Distillation columns column dynamics

In an ideal binary distillation column the dynamics of each tray can be described by first-order systems. Are these capacities interacting or not What general types of responses would you expect for the overhead and bottoms compositions to a step change in the feed composition ... 

Distillation columns are controlled by hand or automatically. The parameters that must be controlled are (/) the overall mass balance, (2) the overall enthalpy balance, and (J) the column operating pressure. Modem control systems are designed to control both the static and dynamic column and system variables. For an in-depth discussion, see References 101—104. 

Whereas there is extensive Hterature on design methods for azeotropic and extractive distillation, much less has been pubUshed on operabiUty and control. It is, however, widely recognized that azeotropic distillation columns are difficult to operate and control because these columns exhibit complex dynamic behavior and parametric sensitivity (2—11). In contrast, extractive distillations do not exhibit such complex behavior and even highly optimized columns are no more difficult to control than ordinary distillation columns producing high purity products (12). 

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 hquid flow on the tube wall the vapor shear ac4s to tliicken 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 Sohman, Schuster, and Berenson [J. Heat Transfer, 90, 267-276... 

FIG. 13-107 Binary distiUatio n column dynamic distillation of ideal binary mixture. 

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. 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

The state variables are the minimal set of dependent variables that are needed in order to describe fully the state of the system. The output vector represents normally a subset of the state variables or combinations of them that are measured. For example, if we consider the dynamics of a distillation column, in order to describe the condition of the column at any point in time we need to know the prevailing temperature and concentrations at each tray (the state variables). On the other hand, typically very few variables are measured, e.g., the concentration at the top and bottom of the column, the temperature in a few trays and in some occasions the concentrations at a particular tray where a side stream is taken. In other words, for this case the observation matrix C will have zeros everywhere except in very few locations where there will be 1 s indicating which state variables are being measured. 

In the distillation column example, the manipulated variables correspond to all the process parameters that affect its dynamic behavior and they are normally set by the operator, for example, reflux ratio, column pressure, feed rate, etc. These variables could be constant or time varying. In both cases however, it is assumed that their values are known precisely. 

While we laud the virtue of dynamic modeling, we will not duphcate the introduction of basic conservation equations. It is important to recognize that all of the processes that we want to control, e.g. bioieactor, distillation column, flow rate in a pipe, a drag delivery system, etc., are what we have learned in other engineering classes. The so-called model equations are conservation equations in heat, mass, and momentum. We need force balance in mechanical devices, and in electrical engineering, we consider circuits analysis. The difference between what we now use in control and what we are more accustomed to is that control problems are transient in nature. Accordingly, we include the time derivative (also called accumulation) term in our balance (model) equations. 

Mutalib MIA and Smith R (1998) Operation and Control of Dividing Wall Distillation Columns Part I Degrees of Freedom and Dynamic Simulation, Trans IChemE, 76A 308. 

Procedure Cholinesterase activity in analyzed tissue or the matrix (biotest with immobilized AChE) is determined in the incubation media [consisting of substrate ATCh - 34 mmol maleate buffer 0.1 M, pH = 6.0- 6.5 ml sodium citrate 0.1 M - 0.5 ml CuS045H20 0.03M -1.0 ml distilled H20 (or inhibitor in variant with toxin analyzed) -1.0 ml potassium ferricyanide 0.005 M -1 ml.] Volume of incubation media in one test - 400 mcl. As a blank (control sample), a treatment of the exposure without the substrate is used. If inhibitory effects of allelochemical (or any toxin) are analyzed, before the substrate addition the sample was preliminary exposed to allelochemical inhibitor. Two methods for the AChE-biotests may be recommended (i) in microcells ( stationary conditions ) and (ii) in flowing columns-reactors ( dynamic conditions ). 

Other synonyms for steady state are time-invariant, static, or stationary. These terms refer to a process in which the values of the dependent variables remain constant with respect to time. Unsteady state processes are also called nonsteady state, transient, or dynamic and represent the situation when the process-dependent variables change with time. A typical example of an unsteady state process is the operation of a batch distillation column, which would exhibit a time-varying product composition. A transient model reduces to a steady state model when d/dt = 0. Most optimization problems treated in this book are based on steady state models. Optimization problems involving dynamic models usually pertain to optimal control or real-time optimization problems (see Chapter 16)... 

Skogestad, S. Dynamic and Control of Distillation Columns—A Critical Survey. Modeling Identification Control 18 177-217 (1997). 

In many operations, for instance in a distillation column, it is necessary to understand the fluid dynamics of the unit, as well as the heat and mass transfer relationships. These factors are frequently interdependent in a complex manner, and it is essential to consider the individual contributions of each of the mechanisms. Again, in a chemical reaction the final rate of the process may be governed either by a heat transfer process or by the chemical kinetics, and it is essential to decide which is the controlling factor this problem is discussed in Volume 3, which deals with both chemical and biochemical reactions and their control. 

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. 

Example The location of the best temperature-control tray in a distillation column is a popular subject in the process-control literature. Ideally, the best location for controlling distillate composition xa with reflux flow by using a tray temperature would be at the top of the column for a binary system. See Fig. 8.9o. This is desirable dynamically because it keeps the measurement lags as small as possible. It is also desirable from a steadystate standpoint because it keeps the distillate composition constant at steadystate in a constant pressure, binary system. Holding a temperature on a tray farther down in the column does not guarantee that x will be constant, particularly when feed composition changes occur. 

To illustrate the concept, consider a single distillation column with distillate and bottoms products. To produce these products while using the minimum amount of energy, the compositions of both products should be controlled at their specifications. Figure 8.13u shows a dual composition control system. The disadvantages of this structure arc (1) two composition analyzers are required, (2) the instrumentation is more complex, and (3) there may be dynamic interaction problems since the two loops are interacting. This system may be difficult to design and to tune. 

Figure 11.5a shows a typical implementation of feedforward controller. A distillation column provides the specific example. Steam flow to the reboiler is ratioed to the feed flow rate. The feedforward controller gain is set in the ratio device. The dynamic elements of the feedforward controller are provided by the lead-lag unit. 

The distillation column used in this example separated a binary mixture of propylene and propane. Because of the low relative volatility and large number of trays, the dominant time constant is very large (500 minutes). Despite this large time constant, a sampling period of 9.6 minutes gave poor results. The period had to be reduced to 1,8 minutes to get good identification, both dynamic and steadystate gain. 

M.I. Abdul-Mutalib and R. Smith. Operation and control of dividing wall distillation columns. Part I Degrees of freedom and dynamic simulation. Trans. IchemE, 76(Part A) 308-318, f998. 

De Wolf, S. Jager, J. Kramer, H.J.M. Eek, R. Bosgra, O.H. Proc. IFAC Symp. on Dynamics and Control of Chemical Reactors. Distillation Columns and Batch Processes. Maastricht, The Netherlands, I989. 

Operation of a batch distillation is an unsteady state process whose mathematical formulation is in terms of differential equations since the compositions in the still and of the holdups on individual trays change with time. This problem and methods of solution are treated at length in the literature, for instance, by Holland and Liapis (Computer Methods for Solving Dynamic Separation Problems, 1983, pp. 177-213). In the present section, a simplified analysis will be made of batch distillation of binary mixtures in columns with negligible holdup on the trays. Two principal modes of operating batch distillation columns may be employed ... 

Balchen. J.G. Dynamics and Control of Chetmcal Reactors, Distillation Columns, and Batch Processes Selected Pafwrs from the 3rd fFAC Symposium. Maryland. U.S.A., Elsevier Science, New York, NY. 1993. 

The degree of variation around the steady state to which systems can be subjected such that it is possible to approximate them by using linear relationships (e.g. as in equation 7.24) differs from system to system. The dynamics of a highly non-linear reactor might be described satisfactorily by a linear analysis for perturbations of up to 3 per centother hand the dynamics of some distillation columns have been shown to remain reasonably linear in the face of variations of 25 per cent in some process variables00. 

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 ... 

Many chemical and biological processes are multistage. Multistage processes include absorption towers, distillation columns, and batteries of continuous stirred tank reactors (CSTRs). These processes may be either cocurrent or countercurrent. The steady state of a multistage process is usually described by a set of linear equations that can be treated via matrices. On the other hand, the unsteady-state dynamic behavior of a multistage process is usually described by a set of ordinary differential equations that gives rise to a matrix differential equation. 

Dow Corning has reported monitoring the concentration of a chlorosilane distillation stream with Raman spectroscopy. On-line GC was used, but the 20-60-minute response time proved too slow to detect important column dynamics. The on-line GCs also required extensive maintenance due to the hydrochloric acid in the stream. The Raman system is used to predict the concentration of nine species. Many could not be detected or distinguished by NIR.69... 

PID controller tunings for this model have been given by a number of researchers [9-13], Chen and Fruehauf [9] have given an industrial example of the level control in a distillation column where the open loop dynamics follows the IPTD model with parameters kp = 0.2 and d = 1A min. 

Ranzi E, Rovaglio M, Faravelli T, Biardi G. Role of energy balances in dynamic simulation of multicomponent distillation columns. Computers Chem Eng 1988 ... 

The dynamic behavior of processes (pipe-vessel combinations, heat exchangers, transport pipelines, furnaces, boilers, pumps, compressors, turbines, and distillation columns) can be described using simplified models composed of process gains, dead times, and process dynamics. 

Finally, nonlinear wave can also be used for nonlinear model reduction for applications in advanced, nonlinear model-based control. Successful applications were reported for nonreactive distillation processes with moderately nonideal mixtures [21]. For this class of mixtures the column dynamics is entirely governed by constant pattern waves, as explained above. The approach is based on a wave function which can be used for the approximation of the concentration profiles inside the column. The wave function can be derived from analytical solutions of the corresponding wave equations for some simple limiting cases. It is given by... 

Y.-L Hwang, On the nonlinear wave theory for dynamics of binary distillation columns. 

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. 

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