameters (Tp=I700K) 529 G.S.Liu et al. Comparison of the two zype reaction rate equations Using the L-H equation, the distributions of C02 and CO relative partial pressure (ratio of the partial pressure to the total pressure on the surface) within the particle were obtained by numerical calculation of equation (7). It is shown in figure l(a) that the COz partial pressure decreases when the position moves inward from the particle surface to the particle centre, while the partial pressure of the product gas, CO, partial pressure increases significantly. The reaction rate exhibits a large variation from the surface to the centre as seen in figure I@), due to the assumption that the reaction rate is dependent on both the partial pressure of CO2 and CO. For comparison, the CO2 distribution and reaction rate were also calculated using n-th order equation in the way similar to the calculation discussed above, which can also be obtained elsewhere [7]. The intrinsic reaction rate using n-th order rate equation is expressed as: R,= 5.2exp(-243300 ~r)pO.’ (g/cm2.s). Using this equation, the calculated reaction CfJI rate on the particle surface is close to that calculated using L-H equation. As seen in figure l(a), the C02 partial pressure is similar to the case of using LangmuirHinshelwood equation, while as shown in figure l(b) the reaction rate profile is flatter due to the rate dependence on C02 partial pressure only. Reaction rate distributions were also obtained using L-H and n-th order equations at the particle temperature of 15OOK. No such deviation as indicated in figure l(b) was observed since the reaction is chemical reaction controlled using either L-H or nth order equation. The reaction rate calculated using n-th order equation however is higher than that using L-H expression. Overall conversion Overall conversion is the total carbon conversion of the particle which is calculated from the following equation 530 Modeling of intra-particle C-carbondioxide reaction Overall conversion Xchanging with residence time t is shown in figure 3. From initial to about 3-5 seconds, the overall conversion increases monotonically with the increase in the residence time, and then the profile becomes flat with further increase due to the decrease of the reaction surface area, which will be discussed below. The overall conversions at different particle structure parameters, N,are also indicated in figure 3. Assuming the uniform pore size distribution, the particle structure parameter yois a function of the initial porosity 6 only, shown as follows [3]: 1 yo =-ln(l-Eg) (9) As shown in figure 3, the particle with large initial porosity has low carbon conversion rate. This phenomenon can be explained that with the same initial internal surface area, the particle with small porosity contains relatively small pores. During the reaction, the small pores produce more internal surface area than large pores at the same gasified carbon, which lead to high reaction rate. Local CO,partial pressure In the calculation, it is assumed that the diffusion of C02 from the particle surface to the centre is rapid, in other words, C02 reaction and diffusion are assumed in the quasi-steady state at any time. As shown in figure 4(a), the C02 partial pressure distribution is similar to that indicated in figure l(a). As the residence time increases, the distribution becomes uniform within the particle. Local su$ace area Figure 4(b) shows that the local surface area (i.e. the surface area at different position) changes with the position within the particle at different residence time. The deviation of the surface area between the particle surface and the centre is observed, and become significant with the residence time increases. As can be seen in the figure, at each position the surface area decreases with an increase in residence time 53I G.S. Liu et al. due to the collapse of the pore wall. These results are similar to that presented by Bhatia et a1.[2]in the case of small particle structure parameter fi. 0.81 1 l2 0.80 $ 0.79 5uo 0.78 -----_ ----_ 3 0.8 :---- 0.77 m 0.76 3 0.75 -l=o.os ---- e 3 . 0 ~ 0.74 - ........ e 6 . 0 ~ -..-.. m.os I 0.73 I 0.72 0.0 0.2 0.4 0.6 Radial position xR0 0.8 0.16 fm -- - 0.4 * 0.0 L 0.0 1.0 -_-_ - 02 1.0 I --. .................. -.__ ..-.._ ..-..-.. -.. --.---- .- - -.-.___ *-. .-. 0.6 n P I 02 0.4 0.6 0.8 Radial position ~830 , 1.0 I 0.14 -: 0.12 0.10 p! s 0.08 0 C 2 0.06 a, = 0.04 0.02 0.00 1I f I 0.0 02 0.4 0.6 Radial position xR0 0.8 1.0 ::I,, 0.0 0.0 02 0.4 , 0.6 , I 0.8 1.0 Radial position xR0 Figure 4. Disnibutions of (a) C02 relative partial pressure, (b) surjace area, (c) reaction rate, and (d) carbon conversion within the particle at direrent residence time. Line notation as in Figure (a) (Tp=1700K) Local reaction rate It is very interesting when one looks at the distribution of the local reaction rate the reaction rates at the shown in figure 4(c). At the residence time of 0.0 and 3.0~~ particle surface are higher than those at the particle centre, while they are lower at the 532 Modeling of intra-particleC-carbon dioxide reaction times of 6.0 and 9.0s. This phenomenon can be explained by the distributions of the surface area and the COZpartial pressure. At times of 0.0 and 3.0s, the distribution of C 0 2 partial pressure dominates the reaction rates, while at the times of 6.0 and 9.0s, the distribution of surface area plays an important role in the calculation of reaction rates. Also it is seen that the reaction rate decreases with the time increases at any position in the particle. Local carbon conversion The carbon conversion at the particle surface is higher than that at the particle centre at each residence time. At the time of 9.0s, the deviation of the carbon conversion between the particle surface and the particle centre is about lo%, while at the time of 3.0s, the difference is 18%. Using n-th order equation, a similar result has been reported by Bhatia er al. [2]. Effetivenessfactor Effectiveness factor, which is defined as the ratio of the internal surface area involved in the reaction to the total surface area, is usually employed in the determination of the overall reaction rate of the char particle. Once the solution of the equation (7) is obtained, the effectiveness factor can be calculated using the following equation: Where & is the modified Thiele modulus. For comparison, the effectiveness factors based on the n-th order equation at the same conditions are also obtained from the well-known Thiele analysis [7]: 533 G.S.Liu et al. Table 1 shows the effectiveness factors calculated using both expressions at different bum-off and the same particle temperature of 1700K. For LangmuirHinshelwood kinetic, the reaction is controlled by combination of reaction and diffusion control when the carbon bum-offis less than 75%, which corresponds to the effectiveness factors from 78.4% to 94.2%. It will be transferred to reacton control with the further increase in the bum-off. At the same conditions, for n-th order equation, the effectiveness factors are nearly 1 .O over the whole range of the bum-off, which means the reaction is almost chemical reaction control. Table I. Comparison of calculated effectiveness factors at direrent burn-of using Langmuir-Hinshelwood and n-th order equation, respectively Bum-off(%) VusingL-H qusing n-th I0 I .784 I .989 15 30 40 55 65 75 85 .796 .814 .838 .867 .902 .942 .985 .99 .991 .992 .994 .995 .996 .997 Conclusions 1. A large deviation of reaction rate is shown between using the n-th order equation and the Langmuir-Hinshelwood expression. A large variation of reaction rate between the particle surface and the particle centre is also indicated when the Langmuir-Hinshelwood expression is applied, while the profile of reaction rate within the particle obtained using the n-th order equation is much flatter. At the particle temperature of 1500K, reaction rate profiles obtained using both two methods are uniform, however, the deviation between two approaches still exists. 2. The overall carbon conversion increases monotonically as an increase in the residence time. This trend becomes insignificant with further increase in residence time. The conversion rate with high particle structure parameter is higher than that with low particle structure parameter. 534 Modeling of intra-particle C-carbon dioxide reaction 3. The C02 partial pressure distribution in the particle becomes uniform with an increase in residence time. The surface area decreases with the time increases, however, the surface area at the particle surface is lower than that at the particle centre at any time. The Reaction rate also decreases with the time increases, at the time of 0.0 and 3.0s, the reaction rate at particle surface is higher than that at the particle centre, while it is lower at the time of 6.0 and 9.0s. These different trends are attributed to the distributions of C02 particle pressure and surface area respectively. The carbon conversion distribution becomes uniform in the particle as the time increases. 4. A small deviation of the effectiveness factors obtained between using Langmuir- Hinshelwood and n-th order equation is shown when the carbon burn-off is between 0-85%. For the Langmuir-Hinshelwood expression, the reaction is controlled by combination of reaction and &&ion when the bum-off is less than 75%, and then will be transferred into reaction control with the further increase in bum-off. At the same conditions, for n-th order equation, the effectiveness factor is nearly 1.O over the whole range of the burn-off. Acknowledgements The authors wish to acknowledge the financial support provided by the Cooperative Research Centre for Black Coal Utilization, which is funded in part by the Cooperative Research Centres Program of the Commonwealth Government of Australia. Nomenclature Dco D,-a kl k2 k3 Kl K2 kc MC pco CO diffusion coefficient C02diffision coefficient Reaction rate constant Reaction rate constant Reaction rate constant Transformed reaction rate constant Transformed reaction rate constant Reaction rate constant Carbon molecule weight CO partial pressure 535 G.S. Liu et al. Pcm p*.* R C02 partial pressure Total pressure at particle surface Gas constant RO Particle radius Ri Intrinsic reaction rate S Surface area SO Initial surface area t Reaction time T Particle temperature VP Particle volume X Distance from particle centre X Carbon conversion Greek symbols h Modified Thiele Modulus Thiele Modulus 4 Initial porosity Y O Particle structure parameter w Transformation parameter Y Stoichiometriccoefficient Q Effectiveness factor Subscript 0 Initial or particle centre Local position within the particle Local OveraZZ Overall reaction S Particle surface t Total es References 1. 2. 3. 4. 5. 6. 7. Bhatia, S. K., and Perlmutter, D. D., 1980, A random pore model for fluid-solid reactions: I. Isothermal, kinetic control, AIChE J., 26,379 Bhatia, S. K., and Perlmutter, D. D., 1981, A random pore model for fluid-solid reactions: 11. Diffusion and ininsport effects, AIChE J.,27,247 Bhatia, S. K, and Perlmutter, D. D., 1981, The effect of pore structure on fluid-solid reactions: application to the SO*-lime reaction, AIChEJ., 27,226 Blackwood, J. D., and Ingerne, A. J., 1960, Reaction of carbon with carbon dioxide at high pressure, Aust. J. Chem., 13, 194 Bliek, A., 1984, Mathematical modeling of a concurrent fixed bed coal gasifier, PhD thesis, Eindhoven, The Netherlands Roberts, G. W., and Sattertield, C. N., 1965, Effectiveness factor for porous catalysts. LangmuirHinshelwood kinetic expressions, Ind. Eng. Chem. Fundamentals, 4,288 Satterfield, C. N., 1970, Mass transfer in heterogeneous catalysis, MIT Press 536

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