Distillation dynamic model

C. Noeres, Catalytic Distillation Dynamic Modeling, Simulation and Experimental Validation, Ph.D. Thesis, University of Dortmund, Germany, 2002. 

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. 

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. 

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)... 

S. Hernandez and A. Jimenez. Design of optimal thermally - coupled distillation systems using a dynamic model. Trans. IchemE, 74(Part A) 357-362, 1996. 

Schneider R, Noeres C, Kreul LU, Gorak A. Dynamic modeling and simulation of reactive batch distillation. Computers Chem Eng 1999 23 S423-S426. 

The advanced process control strategies that are most applicable to the optimization of the distillation process are usually based on white-box modeling, where the theoretical dynamic models are derived on the basis of the mass, energy, and momentum balances of this well-understood process. Although the optimization techniques described here can improve productivity and profitability by 25%, this goal will only be achieved if the distillation process is treated as a single and integrated unit operation and the variables, such as flows, levels, pressures, etc., become only constraints, and the controlled and optimized variables are productivity and profitability. 

A. Kienle, Low-order dynamic models for ideal multicomponent distillation processes using nonlinear wave propagation theory. Chem. 

The optimal control of a process can be defined as a control sequence in time, which when applied to the process over a specified control interval, will cause it to operate in some optimal manner. The criterion for optimality is defined in terms of an objective function and constraints and the process is characterised by a dynamic model. The optimality criterion in batch distillation may have a number of forms, maximising a profit function, maximising the amount of product, minimising the batch time, etc. subject to any constraints on the system. The most common constraints in batch distillation are on the amount and on the purity of the product at the end of the process or at some intermediate point in time. The most common control variable of the process is the reflux ratio for a conventional column and reboil ratio for an inverted column and both for an MVC column. 

Table 6.7. Results for Ternary Distillation (Detailed Dynamic Model)"1.

In this separation, there are 4 distillation tasks (NT-4), producing 3 main product states MP= D1, D2, Bf) and 2 off-cut states OP= Rl, R2 from a feed mixture EF= FO. There are a total of 9 possible outer decision variables. Of these, the key component purities of the main-cuts and of the final bottom product are set to the values given by Nad and Spiegel (1987). Additional specification of the recovery of component 1 in Task 2 results in a total of 5 decision variables to be optimised in the outer level optimisation problem. The detailed dynamic model (Type IV-CMH) of Mujtaba and Macchietto (1993) was used here with non-ideal thermodynamics described by the Soave-Redlich-Kwong (SRK) equation of state. Two time intervals for the reflux ratio in Tasks 1 and 3 and 1 interval for Tasks 2 and 4 are used. This gives a total of 12 (6 reflux levels and 6 switching times) inner loop optimisation variables to be optimised. The input data, problem specifications and cost coefficients are given in Table 7.1. 

In this problem, there are 3 outer loop decision variables, N and the recovery of component 1 from each mixture (Re1 D1B0, Re D2,BO)- Two time intervals for reflux ratio were used for each distillation task giving 4 optimisation variables in each inner loop optimisation making a total of 8 inner loop optimisation variables. A series of problems was solved using different allocation time to each mixture, to show that the optimal design and operation are indeed affected by such allocation. A simple dynamic model (Type III) was used based on constant relative volatilities but incorporating detailed plate-to-plate calculations (Mujtaba and Macchietto, 1993 Mujtaba, 1997). The input data are given in Table 7.3. 

In this section optimal operation problem of BREAD processes is presented as a proper dynamic optimisation problem incorporating a detailed dynamic model (Type V- CMH). The problem formulation and solution exploit the methods developed for non-reactive batch distillation by Mujtaba and Macchietto (1991, 1993,1998). These methods are also discussed in Chapters 5 and 6. 

The four experiments done previously with Rnp (= 0.5, 1, 3, 4) were used to train the neural network and the experiment with / exp = 2 was used to validate the system. Dynamic models of process-model mismatches for three state variables (i.e. X) of the system are considered here. They are the instant distillate composition (xD), accumulated distillate composition (xa) and the amount of distillate (Ha). The inputs and outputs of the network are as in Figure 12.2. A multilayered feed forward network, which is trained with the back propagation method using a momentum term as well as an adaptive learning rate to speed up the rate of convergence, is used in this work. The error between the actual mismatch (obtained from simulation and experiments) and that predicted by the network is used as the error signal to train the network as described earlier. 

Figure 12.6 also shows the instant distillate composition profile for / exp = 2 (which is used to validate the network) using the simple model coupled with the dynamic model for the process-model mismatches (curve C). The predicted profile (curve C) shows very good agreement with the experimental profile (curve B). Similar agreements have been obtained for the accumulated distillate amount and composition profiles (Greaves, 2003). 

The digital simulation of an extractive distillation column was performed in order to understand the dynamic behaviour of the system. Based on this results a considerably simplified dynamic model of sufficient accuracy could be developed. This model was employed in the design of a state observer and of an optimal control. After implementation in the large scale plant this new control system has proved to be highly efficient and reliable. 

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... 

Divided Wall Distillation Column Dynamic Modeling And Control... 

Keywords divided wall distillation column, dynamic modeling, optimal startup control... 

Distillation control schemes may be analyzed either on a steady-stale (sensitivity analysis) or on a dynamic basis. The latter requires a dynamic model that takes into account the dynamic response of the column and the control loope. An example of a dynamic model is described by McCune and Gailier,6 but il should be apparent from the material presented enrlier that the holdup characteristics of distillation columa devices can vary widely, and snch variation should be accommodated by the model. The development of the naw high-efficiency packings has caused a new look at the system dynamics when the liquid holdup in the column is quite low, and thus the existing models for trays may not be adjustable to application to packings. The use of a tray-type dynamic model is described in the article by Gailier and McCune 7 so work to date has been reported for packed column dynamic models. 

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 dynamic model of a distillation column can be assembled from simpler units, as trays, heat exchangers (condenser, reboiler), reflux drum, valves and pumps (Fig. 4.5). Tray modelling has to answer two issues (1) accurate description of material and energy holdup, and (2) accurate pressure drop calculation. 

Figure 4.5 Dynamic model for a distillation column Tray modelling...

Consider the separation of a benzene/toluene mixture by distillation in a tray column. Study the building of a dynamic model and explore the behaviour of the separation without purity control. 

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