ponchon-savarit Toolbox for GNU-Octave

Installing and Loading ponchon-savarit

# e.g. this call installs version 1.0.0
pkg install https://github.com/aumpierre-unb/Ponchon-Savarit-for-GNU-Octave/archive/refs/tags/v1.0.0.tar.gz
pkg load ponchon-savarit

Citation of ponchon-savarit

You can cite all versions (both released and pre-released), by using DOI 10.5281/zenodo.7133683. This DOI represents all versions, and will always resolve to the latest one.

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The following is a very short introduction to the ponchon-savarit toolbox for GNU Octave.

This text is divided in two main sections: The Theory and The ponchon-savarit Toolbox.

The Theory

The Ponchón-Savarit graphical method is a method to calculate the number of theoretical stages of equilibrium of a distillation column for a two component mixture. It allows for variations on the heat of vaporization, the most demanding premise of the McCabe-Thiele method. Ponchón-Savarit method demands that the column be adiabatic, except for its bottom and top, where there must heat exchange in order to maintain reflux streams.

Distillation is a unit operation based on the difference of volatility to separate different chemical species of a mixture and on gravity to separate vapor and liquid streams. There are several types of distillation.

Typically, continuous distillation is performed in a vertical column fed at its intermediate section while products at its top and bottom are recovered. As a rule of thumb, the higher the column, the higher the number of stages of equilibrium and the best is the separations of the components of the mixture fed.

Theoretical Stage of Equilibrium

A theoretical stage of equilibrium is an abstract control volume such that the effluent currents are all in thermodynamic equilibrium. All multistage operations are based on the concept of stage of equilibrium.

Material and Enthalpy Balances

The global and specific material balances and the enthalpy balance for any equilibrium stage n are given by

$$ V_{n-1} - L_n = V_n - L_{n+1} $$

$$ V_{n-1}\ y_{n-1} - L_n\ x_n = V_n\ y_n - L_{n+1}\ x_{n+1} $$

$$ V_{n-1}\ H_{n-1} - L_n\ h_n = V_n\ H_n - L_{n+1}\ h_{n+1} $$

where L_n+1 and V_n are the liquid and the vapor streams, x_n+1 and y_n are compositions of liquid and vapor streams, and h_n+1 and H_n are the material enthalpy of liquid and vapor streams.

For any theoretical stage of the rectifying section,

$$ {\it\Delta} = V_n - L_{n+1} $$

$$ {\it\Delta}\ x_{\it\Delta} = V_n\ y_n - L_{n+1}\ x_{n+1} $$

$$ {\it\Delta}\ h_{\it\Delta} = V_n\ H_n - L_{n+1}\ h_{n+1} $$

where ${\it\Delta}$, x_{${\it\Delta}$} and h_{${\it\Delta}$} are the upcolumn stream of the rectifying section, its global composition and its enthalpy. Combining the three balances, one has

$$ {L_{n+1} \over V_n} = {y_n - x_\Delta \over x_{n+1} - x_\Delta} = {H_n - h_\Delta \over h_{n+1} - h_\Delta} $$

Also, the material balances at the top of the column are

$$ D = V_n - L_{n+1} $$

$$ D\ x_D = V_n\ y_n - L_{n+1}\ x_{n+1} $$

where D, x_D and h_D are the distillate stream and its composition. It follows that ${\it\Delta}$ = D and x_{${\it\Delta}$} = x_D.

The ratio between the distillate D and the refluxing current L_N+1 is the reflux ratio at the top of the column,

$$ R = {L_{N+1} \over D} = {L_{N+1} \over {\it\Delta}} $$

Given the enthalpy diagram of the vapor and the liquid at equilibrium and the composition of the distillate x_D and the reflux ratio R it is possible to calculate x_{${\it\Delta}$}. It is then possible to calculate x_n+1 from y_n and L_n+1 from V_n for any stage n of the rectifying section.

The balances of the column is given by

$$ F = {\it\Delta} + {\it\Lambda} $$

$$ F\ x_F = {\it\Delta}\ x_{\it\Delta} + {\it\Lambda}\ x_{\it\Lambda} $$

$$ F\ h_F = {\it\Delta}\ h_{\it\Delta} + {\it\Lambda}\ h_{\it\Lambda} $$

where x_F and h_F are the composition and the enthalpy of the feed and ${\it\Lambda}$, x_{${\it\Lambda}$} and h_{${\it\Lambda}$} are the downcolumn stream of the stripping section and its composition and enthalpy.

The enthalpy of the feed h_F can be calculated from the composition x_F and the quality q of the feed,

$$ (1 - q)\ y_n + q\ x_{n+1} = x_F $$

$$ (1 - q)\ H_n + q\ h_{n+1} = h_F $$

So that

$$ {{\it\Lambda} \over {\it\Delta}} = {x_{\it\Delta} - x_F \over x_F - x_{\it\Lambda}} = {h_{\it\Delta} - h_F \over h_F - h_{\it\Lambda}} $$

Analogously to the rectifying section, ${\it\Lambda}$ = B and x_{${\it\Lambda}$} = x_B, where B and x_B are the column's bottom product and its composition.

The ponchon-savarit Toolbox

ponchon-savarit provides the following functions:

• stages
• refmin
• qR2S
• qS2R
• RS2q

stages

stages computes the number of theoretical stages of a distillation column using the Ponchón-Savarit method given a x-h-y-H matrix of the liquid and the vapor fractions at equilibrium and their enthalpies, the vector of the fractions of the products and the feed and two paramaeters aong the feed quality, the reflux ratio at the top of the column and the reflux ratio at the bottom of the column.

Syntax:

N=stages(data,X,q,R,:[,fig=true])
N=stages(data,X,q,:,S[,fig=true])
N=stages(data,X,:,R,S[,fig=true])

By default, stages plots a schematic diagram of the solution, fig = true. If fig = false is given, no plot is shown.

By default, stages plots a schematic diagram of the solution, fig = true.

Examples:

Compute the number of theoretical stages of a distillation column for acetone and methanol from the bottom to the top of the column given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 93 %, the composition of the feed is 41 %, the composition of the bottoms is 7 %, the feed is a saturated liquid and the reflux ratio at the top of the column is 55 % higher that the minimum reflux ratio, and plot a schematic diagram of the solution:

data=[2.5e-4 3.235 1.675e-3 20.720; # enthalpy in kcal/mol
      0.05   2.666 0.267    20.520;
      0.1    2.527 0.418    20.340;
      0.15   2.459 0.517    20.160;
      0.2    2.422 0.579    20.000;
      0.3    2.384 0.665    19.640;
      0.4    2.358 0.729    19.310;
      0.5    2.338 0.779    18.970;
      0.6    2.320 0.825    18.650;
      0.7    2.302 0.87     18.310;
      0.8    2.284 0.915    17.980;
      0.9    2.266 0.958    17.680;
      1.     2.250 1.       17.390];
x=[0.93;0.41;0.07];
[r,s]=refmin(data,x,q=1)
N=stages(data,x,q,R=1.55*r)

Compute the number of theoretical stages of a distillation column for oxygen and nitrogen from the bottom to the top of the column given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 88 %, the composition of the feed is 44 %, the composition of the bottoms is 8 %, the feed quality is 55 % and the reflux ratio at the bottom of the column is 46 % higher that the minimum reflux ratio and plot a schematic diagram of the solution:

data=[0.    0.420 0.    1.840; # enthalpy in kcal/mmol
      0.075 0.418 0.193 1.755;
      0.17  0.415 0.359 1.685;
      0.275 0.410 0.50  1.625;
      0.39  0.398 0.63  1.570;
      0.525 0.378 0.75  1.515;
      0.685 0.349 0.86  1.465;
      0.88  0.300 0.955 1.425;
     1.    0.263 1.    1.405];
x=[0.88;0.44;0.08];
[r,s]=refmin(data,x,q=0.55)
N=stages(data,x,q,:,S=1.46*s)

Compute the number of theoretical stages of a distillation column for oxygen and nitrogen from the bottom to the top of the column given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 92 %, the composition of the feed is 59 %, the composition of the bottoms is 9 %, the reflux ratio at the bottom of the column is 1.9, the reflux ratio at the top of the column is 1.5:

data=[0.    0.420 0.    1.840; # enthalpy in kcal/mmol
      0.075 0.418 0.193 1.755;
      0.17  0.415 0.359 1.685;
      0.275 0.410 0.50  1.625;
      0.39  0.398 0.63  1.570;
      0.525 0.378 0.75  1.515;
      0.685 0.349 0.86  1.465;
      0.88  0.300 0.955 1.425;
      1.    0.263 1.    1.405];
x=[0.92;0.59;0.09];
q=RS2q(data,x,R=1.5,S=1.9)
N=stages(data,x,:,R,S,fig=false)

refmin

refmin computes the minimum value of the reflux ratio of a distillation column using the Ponchón-Savarit method given a x-h-y-H matrix of the liquid and the vapor fractions at equilibrium and their enthalpies, the vector of the fractions of the products and the feed and the feed quality.

Syntax:

[R,S]=refmin(data,X,q)

If feed is saturated liquid q = 1, q is reset to q = 1 - 1e-10.

Examples:

Compute the minimum value of the reflux ratio of a distillation column for oxygen and nitrogen given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 88 %, the composition of the feed is 46 %, the composition of the column's bottom product is 11 % and the feed quality is 52 %:

data=[0.    0.420 0.    1.840; # enthalpy in kcal/mmol
      0.075 0.418 0.193 1.755;
      0.17  0.415 0.359 1.685;
      0.275 0.410 0.50  1.625;
      0.39  0.398 0.63  1.570;
      0.525 0.378 0.75  1.515;
      0.685 0.349 0.86  1.465;
      0.88  0.300 0.955 1.425;
      1.    0.263 1.    1.405];
x=[0.88;0.46;0.08];
[r,s]=refmin(data,x,q=0.52)

Compute the minimum value of the reflux ratio of a distillation column for acetone and methanol given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 88 %, the composition of the feed is 46 %, the composition of the column's bottom product is 11 % and the feed is a saturated liquid:

data=[2.5e-4 3.235 1.675e-3 20.720; # enthalpy in kcal/mol
      0.05   2.666 0.267    20.520;
      0.1    2.527 0.418    20.340;
      0.15   2.459 0.517    20.160;
      0.2    2.422 0.579    20.000;
      0.3    2.384 0.665    19.640;
      0.4    2.358 0.729    19.310;
      0.5    2.338 0.779    18.970;
      0.6    2.320 0.825    18.650;
      0.7    2.302 0.87     18.310;
      0.8    2.284 0.915    17.980;
      0.9    2.266 0.958    17.680;
      1      2.250 1        17.390];
x=[0.88;0.46;0.08];
[r,s]=refmin(data,x,q=1)

qR2S

qR2S computes the reflux ratio at the bottom of a distillation column using the Ponchón-Savarit method given a x-h-y-H matrix of the liquid and the vapor fractions at equilibrium and their enthalpies, the vector of the fractions of the products and the feed, the feed quality and the reflux ratio at the top of the column.

Syntax:

S=qR2S(data,X,q,R)

Examples:

Compute the reflux ratio at the bottom of a distillation column for acetone and methanol given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 93 %, the composition of the feed is 41 %, the composition of the bottoms is 7 %, the feed is a saturated liquid and the reflux ratio at the top of the column is 2:

data=[2.5e-4 3.235 1.675e-3 20.720; # enthalpy in kcal/mol
      0.05   2.666 0.267    20.520;
      0.1    2.527 0.418    20.340;
      0.15   2.459 0.517    20.160;
      0.2    2.422 0.579    20.000;
      0.3    2.384 0.665    19.640;
      0.4    2.358 0.729    19.310;
      0.5    2.338 0.779    18.970;
      0.6    2.320 0.825    18.650;
      0.7    2.302 0.87     18.310;
      0.8    2.284 0.915    17.980;
      0.9    2.266 0.958    17.680;
      1.     2.250 1.       17.390];
x=[0.93;0.41;0.07];
S=qR2S(data,x,1,2)

Compute the reflux ratio at the bottom of the column of a distillation column for oxygen and nitrogen given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 88 %, the composition of the feed is 44 %, the composition of the bottoms is 8 %, the feed quality is 55 % and the reflux ratio at the top of the column is 2:

data=[0.    0.420 0.    1.840; # enthalpy in kcal/mmol
      0.075 0.418 0.193 1.755;
      0.17  0.415 0.359 1.685;
      0.275 0.410 0.50  1.625;
      0.39  0.398 0.63  1.570;
      0.525 0.378 0.75  1.515;
      0.685 0.349 0.86  1.465;
      0.88  0.300 0.955 1.425;
      1.    0.263 1.    1.405];
x=[0.88;0.44;0.08];
S=qR2S(data,x,0.55,2)

qS2R

qS2R computes the reflux ratio at the top of a distillation column using the Ponchón-Savarit method given a x-h-y-H matrix of the liquid and the vapor fractions at equilibrium and their enthalpies, the vector of the fractions of the products and the feed, the feed quality and the reflux ratio at the bottom of the column.

Syntax:

R=qS2R(data,X,q,R)

Examples:

Compute the reflux ratio at the top of a distillation column for acetone and methanol given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 93 %, the composition of the feed is 41 %, the composition of the bottoms is 7 %, the feed is a saturated liquid and the reflux ratio at the bottom of the column is 1.7:

data=[2.5e-4 3.235 1.675e-3 20.720; # enthalpy in kcal/mol
      0.05   2.666 0.267    20.520;
      0.1    2.527 0.418    20.340;
      0.15   2.459 0.517    20.160;
      0.2    2.422 0.579    20.000;
      0.3    2.384 0.665    19.640;
      0.4    2.358 0.729    19.310;
      0.5    2.338 0.779    18.970;
      0.6    2.320 0.825    18.650;
      0.7    2.302 0.87     18.310;
      0.8    2.284 0.915    17.980;
      0.9    2.266 0.958    17.680;
      1.     2.250 1.       17.390];
x=[0.93;0.41;0.07];
R=qS2R(data,x,1,1.7)

Compute the reflux ratio at the top of a distillation column for oxygen and nitrogen given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 88 %, the composition of the feed is 44 %, the composition of the bottoms is 8 %, the feed quality is 55 % and the reflux ratio at the bottom of the column is 1.3:

data=[0.    0.420 0.    1.840; # enthalpy in kcal/mmol
      0.075 0.418 0.193 1.755;
      0.17  0.415 0.359 1.685;
      0.275 0.410 0.50  1.625;
      0.39  0.398 0.63  1.570;
      0.525 0.378 0.75  1.515;
      0.685 0.349 0.86  1.465;
      0.88  0.300 0.955 1.425;
      1.    0.263 1.    1.405];
x=[0.88;0.44;0.08];
R=qS2R(data,x,0.55,1.3)

RS2q

RS2q computes the feed quality of a distillation column using the Ponchón-Savarit method given a x-h-y-H matrix of the liquid and the vapor fractions at equilibrium and their enthalpies, the vector of the fractions of the products and the feed, the reflux ratio at the top of the column and the reflux ratio at the bottom of the column.

Syntax:

q=RS2q(data,X,q,R)

Examples:

Compute the feed quality of a distillation column for acetone and methanol given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 93 %, the composition of the feed is 41 %, the composition of the bottoms is 7 %, the reflux ratio at the top of the column is 2 and the reflux ratio at the bottom of the column is 1.7:

data=[2.5e-4 3.235 1.675e-3 20.720; # enthalpy in kcal/mol
      0.05   2.666 0.267    20.520;
      0.1    2.527 0.418    20.340;
      0.15   2.459 0.517    20.160;
      0.2    2.422 0.579    20.000;
      0.3    2.384 0.665    19.640;
      0.4    2.358 0.729    19.310;
      0.5    2.338 0.779    18.970;
      0.6    2.320 0.825    18.650;
      0.7    2.302 0.87     18.310;
      0.8    2.284 0.915    17.980;
      0.9    2.266 0.958    17.680;
      1.     2.250 1.       17.390];
x=[0.93;0.41;0.07];
q=RS2q(data,x,2.1,1.7)

Compute the feed quality of a distillation column for oxygen and nitrogen given a matrix that relates the liquid and the vapor fractions and their enthalpies at equilibrium, the composition of the distillate is 88 %, the composition of the feed is 44 %, the composition of the bottoms is 8 %, the reflux ratio at the top of the column is 2 and the reflux ratio at the bottom of the column is 1.3:

data=[0.    0.420 0.    1.840; # enthalpy in kcal/mmol
      0.075 0.418 0.193 1.755;
      0.17  0.415 0.359 1.685;
      0.275 0.410 0.50  1.625;
      0.39  0.398 0.63  1.570;
      0.525 0.378 0.75  1.515;
      0.685 0.349 0.86  1.465;
      0.88  0.300 0.955 1.425;
      1.    0.263 1.    1.405];
x=[0.88;0.44;0.08];
q=RS2q(data,x,2,1.3)

See Also

McCabe-Thiele-for-GNU-Octave, Psychrometrics-for-GNU-Octave, Internal-Fluid-Flow-for-GNU-Octave.

Copyright © 2022 2023 Alexandre Umpierre

email: aumpierre@gmail.com