plotG(vx,vy,char,size,color)

0b52a923-6b4d-44de-869f-81ff385f05ab 15 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

xL 0 0.0917 0.1842 0.2779 0.3732 0.4703 0.5699 0.6721 0.7776 0.8867 1111 mat :

xV 0 0.1543 0.2943 0.4188 0.5315 0.6327 0.7236 0.8049 0.8776 0.9424 1111 mat :

data xL xV augment :

4 appVersion 0.98.6179.21440 ≡

Benzene purity in distillate
Benzene purity in bottom
Benzene fraction in feed
'q' value
Reflux ratio xD 97 % * : xB 2 % * : xF 40 % * : q 1.5 : R 3.5 : 51 sys

x qline x q q 1 - / * xF q 1 - / - : x top_op x R 1 R + / * xD 1 R + / + : 21 sys

System data given by Valentino [20201119]

x bottom_op x R xF xB - (* q xD xB - (* + q xD xB - (* R xF xB - (* + xD - xF + / * xB xF xD - (* q xD xB - (* R xF xB - (* + xD - xF + / + :

incorrect

jnct xD q 1 - (* xF R 1 + (* + q R + / : 0.457

x operating_line x bottom_op x jnct ≤ x top_op jnct x ≤ cases :

x jnct <

jnct x <

Thiele(X,Y,0) "K" .... Thiele(X,Y,1) "Table"

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

data List collects index list select 111 range : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

select the support points XY data :

length Thiele j XY rows : 11

Thiele on length of support points 'j' K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

Cfr(K,X,x) Expansion

symbolic expansion of Thiele continued fraction algo style K X x Cfr K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el x X 10 el - K 11 el / + / + / + / + / + / + / + / + / + / +

recast the Cf on the system  [K,X,x] x Cf K X x Cfr :

data set vx data 1 col : vy data 2 col : 21 sys

support points X XY 1 col : Y XY 2 col : 21 sys

Thiele K's coeff's
@ support points X X Y 0 Thiele 00 0.0917 0.5943 0.1842 2.9277 0.2779 0.3913 - 0.3732 0.4692 - 0.4703 1.1534 - 0.5699 4.3393 - 0.6721 0.0613 0.7776 2.5357 0.8867 0.8674 1 0.2305 112 mat

Thiele K's continued fraction K X Y 0 Thiele 2 col : 0 0.594296824 2.927667067 0.391282005 - 0.469188818 - 1.153434717 - 4.339276852 - 0.06130733 2.535741076 0.867401426 0.230455988 111 mat

data UnestRow v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

x Th 10 x ≤ (x 1 ≤ (& cases :

x Op 10 x ≤ (x 1 ≤ (& cases :

TraySystem

u xB Cf : op x operating_line u - x 01 solve : 21 line

Tray 1 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 2 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 3 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 4 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 5 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 6 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 7 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 8 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 9 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 10 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 11 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 12 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 13 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 14 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 15 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 16 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 17 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 18 el u op 12 mat :

u op Cf : op x operating_line u - x 01 solve : 21 line

Tray 19 el u op 12 mat :

i 119 range : Tray Tray i el : tray Tray UnestRow : u tray 1 col : v tray 2 col : 12 mat 41 sys

i 1 u rows range C i el u i el u i el 21 mat : for

i 1 v rows range O i el v i el v i el 21 mat : for

C C UnestRow : O O UnestRow : 12 mat C C 2 C rows range 1 el : O O 1 O rows 1 - (range 1 el : strip O C augment : 41 sys

plotStrip x Cf x Th * x operating_line x Op * strip jnct 0.571 + 100 black 15 mat 0.0351 0.032 + 40 black 15 mat 0.9714 0.972 + 40 black 15 mat 61 sys :

0.457 bottom_op 0.457 operating_line 21 mat 0.571 0.571 21 mat

Tray 1 el Tray 19 el 21 mat 0.0351 0.032 12 mat 0.9714 0.9719 12 mat 21 mat

plotStrip

x operating_line x bottom_op x jnct < x top_op jnct x < cases :

from incomplete equalities jnct operating_line

Binary fractional distillation is a means of separating two liquid components via a distillation column (which contains a number of trays, or stages). It's a concept encountered by virtually every Chemical & Process Engineering student. This application calculates the required number of theoretical stages for a set of specified operating parameters via the McCabe-Thiele method. It plots the classic McCabe-Thiele diagram and evaluates the minimum and actual reflux ratio, and the thermodynamic state of the feed.

This disabled collapsed section exposes the possible glitches. Amongs all the projects I have done, very few glitches appeared, and only one in those cases. They appear in data sets that under the hood aren't true. In this demo Thiele-McCabe, we find 3 . We prove it otherwise applying Thiele on the 4 point circle.

About glitches

x q 0.8854 3.5503 x 3.1319 + 5.6411 x 0.7899 - 7.1605 107 -^* x 0.8028 - 0.1325 x 0.1443 + 0.0443 x 0.5729 - / + / + / - / + / + :

x Cf x q ≡

h 0.25 :

x f x q :

Infinitesimal 1rst derivative x h f D1 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / :

x h f D1 x Th *

default acc [100] x q x 01 int 0.6077

Σ U 01 0.025 range : i 1 U rows range Cumul i el x q x U 1 el U i el int eval : for U Cumul augment 31 line :

x q x Th * Σ 0.5 x h f D1 * x Th * 3 1 sys

0.885400 3.550069 x 3.131823 + 5.640881 x 0.789885 - 7.260077 107 -^* x 0.795416 - 0.126512 x 0.141263 + 0.046397 x 0.577258 - / + / + / - / + / +

Thiele 00 0.0917 0.5943 0.1842 2.9277 0.2779 0.3913 - 0.3732 0.4692 - 0.4703 1.1534 - 0.5699 4.3393 - 0.6721 0.0613 0.7776 2.5357 0.8867 0.8674 1 0.2305 112 mat :

x Th 10 x ≤ (x 1 ≤ (& cases :

Glitches are not uncommon Thiele. Mostly observed wrt not true data.

X Thiele 1 col : K Thiele 2 col : 12 mat

x f K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el x X 10 el - K 11 el / + / + / + / + / + / + / + / + / + / + :

x f x diff x Th * QED 4 points circle absent of glitches

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

data 1 - 0 0.86602540378444 - 0.5 0.5 - 0.86602540378444 0142 mat :

length Thiele j data rows : 4

X data 1 col :

Y data 2 col :

Continued on length 'j'  of support points 'X' j K X x Thiele Optimiz NONE j <= rows(k) N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 71 line :

Optimiz NONE ... Export the RHS member 4 K X x Thiele 0 x 1 - (- 594310000 / x 2165063509461125000000000000 / - (- 2927710000 / x 12 / - (- 391310000 / - / + / + / +

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

X Y 0 Thiele 1 - 0 0.86602540378444 - 0.26794919243112 0.5 - 1.18301270189221 0 1.34969465094621 1014^* 42 mat

K X Y 0 Thiele 2 col (: 0 0.26794919243112 1.18301270189221 1.34969465094621 1014^* 41 mat

data data . 14 black plot :

x c 11 - x ≤ (x 0 ≤ (& cases :

x f K 1 el x 1 - (- K 2 el x 2165063509461125000000000000 / - (- K 3 el x 12 / - (- K 4 el / + / + / + :

accuracy of 4 points fit is not the question. Rather derivative glitches ... none to be seen.

0.25 x f x diff x c * ( * x f x c * data 1 x 2 ^ - sqrt ± 7 1 sys

The 4 points Thiele circle ... no glithes

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

data 1 - 0 0.86602540378444 - 0.5 0.5 - 0.86602540378444 0142 mat :

x Th 11 - x ≤ (x 0 ≤ (& cases :

Circle data . 14 black plot :

K 0 0.26794919243112 1.18301270189221 1.34969465094621 1014^* 41 mat :

x f K 1 el x 1 - (- K 2 el x 2165063509461125000000000000 / - (- K 3 el x 12 / - (- K 4 el / + / + / + :

1 x f x diff x Th * ( *

accuracy of 4 points fit is not the question. Rather derivative glitches ... none to be seen.

0.25 x f x diff x Th * ( * x f x Th * Circle 1 x 2 ^ - sqrt ± 7 1 sys