A major shortcoming of polynomial approximation in the medelling of distillation columns isthe difficulty encountered while choosing the number and location of collocation points,which are usually doneby rule of the thumb,inevitably giving rise to high dimensionality and longer computation time for the resultingmodel.In order to take full advantage of polynomial approximation in the modelling of complicatedmulticomponent distillation columns,modifications must be made to the model reduction procedure originallyproposed by Cho.This is achieved by putting in special polynomials to each of the variable profiles.Furthermore,the number and location of the collocation points can be determined by the optimization of anappropriate objective function.This would bring about less dimensionality and less computation time for theresulting reduced--order model as compared with Cho’s procedure while its accuracy is still kept excellent.Theeffectiveness of such modifications is illustrated by two simulation examples.Both order reduction and accuracyimprovement are remarkably indicated for steady state and dynamic state simulations of distillation columns.

Using lattice-fluid model,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.A two-stepprocess is deslgned to form a real polymer solution containing a solvent and a polydisperse polymersolute occupying a volume at fixed temperature and pressure.In the first step,close-packed purecomponents including solvent and polymers with different molar masses or different chain lengths aremixed to form a closed-packed polymer solution.In the second step,the close-packed mixture,con-sidered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a vol-ume dependent on temperature and pressure.Revised Freed’s model developed previously is adoptedfor both steps.Besides pure-component parameters,a binary size parameter c_r and a binary energyparameter ε_(12) are used.They are all temperature dependent.The discrete-multicomponent approach isadopted to derive expressions for chemical potentials,spinodals and critical points.The continuousdistribution function is then used in calculations of moments occurring in those expressions.Computation procedures are established for cloud-point-curve,shadow-curve,spinodal and criti-cal-point calculations using standard distribution or arhitrary distribution on molar mass or on chainlength.Illustrative examples are also presented.

In an internal loop airlift reactor of 55L working volume,the gas-liquid volumetric oxygenmass transfer coefficient k_Lα,gas holdup ε_G and liquid circulation time t_c were measured with the sol-ution of carboxymethyl cellulose(CMC)to simulate the performance of a reactor with highly viscousbroth.Electric conductivity and oxygen probes were used to measure the local gas holdup,liquidcirculation time and oxygen mass transfer coefficient in the individual sections of the reactor(riser,downcomer and the gas-liquid separating section at the top of the reactor)and the total reactor,respectively.The values of k_Lαfor the riser,downcomer and separation sections of the reactor were alsoestimated and compared with that for the total reactor.The results show that,both k_Lαand ε_G in-crease but t_c decreases with increasing gas velocity.Correlations and comparisons with works reportedin the literature are also presented.Data show that the methods developed for k_Lαmeasurements inthe individual section and total reactor are applicable to the studies of internal loop airlift reactors.

In this work,eight commonly used and recently developed cubic EOSs have beenextensively tested for the calculation of thermodynamic properties,including vapor pressure,vaporand liquid densities and heat of vaporization for 26 pure CFCs and their alternatives.The modifiedDu-Guo EOS is recommended for the vapor-liquid equilibria calculations of mixtures for its goodaccuracy.A method for the development of the optimized mixture compositions of CFC alternativeshas been proposed by using minimization of deviations between the vapor pressures of CFC and thealternative mixtures of interest.As examples,two binary mixtures R22-R142b and R22-R152a,and aternary R22-R142b-R152a have been tested.The results show that the vapor pressure of R12 can bewell duplicated by a mixture refrigerant with the optimized composition.On the other hand,thedeviations between the heat of vaporization are somewhat apparent within 10 percent.Moreover,allthe mixtures discussed here are of the characteristics of being near azeotropic,and promisingrefrigerants to replace R12,as far as their thermodynamic properties are concerned.

Here we review a new class of mixing rules that have extended range of mixtures and condi-tions that can now be described by equation of state models.One characteristic of these mixing rulesis that they simultaneously satisfy the boundary conditions of producing a second virial coefficientthat is quadratic in mole fraction,and a free energy of mixing like that of an activity coefficientmodel at high density,though the mixing rule is itself independent of density.We show that usingthis mixing rule,various asymmetric,highly nonideal mixtures can be accurately described.Oneserendipitous result is that the parameters in this mixing rule model are almost independent oftemperature,which allows accurate extrapolations of phase behavior to be made over large ranges oftemperature and pressure.