Shortcut Model

The rigorous model of batch distillation operation involves a solution of several stiff differential equations and the semirigorous model involves a set of highly nonlinear equations. The computational intensity and memory requirement of the problem increase with an increase in the number of plates and components. The computational complexity associated with these models does not allow us to derive global properties such as feasible regions of operation, which are critical for optimization, optimal control, and synthesis problems. Even if such information is available, the computational costs of optimization, optimal control, or synthesis using these models are prohibitive. One way to deal with these problems associated with these models is to develop simphfied models such as the shortcut model. 

At any instant of time. Equations 4.12, 4.13, and the differential material balance equation can be used to calculate the bottom composition of aU the components. The following procedure is then used to calculate the distillate composition at that instant. The procedure is repeated at each time step until the stopping criterion is 

Time implicit model equations for the shortcut method 

The constant Ci in the Hengstebeck-Geddes equation is equivalent to the minimum number of plates, Nmin, in the Fenske equation. At this stage, the variable reflux operating mode has Gi and R, the constant reflux has and Ci, and the optimal reflux has, Ci, and R as unknowns. Summation of distillate compositions can be used to obtain Gi for variable reflux and for both constant reflux and optimal reflux operation, and the FUG equations to obtain R for variable reflux and Gi for both constant reflux and optimal reflux operations. The optimal reflux mode of operation has an additional unknown, R, which is calculated using the concept of optimizing the Hamiltonian, formulated using the different optimal control methods. 

The shortcut model is extremely efficient and reasonably accurate for nearly ideal systems and for column with neghgible holdup. For columns with severe holdup 

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It is important to note that in formulating the problem in this way, it is a linear formulation, guaranteeing (within the bounds of the assumptions made) a global optimum solution. The potential problems associated with nonlinear optimization have been avoided. Even though the models are nonlinear, the problems associated with nonlinear optimization have been avoided. The approach can use either shortcut models or detailed models and the linearity of the optimization is maintained. 

The shortcut model is developed based on the assumption that batch distillation operation can be represented by a series of continuous distillation operation of short duration and employs modified Fenske-Underwood-Gilliland (FUG) shortcut model of continuous distillation (Diwekar and Madhavan, 1991a,b Sundaram and Evans, 1993a,b). Starting with an initial charge (B0, xB0) at time f=fo and for a small interval of time At = t, - t0, the batch distillation column conditions at to and ts is schematically shown in Figure 4.1 (Galindez and Fredenslund, 1988). 

Table 4.2. Simulation by Shortcut Model of Sundaram and Evans (1993a)...

The reactor and separation systems described above can be assembled in a flowsheet In a preliminary simulation, the goal is closing the material balance with recycles. In a first approach shortcut models may be used to simulate the distilla-... 

Rmin and the corresponding number of trays calculated ( 2N J. The shortcut models were replaced by rigorous RADFRAC units, where the reflux and distillate feed ratio were adjusted by means of design specifications, in order to meet the desired separation. The trays were sized using Aspen s facilities. Finally, the dimensions of the reflux drum and column sump were found based on a residence time of 5 min and aspect ratio H D = 2 1. Table 9.7 presents the results of distillation column sizing. 

Because of the low success rate for the commercialization of new processes, we will continue to develop new processes by proceeding through a hierarchy of designs, and therefore we will still need shortcut models. To decide whether simple models are applicable in a particular situation, we can develop a perturbation solution around a complex model, so that the simple model is the generating solution. With this approach, we can establish an error criterion that will indicate the validity of the simple model. 

The second chapter, by Westerberg and Wahnschafft, further develops the synthesis of nonideal separation sequences through the use of physical insights, artificial intelligence, shortcut models, and geometric constructions. Using a... 

The simplest distillation models to set up are the shortcut models. These models use the Fenske-Underwood-Gilliland or Winn-Underwood-Gilliland method to determine the minimum reflux and number of stages or to determine the required reflux given a number of trays or the required number of trays for a given reflux ratio. These methods are described in Chapter 11. The shortcut models can also estimate the condenser and reboiler duties and determine the optimum feed tray. 

The easiest way to use a shortcut distillation model is to start by estimating the minimum reflux and number of stages. The optimum reflux ratio is usually between 1.05 and 1.25 times the minimum reflux ratio, Rmm, so 1.15 x Rmin is often used as an initial estimate. Once the reflux ratio is specified, the number of stages and optimum feed stage can be determined. The shortcut model results can then be used to set up and initialize a rigorous distillation simulation. 

Shortcut models can also be used to initialize fractionation columns (complex distillation columns with multiple products), as described later. 

The main drawback of shortcut models is that they assume constant relative volatility, usually calculated at the feed condition. If there is significant liquid- or vapor-phase nonideality, then constant relative volatility is a very poor assumption and shortcut models should not be used. 

In this example, a column simulation should be set up using a shortcut model. The shortcut model results will be used to initialize a rigorous model in the example that follows. Determine... 

Figure 4.22 shows the rigorous column simulation. UniSim Design allows the designer to enter any two specifications for the column, so instead of entering the reflux ratio as a specification, we can enter the required recoveries and provide the value of reflux ratio found in the shortcut model as an initial estimate, as shown in Figure 4.23. 

The column converges quickly with the good estimate provided from the shortcut model. The column profiles can be checked by selecting the Performance tab in the column environment and then selecting Plots from the menu on the left and Composition from the list of possible plots, as shown in Figure 4.24. This generates composition profiles like those presented in Figures 4.12 to 4.17. 

In the multi-product shortcut model, it is reasonable to consider the top product from section a to be also the bottom product from section a-1 L7 = = 7 ,... 

One approach involves periodic updating of the shortcut model parameters using... 

The shortcut model is developed in terms of reduced parameters that are not strongly dependent on stream compositions, temperature, and pressure. The shortcut model, represented by Equations 12.33 through 12.37b, is solved in conjunction with reduced equations for calculating enthalpies, vapor-liquid equilibrium coefficients, and effective stripping factors based on the rigorous base case. 

The enthalpies, which in the rigorous model are generally calculated by compositional methods appropriate to the mixture under consideration, are expressed in the shortcut model as a linear function of temperature only ... 

Automatic feedback control is the continuous or repetitive modification of some operating parameters based on measurement data. Due to the dynamic nature of the process, the control algorithm is usually also dynamic and has to be designed carefully to avoid instability. We have to distinguish between two types of process control standard and advanced one. Standard controllers have a static algorithm like PID-controller type or cascade mode for the temperature control. Advanced control schemes use a more sophisticated algorithm that could be based on shortcut models or dynamic process models. 

GadaUa, M., Jobson, M. and Smith, R. (2003) Shortcut models for retrofit design of distillation columns. Chemical Engineering Research and Design, 81, 971-986. 

Yang etal. (2014) optimized a water network for total cost, which consists of annualized investment and operating costs here, shortcut models for treatment units are developed instead of using a fixed contaminant removal model. 

Consider the DME Tower, T-201, in the DME process in Appendix B. Simulate this unit using a shortcut model with different liquid-state activity-coefficient models to determine the required number of stages for the reflux ratio and the recoveries shown in Appendix B. Include no corrections for heat of mixing. Then perform a rigorous column simulation to check the distillate purity. Cotipare the results. 

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