Noncatalytic Gas-solid Reactions Research Articles

Deactivation model for textural effects of kinetics of gas-solid noncatalytic reactions “char gasification with CO 2”

Variation of the reactivity of a solid reactant due to changes in number of working active sites and pore structure was represented by a deactivation model. The model was shown to give good aggreement with the experimental data obtained for the gasification of chars of different lignites. All the kinetic data obtained at different temperatures (800°–950°C) and also for different types of coals were represented with a single generalized relation. The increase of the surface area of the char at the initial stages of gasification did not cause a corresponding increase in the reaction rate. Results indicated that the surface was composed of highly reactive and less reactive sites. It was shown that the reactivity of unit surface area of the solid reactant first showed a rapid decrease due to decrease of number of more reactive sites as the initial stages and then reached to about one fourth of its initial value.

Single pellet reactor for the dynamic analysis of gas-solid reactions “reaction of SO 2 with activated soda”

Single-pellet moment technique which was initially proposed for the measurement of effective diffusivities in porous catalysts and adsorption rate and equilibrium constants was modified for the analysis of gas-solid reactions. In this technique dynamic version of the Wicke-Kallenbach single-pellet cell was used. A pulse of a tracer gas was introduced into stream flowing over one end face of the pellet. In the modified pulse-double response procedure, experimental moments of the response peaks of both reactant and product gases measured in both top and bottom outlet streams of the single-pellet reactor were used for the evaluation of intrapellet rate and equilibrium parameters. Application of the technique to the reaction of SO 2 with activated soda indicated that the value of Thiele modulus decreased from 6.74 to 0.33 by the increase of fractional conversion of Na 2CO 3 to Na 2SO 3 from zero to 0.63. In this range of conversion values a significant variation in pore structure and also a decrease of effective diffusivity of SO 2 from 0.045 cm 2/s to 0.025 cm 2/s was observed. A cell model which considered the changes in pore length and radius with reaction extent and variations in product layer diffusion resistance was shown to be successfully used in the analysis of experimental observations. A review of single-pellet dynamic reactor studies for catalytic and noncatalytic gas-solid reactions was also given.

CHARACTERISTICS OF THE REVERSIBLE REACTION BETWEEN CO2(g) AND CALCINED DOLOMITE

Abstract The noncatalytic gas-solid reaction between calcined dolomite and CO2(g) has been studied in an electrobalance reactor as a function of temperature, pressure, and reactive gas composition. Multicycle tests consisting of as many as ten complete calcination-carbonation cycles were carried out to obtain information on sorbent durability. Surface area, pore volume, and pore size distribution measurements were made to supplement the reaction studies. This reaction is of interest both as a model for studying (he importance of structural property changes in gas-solid reactions, and as the basis for a possible process for the high temperature separation of CO2 from gas streams. Calcined dolomite is a superior sorbent to calcined CaCO3 in that larger fractional conversions of CaO and improved multicycle durability are possible. With CaO obtained from CaCO3, the first-cycle fractional recarbonation was limited to about 0.80, a value which decreased by 15 to 20% in each subsequent cycle. In contrast, the first-cycle fractional recarbonation of CaO in calcined dolomite was typically 0.90 to 0.95, and this value decreased by only 1 to 2% in each subsequent cycle. These advantages are atlributed to the “excess” pore volume created by the original decomposition of MgCO3 in dolomite, and by a reduction in the rate of CaCO3 sintering in the presence of MgO.

Solution of transient problems with steep gradients: Novel front-tracking strategy

A finite element collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. An efficient, parametrically convergent front-tracking procedure is developed based on a balance on a moving front, and the technique is applied and tested for the case of a gas-solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained here for Thiele modulus larger than 50 for the case of slab as well as spherical geometry and found to match the analytical solution when it exists (such as for slab geometry).

Simultaneous shift reaction and carbon dioxide separation for the direct production of hydrogen

Hydrogen production via the reversible water-gas shift reaction normally requires multiple catalytic reaction steps followed by CO 2 separation in order to produce the required H 2 purity. Removal of CO 2 as it is formed via the noncatalytic gas—solid reaction between CO 2 and CaO provides the opportunity to combine reaction and separation into a single processing vessel. Resultant process simplifications include elimination of the need for heat exchangers between catalyst beds as well as the absorption and stripping units required for CO 2 removal (or the pressure swing adsorption unit). Process savings may be realized by reducing the quantity of excess steam to the reactor, and the expensive, sulfur-sensitive shift catalyst is not needed in the 500–600°C range of interest. The combined shift and carbonation reactions were studied in a laboratory-scale fixed-bed reactor containing dolomite sorbent precursor. The effect of shift-carbonation temperature and pressure, synthesis gas composition, space velocity, and composition and properties of the sorbent were studied. The rapid rates of the combined reactions permit equilibrium CO conversion and CO 2 removal to be closely approached. Greater than 0.995 fractional removal of carbon oxides was achieved over a range of reaction conditions.

Modelling gasification reactions including the percolation phenomenon

The analysis of percolative fragmentation for noncatalytic gas—solid reactions, with special emphasis on gasification and combustion of carbonaceous materials, is presented. The description of pore surface area and pore surface enlargement during reaction is based on the random pore model developed by Bhatia and Perlmutter (1980), A.I.Ch.E. J. 26, 379–386; 1981, A.I.Ch.E. J. 27, 247–254). Different reaction regimes between intraparticle diffusion and chemical kinetics control are considered. The inclusion of percolative fragmentation in the Bathia—Perlmutter random pore model allows a more realistic description of changes during gasification of porous solids to be made. The results include the variation of local properties (porosity, surface area and gas concentration) within the particle at different reaction stages as well as the modification of the overall particle properties (particle conversion, percolated mass fraction and reaction rate) with reaction progress.

Shape change of rough particles

In the analysis of solid combustion and other fluid-solid noncatalytic reactions, it is customary to treat reacting particles as spherical to simplify the solution of the relevant reaction-transport equations. The analysis of the spherically symmetric problem is generally assumed to set the correct trends on the effect of various parameters, even when the reacting particles are nonspherical. In this work, the authors analyze reaction and external diffusion for nonspherical, but axially symmetric, particles to determine the change in the shape of a particle due to consumption of the solid material. The shape change can be pronounced over extended conversion even when the initial particle shape is only slightly nonspherical. The most important noncatalytic gas-solid reaction is coal or char combustion. However, under conditions of high Thiele modulus, that is, shrinking core combustion, external heat transfer, as well as mass transfer, needs to be considered. In this note, the authors assume isothermal conditions and consider the external mass-transfer problem only. However, the methodology presented is applicable, with suitable extensions, to simultaneous heat and mass transfer. The latter problem was discussed earlier by Choi and Gavalas (1993) with the focus on coal combustion. Two technique are used to treat the problem ofmore » reacting nonspherical particles. The first is domain perturbation (DP) (Brenner, 1964; Acrivos and Taylor, 1964), the second is the boundary integral technique (BI) (Brebbia and Walker, 1980; Liggett and Liu, 1972).« less

The influence of particle residence time distribution on the reactivity in fluidized bed reactors

The influence of particle residence time distribution on the average conversion rate (or reactivity) of particles undergoing a non-catalytic gas-solid reaction inside a continuously operated fluidized bed reactor is evaluated. A so called β-factor is defined as the ratio of the actual reactivity in the reactor and the reactivity of a batch of particles that react under similar circumstances and that all have a conversion extent equal to the average conversion extent in the reactor. The β-factor concept is elaborated for shrinking core conversion behaviour. According to Heesink et al. (1993), three extreme types of conversion behaviour are distinguished: core reaction limitation, product-layer diffusion limitation and grain reaction limitation. For each type of behaviour a mathematical function is derived that expresses β as function of average particle conversion, maximum attainable conversion (with regard to pore plugging) and a new-defined expansion factor, which is a measure for the expansion (or shrinking) of the reacting solid during conversion. These functions can be easily incorporated in fluidized bed reactor models.

The three-stage model of noncatalytic gas—solid reactions—a supplement

The three-stage model of noncatalytic gas—solid reactions—a supplement

Reactivity, experimental strategy and reaction rate data evaluation in noncatalytic gas-solid systems

Important aspects of noncatalytic gas-solid reactions including mass transfer and pore structure, heat transfer, chemical reaction kinetics and equilibrium, mechanical stresses, phase change and sintering are briefly reviewed. An improved strategy for the determination of reaction kinetics is formulated, akin to the systematic procedure which exists for catalytic systems. The synthesis of titanium nitride is utilized as a case study. The approach includes the use of nonisothermal data in addition to the traditional isothermal data as a crucial step to obtain data with sufficient orthogonality to allow rigorous evaluation of competing rate laws. Two particle morphologies are tested and experiments are conducted over a wide range of conversion, temperature and heating rate. Four kinetic laws are evaluated by nonlinear optimization using the BET surface area as a measure of reactivity. The logarithmic law provides a surprisingly good fit of the experimental data. The apparent observed activation energy is a function of temperature, conversion and particle size even though the intrinsic activation energy remains constant. This offers an explanation for discrepancies that exist between kinetic parameters obtained in previous investigations.

Reactivity, experimental strategy and reaction rate data evaluation in noncatalytic gas-solid systems

Important aspects of noncatalytic gas-solid reactions including mass transfer and pore structure, heat transfer, chemical reaction kinetics and equilibrium, mechanical stresses, phase change and sintering are briefly reviewed. An improved strategy for the determination of reaction kinetics is formulated, akin to the systematic procedure which exists for catalytic systems. The synthesis of titanium nitride is utilized as a case study. The approach includes the use of nonisothermal data in addition to the traditional isothermal data as a crucial step to obtain data with sufficient orthogonality to allow rigorous evaluation of competing rate laws. Two particle morphologies are tested and experiments are conducted over a wide range of conversion, temperature and heating rate. Four kinetic laws are evaluated by nonlinear optimization using the BET surface area as a measure of reactivity. The logarithmic law provides a surprisingly good fit of the experimental data. The apparent observed activation energy is a function of temperature, conversion and particle size even though the intrinsic activation energy remains constant. This offers an explanation for discrepancies that exist between kinetic parameters obtained in previous investigations.

A grain size distribution model for non-catalytic gassolid reactions

A new model to describe the non-catalytic conversion of a solid by a reactant gas is proposed. This so-called grain size distribution (GSD) model presumes the porous particle to be a collection of grains of various sizes. The size distribution of the grains is derived from mercury porosimetry measurements. The measured pore size distribution is converted into a grain size distribution through a so-called pore-tosphere factor whose value is also derived from the porosimetry measurements. The grains are divided into a number of size classes. For each class the conversion rate is calculated either according to the shrinking core model, involving core reaction and product layer diffusion as rate-determining steps or according to a new model in which some reaction at the grain surface is assumed to be limiting. The GSD model accounts for the phenomenon of pore blocking by calculating the maximum attainable conversion degree for each size class. In order to verify the model, two types of precalcined limestone particles with quite different microstructures were sulphided as well as sulphated. Furthermore, a single sample of sulphided dolomite was regenerated with a mixture of carbon dioxide and steam. For each reaction good agreement was attained between measured and simulated conversion vs. time behaviour.

Modelling of non-catalytic reactions in a gas-solid trickle flow reactor: dry, regenerative flue gas desulphurisation using a silica-supported copper oxide sorbent

A one-dimensional, two-phase dispersed plug flow model has been developed to describe the steady-state performance of a relatively new type of reactor, the gas-solid trickle flow reactor (GSTFR). In this reactor, an upward-flowing gas phase is contacted with as downward-flowing dilute solids phase over an inert packing. The model is derived from the separate mass heat balances for both the gas and (porous) solids phases for the case of a non-catalytic gas-solid reaction, which is first-order in the gaseous reactant. The reaction rate may also depend on the solid reactant concentration, but this concentration is assumed to be low and uniform throughout the solids volume. From the model, axial profiles can be calculated numerically for the four independent variables, viz. the gas-phase and solids-phase temperatures and the concentrations of the gaseous and solid reactant. Under isothermal conditions, the model equations can be solved analytically; the resulting expressions for the axial profiles of the gaseous and solid reactant are presented. The model is applied to predict the flue gas desulphurisation performance of a full-scale GSTF absorber in a dry, regenative process for the simultaneous removal of SO x and NO x from flue gases. In this process, to be operated at 350–400°C, the sorbent material consists of a porous silica support (spherical particles, 1.5mm diameter) with 7.5 wt% CuO deposited on this support by an ion-exchange technique. The model calculations are based on experimental findings from previous studies regarding reaction kinetics, hydrodynamics of the two-phase flow, gas-solids mass transfer and testing of the integrated process in a bench-scale plant. It appears that SO 2 removal efficiencies over 95% can be achieved in a GSTF absorber with a length of 15 m. Furthermore, the model predicts a large temperature peak for both phases in the absorber if the heat capacity ratio(defined as the ratio of mass flux times specific heat capacity for both phases) is close to one. This large temperature peak is due to the occurrence of the exothermic reaction of SO 2 with CuO in combination with efficient counter-current gas-solids heat exchange. Several parameters influencing the magnitude and axial position of the maximum gas-phase and solids-phase temperatures are discussed.

Calcium acetate as a sorbent precursor for the removal of carbon dioxide from gas streams at high temperature

The feasibility of a process for the high-temperature, high-pressure separation of CO 2 from coal-derived gas streams based upon the noncatalytic gas-solid reaction CaO(s)+CO 2(g) ⇆ CaCO 3(S) is being investigated. Earlier studies have shown that complete carbonation cannot be achieved and that sorbent performance deteriorates as the number of calcination-carbonation cycles increases, problems which are attributed to the variation of the pore structure of the sorbent in the oxide and carbonate forms. Hydrated calcium acetate has been found to be superior to calcium carbonate as a sorbent precursor. Calcium acetate decomposes in a step-wise fashion beginning with the loss of water of hydration, followed by acetate decomposition to CaCO 3, and finally calcination to CaO. The more open structure of the resultant CaO permits complete carbonation to occur and improves multicycle durability. Further increases in durability, but with a reduced CO 2 capacity, appear possible using dolomite or calcium magnesium acetate precursors. Kinetic results obtained from a high-pressure electrobalance reactor comparing the behavior of sorbent precursors and examining the effect of reaction temperature, pressure, and gas composition as well as structural property data are presented.

Solution of moving boundary problems for gas—solid noncatalytic reactions by orthogonal collocation—revisited

The validity of the method introduced by Duduković and Lamba (1978) for treatment of gas—solid reactions with a moving boundary is confirmed.

ANALYTICAL APPROXIMATE SOLUTIONS OF CERTAIN GAS-SOLID REACTION MODELS IN PELLETS

Abstract A method to obtain analytical approximate solutions of a certain class of non-catalytic gas-solid reaction models in pellets is presented. Analytical estimates of the error are given based on upper and lower bounds of the exact solutions. The method is illustrated by application to different models of gas-solid reactions. Good results are obtained for both linear and non-linear gas kinetics when moderate values of the Thick- Modulus are used.

On the free boundary problem in the wen-langmuir shrinking core model for noncatalytic gas-solid reactions

We prove a local result in time for the existence and uniqueness of the solution of the free boundary problem in the shrinking core model for noncatalytic gas-solid reactions. We impose free boundary conditions of the type $$\begin{gathered} u_x (s(t),t) = g(u(s(t),t)),0< t \leqslant T, \hfill \\ \dot s(t) = f(u(s(t),t)),0< t \leqslant T, \hfill \\ \end{gathered} $$ with general functions g and f which satisfy the assumptions $$\begin{gathered} g 0f' > 0,f(0) = 0. \hfill \\ \end{gathered} $$ The Wen and Langmuir conditions are given by,f(x)=-g(x)=x n (n>0) andf(x) =-g(x)=a x n /(b+cx n ) (a,b,c,n>0), respectively, which both fulfill the above assumptions.

Appliction of integral transformation and orthogonal collocation in gas—solid non-catalytic reaction with varying diffusivity, temperature and bulk gas concentration

An integral transformation and orthogonal collocation are used in the solution of gas—solid non-catalytic reaction with varying diffusivity, temperature and bulk gas concentration. A coordinate transformation is applied in the stage when boundary varies with time. These manipulations reduce the nonlinear initial-boundary problem in time and space to a set of ordinary differential equations in time with given initial conditions. Formulations for different types of gas—solid non-catalytic reactions are given. In addition to the wider range of application, the present method is more refined than that of Duduković and Lamba (1978, Chem. Engng Sci., 33, 303-314) in spite of their similarities in some aspects. Furthermore this method has corrected the mistakes of Dudukovic and Lamba in dealing with stage II of the reaction process. The comparison between the results obtained from the model with varying diffusivity and those from that with constant diffusivity shows that the errors introduced by constant diffusivity simplification can be very large when the internal diffusional resistance is not significally small, and that this tendency increase with the increase of the Thiel modulus.

Statistical modeling of fluid-solid reactions in porous media

We discuss statistical modeling of fluid-solid reaction processes in porous media. We show that ideas from modern statistical physics of disordered media, such as the concepts of percolation theory, aggregation processes, dynamic scaling and universality and random walk representation of diffusion processes are potent tools for studying of such processes in porous media. As examples, we briefly describe how such ideas and concepts can be used fruitfully to model non-catalytic gas-solid reactions processes, and the phenomenon of catalyst deactivation with pore plugging. The application of our method to other problems of interest is also discussed.

Lateral non-uniformities of solids and gas concentrations in fluidized bed reactors

It is the interrelation between mixing of solid particles and gas—solid reactions in fluidized beds which is of particular significance for the design and operation of fluidized bed reactors for non-catalytic gas—solid reactions. A model for the calculation of the distribution of a solid reactant over the cross-sectional area of the fluidized bed under conditions of gas—solid reactions is developed. The general tendencies are illustrated with the examples of coal gasification and coal combustion, respectively. Detailed calculations have been carried out for the combustion of coal in an atmospheric fluidized bed combustor. As reactions, the combustion of char and volatiles and the release and capture of sulfur dioxide are taken into account. The steady state size distribution of the coal particles in the combustor and an effective reaction rate constant based on this size distribution are evaluated. The influence of the mechanisms of attrition and elutriation as well as that of the Sherwood number on this rate constant are shown. The performance of the model is demonstrated by an application of the 20-MW pilot plant of Tennessee Valley Authority to the geometry and the operating conditions. On this plant detailed measurements of oxygen, carbon dioxide and sulfur dioxide profiles above the bed surface have been carried out. A good agreement between these measurements and the predictions of the model is obtained.