Distillation columns liquid dynamics

In a packed distillation column, the vapour stream rises against the downward flow of a liquid reflux, and a state of dynamic equilibrium is set up in a steady state process. 

You may wonder why we would ever be satisfied with anything less than a very accurate integration. The ODEs that make up the mathematical models of most practical chemical engineering systems usually represent a mixture of fast dynamics and slow dynamics. For example, in a distillation column the liquid flow or hydraulic dynamic response occurs fairly rapidly, of the order of a few seconds per tray. The composition dynamics, the rate of change of hquid mole fractions on the trays, are usually much slower—minutes or even hours for columns with many trays. Systems with this mixture of fast and slow ODEs are called stiff systems. 

A distillation process. The behaviour of liquid and vapour streams in any stagewise process can usually be approximated by a number of non-interacting first order systems in series. For example, Rose and Williams021 employed a first order transfer function to represent the dynamics of liquid and vapour flow in a 5-stage continuous distillation column. Thus for stage n in Fig. 7.17 ... 

In what follows, we begin by introducing two examples of process systems with recycle and purge. First, we analyze the case of a reactor with gas effluent connected via a gas recycle stream to a condenser, and a purge stream used to remove the light impurity present in the feed. In the second case, the products of a liquid-phase reactor are separated by a distillation column. The bottoms of the column are recycled to the reactor, and the trace heavy impurity present in the feed stream is removed via a liquid purge stream. We show that, in both cases, the dynamics of the system is modeled by a system of stiff ODEs that can, potentially, exhibit a two-time-scale behavior. 

Lehtonen et al. (1998) considered polyesterification of maleic acid with propylene glycol in an experimental batch reactive distillation system. There were two side reactions in addition to the main esterification reaction. The equipment consists of a 4000 ml batch reactor with a one theoretical plate distillation column and a condenser. The reactions took place in the liquid phase of the reactor. By removing the water by distillation, the reaction equilibrium was shifted to the production of more esters. The reaction temperatures were 150-190° C and the catalyst concentrations were varied between 0.01 and 0.1 mol%. The kinetic and mass transfer parameters were estimated via the experiments. These were then used to develop a full-scale dynamic process model for the system. 

Any of the global Newton methods can be converted to a relaxation form in Ketchum s method by making both the temperatures and the liquid compositions time dependent and by having the time step increase as the solution is approached. The relaxation technique should be applied to difflcult-to-solve systems and the method of Naphtali and Sandholm (42) is best-suited for nonideal mixtures since both the liquid and vapor compositions are included in the independent variables. Drew and Franks (65) presented a Naphtali-Sandholm method for the dynamic simulation of a reactive distillation column but also stated that this method could be used for finding a steady-state solution. 

Let us derive a dynamic model of the process with control structure CS2 included. A rigorous model of the reactor and the two distillation columns would be quite complex and of very high order. Because the dynamics of the liquid-phase reactor are much slower than the dynamics of the separation section in this process, we can develop a simple second-order model by assuming the separation section dynamics are instantaneous. Thus the separation section is always at steady state and is achieving its specified performance, i.e, product and recycle purities are at their setpoints. Given a flowrate F and the composition zA/zB of the reactor effluent stream, the flowrates of the light and heavy recycle streams D, and B-L can be calculated from the algebraic equations... 

Tables 11.5 to 11.7 contain process stream data. These data come from the TMODS dynamic simulation and not from a commercial steady-state simulation package. The corresponding stream numbers are shown on the flowsheet in Fig. 11.1. Tables 11.8 to 11.10 list the process equipment and vessel data. In the simulation, all gas is removed in a component separator prior to the distillation column. This involves the liquid from the separator and the absorber. The gas is sent back and combines with the vapor product from the separator to form the vapor feed to the absorber. Figure 11.2a shows the temperature profile in the azeotropic distillation column.

We have designed and implemented a reactive divided wall distillation column for the production of ethyl acetate from acetic acid and ethanol. Important aspects derived from steady state simulation were considered for instance, a side tank was implemented in order to split the liquid to both sides of the wall and a moving wall inside the column that allows to fix the split of the vapor stream. The dynamic simulations indicate that it is possible to control the composition of the top and bottoms products or two temperatures by manipulating the reflux rate and the heat duty supplied to the reboiler, respectively. The implementation of the reactive divided wall distillation columns takes into account important aspects like process intensification, minimum energy consumption and reduction in Carbon Dioxide emission to the atmosphere. 

The distillation column used in this study is designed to separate a binary mixture of methanol and water, which enters as a feed stream with flow rate F oi and composition Xp between the rectifying and the stripping section, obtaining both a distillate product stream D oi with composition Ad and a bottom product stream 5vo/ with composition Ab. The column consists of 40 bubble cap trays. The overhead vapor is totally condensed in a water cooled condenser (tray 41) which is open at atmospheric pressure. The process inputs that are available for control purposes are the heat input to the boiler Q and the reflux flow rate L oi. Liquid heights in the column bottom and the receiver drum (tray 1) dynamics are not considered for control since flow dynamics are significantly faster than composition dynamics and pressure control is not necessary since the condenser is opened to atmospheric pressure. 

This example is intended to demonstrate the process dynamics methodology as implemented on a single equilibrium stage. A stream of light hydrocarbons is sent to a distillation column where the C3 s and lighter components are separated from the C4 s. Since the feed composition fluctuates substantially, it is sent to a flash drum located upstream of the column in order to attenuate the composition fluctuations and thereby improve the column controllability. The vapor and liquid products from the flash drum are then sent to different trays in the column. 

Many industrial separation processes are based on phase equilibria. By this we mean that the various components of the mixtures present in the (vapor, liquid, solid) phases are in equilibriinn. This is a dynamic equilibriinn and equal mnnbers of components are being transferred continuously from one phase to the other thus the concentrations at equilibriinn do not change. To design the separation processes in industry, e.g., finding the height and number of trays of a distillation column, we need to know the concentrations at equilibrium at any temperature and pressure. 

Dynamic simulation of distillation column needs also tray sizing. We considered sieve trays with 0.4 m diameter of and 0.05 m static liquid height. 

After developing a robust steady-state simulation, the next step is the sizing of units whose dynamics is considered. Typically these are units with a significant material inventory, as flash vessels, distillation columns, and liquid-phase reactors. Heat exchangers, pumps and compressors may be considered in many situations as reaching fast steady state. 

Vertical in-tube condensers are often designed for reflux or knock-back application in reactors or distillation columns. In this case, vapor flow is upward, countercurrent to the liquid flow on the tube wall the vapor shear acts to thicken and retard the drainage of the condensate film, reducing the coefficient. Neither the fluid dynamics nor the heat transfer is well understood in this case, but Soliman, Schuster, and Berenson [/. Heat Transfer, 90, 267-276... 

Figure 21.2 shows the LV configuration for the two-point composition control of a binary distillation column discussed in Example 20.9. After assigning manipulated variables to regulate the vapor and liquid inventories, the boilup rate, V, and the reflux flow rate, L, remain available to control the distillate and bottoms product compositions, and Xg, respectively. To assess the controllability and resiliency of this configuration, the disturbances are taken to be the feed composition, Xp, and the flow rate, F. The column dynamics are approximated by a linear model in transfer function form (Sandelin et al., 1990) ... 

The process dynamics of a few process variables can be characterized as an integrating process response. One example is the response of the liquid level in the bottom of a distillation column when liquid is being pumped out with a centrifugal pump and the liquid flow rate is restricted by an automatic valve after the pump. The column base liquid level may be steady with an initial automatic valve position, and opening the valve to a new position will increase the liquid flow rate. The difference between the two flow rates will be integrated over time as seen by the response in liquid level going down. Eventually, the column base liquid level will go to zero... 

Fig. 10.21. Liquid flow through a distillation column. The equations for the dynamic behavior become therefore ...

In chapter 16 the liquid dynamics for a distillation column were derived. In section 16.8 it was shown that the response of the bottom hold-up to vapor flow changes can be written as ... 

Wang XL, Liu CT, Yuan XG, Yu KT (2004) Computational fluid dynamics simulation of three-dimensional liquid flow and mass transfer on distillation column trays. Ind Eng Chem Res 43(10) 2556-2567... 

The phenomenon of overshoot or inverse response results from the zero in the above example and will not occur for an overdamped second-order transfer function containing two poles but no zero. These features arise from competing dynamic effects that operate on two different time scales (ti and T2 in Example 6.2). For example, an inverse response can occur in a distillation column when the steam pressure to the reboiler is suddenly changed. An increase in steam pressure ultimately will decrease the reboiler level (in the absence of level control) by boihng off more of the liquid. However, the initial effect usually is to increase the amount of frothing on the trays immediately above the reboiler, causing a rapid spillover of liquid from these trays into the reboiler below. This initial increase in reboiler liquid level, is later overwhelmed by a decrease due to the increased vapor boil-up. See Buckley et al. (1985) for a detailed analysis of this phenomenon. 

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