Expoert scalar Thiele on length of data support points

0a074b74-3ba4-4eb0-962f-ce95482d9d6a 242 4 5 decimal

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

pTM January 2023 Thermo calc Vapor-Solid Distribution

System

Sys AB_:

PC 1760 / :

Constants

Ro 8.314 :

T0K 273.15 :

HSC 2 :

Temperature

T 800 T0K + :

P 50 :

Torr

Energy

T ΔGA 4001000 * T 190 * - :

A-B Ωi

Ωi 2500 :

T ΔGB 3801000 * T 210 * - :

Flows

ϕpt 50 :

ϕtl 12500 :

ϕB ϕpt 0.01 * :

ϕH2 ϕtl ϕpt - :

pzpt ϕpt ϕtl / P PC / * :

pzH2 ϕH2 ϕtl / P PC / * :

pzB ϕB ϕtl / P PC / * :

Partial Pressuresatm

pzB pzA pzpt pzB - :

xv pzB pzpt / :

Mole fraction vapor

pzB pA pB x pzB pB - pzB pzA pA - pzB + pB - / :

Mole fraction solid

pzB pA pB aA 1 pzB pA pB x - (e Ωi Ro T * / pzB pA pB x (2^*^* :

Activities

pzB pA pB aB pzB pA pB x e Ωi Ro T * / 1 pzB pA pB x - (2^*^* :

K0A e T ΔGA Ro T * / -^:

K0B e T ΔGB Ro T * / -^:

EquilibriumConstants

pzB pA pB KA pzB pA pB aA 2 pzB pzA pA - (* (2^* pA / :

111 KA 90000

pzB pA pB KB pzB pA pB aB 2 pzB pB - (* (2^* pB / :

222 KB 0

pzB 1.52

x y KA 1 pzB x y aA 2 pzB pzA x - (* (2^* x / * : x y KB 1 pzB x y aB 2 pzB y - (* (2^* y / * : 21 sys

x 0 KA x 0.001 KB 2 1 sys

data list ListCollect collects index list select list : 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 :

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 :

x 0 KA x 0.0001 KB - x 32128 solve 34.1369

x 0 KA x 0.02 KB - x 64128 solve 120.7539

sol_1 u 0.0001 0.005 0.00025 range : i 1 u rows range y i el x 0 KA x u i el KB - x 32128 solve : for u y augment 31 line :

sol_2 U 0.0001 0.01 0.00025 range : i 1 U rows range Y i el x 1 KA x U i el KB - x 32128 solve : for U Y augment 31 line :

isolate/save sol_1 sol_1 eval :

isolate/save sol_2 sol_2 eval :

list 1247121930456019 mat :

sol_2 sol_2 rows row 0.01 113.7842 12 mat

data sol_2 list ListCollect :

plot sol_1 sol_2 data . 14 black plot 31 sys :

plot

j data rows : 9

Expoert scalar Thiele on length of data support points

Thiele on length of support points 'j' 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 :

symbolic expansion of Thiele 'Cfr' algo style j 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 / + / + / + / + / + / + / + / +

Thiele(X,Y,Δ) ..... plot(data,char,size,clr)

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 :

j 8 :

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 :

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 data 1 col : Y data 2 col : 12 mat

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

Thiele K's coefficients @ support points X X Y 0 Thiele

will expand Thiele Table @ support points  [X,Y] X Y 1 Thiele

Thiele K's continued fraction K X Y 0 Thiele 2 col :

store/isolate K K 6 round vectorize eval :

x λ 10 x ≤ (x 0.0125 ≤ (& cases :

Thiele on length of support points 'j' K X x Cfr j K rows 1 - : N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (1 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 61 line :

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

x Cf data 2 1 sys

◄ NUMERIC ▲

It looks strangely Water Saturation °C(bar) In short: the system solves for 'y' given 'x' wrt the system KB(x,y) ... suggestive of coding the solve bloc, not limited to this demo. Please, don't hesitate for more collaboration. Salut Pierre ... be good [I love that Irish]

Thiele supports derivative(s).

x Cf x diff x λ *

K 34.291412 8106 -^* 60.595904 0.000103 22.722051 0.000621 11.628804 0.002608 6.985686 91 mat

Export Thiele project as stand alone entity

renew 'K & X'

K 34.291412 8106 -^* 60.595904 0.000103 22.722051 0.000621 11.628804 0.002608 6.985686 91 mat :

Export the Tiele system for else document
copied/pasted from scalar turquoise above. 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 0.0001 0.00025 0.00055 0.001 0.00175 0.0028 0.00445 0.0067 0.00895 91 mat :

x y Part1 x y KA (: 425 y * - 38 + 25152 - x + y + (* + (* e 400003825 y * - (2^* 89221691152 - x + y + (2^* /^* 376225 x * - (2^* 15625152 - x + y + (* x * /

x y Part2 x y KB (: 425 y * - 38 + (3^* e 400003825152 - x + (* + (2^* 89221691152 - x + y + (2^* /^* 15625152 - x + y + (* y * / -

Given

x Target pA pB 12 mat x 1 el x 2 el 12 mat : pzB pA pB KA K0A - pzB pA pB KB K0B - 21 mat 21 line :

Jx x Target x 12 range el vectorize Jacob :

x J Jx eval :

K0A 2.8483 1010 -^*

ε 1012 -^:

Solve

pzB Guess f sol Guess 0 ε Target J al_nleqsolve : sol Target normi ε sqrt ≤ sol 00 stack if 21 line :

K0B 2.9705 108 -^*

Guess 0 0.1 21 mat :

pA pB 21 mat pzB Guess f : #

Output

110 f #

pA pB 21 mat Target #

pzpt 152

pzB pzA pA pzB pzA pA - xv pzB pB pzB pB - pzB pA pB x 24 mat #

k IP MTX 5 k el MTX 5 k 1 - el - MTX 6 k el MTX 6 k 1 - el - / MTX 5 k 1 - el MTX 5 k 2 - el - MTX 6 k 1 - el MTX 6 k 2 - el - / < :

Program

N 100 :

ko 0 :

Guess pA pB 21 mat :

Guess #

Start Guess :

k 1 N 1 - (range pz 1 el ϕpt ϕtl / 1 k N / - (* : pz 2 el ϕpt ϕtl / k N / * : k 2 > Guess MTX 4 k 1 - el MTX 5 k 1 - el 21 mat : Guess Start : if Mp pz 2 el Guess f : MTX 1 k el k : MTX 2 k el pz 1 el : MTX 3 k el pz 2 el : MTX 4 k el Mp 1 el : MTX 5 k el Mp 2 el : MTX 6 k el pz 2 el pz 1 el pz 2 el + / : MTX 7 k el pz 2 el Mp 1 el Mp 2 el x : n 12 range Mp n el 0 < M8 k el Negative : continue if for n 12 range pz n el Mp n el - 0 < M8 k el Negative : continue if for ko 0 ≡ (k 2 > (& (k IP & ko k 2 - : continue if 141 line for

Mp pzB Guess f : #

Mp pzB Start f : #

Export

FLNM Sys var2str P var2str_T T0K - var2str_ϕtl var2str_ϕpt var2str concat :

FLNM AB_50_800_12500_50

MTX FLNM exportData.CSV 1 ≡

Plot

XX MTX 4 el :

YY MTX 5 el :

XX YY augment XX ko el YY ko el o augment 2 1 sys

Display MTX

MTX

k 1 N 1 - (range pzA ϕpt ϕtl / 1 k N / - (* : pzB ϕpt ϕtl / k N / * : k 2 > Guess M4 k 1 - el M5 k 1 - el 21 mat : Guess Start : if MTX 1 k el k : MTX 2 k el pzA : MTX 3 k el pzB : MTX 4 k el pA : MTX 5 k el pB : MTX 6 k el pzB pzA pzB + / : MTX 7 k el pzB pA pB x : pA 0 < M8 k el Negative : continue if pB 0 < M8 k el "Negative" : continue if pzA pA - 0 < M8 k el Negative : continue if pzB pB - 0 < M8 k el "Negative" : continue if ko 0 ≡ (k 2 > (& (k IP & ko k 2 - : continue if 151 line for

Removed from program

pA pB 21 mat pzB pA pB 21 mat f :