ENPE_381_Set-1-2010-Solution

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Petroleum System Engineering Faculty of Engineering University of Regina Natural Gas Engineering, ENPE 381 Problem Set # 1 Due : May 10, 2010 1. A natural gas has the following composition: Component C 1 C 2 C 3 i-C 4 n-C 4 i-C 5 n-C 5 C 6 C 7 + H 2 S CO 2 N 2 Mole % 74.62 8.99 5.11 1.03 1.69 0.69 0.76 0.95 3.34 0 2.49 0.16 C 7 + molecular weight = 126 lbm/lbm-mol, C 7 + gravity = 0.772 a. The average molecular weight, M a , of the gas mixture. Components Mole.% Yi Mole.% Yi Mi Mi yi hydrogen sulfide 0.00 0.00 34.08 0.00 Carbon Dioxide 2.49 2.49 44.01 1.10 Nitrogen 0.16 0.16 28.01 0.04 Methane 74.62 74.75 16.04 11.99 Ethane 8.99 9.01 30.07 2.71 Propane 5.11 5.12 44.10 2.26 i-butane 1.03 1.03 58.12 0.60 n-butane 1.69 1.69 58.12 0.98 i-pentane 0.69 0.69 72.15 0.50 n-pentane 0.76 0.76 72.15 0.55 hexane 0.95 0.95 86.18 0.82 hepatane plus 3.34 3.35 126.00 4.22 99.83 100.00 25.77 b. The specific gravity, g γ , of the gas mixture. Gas Sp.gr.= 0.8897311
c. The pseudocritical pressure, P pc , and the pseudocritical temperature, T pc , using the calculated gas gravity. d. The pseudocritical properties of the C 7+ fraction. TbC7+= 759.74048 TpcC7+= 1089.0443 PpcC7+= 388.08173 e. The pseudocritical pressure, P pc , and the pseudocritical temperature, T pc , using the simple mixing rules, Critical Critical Composition Composition Components pressure, psia temp., deg R (mole fraction) (mole fraction) P c x y i T c x y i C 1 668 343 0.7462 0.7475 499.31 256.38 C 2 708 550 0.0899 0.0901 63.7576 49.529 C 3 616 666 0.0511 0.0512 31.5312 34.091 nC 4 551 765 0.0169 0.0169 9.32776 12.951 iC 4 529 735 0.0103 0.0103 5.45798 7.5834 nC 5 489 845 0.0076 0.0076 3.72273 6.4329 iC 5 490 829 0.0069 0.0069 3.38676 5.7298 nC 6 437 913 0.0095 0.0095 4.15857 8.6883 nc 7+ 388.08173 1089.0443 0.0334 0.0335 12.984 36.436 nC 8 361 1024 0 0.0000 0 0 nC 9 332 1070 0 0.0000 0 0 nC 10 304 1112 0 0.0000 0 0 CO 2 1071 548 0.0249 0.0249 26.7133 13.668 H 2 S 1306 672 0.0000 0.0000 0 0 N 2 493 227 0.0016 0.0016 0.79014 0.3638 Ma = 0.9983 1.0000 661.14 431.86 γ = P pc T pc
f. The pseudocritical pressure, P pc , and the pseudocritical temperature, T pc , using Stewart et al mixing rules. J= 0.66941752 K= 17.2973624 Tpc (R ) 447.634611 Ppc (psia) 668.1946824 Z @ (300F, 3758.6psia) 0.904258825 Mw 25.76666273 Gas Gravity 0.889425707 g. Correct the pseudocritical pressure, P pc , and the pseudocritical temperature, T pc obtained in part f. ε 4.003 Correctet P pc and T pc 655.013 427.85 h. The pseudocritical pressure, P pc , and the pseudocritical temperature, T pc , using McCain’s method. Tpc (R ) 443.9354457 Ppc (psia) 634.9397636 Z @ (180F, 1000psia) 0.829005499 Mw 25.82443454 Gas Gravity 0.891419901 i. Use the results of part h to build a table of the following gas properties at a temperature of 249 o and pressure of 500, 1000, 1400, 2000, 2500, and 3000 psia: z factor, gas density, ρ g , and gas formation volume factor, B g .
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