he followng ae appendes A, B1 and B2 of ou pape, Integated Poess Modelng and Podut Desgn of Bodesel Manufatung, that appeas n the Industal and Engneeng Chemsty Reseah, Deembe (2009). Appendx A. An Illustaton of How to Aess NIS DE When Applyng Aspen Plus to Develop a Bodesel Poess Model o aess NIS DE Data Engne n Aspen Plus veson 2006.5 o V7.0 Step 1. Ente the ME n the omponent lst Step 2. Go to ools -> NIS hemo Data Engne (DE) 1
Step 3. Selet the omponent Step 4. Cl Evaluate now 2
Step 5. he use an aess the value of a spef popety, eq. Lqud Densty 3
Appendx B Pedton Methods and NIS DE Equatons fo hemophysal Popetes B.1 Pedton Methods fo hemophysal Popetes b,, P, ω: Constantnou and Gan Method 29 Requed data: stutue b (K) 204.359 ln[ N tb1 + W M tb2] (B.1) (K) 181.128 ln[ N t1 + W M t2] (B.2) -2 P (ba) [ N p1 + W M p2 + 0.10022] + 1.3705 (B.3) ( 1/0.505) ω 0.4085 ln N ω1 + W M ω2 + 0.10022 + 1.1507 (B.4) whee W 0 when only applyng fst-ode and W 1 when applyng fst-ode and seond-ode. able B.1. Constantnou and Gan Contbutons of b,, P fo glyede 4
: Wlson and Jaspeson Method 29 Requed data: b and stutue (K) b 0.2 [0.048271+ N Δt + M Δt] (B.5) able B.2. Wlson and Jaspeson Contbutons of fo glyede b,, P : Dohn and Bunne Method A 34 Requed data: b and V L, 20 b a (B.6) b ( 2) ( 1) a Ωa a ( b) Ωb (1) (2) Ω ( b V b ) (B.7) b L, 20 b + Ωb a 1 (K) (B.8) Ω b R P b 2 (Pa) ( ) a a a Ω (B.9) Ω b 3 Log(101.3 Pa/P ) ω 1 (B.10) 7 ( / 1) b 5
whee Ω a 0.45724, Ω b 0.0778, a (1) 21.26924 J/mol-K, a (2) 0.913049, b (1) 0.02556188 K -1, b (2) 0.168721 m 3 mol -1, R 8.314 J/mol-K, V L, 20 s lqud densty at 20 b,, P, ω: Dohn and Bunne Method B 34 Requed data: vapo pessue at any tempeatue (P sat at 1 ) and V L, 20 b a (B.11) b ( 2) ( 1) a Ωa a ( b) Ωb (1) (2) Ω ( b V b ) (B.12) b L, 20 b + Ωb a 1 (K) (B.13) Ω b R P b 2 (Pa) ( ) a a a Ω (B.14) Ω b sat 3 Log(P at 1/P ) ω 1 (B.15) 7 ( / 1) 1 6
Fgue B.1. Iteaton step of Dohn and Bunne Method to pedt b,, P andω Dohn and Bunne 34 use Joba 29 method to obtan the ntal guesses of and P. Joba method fo and P : b (K) 198 + N tb (B.16) 7
(K) b 0.584 + 0.965 N t N t (B.17) P (Ba) 0.113 + 0.0032 Ntotal atoms N p (B.18) 2 2 1 able B.3. Joba Goup Contbutons of and P fo glyede P vap : Ambowse and Walton Method 29 Requed data:, P, ω P ln( P (B.19) f f f (0) (1) (2) vap ) f (0) (1) 2 ( ) + ω f ( ) + ω f (2) ( ) 1.5 2.5 5 5.97616 τ + 1.29874 τ 0.60394 τ 1.06841 τ ( ) (B.20) 1.5 2.5 τ + 1.11505 τ 5.41217 τ 7.44628 5 5.03365 τ ( ) (B.21) 1.5 2.5 5 0.64771 τ + 2.41539 τ 4.26979 τ + 3.25259 τ ( ) (B.22) τ 1 (B.23) whee s edued tempeatue. P vap : Cean and Meelles Method 37 8
Requed data: Stutue ln(p, vap, Pa) 1 ξ 2 N M A N 1 B + A 1 1.5 2 C B + 1 2 1.5 ln() - D1 + (B.24) C2 ln() - D2 + Q Q ξ q + (B.25) β q α + γ ln() δ (B.26) 1.5 ξ + (B.27) 1 f0 N f1 ξ (B.28) 2 s0 + Ns s1 whee s tempeatue n Kevn, M s moleula weght and A 1, B 1, C 1, D 1, A 2, B 2, C 2, D 2 ae goup ontbuton tems. N s the total numbe of abon atoms n the moleule and N s s the numbe of abons of the substtute faton. Fo example, N s of lau ad han, -OOC-(CH 2 ) 10 -CH 3, s 11. able B.4. Cean and Meelles Contbutons of Vapo Pessue ρ L : Halvosen Method 35 fo tglyedes Requed data:, P, Z RA of the fatty ads 9
x ( x MW ), ( x Z ) RA, G ρ + F (B.29) R x, P, 2 / 7 [1+ (1 ) ] (B.30) G MW 3 x MW + 38.0488 (B.31) G G F 0.0236 + 0.000082 875 MW when MW 875 (B.32) G G F 0.0236 + 0.000098 875 MW when MW 875 (B.33) whee x s mola faton of the th fatty ad han n the tglyede moleule, MW s the moleula weght of the th fatty ad,, s the tal tempeatue of the th fatty ad, P, s the tal pessue of the th fatty ad and Z RA, s the Raett paamete of the th fatty ad. able B.5. Requed Paametes fo Halvosen Method of ρ L Pedton Example: fnd the densty of tolen (18:1) at 20 10
Poedue: 1. olen s pue tglyede whh s omposed of thee ole ad hans (18:1). 2. x MW 1 MW 282.46 (g / mol) 0.28246 (g/mol) 18:1 x, 1 18:1 3. 6.4217 E - 04 (K / Pa) P P, 18:1 4. x Z 1 Z18:1 0.223 and RA, x, 1,18:1 293.15 819.41 3.5776E - 01 [1+(1 ) 2/7 ] [1+(1 5. ( x Z ) ( 1 Z ) 5.9437E - 02 RA, 18:1 ) 2/7 ] 6. G MW 3 x MW 885.4288 (g/mol) + 38.0488 3 (1 282.46) + 38.0488 G 3 7 F 0.0236 + 0.000082 875 MW 2.4455E - 02 (g/m ) 2.4455E01 (g/m 8. ρ G g ( ) 3 m R x P, ( x MW ), ( x Z ) RA, g 0.28246 ( mol 3 Pa - m 8.314 ( ) 6.4217E - K - mol g 914.66 3 m ) K 04 ( Pa 2/7 [1+(1 ) ] + F 9. he expemental value s 912.6 g/m 3 and the ARD s 0.23%. g + 2.455E01 ( ) 3 m ) 5.9437E - 02 3 ) C P, L : Moad Method 36 fo tglyedes Requed data:, ω of the fatty ads 11
G C P, L C IG p, mx x, ( 1 ) 1 1.45 + 0.45 + + R 0.25 ω mx 17.11 + 25.2 ( 1 ) 1/3 + 1.742 ( 1 ) (B.34) (B.35) C IG IG, p, mx x Cp, (B.36) ω mx x ω (B.37) MW mx x MW (B.38) MW G 3 x MW + 38 (B.39) G G F 0.2386 0.0005 850 MW when MW 850 (B.40) G G F 0.3328 + 0.0001 850 MW when MW 850 (B.41) whee R1.987 Cal/K-mol and the unt of heat apaty s Cal/K-mol. able B. 6 lsts the equed paametes of fatty ads. able B.6. Requed Paametes fo Moad Method of C P, L Pedton IG, Cp, s dea gas heat apaty of fatty ad. Moad et al. 36 use Rhan method 76 to IG, estmatec : p, 12
2 N a + N b + N + N d 3 C IG, (B.42) p whee N s the numbe of the gven funtonal goups. he unt of IG, Cp s Cal/K-mol. able B.7. Rhan Contbutons of Ideal Gas Heat Capaty fo Fatty Ad H vap :Vetee method ombned wth Watson elaton 29 Requed data: b,, P ΔH vap, b 0.38 0.5066 ( 1 b ) lnp 0.513 + 2 P R b (B.43) 1 + ln b b b ( 1 ( 1 ) ) 0.38 b ΔH vap ΔH vap, b 1 1 b 0.38 (B.44) whee ΔH vap,b s heat of vapozaton at nomal bolng pont, s edued tempeatue, and b s edued tempeatue at nomal bolng pont 13
B.2 NIS DE Equatons fo hemophysal Popety V L : NIS Raett Equaton 28 R V L C2 (B.45) P Z 1 + 1 RA able B.8. he Paametes of NIS Raett Equaton fo ME NIS DE Raett Equaton (m 3 /mol) C1 (Z RA ) C2 C3 (, K) C4 (P, Pa) C5 C6 C12:0 0.2445916 0.2857143 712 1748839 278 712 C14:0 0.2353773 0.2857143 718 1448599 292 718 C16:0 0.2227887 0.2857143 749 1205875 303 749 C16:1 0.2071558 0.2857143 734 1279721 240 734 C18:0 0.2298488 0.2857143 770 1178960 312 770 C18:1 0.2225078 0.2857143 751 1124671 253 751 C18:2 0.2226222 0.2857143 773 1162805 234 773 C18:3 0.224261 0.2857143 774 1202626 110 774 C20:0 0.1967211 0.2857143 767 1036965 319 767 C20:1 0.2138194 0.2857143 767 990082 636 767 C22:0 0.1841152 0.2857143 785 901921 326 785 C22:1 0.2122916 0.2857143 784 881791 110 784 C24:0 0.183291 0.2857143 804 821192 332 804 C24:1 0.2010567 0.2857143 802 822329 678 802 Paamete C1 C2 C3 C4 C5 C6 Despton Z RA - P lowe uppe Unt N/A N/A K Pa K K V L : NIS hemoml Equaton 28 V L C5 n 1 C (B.46) 1 able B.9. he Paametes of NIS hemoml Equaton fo V L 14
C P, IG : NIS Aly-Lee Equaton 28 C 2 2 C 3/ C 5/ P, IG C1 + C2 C4 Snh( C 3/) + (B.47) Cosh( C 5/) able B.10. he Paametes of NIS Aly-Lee Equaton fo C P, IG fo ME NIS Aly-Lee Equaton (J / mol-k) C1 C2 C3 C4 C5 C6 C7 C12:0 240063.9 542541.1-819 121697.8 0 200 980 C14:0 205454.4 805594.2-574 -442429.9 650 200 980 C16:0 230137.9 910125.1-574 -497826.1-650 200 980 C16:1 234231.9 895310.9-588 -512600-664 200 980 C18:0 267382.2 563286.7-569 596005.8-1600 200 980 C18:1 269559.9 532189.6-577 616279.7-1617 200 980 C18:2 261554.1 984480.8-1271 490798-556 200 980 C18:3 265702.7 972734.7-614 -599483.1-687 200 980 C20:0 278834.7 1117297-1214 609431-536 200 980 C20:1 282797.7 1102514-1240 579972.5-545 200 980 C22:0 299203.3 1224641 564-674861.1-641 200 980 C22:1 307461.3 1206798 1237 638488.9-544 200 980 C24:0 345378.1 741693.7 568 774619.4-1600 200 980 C24:1 347594 710543.1 574 794868.1-1613 200 980 Paamete C1 C2 C3 C4 C5 C6 C7 Despton - - - - - lowe uppe Unt J/mol-K J/mol-K K J/mol-K K K K C P, L : NIS hemoml Equaton 28 C C3 n 1 P, L C 1 (B.48) 15
able B.11. he Paametes of NIS hemoml Equaton fo C P, L C P, L : NIS DE Equaton 28 C P, L n 1 C7 C 5 + C 1 1 C (B.49) 6 1 C 6 NIS DE Equaton (J/mol-K) able B.12. he Paametes of NIS DE Equaton fo C P, L fo ME C1 C2 C3 C4 C5 C6 C7 C8 C9 C12:0 508414.7-1413.503 4.966722-0.004025 8804.63 712 4 278 698 C14:0 974844.7-4513.728 12.42177-0.009581 11780.11 718 4 292 704 C16:0 767706.7-2508.638 7.655214-0.005827 10693.47 749 4 303 734 C16:1 472441.6-168.3002 1.95041-0.001492 7765.68 734 4 240 719 C18:0 689451.7-1677.292 6.066038-0.004698 10924.92 770 4 312 755 C18:1 466346.9 120.4442 1.566388-0.00124 7728.59 761 4 253 746 C18:2 471973.1-38.21093 1.788936-0.001336 7519.56 773 4 234 758 C18:3 498535.9-209.9461 1.964523-0.001379 7539.46 774 4 250 759 C20:0 910960-2927.919 9.154863-0.007013 13838.95 767 4 319 750 C20:1 526862.5 76.54091 1.84262-0.001448 8310.67 767 4 250 750 Paamete C1 C2 C3 C4 C5 C6 C7 C8 C9 Despton - - - - - lowe uppe Unt J/mol-K J/mol-K J/mol-K J/mol-K J/mol-K K N/A K K P vap : NIS Wagne Equaton 28 1.5 C + 1 1 C2 1 C 6 C6 ln(p vap) ln(p ) + (B.50) 2.5 5 C6 + C + 3 1 C4 1 C6 C6 16
able B.13. he Paametes of NIS Wagne Equaton fo P vap fo ME NIS Wagne Equaton (Ba) C1 C2 C3 C4 C5 C6 C7 C8 C12:0-9.694324 2.509544-4.402982-9.230351 14.3745 712 278 712 C14:0-10.32312 0.2486618-0.272116-15.16169 14.1861 718 292 718 C16:0-10.98844 4.20676-8.735103-5.583598 14.0027 749 303 749 C16:1-11.50495 4.414073-9.852489-5.443423 14.0622 734 240 734 C18:0-11.01778 3.60513-9.883088-2.333603 13.9801 770 312 770 C18:1-11.90171 5.368385-10.61564-5.806015 13.933 761 253 761 C18:2-11.17148 4.445311-9.284593-5.08707 13.9664 773 234 773 C18:3-10.5887 2.436575-6.783611-7.340778 14 774 200 774 C20:0-12.79261 6.579309-14.06263-4.254656 13.8518 767 319 767 C20:1-12.46868 5.523578-12.0696-5.475907 13.8055 767 200 767 C22:0-13.41457 5.666122-13.2316-8.207159 13.7123 785 326 785 C22:1-12.9095 6.159538-13.16899-5.268222 13.6897 784 200 784 C24:0-13.15767 6.335366-13.74519-5.33026 13.6185 804 332 804 C24:1-13.28506 6.719306-14.09176-5.100378 13.6199 802 200 802 Paamete C1 C2 C3 C4 C5 C6 C7 C8 Despton - - - - ln (P ) lowe uppe Unt N/A N/A N/A N/A ln (Ba) K K K H vap : NIS Watson Equaton 28 ln(δ H vap 2 C6 ) C1 + C ln(1 ) 2 C (B.51) 5 C5 able B.14. he Paametes of NIS Watson Equaton fo NIS Watson Equaton (J / mol) H vap fo ME C1 C2 C3 C4 C5 C6 C7 C8 C12:0 18.71476 1.562579-1.321583 0.2647786 712 4 278 712 C14:0 19.11147 2.941289-3.70431 1.327995 718 4 292 718 C16:0 18.36144-0.701121 2.342368-1.24532 749 4 303 749 C16:1 19.10368 2.33551-2.86149 1.05891 734 4 240 734 C18:0 18.34189-0.918448 2.425747-1.143153 770 4 312 770 C18:1 18.67553 0.0416939 1.315343-0.907716 761 4 253 761 C18:2 19.07527 2.26599-2.78663 1.03997 773 4 234 773 C18:3 18.49942-0.978716 3.4717 2.2344 753 4 255 753 Paamete C1 C2 C3 C4 C5 C6 C7 C8 Despton - - - - - lowe uppe Unt N/A N/A N/A N/A K N/A K K 17
18