Showing papers in "Chemical Engineering Science in 1983"

The pinch design method for heat exchanger networks

Abstract: A novel method is presented for the design of heat exchanger networks. The method is the first to combine sufficient simplicity to be used by hand with near certainty to identify “best” designs, even for large problems. “Best” designs feature the highest degree of energy recovery possible with a given number of capital items. Moreover, they feature network patterns required for good controllability, plant layout, intrinsic safety, etc.

A kinetic study of methane hydrate formation

Abstract: The kinetics of methane hydrate formation, after commencement of nucleation, were studied using a semibatch stirred tank reactor. The temperatures studied in the experiments were from 274 to 284 K over a pressure range of 3–10 MPa. The results of the experiments revealed that the formation kinetics were dependent on the interfacial area, pressure, temperature and degree of supercooling. The history of water sample affected the induction delay times for nuclei formation, but it had no observable effects on the overall kinetics of hydrate formation after the nucleation had commenced. A consistent semi-empirical model was formulated to correlate the experimental kinetic data.

Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Isolas and other forms of multistability

Abstract: Autocatalytic reactions are often complicated, and analyses of their behaviour in open systems can seem too particular to permit useful generalisation. We study here the simplest of circumstances (uniform temperatures and concentrations in the isothermal CSTR) and the simplest of reaction schemes: (i) quadratic autocatalysis ( A + B →2 B ); and (ii) cubic autocatalysis ( A + 2 B →3 B ). The catalyst B may be stable or have a finite lifetime (B→ inert products). Allowing for this finite lifetime adds another dimension to the interest. The phenomena encountered include multistability, hysteresis, critical extinctions, critical ignitions, and anomalous relaxation times (though infinite values do not arise). Patterns of stationary states as function of residence time can show isolas and mushrooms. All these aspects yield to simple algebraic analysis. The presence of the catalyst B in the inflow can make qualitative differences of a kind parallelled by an additional, non-catalytic reaction of the same stoichiometry (e.g. A → B ). Invoking the reversibility of the reactions neither increases nor diminishes their variety, and thermodynamic considerations have little to do with the many different patterns of reactivity displayed. The local stability of the various stationary states has also been characterized. Quadratic autocatalysis shows limited variety (stable node, stable focus); cubic autocatalysis generates all the kinds of stationary state possible in a two-variable system. Again all the algebra is straightforward if not always simple. Sustained oscillatory behavior (limit cycles) also occur. All these remarks relate to isothermal systems, but there are the most striking parallels between isothermal autocatalysis and the exothermic, first-order reaction in the CSTR. Behaviour with an autocatalyst of complete stability corresponds to perfect heat insulation (adiabatic operation) in the non-isothermal, exothermic system.

A study on the reaction between CO2 and alkanolamines in aqueous solutions

Abstract: Literature data on the rates of reaction between CO2 and alkanolamines (MEA, DEA, DIPA, TEA and MDEA) in aqueous solution are discussed. These data induced us to carry out absorption experiments of CO2 into aqueous DEA, DIPA, TEA and MDEA solutions from which the respective rate constants The results for DEA and DIPA were analysed by means of a zwitterion-mechanism which was derived from the mechanism originally proposed by Danckwerts [1 The reaction rate of CO2 with aqueous TEA and MDEA solutions shows a significant base catalysis effect which is also reported by Donaldson and Nguy

Design of resilient processing plants—III: A general framework for the assessment of dynamic resilience

Abstract: With increased process integration it has become very important to evaluate and compare the dynamic operability characteristics (dynamic resilence) of alternate designs. Based on recent results in multivariable frequency response theory a new framework is developed for this purpose. It is shown that dynamic resilence is determined by characteristics inherent in the system and that it is independent of the imposed controller structure and type. This gives the new method considerable intuitive appeal and allows it to avoid the lengthy optimization procedures which are typical for the previously published techniques.

Evaluation of steady flow profiles in rectangular and circular packed beds by a variational method

Abstract: The Brinkman-equation is solved by an equivalent variational problem in order to obtain steady flow profiles which satisfy the conditions w = 0 and e = 1 at the container wall of a packed bed. The quite large deviations between calculated and measured profiles are fully explained. An analytical expression is developed with sufficient accuracy. The main body of calculations is performed for isothermal flow, however flows under non-isothermal conditions also are considered.

Minimum utility usage in heat exchanger network synthesis : a transportation problem

Abstract: This paper formulates the minimum utility calculation for a heat exchanger network synthesis as a “transportation problem” from linear programming, allowing one to develop an effective interactive computing aid for this problem. The approach is to linearize cooling/heating curves and partition the only at potential pinch points. In this formulation user imposed constraints are readily included, the latter permitting selected stream/stream matches disallowed in total or in part. By altering the formulation of the objective function, the paper also shows how to solve a minimum utility cost problem, where each utility is available at a single temperature level. A procedure is included to handle a utility which passes through a temperature change when being used. Extending the partitioning procedure permits the formulation to accommodate match dependent approach temperatures, an extension which is useful when heat transfer through a third fluid only is allowed for some matches.

Dynamic modeling and reaction invariant control of pH

Abstract: A systematic treatment of the dynamics and control of acid-base reactions is presented. A state model consisting of mass balances for the species present is formed. Through a linear transformation of the concentration vector a new model is set up. The state vector of this model is partitioned into a reaction invariant and a reaction variant part. The model is thus split into two parts, one describing the physical properties of the reactor system independent of chemical reactions, the other describing the chemical reactions. For fast acid-base reactions the reaction invariant part of the model is sufficient to define the thermodynamic state of the system. The reaction rate vector is thus eliminated from the model. In this case the reaction variant part of the model consists of a static equation, relating pH to the reaction invariant state variables. The model obtained provides a sound basis for design of control loops for feedback and feedforward control of pH. As a direct application a new scheme for adaptive control of pH is proposed.

Dispersion in pulsed systems—III: Comparison between theory and experiments for packed beds

Abstract: The theoretical development put forth in Part II of this paper is applied to several two-dimensional, spatially periodic porous media in order to determine components of the dispersion tensor for Peclet numbers ranging from 1 to 104. The calculated longitudinal dispersion coefficients show reasonable agreement with experimental data for a packed bed of spheres in a cubic array. This provides support for the theory developed in Part II; however, for randomly packed beds the experimental values of the longitudinal dispersion coefficient are smaller than those predicted using the spatially periodic model. In addition, the functional dependence on the Peclet number for the experimental data differs considerably from that predicted by the theory. The dependence of the dispersion coefficient on distance is discussed from the point of view of the results presented in Part I, and some recent experimental observations and calculated results for the effect of particle size distribution are given. In addition, our calculated values for the lateral dispersion coefficient are compared with experimental values and are found to be too small by about three orders of magnitude at a Peclet number of 103.

A unified model for particulate expansion of fluidised beds and flow in fixed porous media

Abstract: A model is derived for a fluidised bed that enables its steady state particulate expansion to be predicted as a function of superficial velocity from the initial (packed bed) condition to the final fully expanded (single suspended particle) state These predictions are in good agreement with the empirical correlations and functional dependencies found by Richardson and Zaki[1,2] over the full range of flow conditions The derivations incorporat revisions in the form of the pressure drop correlations for flow in porous media that are justified on theoretical and empirical grounds

Dispersion in pulsed systems—II: Theoretical developments for passive dispersion in porous media

Abstract: A general theory is developed that allows one to calculate the dispersion tensor for pulsed systems in spatially periodic porous media. The analysis has its origin in the original work of Taylor, and the results quite naturally reduce to the Taylor-Aris result for passive dispersion when applied to the case of laminar flow in a tube. In Part III the theory is compared with axial dispersion data for packed beds.

Heat integration of distillation columns into overall processes

Abstract: There are many well-known schemes for better energy efficiency in distillation. Examples are thermal coupling, multiple effect, heat pumping, etc. Usually these schemes are discussed for individual columns in isolation, independently from the overall process they are a part of. This paper puts the design of individual distillation columns into context with the heat integration for the overall process. An insight is discussed w Generally, the paper defines good integration as a column not crossing the heat recovery pinch of the process and either the reboiler or the condenser

Mixing in mechanically agitated gas-liquid contactors, bubble columns and modified bubble columns

Abstract: Mixing time measurements were made in 300 and 1000 mm i.d. mechanically agitated contactors with different types of impellers, located at different heights from the bottom of the vessel. Mixing time measurements were also made in 150, 200, 385 and 1000 mm i.d. bubble columns with varying liquid heights. Transient pH measurement and conductivity measurement were used to measure the mixing times. Impeller speed was varied in the range of 3.33–20 r/sec in the case of mechanically agitated contactors and gas superficial velocity was varied in the range of 10–250 mm/sec in bubble columns. Effect of physical properties of the fluid (surface tension, ionic strength, liquid viscosity) and that of the non-Newtonian behavior on mixing time was studied. Mixing time in the presence of drag reducing agents was also investigated. In the range of variables covered in this work mixing time in mechanically agitated contactors and bubble columns was found to be in the range of 4–6 Mixing time predictions based on the longest loop length and circulation velocity are made in the presence and absence of a gas for mechanically agitat A procedure is given for the prediction of the critical impeller speed for gas phase dispersion in mechanically agitated contactors.

Multiplicity features of reacting systems. Dependence of the steady-states of a CSTR on the residence time

Abstract: Singularity theory with a distinguished parameter, as developed by Golubitsky and Schaeffer, is a very useful tool for predicting the influence of changes in a control or design variable on the steady-states of lumped-parameter systems. The theory is used to construct various bifurcation diagrams describing the influence of changes in the residence time on the temperature in a CSTR in which several reactions occur simultaneously. The number of different bifurcation diagrams increases very rapidly with increasing number of reactions. The predictions of this local theory provide important theoretical guidance in the global analysis of the multiplicity features.

The kinetics of adsorption of surface active agents at gas-liquid surfaces

Abstract: A general model of adsorption of surfactants at a gas-liquid surface has been developed, which accounts for both the diffusion in the bulk and the barrier to adsorption. In this model, the activation energy barrier to adsorption is accounted for by means of a kinetic expression. A numerical scheme for the solution of the resulting equation of the diffusion-kinetic model is illustrated for the case of the Frumkin isotherm. The model is used to estimate the extent of the adsorption barrier from the dynamic surface tension data of two aqueous surfactant systems reported in the literature. A simplification of the diffusion-kinetic model is proposed which accounts for diffusion in the bulk using diffusion-penetration theory. The simplified model compares very well with the exact model, especially for high barrier resistances.

Synthesizing heat exchanger networks having restricted stream/stream matches using transportation problem formulations

Abstract: This paper presents an algorithm which is readily computer implementable for the synthesis of heat exchanger networks. The algorithm permits the user to impose constraints disallowing in part or in total the matching of any of the stream pairs. Earlier work showed how to discover minimum utility use for these restricted match problems. Constraining utility use to any feasible limit desired, this paper shows how to discover networks requiring the fewest stream/stream matches and among those to discover networks of simply topology. If required, the algorithm will generate cyclic and/or split stream networks. The algorithm involves the formulation, solving and post processing of a series of linear “transportation” problems. Such problems are linear programming problems of special structure which can be solved extremely rapidly using existing computer codes.

Dispersion in pulsed systems—I: Heterogenous reaction and reversible adsorption in capillary tubes

Abstract: The dispersion of a pulse of solute in a capillary tube undergoing irreversible, heterogeneous reaction or reversible adsorption at the tube wall is considered in order to test certain concepts regarding the construction of dispersion equations. To compare theory and experiment, computer experiments have been performed which indicate that the time dependence of the coefficients in a general dispersion equation may be quite complex. For sufficiently long times the computer experiments provide confirmation of the well-established Taylor-Aris result in addition to providing the first experimental proof of the Golay theory for reversible adsorption.

Floc breakage in agitated suspensions: Effect of agitation rate

Abstract: A population balance equation that governs the floc size distribution in turbulent flow, incorporating both the splitting and erosion mechanisms of floc breakage has been presented in previous studies[6,7]. Experiments have been conducted in which transient floc size distributions of dilute suspensions of Kaolin-hydrous ferric-oxide flocs undergoing breakage in agitated batch system are obtained over turbulent microscale shear rates ranging from 60 to 400 sec −1 . Floc size distributions over a range of floc diameters from about 1 to 100 μ m are measured by overlapping techniques, including computerized optical scanning of photographs and rapid electronic sizing of individual flocs using a light blockage transducer. The experimentally determined size distributions are then fit to those computed from the population balance equation, using constrained nonlinear least squares. The splitting frequency of parent flocs is found to vary as the 0.33 power of the parent floc volume and 0.71 power of the shear rate. The average number of daughter fragments produced upon splitting of individual flocs is found to be about 2.5. The mean and standard deviation of the daughter fragments produced upon splitting are found to be in fixed ratio to one another, independent of the parent floc size and shear rate. An appropriately nondimensionalized coefficient characterizing floc erosion has been found to be independent of shear rate.

Particle growth mechanisms in fluidised bed granulation—I: The effect of process variables

Abstract: Two types of product granule have been identified in an experimental study of batch fluidised bed granulation; agglomerates which consist of two or more, and usually several, initial particles; and layered granules, which consist of single primary particles with dried feed material adhering to the surface. Increasing the excess fluidising gas velocity, in the range U-U mf = 0.15-0.525 m s −1 , resulted in decreased particle growth rates and, depending upon the binder material, a change in product morphology from agglomerates to layered granules. Similar changes resulted from increasing the mean size of the starting material. Thus, a mechanism of particle growth is proposed in which the strength of inter-particle bridges and the extent of fluid drag and inertial forces on particles determine the equilibrium granule form and size. However, if the initial particles are porous this mechanism may break down since liquid may enter intra-particle pores and be unavailable for the initial formation of liquid bonds.

The use of a new model of micromixing for determination of crystal size in precipitation

Abstract: The course of the precipitation process and the size distribution of the solid particles obtained depend significantly on the intensity of mixing in the crystallizer. The authors have used a new model of micromixing, based on the spectral interpretation of mixing in the isotropic, homogeneous turbulent field to evaluate the influence of the intensity of mixing on the rate of precipitation and on the particle size of the product obtained in a stirred vessel with ideal macromixing The results obtained from the model are in good agreement with the experimental results obtained for the precipitation of BaSO 4 .

Tracer dispersion in a laboratory air-lift reactor

Abstract: Measurements of single-circulation Bodenstein numbers are reported for a laboratory concentric-tube air-lift reactor operating with air—water mixtures. The Bodenstein numbers for three different lengths of draught tubes fall with increasing gas throughput but tend to a constant value when dispersion in the gas disengagement section becomes important. The change in variance of a pulse of tracer due to its passage through the head section was measured and at high gas throughputs this region approaches well-mixedness. The variation of Bodenstein numbers is determined by mixing in the riser, the downcomer, and the head section. An existing correlation is employed to examine the contribution of each section. Measurements of the influence of additives upon tracer dispersion are reported.

Hindered diffusion of asphaltenes through microporous membranes

Abstract: The relationship between the diffusion coefficient of asphaltenes and pore size was studied experimentally using track-etched mica membranes. The asphaltenes were extracted from Kuwait atmospheric bottoms using criteria of n -pentane insolubility and tetrahydrofuran solubility at 25°C. Data were obtained for asphaltene fractions of narrow size range by using gel permeation chromatography to analyze the diffusion samples. The results show a very strong pore size effect on diffusion coefficient in the range 70–500 A pore radius for asphaltenes whose GPC-equivalent polystyrene molecular weight is 3000 or greater. By properly accounting for the molecular size of the asphaltene fractions, we are able to obtain good agreement between the measured diffusion coefficients and those predicted from a hydrodynamic theory of hindered diffusion.

Modeling of wavy flow in inclined thin films

Abstract: A physical model for the hydrodynamic mechanisms associated with gravity rolling waves in thin liquid films is presented. The model is based on a periodical distortion of the hydrodynamic boundary layer in the wave front, followed by a recovery process in the wave trail. One input (frequency) is required for prediction of all other wave variables at the developing region. At the developed region, energy considerations provide an additional relationship for predicting the waves frequency. Thus, a closed-form solution is obtained. The agreement with experimental data is satisfactory for wide ranges of liquid flow rates and inclination.

A mathematical model for continuous fluidized bed drying

Abstract: A mathematical model for continuous drying process in a fluidized bed-dryer is presented. To describe the heat and mass transfer in gas phase, a Kunii—Levenspiel type, three-phase model representing a dilute (bubble) phase, interstitial ga Numerical computation based on this model was done to study the effects of the process parameters as particle and bubble-size, gas velocity, inlet gas

More on the dynamics of a stirred tank with consecutive reactions

Abstract: The literature on the stirred tank reactor with consecutive reactions is reviewed and a census of multiplicity diagrams, bifurcation diagrams and phase portraits is given. The location of the organizing centre, introduced by Balakotaiah and Luss, and some features of the butterfly singularity are discu particularly with reference to variations in the ratio of activation energies. The forms that the regions of attraction of the various steady states ma take in the three-dimensional state space are also discussed.

Sandstone water sensitivity: Existence of a critical rate of salinity decrease for particle capture

Abstract: Ahsbaet-A critical rate of salinity decrease (CRSD) was found to exist in the water sensitivity of Berea sandstone. The CRSD was determined by conducting core. flood experiments in which the salinity was dmreased exponentially by placing mixers of various volumes in the inlet stream. Above the CRSD, drastic reductions in core permeability occur due to a log jam, or bridging effect, at the pore constriction. Below the CRSD, the released clay particles pass through the constriction without being captured and therfore very little reduction in core permeability occurs. A critical particle concentration was also identified above which brideina occurs. Based on the exoerimental observations. a mathematical model was develoued to delineate &e &kms of high and lo& permeability agreement with experimental measurements. reductiohs. The model predictions are in- good

A new sequential experimental design procedure for discriminating among rival models

Abstract: A new procedure to be used in the sequential design of experiments for discriminating among rival models is presented. The procedure consists of a new design criterion and a model adequacy test based on statistical principles. The method is illustrated with examples and compared to previous methods.

Segregation and mixing in liquid fluidized beds

Abstract: Segregation and mixing were studied in beds of binary mixtures of lead glass spherical particles (2 mm with 3 mm; and 2 mm with 4 mm diameter) fluidize by paraffin oil. Concentration profiles were obtained both by measuring pressure gradients in the bed and by sampling. A model for solid mixing, based on the combined effects of diffusive and convective mechanisms, has been used in conjunction with the experimental resu

Modelling of the pressure swing air seperation process

Abstract: A theoretical analysis is given of the separation of oxygen and nitrogen in air by a single column pressure swing gas separation process. The problem treated includes changes in mass flow due to adsorption. The findings are compared with data obtained using molecular sieve adsorbent.