Exercise 4.14

Removing oil from a water/oil mix. In the oil industry, water that mixes with crude oil during production and transportation must be removed. Chemists have found that the oil can be extracted from the water/oil mix electrically. Researchers at the University of Bergen (Norway) conducted a series of experiments to study the factors that influence the voltage (y) required to separate the water from the oil (Journal of Colloid and Inter-face Science, August 1995). The seven independent variables investigated in the study are listed in the table below. (Each variable was measured at two levelsa low level and a high level.) Sixteen water/oil mixtures were prepared using different combinations of the independent variables; then each emulsion was exposed to a high electric field. In addition, three mixtures were tested when all independent variables were set to 0. The data for all 19 experiments are also given in the table. (a) Propose a first-order model for y as a function of all seven independent variables. (b) Use a statistical software package to fit the model to the data in the table. (c) Fully interpret the estimates. (d) Find and interpret s. (e) Find and interpret R2. (f) Conduct a test of overall model utility. (g) Do you recommend using the model in prac-tice? Explain.

1. Removing oil from a water/oil mix. Refer to Exercise 4.14 (p. 189). The researchers concluded that in order to break a wateroil mixture with the lowest possible voltage, the volume fraction of the disperse phase (x1) should be high, while the salinity (x2) and the amount of surfactant (x5) should be low. Use this information and the first-order model of Exercise 4.14 to find a 95% prediction interval for this low voltage y. Interpret the interval.