Simultaneous absorption with reversible instantaneous chemical reaction

The approach presented recently [1] for analyzing absorption and desorption mass transfer problems with instantaneous chemical reaction is extended to the case of simultaneous absorption of two gases, A and A′. The analysis is developed for arbitrary stoichiometry. The following simple case is discussed in detail:A + B₁?B₂A′ + B₁?B₃ where B₁ is the liquid phase reactant and B₂, B₃ the reaction products. The analysis takes into account the “shift” reaction, which for the simple case above is:A + B₃?A′ + B₂This reaction takes place in the region near the interface. The analysis differs from previous work which, with one exception, ignored the “shift” reaction and restricted attention to zero values of the concentrations of B₂ and B₃ in the bulk liquid.The analysis shows that the conditions where the physical driving forces (a_i-a_o) for absorption of both gases are large and positive does not imply that the chemical driving forces (α_i-α_o) are both positive. In fact, it is shown that cases arise where one component may desorb even though its physical driving force is positive.A simplified thermodynamic model useful for extrapolation of mixed CO₂ and H₂S equilibrium data in amine solutions to very low values of acid gas loading in solution is developed. Tower profiles for simultaneous absorption of CO₂ and H₂S in monoethanolmine solution are considered in light of the new analysis. The good kinetic selectivity measured for H₂S at the absorber lean end is due to the fact that carbon dioxide is not absorbed in the instantaneous reaction regime. At the absorber rich end, where a temperature bulge develops, CO₂ is absorbed in the instantaneous regime, causing H₂S to be desorbed even though its physical driving force favors absorption.     

Enhancement of absorption of a gas into a stagnant liquid in which a heterogeneously catalysed chemical reaction occurs

The CBS method[1, 2] is applied to measure the enhancement factor for the absorption of pure hydrogen from a gas bubble of constant size into a sta     

Further consideration on chemical absorption mechanism by aqueous slurries of sparingly soluble fine particles

The absorption rates of SO₂ into an aqueous slurry of Mg(OH)₂ and an aqueous slurry of CaCO₃ with adding MGSO₄, were theoretically derived in terms of the two-reaction-plane model. Experimental absorption rates of dilute S0₂ into above slurries can be predicted by the proposed model in which there is no particle suspending in between the gas-liquid interface and the primary reaction plane.     

The use of a computer algebra system in the analysis of chemical engineering problems

Computer algebra systems are powerful processors designed to treat formal mathematical expressions. Routine features include many operations that occur frequently in the analysis of engineering problems, and provide the analyst with a powerful and reliable tool for manipulating algebraic, differential and integral equations. The power and general utility of one particular computer algebra system is first demonstrated on two elementary examples—the first involving the solution of an ordinary differential equation by weighted residual techniques, and the second, a perturbation solution of Duffing's equation. Ideas stemming from these examples are then applied to a current research problem involving the determination of the amplitude and frequency of self-sustained density wave oscillations in a once-through evaporator. All examples show the power of this system in handling large amounts of tedious algebra with relative ease, thus eliminating the potential for manual error.     

Residence time distribution of plug flow in a finite packed-bed chemical reactor

The residence time distributions in a finite packed-bed chemical reactor under plug flow conditions have been studied. Analysis was performed upon the well-known axial dispersion model in one dimension. Of paramount importance it was to construct a high order approximate solution to the corresponding initial-boundary value problem which appeared to be extremely convenient for fast numerical calculations. To this purpose singular perturbation techniq were applied using the reciprocal of the Péclet number as a small parameter. An error analysis was subsequently established for the special case of a pulse-function tracer input. The so-called “tailing phenomenon” of the response curve was simulated by an appropriate parameter-depending boundary condition of diffusion type.     

Application of a numerical laplace transform inversion technique in the theory of multiphase flow systems

An isothermal, one-dimensional reactor of infinite length is considered where an arbitrary number of co-current phases flow with different rates containing also a solute. Interphacial reaction between the solutes as well as axial diffusion with different diffusivities are supposed to take place. Defining the overall flux as the response in such a system, the impulse response is, as a rule, equal to the density of the residence time distribution. A straightforward algorithm to determine explicitly the impulse response has been developed based on a numerical Laplace transform inversion technique. An application to the general two-phase system is shown.     

Mass transfer with chemical reaction in a foam bed contactor

On the basis of dodecahedral structure of a foam bed, a model to predict conversion in a foam bed contactor with mass transfer with chemical reaction has been developed. To verify the proposed model, experiments have been carried out in a semi-batch apparatus for the absorption of lean CO₂ gas in a foam of sodium hydroxide solution. The proposed model predicts fairly well the experimentally found absorption values.     

Equilibrium theory of a pressure swing adsorption process

An equilibrium theory of the separation of two-component gaseous mixtures via the pressure swing adsorption process known as heatless adsorption is presented. Both components of the mixture are adsorbable. One is present at a trace level and is preferentially adsorbed.Principal predictions of the theory for the condition of complete removal of the trace component from the high pressure product stream when using the least possible amount of adsorbent are as follows. When the separation factor is large, high recovery of purified high pressure product is obtained and blowdown and purge losses are small. Recovery is increased and losses decreased by increasing the pressure ratio. Conversely, recovery of the purif high pressure product is small and blowdown and purge losses are large when the separation factor is small. In this case the use of high pressure ratio not improve performance.The trace level component in the combined blowdown and purge stream is derived increasingly from the blowdown as the pressure ratio is increased.     

Application of a variable-order semi-implicit Runge-Kutta method to chemical models

A semi-implicit Runge-Kutta method is proposed and application is made to models of chemical kinetics. The presented algorithm GRKV4 is based on an A-stable formula with variable order up to four and possesses an automatic stepsize control. The range of application of GRKV4 is discussed.     

Oscillatory and chaotic behaviour of a forced exothermic chemical reaction

An exothermic reaction takes place in a continuous stirred reactor, the cooling temperature of which is varied with time. It is shown that with an increase in the amplitude of the forcing that quasiperiodic behaviour occurs, followed by a sequence of period doubling bifurcations leading to chaos. Furthermore, multiple oscillatory states can arise, where both states are periodic or one state periodic and the other chaotic.     

Simultaneous absorption of two gases reacting between themselves in a liquid—II: Approximate solutions

An attempt has been made to analyse the hitherto existing approximate solutions of nonlinear differential equations representing a mass balance of two gases which react between themselves in an inert liquid. New approximate analytical solutions of the problem have been obtained and compared with the numerical and the existing approximate solutions in order to show the best approximations and the most convenient mathematical formulas for calculating the concentration profiles and the enhancement factors.     

Simultaneous absorption of two gases reacting between themselves in a liquid—I exact solutions

Simultaneous absorption and irreversible second order chemical reaction of two gases in an inert liquid have been considered. The nonlinear differential equations describing the absorption process have been solved analytically for particular cases by the use of the Weierstrass elliptic function and Airy functions. It is impossible to obtain a general analytical solution and therefore the accurate numerical solution for the diffusion-reaction process based on the film theory has been developed. The approximate formula for the enhancement factor E_A, in the range of large values of the dimensionless parameter M is given.     

A new attempt for the evaluation of the absorption constant of ozone in water

The ozone absorption constants in water at temperatures ranging from 0.5 to 41°C are evaluated by means of an experimental procedure which preserves equilibrium conditions. Ozone analyses are performed according to the previously checked methods of thermal decomposition and batch iodometry.Results confirm that ozone solubility in water adheres to Henry's law and allows the heat of solution to be evaluated.     

Dynsyl: a general-purpose dynamic simulator for chemical processes

DYNSYL was developed at Lawrence Livermore Laboratory (LLL) in order to provide a means of simulating chemical process dynamics in nuclear fuel processing systems. The program is a modification of DYNSYS with several new subroutines for process unit simulation. The program can be used to generate process data or to provide estimates of process performance; it simulates both steady-state and dynamic behavior. This report describes the overall structure of DYNSYL and includes some example problems.     

Temperature-dependent physical properties in physical gas absorption

A solution for interface temperature rise in physical gas absorption due to heat of solution was obtained by Danckwerts [1,2] with the limitation that the pertinent physical properties—diffusion coefficient, solubility of the gas and thermal conductivity of the liquid remained constant. This paper complements Danckwerts' contribution by considering the pertinent physical properties as temperature-dependent, the dependence being of the form:$\text{Q}\text{Qi}$ = exp [γ_Q(T ? T_i)]. Wagner [3] has obtained solutions for unsteady-state diffusion when the diffusion coefficient is similarly dependent on concentration. Wagner's solutions are adapted to provide a solution for the present problem. Two approximate solutions, one valid at high Lewis Number and the other when Lewis Number approaches unity are also presented. For the normal values of activation energies, Danckwerts' model is shown to be accurate when interfacial temperature rise is less than one percent of the absolute temperature of bulk liquid. The extent of departure from the Danckwerts' model is shown to depend on combinations of activation energies of the pertinent physical properties.     

On the dynamics of a stirred tank with consecutive reactions

The pattern of multiplicities of the steady states of a stirred tank reactor in which A → B → C takes place has been known for some time to be complex. We show that even in regions of parameter space for which there is only one steady state the dynamical behavior can be very complicated. Since the number of parameters is very large a complete exploration of the space is impossible, but by careful transection of a small, but significant, region we show that repeated bifurcation of limit cycles leads into a pattern of periodic and chaotic behaviour that returns to a simple limit cycle and then reflects itself.     

An improved algorithm for diagnosis of system failures in the chemical process

The detailed techniques for improving the efficiency of a fault-diagnosis algorithm can be based on the signed directed graph. This graph represents the structure of the system, and the pattern on the graph represents a state of the system. The usefulness of the improved algorithm is demonstrated using a model of a chemical process comprising a reactor, a heat exchanger and a distillation tower.     

Computation of restricted chemical equilibria

It is shown that the method for computation of simultaneous phase and chemical equilibria proposed by Castillo and Grossman can be extended easily for handling restricted chemical equilibria calculations. Equality and inequality constraints that represent limited experimental information on the chemical reaction are incorporated in the nonlinear programming formulation for minimizing the Gibbs energy. Three numerical examples are presented which illustrate the effectiveness of the proposed approach.