Solve the following BVP-ODE with the Finite-Difference, Shooting, and Successive Over- relaxation Methods. Use a step size of 0.01. You may use MATLAB or Excel/VBA to solve these BV-ODES. Remember to completely annotate your programs and turn in your complete programs and output. Also turn in a complete description of your algorithm that you used in the program, i.e., as shown in the notes and examples in class. Compare and contrast the use of all three BVPnumerical methods that were used to solve this problem.

1. A drillstring consists of 9,000 ft 5 in, 19.5 lbm/ft drillpipe, and1,000 ft of 8 in OD, 3in ID drill collars. What is the: (a) Volume of the drillpipe in bbl. (b) Volume of the drill collars in bbl (c) Number of pump cycles required to pump surface mud to the bit(duplex pump, 6 in liners, 2.5 in rods, 16 i strokes, pumping at 85 % volumetric efficiency). (d) Displacement of drillpipes in bbl/ ft (e) Displacement of drill collars in bbl/ft.

3. What do you mean by Reid vapor pressure. How is performance of a spark ignition motor engine effected if the fuel's Reid vapor pressure is too high or too low ?

Relative permeability measurements are made on three core samples. The measured data are summarized below: Core sample 1 h = 1 ft k = 100 mD Soc= 0.35 Swc= 0.25 Water Saturation Sw 0.20 0.25 0.30 0.40 0.50 0.60 0.65 0.72 *Value at critical saturation Core sample 2 h = 1 ft k=80 mD 0.850* 0.754 0.557 0.352 0.131 0.000 Soc= 0.28 Swc = 0.30 Core sample 1 Kro Krw Core sample 2 Kro Krw 0.000 0.018 0.800 0.092 0.593 0.198 0.393 0.327 0.202 0.400* 0.111 0.000 0.000 0.077 0.191 0.323 0.394 0.500* Core sample 3 h = 1 ft k=150 mD Soc= 0.35 Swc = 0.20 Core sample 3 Krw 0.000 0.008 0.027 0.088 0.176 0.286 0.350* Kro 1.000* 0.872 0.839 0.663 0.463 0.215 0.000 It is believed that a connate water saturation of 0.27 and critical oil saturation of 30% better describe the formation. Generate Oil and water relative permeability data using new critical saturation. Plot the averaging relative permeability data. Using data given, de-normalize the data to generate the required relative permeability data.

A mixed hydrocarbon stream must be distilled in a continuous distillation column. The flow rate of the feed is 1000 kmol/h. The feed enters as a liquid at its boiling point. The feed mixture containing six components (CH4 = 0.032, C2H4 = 0.068, C2H6 = 0.17, C3H6= 0.30, C3H8 = 0. 32, n-C4H10 = 0.11) is to be separated by distillation. It is desired to recover 98.5% mole fraction of the light key in the distillate and 98% of the heavy keyin the bottom product. The average relative volatility (a) values are given in Table 1.The a can be assumed to remain constant with any temperature variation. 1.Determine the light key (LK) and heavy key (HK). 2.Use Underwood's method to determine the minimum reflux ratio (the 0 valuesto try are 1.1.1.17 and 1.2).(15) Use the Fenske equation to determine the minimum number of trays.

The following PVT data are from a volumetric oil reservoir at an initial pressure of 2000 psia.The connate water saturation is 25%. Assume negligible rock and water compressibilities. 1. Was this reservoir initially saturated or under saturated? Why? 2. When the reservoir pressure fell to 1500 psia, the cumulative production of oil and gas were 7.5 MMstb and 9.5 Bscf respectively. Estimate the initial oil in place. 3. What was the initial reservoir pore volume?

Solve the following BVP-ODE with the Finite-Difference, Shooting, and Successive Over- relaxation Methods. Use a step size of 0.01. You may use MATLAB or Excel/VBA to solve these BV-ODES. Remember to completely annotate your programs and turn in your complete programs and output. Also turn in a complete description of your algorithm that you used in the program, i.e., as shown in the notes and examples in class. Compare and contrast the use of all three BVPnumerical methods that were used to solve this problem. A chemical reactor with axial dispersion is governed by the following equations: