Showing papers in "Aiche Journal in 1981"

A random pore model for fluid‐solid reactions: II. Diffusion and transport effects

Abstract: The prior random pore model for kinetically controlled fluid-solid reaction (Bhatia and Perlmutter, 1980) is generalized to include transport effects arising from boundary layer, intraparticle, and product layer diffusion. Numerical solutions are presented for a variety of conditions. The results show that the rate and surface area maxima predicted in the kinetic regime are shifted to lower conversions as intraparticle or product layer diffusional resistances increase. In addition, with increasing temperature a decrease in the overall reaction surface is predicted, in agreement with experimental findings (Kawahata and Walker, 1962). For reactions accompanied by an increase in the volume of the solid phase, it is shown that incomplete conversion may be expected, the ultimate conversion decreasing with an increase in the intrapellet diffusional resistance. Optimal temperatures for such reactions are also identified.

A review of process synthesis

Abstract: Process synthesis is the step in design where the chemical engineer selects the component parts and how to interconnect them to create his flowsheet. This paper reviews the rapidly growing process synthesis literature of over 190 articles, almost all of which have been produced in the last decade. The paper first introduces the nature of the synthesis problem and outlines the variety of approaches which have appeared to solve aspects of it. The problems include developing a representation, a means to evaluate alternatives, and a strategy to search the almost infinitely large space of possible alternatives. As the article demonstrates, effective solutions are very dependent on the nature of the synthesis problem being addressed. The article covers in detail the following five synthesis topics: chemical reaction paths, separation systems, heat exchanger networks, complete flowsheets, and control systems. Readily apparent are the development of industrially significant insights to aid in the design of heat exchanger networks. Reasonable progress exists in the synthesis of separation systems based on nearly ideal distillation technology and in the development of computer aids by chemists for reaction path synthesis leading to desired complex organic molecules. More work is needed for the remaining areas to become industrially significant.

Wall effects in laminar flow of fluids through packed beds

Abstract: A model which accounts for the effect of a confining wall and the resulting voidage variations near it on the flow behavior in packed columns is proposed. The model, which is restricted to columns randomly packed with spheres of uniform size, reasonably describes the pressure drop-flow rate relationship for both linear and non-Newtonian fluids. The mass flux distribution is also studied in order to provide an insight into processes in which the flow behavior near the wall may be important.

Pressure fluctuations in a fluidized bed

Abstract: An on-line statistical study of the pressure fluctuations in fluidized beds was conducted by using pressure transducers, a correlation and probability analyzer and a Fourier transform analyzer. The causes of the fluctuations were explored, and the effects of the gas velocity, bed height, particle size and distributor design on the major frequency and amplitude of the fluctuations were investigated. The results indicate that the motion of bubbles appears to be the major cause of the pressure fluctuations in the upper portion of a fluidized bed. In the lower portion, the combined effects of the formation of large bubbles in the middle portion of the bed, the formation of small bubbles near the distributor, and the jet flow immediately above the distributor appear to be the major causes of pressure fluctuations.

The effect of pore structure on fluid‐solid reactions: Application to the SO2‐lime reaction

Abstract: The effect of varying pore structures on the kinetics of fluid-solid reactions is investigated through the random pore model developed in prior papers (Bhatia and Perlmutter, 1980, 1981). By considering several idealized pore-size distributions it is shown that a solid having a uniform pore size is intrinsically less reactive than one possessing a pore-size distribution. For solids with bimodal pore size distributions optimal structures are shown to exist for which the reactivity is a maximum. Numerical solutions were obtained to the model equations for various values of the parameters characterizing the pore structure, the diffusion, and the chemical kinetics. The results show that the conversion-time behavior and the expected ultimate conversion can be very sensitive to variations in surface area and porosity for reactions accompanied by an increase in volume of the solid phase. These findings are in agreement with experimental literature on the SO2-lime reaction (Ulerich et al., 1978; Borgwardt and Harvey, 1972; Potter, 1969; Falkenberry and Slack, 1968) and the model is shown to fit the data of Borgwardt (1970), and of Hartman and Coughlin (1974, 1976). It is seen that this reaction is diffusion controlled under the conditions of Hartman and Coughlin, in consonance with their own finding using the grain model, and a prior Pigford and Sliger (1973) interpretation. The temperature behavior of the diffusion coefficient in the product layer suggests the participation of an activated process, possibly a solid state diffusion step.

Adsorption of binary and ternary hydrocarbon gas mixtures on activated carbon: Experimental determination and theoretical prediction of the ternary equilibrium data

Abstract: Experimental binary and ternary equilibrium data for the adsorption of hydrocarbon mixtures of methane, ethane, ethylene, and propylene on activated carbon at 20°C are presented and discussed. Reproduction of binary adsorption equilibria and prediction of ternary adsorption equilibria exclusively with data of binary systems have been carried out using a real adsorbed solution theory, which requires the calculation of the activity coefficients for the components in the adsorbed phase. Predicted equilibrium data are found to be in excellent agreement with experimental values using Wilson and UNIQUAC equations to calculate the activity coefficients. The real absorbed solution theory provides a much more accurate method for predicting multicomponent adsorption equilibria than the ideal adsorbed solution theory.

Collection efficiency of cyclone separators

Abstract: Based on terLinden's (A. J. terLinden, “Investigations into Cyclone Dust Collectors,” IME Proc., 160, 233, 1949) experimental observations, a three-region model is proposed for the fluid flow in a cyclone. Within each region, turbulence is assumed to promote mixing of the suspended particles. Incorporation of this mixing concept into the three-region model allows an analytic expression for the collection efficiency of the cyclone to be developed. The theoretical result is compared with data obtained in the high temperature, high pressure exhaust from a pressurized fluidized bed combustor.

Slow migration of a gas bubble in a thermal gradient

Abstract: The steady migration velocity of a gas bubble placed in a liquid with a linear temperature field in the absence of gravity is obtained for small Marangoni Numbers using a matched asymptotic expansion procedure for solving the governing equations. A result good to 0(N) is obtained, and in the limiting case of zero Marangoni Number, the results of Young, Goldstein and Block are recovered.

Local hold-up and liquid velocity in air-lift reactors

Abstract: Measurements of local hold-up and liquid recirculation rate in an air-lift reactor were performed with two types of gas spargers using a manometric technique. A simple exponential function correlated properly the liquid velocity measured to the gas flow rate. The local hold-up varied appreciably along the column and showed a maximum in most of the cases. A simple linear relationship correlated the local gas velocity with the total flow rate of the mixture.

A branched pore kinetic model for activated carbon adsorption

Abstract: A branched pore kinetic model for aqueous phase activated carbon adsorption is presented in which the carbon particle is separated into rapidly and slowly diffusing regions. The model was developed to overcome problems arising from a single rate parameter analysis and is shown to describe experimental data well. In addition to very different rates of transport in the two regions, parameters estimated by regression analysis indicated differences in the adsorptive charac- teristics. As an approximation to the microscopic description of the diffusional process, a model has been developed in this work which divides the carbon particle into two regions of different diffusion rates. The regions are loosely termed macropores and micropores. (These terms should not be confused with their conventional uses to define certain pore size ranges.) Relatively rapid diffusion and adsorption occur in the macropores, and the remaining slow approach to equilibrium occurs in the mi- cropores. The micropores are assumed to be homogeneously distrib- uted throughout the particle and to branch off the larger mac- ropore network which is responsible for radial transport. A schematic diagram of the proposed model is shown in Figure 2. In many respects, the model is similar in form to the dual rate models developed for catalysts of pelletized microporous parti- cles or for molecular sieves (Furusawa and Smith, 1973b; Ruckenstein et al., 1971; Shah and Ruthven, 1977). However, it is not possible to define the dimensions of the microporous sub-units when dealing with activated carbons. Thus, a lumped parameter approach was used to describe diffusion in the micropores. A surface diffusion mechanism was assumed to be responsible for transport in the macropores. Batch kinetic experiments were conducted over extended periods using a closed system, liquid-phase Carberry reactor to obtain accurate data for evaluation of the model parameters. CONCLUSIONS AND SIGNIFICANCE Experimental data collected for the adsorption of phenolics onto activated carbon are accurately described by the pro- posed model. The data show that the observed behavior during a batch kinetic experiment, if followed for a sufficiently long period, is not consistent with a single intraparticle diffusion rate model. Furthermore, by viewing activated carbon adsorp- tion as a dual mechanism rather than as a single mechanism process, equilibrium isotherms and relatively short-term batch kinetic data can be shown to be compatible. From the model parameters which were obtained by regression analysis of the data, several conclusions can be drawn. Measured surface diffusion coeffwients within the macro- pore network are comparable to previously reported

Effects of molecular size and configuration on diffusion in microporous membranes

Abstract: Effects of molecular size and configuration on hindered diffusion were examined by measuring diffusion of two series of uncharged macromolecules through track-etch membranes with uniform and well-defined pore geometry. At any given Stokes-Einstein radius, diffusivities in small pores were lower for ficoll (crosslinked structure) than for dextran (more nearly linear structure).

An analytical Carnahan‐Starling‐van der Waals model for solubility of hydrocarbon solids in supercritical fluids

Abstract: Data have been taken by a new flow technique for the solubility of nonpolar hydrocarbons in nonpolar supercritical fluids. These results for molecularly simple molecules provide a basis for the analytical representation of such systems by relatively simple equations of state. 16 refs.

Evaluation of liquid‐solid contacting in trickle‐bed reactors by tracer methods

Abstract: The use of dynamic (tracer) methods for the evaluation of liquid-solid contacting and holdup in trickle-bed reactors is illustrated. It is shown that both the fraction of external catalyst area wetted and the fraction of total catalyst wetted by liquid can be obtained. External contacting efficiency and dynamic liquid saturation are correlated in terms of the appropriate dimensionless groups over the range of variables typical for trickle-flow operation. The relationship between catalyst contacting efficiency and catalyst utilization is outlined.

Kinetics of nonisothermal sorption: Systems with bed diffusion control

Abstract: A theoretical model is presented to describe the kinetics of nonisothermal sorption for a system in which the main resistance to mass transfer is the macrodiffusional resistance of the absorbent particle bed while the main resistance to heat transfer is the resistance at the external surface of the adsorbent sample. The model is used to interpret experimental kinetic data for the sorption of several hydrocarbons in 10X and 13X zeolite crystals. By varying the configuration of the sample bed and the size of the zeolite crystals it is shown that, for n-heptane and iso-octane in 13X, the intracrystalline diffusional resistance is negligible even in 40-μm crystals. The assumption of intracrystalline diffusion control which has been made in earlier kinetic studies of similar systems is therefore incorrect.

Calculation of critical points from cubic two-constant equations of state

Abstract: A computational modification of the Heidemann-Khalil method for calculating the critical temperatures and pressures for general phase-equilibrium problems greatly reduced the computing time for simple two-constant cubic equations of state. For systems where the unlike binary interaction parameters can be derived from the pure-component parameters using the geometric mean values, a further simplification lowers the computing times to a few milliseconds, regardless of the number of components.

Optimal operation of integrated processing systems. Part I: Open‐loop on‐line optimizing control

Abstract: A method for tracking the economically optimal operating conditions of a chemical process in the presence of constraints is developed. The technique is based on an on-line search rather than a fundamental model. The most profitable operating point is found by fitting a dynamic model of the process based on data obtained from experimental moves on the plant. This model is used to compute gradients of the economic objective and of the constraints so that a direction of economic improvement inside the allowed operating region of the plant is always obtained. Constraint violations during the transients are prevented by a multivariable regulator. A new regulation method (Internal Model Control) is used which permits explicit handling of constraints and which can be made robust against modelling errors. This combined optimization/regulation approach is tested in a demonstrative simulation example and shown to be reliable for following a moving optimum and safely handling complex constraint moves.

Revision of kynch sedimentation theory

Abstract: Much of the theory of gravity sedimentation has been based on the work of Coe and Clevenger (1916) and Kynch (1952). They provided methods for obtaining rates of sedimentation in batch, static tests which are presently used for design of continuous thickeners. Kynch assumed that a first order partial differential equation controlled the entire sedimentation process. His equation was based on: (1) continuity balance; and (2) sedimentation velocity being a unique function of solid particulate concentration. A general solution was presented in the form of volume fraction of solids ϕs = f(x − vt). During the constant rate fall of the upper interface, the boundary condition of uniform initial concentration combines with the Kynch equations to adequately describe the sedimentation phenomena. Kynch ignored the sediment rising from the bottom of the settling chamber, and assumed that the characteristics y = x − vt originated at the origin of coordinates (height, time) during the first falling rate period. The characteristics actually originate at the surface of the rising sediment where the upward liquid velocity affects the rate of fall of the particulates. New equations have been derived based upon the assumption that the characteristics emanate from the rising sediment.

Bacterial film growth in adsorbent surfaces

Abstract: Simultaneous biological and activated-carbon treatment of organic wastewaters appears promising. The effects of bacterial film growth on adsorbent particles is investigated by laboratory work and mathematical modelling. Regeneration of the adsorbent due to film growth does occur, but faster than predicted. The discrepancy reflects uncertainty about the structure of bacterial films.

Evolutionary synthesis of separation processes

Abstract: This paper deals with the problem of finding, among many alternatives, the sequence of separation units that will isolate desired products from given feed at the minimum cost. Multicomponent products can be specified. An evolutionary procedure is presented. This method consists of two phases. In the first phase, a good initial structure is created by heuristic methods. In the second phase, the initial structure is successively modified by making evolutionary structural changes. This logic has been programmed on a digital computer and has been tested on several problems.

Liquid film flowing slowly down a wavy incline

Abstract: A viscous lamina of given mean thickness flows down a wavy incline. Assuming low Reynolds number and small perturbations due to the wavy striations, the velocity profiles and the free surface profile are determined. It is found that the amplitude and phase shift of the free surface depend, in a complicated manner, on the surface tension and the wave length and orientation of the wavy striations. The motion of a particle on the free surface experiences drift which is also a function of the surface tension, the amplitude, wave length and orientation of the wavy incline.

Modeling the flow of viscoelastic fluids through porous media

Abstract: A tube with sinusoidal axial variations in diameter has been used as a first step toward modeling the flow channels of a porous medium in such a way that appreciable Lagrangian unsteadiness is present. Experiments with dilute aqueous solutions of a polyacrylamide (Dow Separan AP-30) show that the Lagragian unsteadiness gives rise to an increase in resistance to flow through the sinusoidal channel relative to that predicted for a purely viscous fluid. The increase in pressure drop can occur as a consequence of fluid elasticity, without any observable secondary flow. At sufficiently high flow rates, secondary flow appears. 20 references.

SO2 absorption into aqueous solutions

Abstract: The absorption rate of SO2 from a gas mixture of SO2 and N2 into pure water, HCl, and NaCl solutions has been measured at 25°C in a continuous stirred vessel with an unbroken gas-liquid interface. The rates of the liquid-phase mass transfer are accurately modeled by the theory of surface renewal with the instantaneous, reversible hydrolysis of dissolved SO2. The theory and results are applicable to SO2 absorption from waste gases.

An explicit equation for particle settling velocities in solid‐liquid systems

Abstract: Zanker has recently presented nomographs for determining particle settling velocities in solid-liquid systems. These nomographs were based on the general correlations developed by Barnea and Mizrahi and Barnea and Mednick. This work presents an equation directly computing particle settling velocities, eliminating the uncertainty associated with nomographs.

Analysis of control‐output interactions in dynamic systems

Abstract: A general theory for examining the dynamic as well as static interactions among inputs and outputs in a multivariable control system has been developed. Both state space and frequency domain approaches are used, and at steady state the interaction equations assume the same form as the relative gain array developed by Bristol. Implications of selecting input-output pairings with regard to steady state vs. dynamic consideration are discussed. The application of the method of analysis to a distillation column control system is presented.

Interpretation of surface flow phenomenon of adsorbed gases by hopping model

Abstract: The mechanism of surface flow of adsorbing gas molecules through the porous adsorbent is interpreted, and a new hopping model is derived by separately taking into account the hopping behaviors of monolayer and multilayer molecules. The reported experimental results containing the data measured here are correlated well. Finally, some considerations are given to the two experimental constants appearing in the model.

Measurement and application of limiting activity coefficients

Abstract: Infinite dilution activity coefficients (γ∞) in binary liquid mixtures are data of wide practical and theoretical applicability, but their extensive use has been hindered by the experimental limitations of classical vapor-liquid equilibrium techniques. Two new experimental methods for accurate γ∞ determinations are presented. These techniques, both faster and more accurate than classical methods, are complementary, and their applicability to different types of binary systems is discussed.

A framework for description of mechanical mixing of fluids

Abstract: Mechanical mixing of fluids interpreted as deformation of contact interfaces between materials or originally designated material surfaces, can be described by continuum mechanical arguments. The idea is developed at two levels. Part I: Exact kinematical description of mixing of fluids with negligible interfacial tension. Part II: Description of mixing of fluids with negligible interfacial tension in terms of intermaterial area density. The approach provides a unified mathematical description of the mechanical mixing of fluids.

An experimental investigation of stability and multiplicity of steady states in a biological reactor

Abstract: The existence of multiple stable and unstable steady states in a continuous stirred tank biological reactor (CSTBR) was demonstrated experimentally for the first time. These experiments resulted in the determination of growth rate, yield and intermediate metabolite concentration data entirely from continuous culture. This information was used to qualitatively interpret the stability behavior in terms of the biochemistry and bioenergetics of substrate metabolism.