One of the most promising methods for extracting crude oil employs a carbon dioxide (CO) flooding...

  

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One of the most promising methods for extracting crude oil employs a carbon dioxide (CO) flooding technique. When flooded into oil pockets, CO2 enhances oil recovery by displacing the crude oil. In a microscopie investigation of the CO2 flooding process, flow tubes were dipped into sample oil pockets containing a known amount. The oil pockets were flooded with co, and the percentage of oil displaced was recorded. The experiment was conducted at three different flow pressures and three di fferent dipping angles. The displacement test data are recorded in Table 2. Table 2 Pressure (xi) (Pounds per Square Inch) Dipping Angle (x2) (Degrees) Oil Recovery (y) (Percentage) 1000 60.58 72.72 79.99 1000 15 1000 30 1500 66.83 1500 15 80.78 1500 30 89.78 2000 69.18 2000 15 80.31 2000 30 91.99 a.) Write a complete sccond-order model with interaction relating percentage oil recovery y to pressure x, and dipping angle xz. b.) It is believed that the second order terms can be left out of the model. Write a complete first order model with interaction relating percentage oil recovery y to pressure xi and dipping angle x2. c.) Microsoft Excel was used to obtain the two models in questions a.) and b.) and the following results was obtained: SUMMARY OUT PUT FOR QUESTION 2 Regression Statistics Multiple R R Square 0.981851006 0.964031398 Adjusted R Square 0.942450237 Standard Error 2.508384606 Observations 9. ANOVA df Significance F MS Regression Residual 3 843.1908333 281.0636111 44.67004274 0.000493383 5 31.45996667 6.291993333 Total 8 874.6508 Coefficients Standard Error t Stat Upper 95% P-value Lower 95% Intercept X Variable 1 X Variable 2 X Variable 3 54.5 5.034158413 10.82603993 0.000116695 41.55930497 67.44069503 0.007696667 0.003238311 2.376753688 0.06341952 -0.000627662 0.016020995 0.554111111 0.259962823 2.131501365 0.086240036 -0.114143507 1.222365729 0.000113333 0.000167226 0.67772701 0.528031686 -0.000316533 0.0005432 SUMMARY OUT PUT FOR QUESTION 2 Regression Statistics Multiple R R Square Adjusted R Square 0.986458697 Standard Error 0,997457774 0.994922012 1.216753422 Observations ANOVA Significance F 5 870.2093333 174.0418667117.5570232 0.001223007 df MS Regression Residual 3 4.441466667 1.480488889 Total 8 874.6508 Coefficients Standard Eror t Stat Lower 95% Upper 95% P-value Intercept X Variable 1 X Variable 2 X Variable 3 X Variable 4 X Variable 5 26.19333333 7.579656577 3.45574144 0.040766103 2.071460635 50.31520603 0.047716667 0.010443308 4.56911419 0.019666674 0.014481369 0.080951965 0.760111111 0.170474187 4.4588047190.021002747 0.217585654 1.302636568 0.000113333 8.11169E-05 1.397160649 0.256772122 -0.000144817 0.000371484 -1.334E-05 3.4415E-06-3.876218589 0.030400321 -2.42924E-05-2.38761E-06 -0.006866667 0.003823887-1.795729451 0.170407335 -0.019035993 0.00530266 Is there sufficient evidence to support the statement made in b.)? Motivate your answer statistically. Use a = 0.05. One of the most promising methods for extracting crude oil employs a carbon dioxide (CO) flooding technique. When flooded into oil pockets, CO2 enhances oil recovery by displacing the crude oil. In a microscopie investigation of the CO2 flooding process, flow tubes were dipped into sample oil pockets containing a known amount. The oil pockets were flooded with co, and the percentage of oil displaced was recorded. The experiment was conducted at three different flow pressures and three di fferent dipping angles. The displacement test data are recorded in Table 2. Table 2 Pressure (xi) (Pounds per Square Inch) Dipping Angle (x2) (Degrees) Oil Recovery (y) (Percentage) 1000 60.58 72.72 79.99 1000 15 1000 30 1500 66.83 1500 15 80.78 1500 30 89.78 2000 69.18 2000 15 80.31 2000 30 91.99 a.) Write a complete sccond-order model with interaction relating percentage oil recovery y to pressure x, and dipping angle xz. b.) It is believed that the second order terms can be left out of the model. Write a complete first order model with interaction relating percentage oil recovery y to pressure xi and dipping angle x2. c.) Microsoft Excel was used to obtain the two models in questions a.) and b.) and the following results was obtained: SUMMARY OUT PUT FOR QUESTION 2 Regression Statistics Multiple R R Square 0.981851006 0.964031398 Adjusted R Square 0.942450237 Standard Error 2.508384606 Observations 9. ANOVA df Significance F MS Regression Residual 3 843.1908333 281.0636111 44.67004274 0.000493383 5 31.45996667 6.291993333 Total 8 874.6508 Coefficients Standard Error t Stat Upper 95% P-value Lower 95% Intercept X Variable 1 X Variable 2 X Variable 3 54.5 5.034158413 10.82603993 0.000116695 41.55930497 67.44069503 0.007696667 0.003238311 2.376753688 0.06341952 -0.000627662 0.016020995 0.554111111 0.259962823 2.131501365 0.086240036 -0.114143507 1.222365729 0.000113333 0.000167226 0.67772701 0.528031686 -0.000316533 0.0005432 SUMMARY OUT PUT FOR QUESTION 2 Regression Statistics Multiple R R Square Adjusted R Square 0.986458697 Standard Error 0,997457774 0.994922012 1.216753422 Observations ANOVA Significance F 5 870.2093333 174.0418667117.5570232 0.001223007 df MS Regression Residual 3 4.441466667 1.480488889 Total 8 874.6508 Coefficients Standard Eror t Stat Lower 95% Upper 95% P-value Intercept X Variable 1 X Variable 2 X Variable 3 X Variable 4 X Variable 5 26.19333333 7.579656577 3.45574144 0.040766103 2.071460635 50.31520603 0.047716667 0.010443308 4.56911419 0.019666674 0.014481369 0.080951965 0.760111111 0.170474187 4.4588047190.021002747 0.217585654 1.302636568 0.000113333 8.11169E-05 1.397160649 0.256772122 -0.000144817 0.000371484 -1.334E-05 3.4415E-06-3.876218589 0.030400321 -2.42924E-05-2.38761E-06 -0.006866667 0.003823887-1.795729451 0.170407335 -0.019035993 0.00530266 Is there sufficient evidence to support the statement made in b.)? Motivate your answer statistically. Use a = 0.05.

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