General approach for multicomponent distillation.

Consider the case of the distillation of a multicomponent mixture in a multistage distillation column.  As before, the number of degrees of freedom is determined by the discription rule (i.e., D.O.F. = number of variables set during construction or controlled during operation by independent means).  In particular, when a partial condenser and reboiler are used, we have D.O.F. = N + 8, where N is the number of components.  Generally, all the variables associated with the feed, such as its composition, flow rate and enthaply are set, as is the column pressure, which leaves four degrees of freedom and two basic types of problems (design and simulation) as was the case for a binary distillation.

For a design problem, the goal is to determine the number of plates needed and the location of the feed plate, and the following is generally specified

Separation variable #1 (e.g., the recovery of the light key component in the top (distillate) product.

Separation variable #2 (e.g., the recovery of the heavy key component in the bottom product.

The reflux ratio.

The final degree of freedom is then used in a one dimensional optimization search to determine the minimum number of total plates that are possible. This final degree of freedom is usually taken as the location of the feed plate from either the top or bottom of the column.

For a simulation problem the goal is to determine the compositions of the top and bottom products and the following is generally specified:

The number of plates above the feed plate.

The number of plates below the feed plate

One external flow, such as the flowrate of the top product.

One interal flow, such as the reflux flow from the condenser (or the reflux ratio).

Generally, in a multicomponent distillation column, only two components will exist in significant quantities in both the bottom and top products.  These are the two key components.  The heavy non-key components will essentially all end up in the bottom product while the light non-key components will essentially all end up in the top product.  This is why the separation variables described above are given in terms of the key components.

Simulating a mulitcomponent distillation column involves solving a large number of coupled algebraic equations (roughly two for each component on each plate).  One technique for solving these equations is illustrated by the Naphtali and Sandholm method (L. M. Naphtali and D. P. Sandholm, "Multicomponent Separation Calculation by Linearization," AIChE. J. 17, 148-153, 1971) in which all of the equations are solved simultaneously using a multivariable Newton's method after first grouping the equations in a way to simplify the mathematical structure of the problem. This is basically the technique used in the process simulators ChemSep and Aspen.   Alternatively, in some cases the equations describing multicomponent distillation can be solved one equation at time (usually sequentially from one stage to the next stage) and often analytically.  This type of "stage-to-stage" calculation method has the great advantage of simplfying the computer programming needed and eliminating convergence problems.     

Multicomponent stage-to-stage calculation method for design problems: The Lewis-Matheson Method.

Consider the design problem for the special (and very common) case where there are no light non-keys or no heavy non-keys.  For the first case just mentioned, an overall material balance can be used to determine the bottom composition to a high degree of precision since the distribution of the keys is determined by the product specification and all the heavy nonkeys can be assumed to end up in the bottom product.  Conversely, for the second case, an overall material balance can be used to determine the top composition to a high degree of precision since the distribution of the keys is again determined by the product specification and all the light nonkeys can be assumed to end up in the top product.

Using the product composition calculated as just described as the starting point, the material and equilibrium relations can be solved for stage by stage until the opposite end of the column is reached.  This procedure, termed the Lewis Matheson method, is a multicomponent analog of the McCabe Thiele method described earlier, although it must be performed analytically, not graphically.    In particular,  the internal total molar flow are first determined using the reflux information in the problem specification as was the case for the binary problem.  Then, starting from the bottom product, the following equations are used sequentially:

1.  Determine the composition of the vapor rising from the reboiler (or current stage) using a bubble point

calculation, or more simply, if the relative volatility is known, using:

      y_i_p  =   alpha_i  * x_i_p / [sum_j (alpha_j * x_i_p) ]

where i and j are the component indices, p is the current plate number, sum_j denotes the sum over all j, and alpha_j is the relative volatility of component j with respect to an arbitrary reference component, usually chosen to the the least volatile component so that alpha_j is unity or greater.  Vapor flow rates can then be determined using 

      v_i_p = V * y_i_p

2.  Determine the composition of the liquid stream passing the vapor stream just calculation using the following equation if the current location is below the the feed plate:

      l_i_p = v_i_p-1 + x_i_b b

Or the following equation if the current location is above the feed plate:

     v_i_p = l_i_p+1 + x_i_D D

3.  Return to step 1 with p incremented by unity and repeat until the compositions of the key components are those specified for the top product.

The optimal feed plate can be determined by varying the location of the feed plate until the minimum number of total plates is obtained.

The above calculation procedure can be easily implemented using a spreadsheet, as described elsewhere on this website. 

The minimum reflux ratio can be determined computationally by (in the case where the calculaction starts at the reboiler) setting the feed plate high in the column, such as at the 100th plate from the bottom, for the case where the column contains a large total number of plates, such as 200 total plates.  Then, a small reflux ratio is tried initially, and the reflux ratio is then gradually increased until the desired top product composition is just achieved.  Note, however, that the top product composition will be extremely sensitive to the reflux ratio under these conditions, so care must be taken when adjusting the reflux ratio. In practice, the Underwood equations yield a simpler (although approximate) determination of the minimum reflux ratio.

As in the case of binary distillation, the optimal design that minimizes the combination of capital and operating costs is often when the operating reflux ratio is 1.5 times the minimum reflux ratio. 

The Theile-Geddes and relaxation methods for simulation problems.

For the simulation problem, two options are possible that avoid solving large systems of equations simultaneously.   First, the Thiele-Geddes method can be used which involves guessing a temperature profile in the column, then performing a procedure much like the stage-to-stage method described above, except that ratios of flow rates (such as v_i_p/b_i) are determined initially, and then a matching procedure at the feed plate permits the determination of compositions everywhere in the column.  Then, an improved temperature profile is estimated from the liquid phase compositions just calculated and the procedure repeated to achieve an improved solution.  Convergence is achieved when the temperature profile does not change from iteration to iteration. 

Alternatively, the dynamic behavior (i.e., time dependent behavior) of the column can be simulated from some arbitrary starting point to the final steady state.  This last method, often called a relaxation method, is easily implemented on a spreadsheet using Euler's method as described elsewhere on this course website.

• Detailed notes for Chapter 8.

 

• Distillation tutorials by Angelo Lucia. These tutorials, developed by Angelo Lucia at the Unversity of Rhode Island, include discussions of ternary distillation, azeotropic distillation, extractive distillation, and energy efficiency.

 

• ChemSep-LITE. This free software simulates multicomponent distillation, absorption, stripping, liquid-liquid extraction, and single-stage flash processes and was developed by Ross Taylor at Clarkson University and Harry Kooijman at Shell Global Solutions International. Be sure to also look at the rest of the ChemSep website which contains lots of useful information.

 

• COCO.   COCO (CAPE OPEN to CAPE OPEN) is a free suite of computer aided process engineering open source software programs that includes ChemSep as described in the previous link. For maximum software stability, you should uninstall any previous versions of ChemSep on your computer before you install COCO so you have only one copy of ChemSep on your computer. COCO is an example of the newest generation of software for computer-aided chemical process engineering that consists of "plug and play" components that are primarily free.

 

• Multicomponent distillation example problem.   

 

• COCO/ChemSep tutorial. Part 1.   Part 1 of this Youtube tutorial gives a brief overview of COCO and COFE.

 

• COCO/ChemSep tutorial. Part 2.   Part 2 of this Youtube tutorial shows how to use ChemSep within COFE and is based on the example distillation problem given above.

 

• COCO/ChemSep tutorial. Part 3.   Part 3 of this Youtube tutorial shows how to incorporate an Excel spreadsheet model into COFE and is based on the example distillation problem given above.

 

• Troubleshooting and usage guide for COFE.   

 

• COCO tutorial by Menwar Attarakih   This YouTube tutorial was developed by Menwar Attarakih at the University of Jordan.

 

• Lewis-Matheson stage-to-stage calculator (simple version). For certain types of multicomponent distillation design problems, the Lewis-Matheson method, which is not available in ChemSep or ASPEN, is a superior approach. This Excel spreadsheet, developed by Douglas Frey at UMBC, provides a simple version of this method.

 

• LeMon: Delux version of Lewis-Matheson stage-to-stage calculator. As mentioned in the previous link, for certain types of multicomponent distillation design problems, the Lewis-Matheson method, which is not available in ChemSep or ASPEN, is a superior approach. This Excel spreadsheet, developed by Douglas Frey at UMBC and called LeMon, is a general calculator that accommodates multiple feeds, stage efficiencies, and composition dependent relative volatilities. LeMon can be used as a flow sheet component within COCO. Only a printed version of the speadsheet is given here. Please contact Professor Frey for a working version of this software.