315-AL11-S2023

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Solution AL11-315 Date Student Signature____________ © PETE 315 – Learning Activities by Dr. Maria Barrufet 1/6 PETE 315 – Petroleum Thermodynamics Chapter 12-13 These chapters supplement the material presented in class. The problems assigned are not from the book, particularly the problems related to ternary diagrams which were discussed extensively in class. 1. The following ternary diagram shows the phase behavior of C 1 /C 2- C 6 /C 7 + mixtures at 300 o F and 1,800 psia . You are in charge of analyzing the behavior of a reservoir oil with a composition of 10% C 1 , 60% C 2 -C 6 and 30 % C 7 + . 5,000 moles of the reservoir oil indicated above were mixed with CH 4 at constant pressure and temperature and two phases formed. The resulting overall mixture (z i ) has a methane composition of 40% . Determine a. The molar fraction of gas formed (f v ) b. The number of moles of methane added to the 5,000 moles of oil c. The equilibrium gas and oil compositions. To evaluate f v use methane as the guide, the reason is that because of round off errors in reading you would not get exactly the same value when using the other components. You can also use a ruler and measure the distance (between bubble and dew point compositions along the equilibrium line and overall and liquid compositions). This is equivalent to using the length of the vectors.     ( ) ( ) ( ) ( ) ( ) ( ) v z x z x z x z x f y x y x y x y x − + − + − − = = − − + − + − 2 2 2 1 1 2 2 3 3 2 2 2 1 1 2 2 3 3 Mark all pertinent points ( dilution and equilibrium lines, and equilibrium compositions ) in the graph. Equilibrium Gas Compositions (y i ) Equilibrium Liquid Compositions (x i ) C 1 51 % 33 % C 2 -C 6 40 % 40 % C 7 + 9 % 27 % Total 100 % 100 % f v = 0.39 n C1 added = 2500 1 1 1 1 0.4 0 9 .33 0.51 0.3 3 3 0. v z x f y x − − = = = − − 1 1 1 1 1 0.1 0.1 5000 0.4 5000 o o n n n z n n n  +   +  = = = +  + 

2 © PETE 315 – Learning Activities by Dr. Maria Barrufet 2/6 ( ) 1 1 1 4 2,50 5000 0.1 500 . 0 0 0 3 1 1 0. moles z n z −   = = = − − 2. Using the same diagram used in problem 1 (duplicated below for clarity). Respond to the following questions and MARK your answers in the diagram. a. What is the maximum number of moles of methane ( i.e. C 1 ) that can be added to the 5,000 moles of oil to reach the bubble point and what is the bubble point composition?

3 © PETE 315 – Learning Activities by Dr. Maria Barrufet 3/6 1 1 1 1 1 0.1 0.1 5000 0.34 5000 o o n n n x n n n  +   +  = = = +  +  ( ) ( ) 1 1 1 5000 0.1 5 1 000 0.34 0.1 1 1 0. 818.1 4 8 3 moles x n x − −  = = = − − b. What is the lowest number of moles of methane ( i.e. C 1 ) that can be added to the 5,000 moles of oil to reach the dew point and what is the dew point composition? 1 1 1 1 1 0.1 0.1 5000 0.85 5000 o o n n n y n n n  +   +  = = = +  +  ( ) ( ) 1 1 1 5000 0.1 5 2 000 0.8 0 5,0 1 00 5 . 1 1 0.85 moles y n y − −  = = = − −

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4 © PETE 315 – Learning Activities by Dr. Maria Barrufet 4/6 3. C 1 has been injected in your reservoir at constant T and p. After mixing the equilibrium gas C 1 composition in the reservoir is 71 %. a. What is the molar ratio of (moles of methane injected) /(moles in the reservoir) (use the correct nomenclature for this course). 1 1 1 1 1 0.1 0.1 5000 0.67 5000 o o n n n z n n n  +   +  = = = +  +  ( ) ( ) 1 1 1 5000 0.1 50 , 00 0.67 6 8 636 0.1 6 1 1 7 .3 0. moles z n z − −  = = = − − 1 8636.3 1.73 6 5000 r n molar ratio n  = = =

5 © PETE 315 – Learning Activities by Dr. Maria Barrufet 5/6 b. What is the equilibrium liquid composition in the reservoir? ( ) 0.35,0.24,0.41 x c. What is the molar fraction of gas in the reservoir? (f v ) 1 1 1 1 0.67 0 9 .35 0.71 0 . .3 0 5 88 v z x f y x − − = = = − − Note that when I ask “what is the composition ….” Composition is a vector with 3 components: Mole fractions for C 1 , for C 2 -C 6 and for C 7 + .

6 © PETE 315 – Learning Activities by Dr. Maria Barrufet 6/6 4. ( Individual Bonus: 3 points on most needed exam ) How does the answer in (3) change of instead of injecting pure C 1 you inject a mixture of 80%C 1 and 20% C 2-6 ? – Assume that the equilibrium C 1 gas composition resulting from the resulting mixture is still 0.71. You can visualize this by using the excel file provided in Canvas. Mixture is above the dew-point curve, so the composition is all gas: ( ) 0.71,0.26,0.3 y 1 1 0.8 0.1 5000 0.8 0.71 5000 o s s s s z n n n y n n n +    +   = = = +  +  ( ) ( ) 1 1 5000 0.2 50 8 00 0.71 . 3 ,888. 0 1 0.8 0. . 8 8 0 71 s moles y n y − −  = = = − − 1 33888. 6.78 8 5000 r n molar ratio n  = = = 1 v f =

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