Rj SJVj rf SfLi

vim represents the stoichiometric coefficient of component i in reaction m and sj represents the reaction volume.

9 Modeling of Homogeneous and Heterogeneous Reactive Distillation Processes | 219 The E equations are the phase equilibrium relations

Chemical reaction equilibrium is not considered in many of the early papers because it is more difficult to model. There are, however, some exceptions to this statement and such works are noted in [1].

The S equations are the summation equations

The enthalpy balance is given by

^dp = Vj+iHj+i + Lj-iH^i + FjHf - (1 + rJ)VjHY - (1 + r^Hf - Q (9.6)

The superscripted H are the enthalpies of the appropriate phase. The enthalpy in the time derivative on the left-hand side represents the total enthalpy of the stage but, for the reasons given above, this will normally be the liquid phase enthalpy. Some authors include an additional term in the energy balance for the heat of reaction. However, if the enthalpies are referred to their elemental state then the heat of reaction is accounted for automatically and no separate term is needed.

Under steady-state conditions all of the time derivatives in the above equations are equal to zero.

Some authors include additional equations in their (mostly unsteady-state) models. For example, pressure drop, controller equations, and so on.

Much of the early literature on RD modeling is concerned primarily with the development of methods for solving the steady state EQ stage model. For the most part such methods are more or less straightforward extensions of methods that had been developed for solving conventional distillation problems. The number of examples that illustrate most of the early papers usually is rather limited, both in number as well as in the type of RD process considered (quite often it is an esterification reaction). Only rarely is there any attempt to compare the results of simulations to experimental data. More and more of the more recent modeling studies are carried out using one or other commercial simulation package: Aspen Plus, Pro/II, HYSYS, and SpeedUp are the packages mentioned most often in the published literature [1].

It is well known that real distillation processes do not operate at equilibrium. The conventional way out of this difficulty is to introduce an efficiency factor in to the model equations. There are many different definitions of the stage efficiency; that of Murphree is most often used in EQ stage simulation

where yiL is the average composition of the vapor leaving the tray, yiE is the composition of the vapor entering the tray, and yi is the composition of the vapor in equilibrium with the liquid leaving the tray. Since the mole fractions add to unity, only (n - 1) of the Murphree component efficiencies are independent. For distillation of systems with three or more species, the component efficiencies are almost always unequal to one another and these can routinely assume values greater than unity or less than zero [5].

For packed columns it is common to use the HETP (height equivalent to a theoretical plate). The behavior of HETPs in multi-component mixtures is closely related to the behavior of stage efficiencies.

There are no fundamentally sound methods for estimating either efficiencies or HETPs in RD operations, in which the presence of chemical reactions will have an influence on the component efficiencies. If an efficiency factor of any kind is used it is more often than not treated as an adjustable parameter (or set of parameters) for fitting experimental data. Some authors have obtained good agreement with experimental data in this way [6].

Non-equilibrium Stage Modeling

In recent years the evidence has been growing that distillation (and related) operations are better simulated with non-equilibrium (NEQ) models that take account of mass (and energy) transfer (and sometimes of fluid-flow patterns) in a manner that is more rigorous than is possible with the EQ stage models.

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