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    Problem 13-10 Perform a three-stage separator calculation for the following black oil

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Problem 13-10

Perform a three-stage separator calculation for the following black oil.

            Refer to Excel Spreadsheet for composition chart

Use K-factor of decane for heptane plus. The black oil is produced from a reservoir at its bubble point of 2361 psia at 225°F.

            Primary separator conditions: 250 psig and 160°F

            Second separator conditions: 50 psig and 150°F

            Stock tank conditions: 120°F

Calculate

1. Composition of primary separator gas, mole fraction
2. Specific gravity of primary separator gas
3. Composition of second separator gas, mole fraction
4. Specific gravity of second separator gas
5. Composition of stock tank gas, mole fraction
6. Specific gravity of stock tank gas
7. Primary separator gas oil ratio, scf/STB
8. Second separator gas oil ratio, scf/STB
1. Stock tank gas oil ratio, scf/STB
10. Total gas oil ratio, R_sb, scf/STB
11. Formation volume factor of oil, B_ob, res bbl/STB
50. Gravity of stock tank oil, °API

Compare your answers with laboratory results of

            B_ob = 1.604 res bbl/STB, R_sb = 986 scf/STB

            Ρ_oR = 41.31 lb/cu ft, γ_STO = 38.0°API

            γ_gSP1 = .986, γ_gSP2 = 1.257 and γ_gST = 1.557

Steps

1. Divide each mole fraction by 100 in order to get the summation equal to one.
2. Use appendix A in the back of the book to determine the equilibrium ratios, K, at 250 psig and 160°F (Separator one conditions).
3. Use the square root of methane * ethane to find Carbon Dioxide equilibrium ratio
4. Use Appendix A to find the molecular weight of each component in lb/lb mole
5. To solve for the liquid fraction, X_j, of each component you must use equation 12-17 from the book.
6. My first guess for n_g was .55 and after that I used the “goal seek” tool in excel to find the exact n_g that will give all of the liquid fractions, X_j, a summation equal to one.
7. To find the gas composition fractions, multiply the liquid composition fraction, X_j, with the equilibrium ratio, K_j.
8. The n_L value will be calculated by subtracting the n_g value from one because the summation of n_g and n_L is equal to one.
9. The mass of gas is the summation of gas fraction, Y_j, multiplied by molecular weight M_j,
10. The specific gravity can be taken by dividing the total mass of gas by 29, which equals 1.016813715. A 2.95% error from lab results .986
11. The mole fraction, Z_j, for separator two is equal to the liquid fractions, X_j, from separator one because only the liquid travels to separator two.
12. Find the equilibrium ratios, K_j, using Appendix A, for 50 psig and 140°F (second separator conditions).
13. Again take the square root of methane * ethane to find the equilibrium ratio for carbon dioxide.
14. Using equation 12-17 and a guess of .3 for value of n_g to find the liquid fraction, X_j, and then using the “goal seek” tool in excel to find the exact n_g value that causes the liquid fractions to have a summation of one.
15. Once you have the exact liquid fractions, X_j, multiply them by your equilibrium ratios, K_j, to find the gas fractions, Y_j.
16. Multiply the gas fraction, Y_j, by the molecular weight, M_j, that we found from Appendix A earlier and then take the summation to find the total mass of gas in in separator two.
17. Once you find the total mass, divide that by 29 to get the specific gravity. The calculations gave a specific gravity of 1.27219, which has a 1.194% error from the lab result 1.257.
18. The mole fraction, Z_j, for the stock tank will be equal to the liquid fractions, X_j, calculated from separator two conditions because only the liquid is moved from separator two into the stock tank.
19. Find the equilibrium ratios, K_j, at 0 psig and 140°F ( Stock Tank conditions) using Appendix A.
20. Again take the square root of the equilibrium ratios of methane * ethane to get the equilibrium ratio for carbon dioxide.
21. Then using equation 12-17 and an initial guess of .2 for value of n_g I found the liquid compositions. I then used the “goal seek” tool in excel to change the n_g value so that the summation of liquid fractions was equal to one.
22. Then multiply your liquid fraction, X_j, by your equilibrium ratio, K_j, to find your gas fraction, Y_j.
23. Your gas fraction, Y_j, multiplied by your molecular weight, M_j, gives you you mass of gas and the summation of that gives you the total mass of gas in the stock tank.
24. Divide your total mass by 29 to get a specific gravity of 1.717 and a 9.318% error. This error is a little high and could be due to the fact that we have error in the previous two separator calculations that can cause larger area later.
25. Now using the liquid densities of stock tank oil at STC you can find the liquid volume by multiplying X_j * M_j and dividing the product by the liquid denities. (X_j is the liquid fractions calculated in Step 21 and the liquid densities come from the book on page 381)
26. Take the mass of Propane + by multiplying each liquid fraction, X_j, with each molecular weight, M_j, then take the summation of the liquid masses for Propane + and divide that by the summation of liquid volume for Propane +. This will give you the density of the oil.
27. Calculate your W1 factor by dividing liquid mass of methane by Total Mass of liquid. Use equation 11-2 to calculate your W2 factor.
28. Then take your W1 and W2 factor and use Figure 11-6 to find the density ratio. Multiply your calculated density of oil with your density ratio to get the Pseudoliquid Density.
29. Find the specific gravity of stock tank oil using equation 8-1.
30. Then with the specific gravity and equation 8-2 you can find the gravity of stock tank oil, which was calculated as 38.296°API. That gives a .773% error from the lab result of 38°API.
31. Using equation 13-10 we can calculate gas-oil ratio for separator one.
32. Using equation 13-11 we can calculate gas-oil ratio for separator two.
33. Using equation 13-12 we can calculate gas-oil ratio for Stock Tank.
34. The Total Gas-Oil ratio can be found by summing the results of gas-oil ratios from separator one, separator two, and the stock tank. The calculated Totlal gas-oil ratio, 941.5, had a 4.726% error from lab results 986 scf/STB.
35. Multiply your original Reservoir Mole compositions, Zj, with each components molecular weight, Mj, to find the liquid mass in the reservoir. (You can do this because there is no gas in the reservoir since we are at bubble point).
36. Then divide the liquid masses for propane plus by there liquid densities that we used in Step 25 to get your liquid volume.
37. Sum all of the liquid masses of propane plus and divide this by the summation of liquid volume for propane plus. This will give you the density of propane plus at Reservoir Conditions.
38. Use equation 11-1 and 11-2 to calculate the W1 and W2 at Reservoir conditions.
39. Then use figure 11-6 to find the density ratio and multiply that by the calculated liquid density in Step 37. This is your Pseudoliquid Density.
40. Using chart 11-3, 11-4, and 11-7(Hydrogen Sulfide Adjustment) we cam find the adjustment factors for Pressure and Temperature. After using these adjustment factors we will have our Reservoir Liquid Density, ρ_oR.
41. Our Mass of Liquid in the Reservoir, M_oR, is the summation of results from Step 35.
42. Then using the Liquid Density from Step 40 and Mass of Liquid from Step 41 we use equation 13-14 to calculate Formation volume factor of oil, B_ob.