Distillation column models

The procedure has been tested primarily on realistic distillation column models. This choice was deliberate because most industrial processes have similar gain, deadtime, and lag transfer functions. Undoubtedly some pathological transfer functions can be found that the procedure cannot handle. But we are interested in a practical engineering tool, not elegant, rigorous all-inclusive mathematical theorems. 

For process optimization problems, the sparse approach has been further developed in studies by Kumar and Lucia (1987), Lucia and Kumar (1988), and Lucia and Xu (1990). Here they formulated a large-scale approach that incorporates indefinite quasi-Newton updates and can be tailored to specific process optimization problems. In the last study they also develop a sparse quadratic programming approach based on indefinite matrix factorizations due to Bunch and Parlett (1971). Also, a trust region strategy is substituted for the line search step mentioned above. This approach was successfully applied to the optimization of several complex distillation column models with up to 200 variables. 

By definition, however, we have 2 -C 1. We can thus proceed with the time-scale decomposition and model reduction of the high-purity distillation column model as outlined in Section 7.3, by defining the stretched, fast time scale 72 = t/e2, in which the model becomes... 

Tung, L.S. and Edgar, T. F., "Development and Reduction of a Multivariable Distillation Column Model with Tray Hydraulics,"... 

Fast and satisfactory mass transfer calculations are necessary since we may have to repeat such calculations many times for a rate-based distillation column model or two-phase flow with mass transfer between the phases in the design and simulation process. The generalized matrix method may be used for multicomponent mass transfer calculations. The generalized matrix method utilizes the Maxwell-Stefan model with the linearized film model for diffusion flux, assuming a constant diffusion coefficient matrix and total concentration in the diffusion region. In an isotropic medium, Fick s law may describe the multicomponent molecular mass transfer at a specified temperature and pressure, assuming independent diffusion of the species in a fluid mixture. Such independent diffusion, however, is only an approximation in the following cases (i) diffusion of a dilute component in a solvent, (ii) diffusion of various components with identical diffusion properties, and (iii) diffusion in a binary mixture. 

This is by no means an exhaustive list of the reasons that computer-based simulations fail. Indeed, in many cases it is a combination of more than one of the above factors that leads to difficulty. In those cases it may be necessary to combine several of the strategies outlined above to solve the simulation problem. Often, however, there is no substitute for trial and error. Haas [chap. 4 in Kister (op. cit.), 1992] offers some additional insight on using simulators to solve distillation column models. 

In Examples 5.1 and 5.2 the output variables coincide with the state variables of the two processes. Consequently, in order to develop the input-output model we need only solve the differential equations of the mass and energy balances. This is not always true. Take as an example the binary distillation column model (Example 4.13 and Figure 4.10). For this system we have ... 

Do the same as in Problem III. 1 for the equations describing the dynamic and steady-state behavior of the binary distillation column modeled in Example 4.13. 

A steady-state Plant Simulation Model of an existing plant helped to calibrate the base-case model on a representative operating point. Some details of an industrial process were skipped, but the omission of these details does influence neither the plantwide material balance nor the process dynamics. The units SO, S6 and S7 may be considered black-boxes. Contrary, SI to S5 are rigorous distillation columns, modelled as sieve trays. In steady-state all the reactors are described by stoichiometric approach, but kinetic models are used for Rl and R4 in dynamic simulation. 

Case-Study for Solver Validation Nonequilibrium Distillation Column Model... 

A distillation column model was chosen to test the various solvers. First-principle distillation models yield a tridiagonal block structure, each block... 

Distillation column models are well known to be nonlinear. This implies that a +10% step perturbation in the feed composition could display different dynamics and nonsymmetrical responses to a -10% step perturbation. Six different input sequences were studied and in each case, the computational time for computing the process transient was recorded, for both the open- and closed-loop configurations. 

In this chapter, we discuss both the steady-state design and the dynamic control of divided-wall columns. Aspen simulation tools are used. The industrially important ternary separation of benzene, toluene, and o-xylene (BTX) is used as anumerical example. The normal boiling points of these three components are 353, 385, and 419 K, respectively, so the separation is a fairly easy one with relative volatilities aa/ax/ax of about 1. I2.2I. The feed conditions are a flow rate of 3600 kmol/h, a composition of 30/30/40 mol% B/T/X, and a temperature of 358 K. Chao-Seader physical properties are used in the Aspen simulations. Product purities are 99mol%. All simulations use rigorous distillation column models in Aspen Plus. 

Steady-state simulations are performed in Aspen Plus using Choa-Seader physical properties. Dynamic simulations are performed in Aspen Dynamic using the rigorous RadFrac distillation column model. 

The general distillation column model deals with the modeling of a tray that can also have liquid and vapor feeds and spills (Figure 14.1). 

It is standard practice in the modeling of distillation columns to assume that the liquid is incompressible and perfectly mixed on the trays, and that the vapor and liquid have the same temperature on the tray (thermal equilibrium), whereas the phases could be considered nonequilibrium and some vapor-phase efficiency is sometimes adopted in such cases (e.g., Murphree efficiency). Beyond these possible variants, the basic distillation column model can be reduced to total... 

The regenerator separates the ammonia and water so the top product is almost pure ammonia, which acts as refrigerant, and the bottom product is an ammonia/water mixture which is recycled to the absorber. The regenerator has been simulated with a distillation column model so the duty taken out of the column condenser is used as a heat source in COND ensuring there is sufficient temperature difference. The energy is supplied to the regenerator as saturated steam. 

Luyben and Vinante Kern. Teollisuus, 29, 499 (1972)) developed a distillation column model relating temperatures on the 4th and 17th trays from the bottom of the column (T4, Tij) to the reflux ratio R and the steam flow rate to the reboiler 5 ... 

For the Wood-Berry distillation column model in Example 18.1 ... 

In Section 20.6.1, MPC was applied to the Wood-Berry distillation column model. A MATLAB program for this example and constrained MPC is shown in Table E20.9. The design parameters have the base case values (Case B... 

LI Energy Balance and Parameters for the Reactor/Distillation Column Model (Appendix G)... 

PARAMETERS FOR THE REACTOR/ DISTILLATION COLUMN MODEL (APPENDIX G)... 

Pairing comparison for cases 4, 10, and 18 At this point, the steady-state gain between the distillate flow rate and the distillate composition, gn, will be calculated using the steady-state distillation column model. Perform a step input in the distillate flow rate from 30 to 40 kmol h . Change one of the column specifications from reflux ratio to reboiler duty, specifying a reboiler duty equal to the base case steady-state solution of 4.2 x 10 kJ h . The new specifications for the column should be the same as those given in Table 9.6. 

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