e-book Distillation theory and its application to optimal design of separation units

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About This Item We aim to show you accurate product information. Manufacturers, suppliers and others provide what you see here, and we have not verified it. Pinch point curves are used in heterogeneous systems along with residue curves and phase equilibrium analysis in order to evaluate process feasibility employing the operation leaves Castillo et al.

Phase equilibrium calculation for heterogeneous systems used to be performed using material stability analysis. In this work, an alternative and less complex strategy, based on the knowledge of the partial miscibility region, is presented. Using the tools abovementioned altogether, a method able to assess the process feasibility in single-feed heterogeneous distillation becomes a practical alternative for the analysis of separation systems with partial miscibility.

In addition to the assumptions made in the BVM for homogeneous columns, the model for heterogeneous systems is based on the fact the column is operated within the homogeneous region. Therefore, there is only one heterogeneous stage in the unit, the decanter. A strategy that guarantees that the separation unit operates in the homogeneous region was developed by Pham et al.

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Since the column operates in the homogeneous region, its equations are the same as those for homogeneous columns. The difference between the BVM for homogeneous and heterogeneous systems is the initialization process that must be carried out in the rectifying section for heterogeneous systems in order to ensure that the column will operate in the homogeneous region. On the other hand, constant molar flow CMO assumption was taken into account; although this assumption is not accurate for highly nonideal mixtures, it was used in this work as the main focus is a simplified methodology to evaluate the process feasibility.

Further, the geometrical features presented by heterogeneous systems are another important focus in this work. To illustrate model variables, a schematic for the column is shown in Figure 1. Therefore, the equations for the rectifying and stripping sections are the same as those for single feed homogeneous columns:. In addition to the section column equations, the reflux r and reboil s ratios are related in the same way as those of the homogeneous columns Levy et al.

Although in this model equations for both heterogeneous and homogeneous columns are the same, profiles calculation is different, especially for the rectifying section where the initialization process requires the knowledge of thermodynamic and topologic mixture behavior. Hence, it is necessary to determine accurately the partial miscibility region and the composition of the azeotropes.

As a result, a new variable, p, must be defined in order to calculate the relative proportion of these two liquid phases in the decanter. The relative proportion can be obtained through the lever rule, as follows Pham and Doherty, b :. This condition implies that the distillate stream is only a fraction of the entrainer-lean phase, and the reflux stream includes all the entrainer-rich phase plus the remaining fraction of the entrainer-lean phase. Therefore, this policy allows manipulating the reflux ratio keeping the distillate composition. In this case, the reflux rate is less than the condensation rate of entrainer-rich phase, i.

In addition, this policy requires that the distillate rate be greater than condensation rate of entrainer-lean phase; thus, the distillate stream consists of all the entrainer-lean phase plus the balance of the entrainer-rich phase. Accordingly, there is a unique value of r that satisfy the column mass balances.

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One of the main challenges in heterogeneous distillation is to determine the number of phases under specific conditions of temperature, pressure and composition. Due to the changes in composition throughout the distillation column, it is necessary to verify the number of phases in equilibrium in each column stage. Robust algorithms such as tangent plane criteria Michelsen, have been proposed to determine the number of phases present in a mixture.

A shortcoming of this method and in general of all methods based on Gibbs free energy minimization is the long computation time as well as the complex programming.

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Besides, after the material stability analysis is performed, it is required to calculate the phase equilibrium with the predicted number of phases. Due to the fact that stability analysis adds complexity and computation time, a simpler strategy to solve the phase equilibrium calculation is presented. The strategy is based on the knowledge of heterogeneous regions.

For this purpose, it is necessary to calculate the binodal curve that delimits homogeneous and heterogeneous regions. Variables are grouped in a vector:. The solution determines the VLL binodal along with the vapor line as shown in Figure 2. Using the knowledge on the heterogeneous region, it is possible to determine the number of phases present in each column stage.

Therefore, when distillation profiles, residue and pinch curves are calculated, the model for phase equilibrium calculation must change depending on the region that the profile is crossing. Furthermore, the methodology calculates the complete vapor line that, as considered later, is essential for the design process. After the calculation of the binodal curve, phase equilibrium calculation must be performed to determine the composition of each phase.

For VLLE calculation in heterogeneous systems, a modification of the Rachford and Rice algorithm for vapor-liquid calculations Henley and Seader, was employed, which is based on the principle of chemical potential equality at the equilibrium state; thus, at the condition of VLLE, three phases coexist V: vapor, : liquids and the chemical potential constraint is:. As mentioned above, the calculation of rectifying profiles requires a different initialization process for heterogeneous columns to guarantee the distillation column will operate in the homogeneous region. The knowledge of partial miscibility region is essential in this process step.

For instance, the thermodynamic description for water-acetic acid-amyl acetate system was carried out and is shown in Figure 2. This calculation was performed in Matlab, using the NRTL model Renon and Prausnitz, for liquid phase and the Marek's method Sebastiani and Lacquaniti, for vapor phase, in order to take into account the acetic acid dimerization.

In this system, the mixture to be separated is water-acetic acid, and amyl acetate is considered as entrai-ner in order to achieve the required acid purity. In addition to the partial miscibility region, the vapor line is important for the design of heterogeneous columns due to its thermodynamic implication: each point on the vapor line is in vapor-liquid-liquid equilibrium VLLE. However, the column model performs calculations in distillation columns in which the only heterogeneous stage is the decanter. As a result, the overhead vapor y N should be chosen as a point inside the miscibility region, but not on the vapor line.

Therefore, the composition of the distillate x D is equal to the entrainer-lean phase x lean. Besides, the selection of the overhead vapor y N must be carefully carried out in order to guarantee the separation feasibility. As has been described so far, initialization of rectifying profiles requires to specify some variables and to know the thermodynamic features of the mixture.

The first step is based on the knowledge of the miscibility region and involves the selection of a tie line for the decanter. The second step requires the specification of the overall material balance line, which is determined by x D , F and x B. In the third step, the overhead vapor composition y N is specified, its composition must be on the tie line but not on the vapor line.

Furthermore, y N must be located in the same distillation region of x B , which guarantees that rectifying and stripping profiles can intersect each other and hence, the distillation process becomes feasible. This consideration is irrelevant for systems like water-acetic acid-amyl acetate where the topologic thermodynamic points out the absence of distillation boundaries Figure 2. However, in systems with distillation boundaries, e. Finally, the design specifications are fulfilled when the reboil ratio s is calculated from Equation 4. In this way, after the process to determine the initial point in each profile is completed, the calculations for both rectifying and stripping profiles are estimated with the same methodology used for single feed homogeneous columns Van Dongen and Doherty , Levy et al.

After that, rectifying profile Equation 2 is solved until the profile reaches its fixed point. It is important to mention that the calculation of the rectifying profile implies the calculation of the liquid-vapor equilibrium at each point on the profile. For the stripping profile, the calculation is the same as in homogeneous systems. The design specifications for water-acetic acid-amyl acetate along with its topological features are depicted in Figure 3. Operation leaves are formed by pinch point curves and residue curves.

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The operation leaf delimits all possible operation profiles after specification of feed, and distillate and bottom products. Each column section has one operation leaf that should overlap the other section leaf for the design to be feasible Castillo et al. Therefore, to construct an operation leaf is necessary to specify one product either bottoms or distillate, and feed composition.

Using continuation methods along with the procedure to determine the number of phases it was possible to develop a method for calculating these curves and tracing out operation leaves in heterogeneous systems. Calculation methodology is similar to that for homogeneous systems; main differences are based on the complexity of the correct description of phase equilibrium and the number of phases.

The system of equations that describe a pinch point in a heterogeneous region is bigger than that for homogeneous system. The system of equations for the stripping section is shown as follows:. Equations 16 and 17 represent the liquid-liquid equilibrium. The remaining equations describe column section profile, vapor-liquid equilibrium and molar fraction summation. For the rectifying section, Equation 14 should be changed by its respective expression obtained from Equation 2.

Distillation Theory and Its Application to Optimal Design of Separation Units

Furthermore, it is important to mention that the equations described above must be only used in the heterogeneous region. Before applying the continuation method, the equations and variables are grouped as follows:. The knowledge of the heterogeneous region allows identifying the transition of phases, i.

In this point, the calculation algorithm should be changed and the next pinch point is calculated using the algorithm for homogeneous systems. Stripping and rectifying curves are traced out until they reach constant composition points. These points are the initial values to calculate the residue curves. For residue curves calculation, the algorithm presented by Pham and Doherty a with the proposed methodology to determine the heterogeneous region was employed.

The equation for residue curves is shown below:. When Equation 23 is numerically integrated, heterogeneous residue curves are obtained.