1. A well is being drilled at a depth of 5,000 ft using a Bingham Plastic fluid having a density of 10 lb m/g al, a plastic viscosity of 25 cp and a yield point of 5 lbf/100sqft. The drill string 0 D is 4.5 inches and the hole diameter is 6.5 inches.
(a) Determine the minimum pump flow rate (g al/min) that may cause turbulent flow in the annulus. (10 points).
(b) Determine the frictional pressure loss along the drill string annulus (psi) at the pump flow rate that you obtained in part a, while assuming a turbulent flow in the annulus. (10 points)
(c) Determine the equivalent circulation density (lb m/g al) using the frictional loss that you obtained in part b. (5 points)
2. The following drilling cost data are given:
Bit type             TCI bit    DRI PDC
Bit cost          $ 45,000    $ 70,000
Drilling hours       50             35
Trip ping hours    10             10
Make up hours    1                1
Interval drilled (ft) 1000          1000
Determine the minimum rig cost per hour to justify the use of DRI PDC bit. (15 pts)
3. The bit currently in use has three 12/32 inch nozzles. The driller has recorded that when the 10lbm/gal mud is pumped at a rate of 500 gal/min, a pump pressure of 2500 psig is observed, and when the pump is slowed to a rate of 250 g al/min, a pump pressure of 650 psig is observed.
The pump is rated at 1200 hp and has an overall efficiency of 0.9. The maximum allowable surface pressure is 3200 psi. A minimum flow rate of 100 gal/min is required to keep the cuttings in the annular section suspended.
a. Determine the optimum pump flow rate (g al/min) that maximizes the bit horsepower for the next bit run. (30 pts)
b. Assuming the three nozzles have equal sizes, determine the size of each nozzle to the nearest 32nd of an inch for the optimum pump flow rate that you have found in part a (5 pts). The nozzle efficiency is CD = 0.95.
4. The overburden stress gradient at 1000 ft depth is 0.8 psi/ft. The formation underneath is a thick shale layer with constant compressional wave slowness of 180 us/ft.
a) Estimate the overburden stress gradient at 1200 ft, in (lbm/gal) units. (15 pts)
b) Use Eaton's formula to obtain the pore pressure gradient at 1200 ft in (lb m/gal). (10 pts)
The normal compaction trend can be obtained from the following equation: dtc.n (micro sec/ft) = 62 + 152.6 Exp [-0.0001 z] - 28.1 Exp [-0.0002 7], where Z is depth in ft. Assume the normal pressure gradient is equal to the density of freshwater (SG=1).

1. A well is being drilled at a depth of 5,000 ft using a Bingham P...