Distillation Column
This example shows how to make a simple model for a binary distillation process by combining functionality in the Thermodynamics feature and the Transport of concentrated species interface. In this model the separation of a nonideal mixture of ethanol and water is studied. The required equilibrium relationship is generated using the Equilibrium Calculation functionality available when using the Thermodynamics feature. The model is used to find the optimal design of the column in terms of the length of the stripping and rectifying sections to meet a set of specified distillate and bottoms compositions.
Distillation Background
Distillation is the most prominent separation method in chemical process industries. In a typical application, as shown in Figure 12, a liquid mixture of two or more species is fed into a tall cylindrical column somewhere near the middle. For purpose of illustration, this example is limited to two species. There is a heat source in a collecting vessel or column section at the bottom of the column called the reboiler. Liquid from the feed runs down the column and is heated and partially vaporized in the reboiler. Normally, some of the liquid in the reboiler is continuously removed as the bottoms product. The vapor generated in the reboiler rises up toward the top of the column where it is condensed in an externally cooled vessel or column section called the condenser. Some of the condensed liquid in the condenser is normally removed as the overhead product or distillate. The remainder of the condensed liquid is sent back down the column as reflux. With heat added at the bottom and removed at the top, the temperature decreases from bottom to top of the column that operates at nearly constant pressure.
Figure 12: Packed distillation column schematic.
The separation process inside the column is governed by the difference in tendency to vaporize, or volatility, of two species. Generally, the species with the lower boiling point will vaporize easier and concentrate in the vapor phase. As the liquid flowing down the column contacts the vapor rising up, mass transfer occurs between the phases as each species seeks to reach chemical equilibrium. The equilibrium condition dictates the relative amounts, or composition, of each species that would be in each phase at equilibrium at a certain temperature and pressure. The vapor phase will have a higher composition of the more volatile species at every point in the column. As the vapor phase rises up the column, the equilibrium composition shifts (with decreasing temperature) to drive the vapor phase toward purity in the more volatile component. Similarly, the liquid phase flowing down the column is driven toward purity in the less volatile component.
Inside, the column will have one of two types of internals designed to provide intimate contact between the vapor and liquid phases and facilitate their approach to equilibrium. The column either contains a series of stages or is filled with a specialized packing. A staged column contains a number of horizontal plates or trays with liquid flowing across while vapor bubbles through. In an idealized column, the liquid flowing down after crossing a stage will be in equilibrium with the vapor rising up from that stage. A packed column will contain one or more sections of random or structured packing material made of metal, ceramic, or plastic in specialized shapes. Void spaces inside and between the packing particles allow for high fluid flow rates with limited pressure drop. Ideally, the packing is wet with a thin film of liquid with vapor flowing past the liquid film with a high surface area to promote mass transfer between the phases.
In practice, chemical equilibrium will not be reached due to mass transfer limitations, and with finite column height the distillate and bottoms products will not be completely pure. More stages or a larger height of packing in a column will provide higher purity products but will require a taller, more expensive, column. For a given column height, a higher reflux will provide higher product purity but will yield a lower distillate product flow rate and will require a larger diameter column to accommodate the increased internal flow.
Model Definition
As in virtually all chemical processes, analysis and design of a distillation column requires a combination of mass balances, energy balances, equilibrium relationships, and rate equations. This example considers binary distillation with a saturated liquid feed in a packed column and makes use of two common simplifying assumptions:
1
The molar heats of vaporization of the feed species are equal
2
The heat loss from the column and other heat effects, like heat of solution, are negligible.
These assumptions make it possible to model the process without considering heat effects or energy balances. They also dictate that the liquid and vapor molar flow rates are constant in each column section, the so-called stripping section below the feed and the so called rectifying section above the feed location. That is, for every mole of liquid evaporated within the column, a mole of vapor is condensed. This assumption is known as constant molar overflow and is not as unrealistic in practice as it may seem (Ref. 1).
Considering a saturated liquid feed means that all of the feed joins the liquid in the stripping section such that
(6)
Here Ls is the liquid flow rate from the stripping section into the reboiler, Lr is the liquid flow rate from the condenser into the rectifying section, and F the feed flow rate. Other feed conditions would alter the analysis slightly since some or all of the feed would join the vapor phase in the rectifying section.
The column design task considered here is to determine the height of packing and feed location required to separate a feed of known flow rate and composition into distillate and bottom streams of specified purity. Additional process parameters to be specified include the boil-up rate, or vapor molar flow rate within the column, and the overall gas phase mass transfer coefficient, Kya. In practice, the boil-up rate will depend on the heat input to the reboiler. Specify the boil-up rate as
(7)
That is, the vapor flow rate from the reboiler into the stripping section equals the vapor flow rate into the condenser.
Overall and species mass balances make it possible to calculate the molar flow rates of bottoms, B, and distillate, D, by solving two equations in the two unknowns:
(8)
(9)
where xf, xb, and xd are mole fractions of the more volatile species in the feed, bottoms, and distillate streams, respectively.
The internal liquid flows are then found from:
(10)
along with Equation 6. All of these flow rates are found in the model by algebraic manipulation in the Parameters node under Global Definitions in the Model Builder.
Neglecting any variation in the radial direction, model the distillation column in one dimension using two line segments (see Figure 13). One segment of length, Hs, represents the stripping section, while the other segment of length Hr, represents the rectifying section. The goal of the model is to determine the values of Hs and Hr that provide the specified bottoms and distillate compositions. Assume values of Hs and H = Hs + Hr, solve for the compositions in the vapor and liquid phases at every point in the column, and iterate until the outlet compositions match the design specifications.
Figure 13: One-dimensional model geometry including the boundary conditions for the mole fraction of ethanol in each phase.
To solve for the mass transfer, use two instances of the Transport of Concentrated Species interface, one for the vapor phase and one for the liquid phase. The mass transfer between the phases is accounted for as using a Reacting Source node where the source rate is defined as
(11)
where Kya is an overall gas phase mass transfer coefficient in mol/(m3·s), ye1 is the mole fraction of the more volatile species that would be reached at equilibrium, and M1 is the molar mass of the more volatile species. This provides a mass transfer rate of the more volatile species from the liquid phase to the vapor phase. A similar expression with opposite sign describes the simultaneous mass transfer of the less volatile component in accordance with our constant molar overflow assumption. The value of ye1 at each point is found using an Equilibrium Calculation node added in the Thermodynamic System under Thermodynamics. The mass transfer coefficient will depend on the fluid and packing properties and the local fluid velocities and may vary along the height of the column. Correlations for Kya are available in the literature. In this example, a constant value of Kya = 75 mol/(m3·s) is used for illustrative purposes.
The molar flows of liquid and vapor within the column are accounted for by specifying the velocity in each phase. This lumped parameter model based on an overall gas phase mass transfer coefficient uses an equivalent gas phase velocity for the liquid phase to put them on the same basis. This is essentially a form of scaling the liquid phase velocity to be on the same order of magnitude as the gas phase velocity. To convert a molar flow rate, Lr for example, to a velocity, uLr, assume a column diameter, determine a cross-sectional area, A, and assume ideal gas molar volume at standard conditions for both phases:
(12)
The boundary conditions for this mass transfer problem are shown in Figure 13. You specify the mass fraction of the bottoms in the vapor phase and the mass fraction of the feed and distillate in the liquid phase. Hs and H are varied by guess and check or using a parameter sweep until a solution is found where the liquid phase bottoms composition equals that specified in the vapor phase, and the vapor phase distillate composition equals that specified in the liquid phase.
Results and Discussion
Figure 14 shows the results of an equilibrium calculation, available in Thermodynamics, generating an xy diagram for the ethanol–water system at 1 atm pressure. The NRTL thermodynamic model is used for the liquid phase, while an ideal gas assumption is used for the gas phase.
The calculated results for vapor and liquid phase compositions inside a column designed to separate a 50 mole percent mixture of ethanol in water to yield a distillate of 85 mole percent ethanol and a bottoms product of 5 mole percent ethanol are shown in Figure 15. The required heights found by trial are Hs = 1.2 m and H = 5.7 m. In the model a Parametric Sweep study step was used to compute the column composition when varying the stripping section length. The design criteria to be met in this case is that the ethanol mole fraction in the vapor and liquid phase should coincide at the bottom. Using a section length less than about 1.2 m, the liquid phase mole fraction exiting the column is higher than that of the vapor phase. Correspondingly, for a section longer than 1.2 m, the liquid phase mole fraction is lower than that of the vapor phase. The same analysis can be made for the top of the column. The optimal column height is found when the phase compositions match also at the top.
Figure 16 presents the results from Figure 15 on an xy plot along with the equilibrium curve of Figure 14. Readers familiar with the traditional McCabe–Thiele distillation analysis will note that it is no coincidence that our calculated results trace out straight operating lines for the stripping and rectifying sections that intersect at the feed composition for this case with a saturated liquid feed.
Figure 14: x-y diagram for ethanol–water at 1 atm pressure using the NRTL model.
Figure 15: Mole fraction of ethanol in the vapor and liquid phases as a function of column height for a distillation column designed to separate a 50 mole percent ethanol–water mixture to yield products with xb = 0.05 and xd = 0.85 mole fraction ethanol. Heights required were Hs = 1.2 m and H = 5.7 m.
Figure 16: x-y diagram showing the calculated operating lines within the distillation column described in Figure 12.
Reference
1. E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems, 3rd ed., Cambridge University Press, 2009.
Modeling Instructions
The following step-by-step instructions guide you through the process to set up and solve a distillation column model that simulate the distillation process for water-ethanol mixture. The model accounts for a 1D column geometry, mass transfer, and phase equilibrium calculations.