1. Consider a well that is completed in three zones. Zone 1 is 10 ft thick, has a permeability of 500 md, and has a damaged region with a permeability of 60 md extending one foot into the reservoir. Zone 2 is 20 ft thick, has a permeability of 200 md, and its damaged region having a permeability of 40 md extending 6 inches into the reservoir. Zone 3 is 20 ft thick, has a permeability of 80 md, and its damaged region having a permeability of 30 md extending 5 inches into the reservoir. The well radius is 0.25 ft, the well drains a 60-acre region, and there are no other completion skin effects. What is the overall skin factor for this well? If we injected acid into this well to restore the permeability in the damaged region, what would be the initial distribution of the injected acid into the three layers?

2. If rw = 0.25 ft, h = 165 ft, hw = 75 ft, and zw = 82.5 ft (midpoint of the reservoir), calculate the partial completion skin effect for a vertical well. At which angle of well deviation would the contribution from s𝜃 nullify the effects of sc (i.e., sc+𝜃 ≈ 0)?

3. A vertical well with a wellbore radius of 0.5 ft has been completed through the top half of the pay zone. The pay zone is 1000 ft thick. The perforation density is 2 shots/ft and the perforations are 6in. long, resulting in a perforation skin factor, not considering any damage or other effects, of 6 (sp =6). There also exists a damage zone around the well extending one foot into the formation from the wellbore, in which the permeability is 10% of the undamaged permeability.
Consider a pseudoskin factor of 4.5.
a. What is the total skin factor for this well?
b. If the well is originally perforated in the same zone (top half of the pay zone) to 2 shots/ft and 1.5 ft long, resulting in a perforation skin of 1, what is the total skin?

4. Suppose that 1,000 bbl/day of 16 °API, 5 cp oil is being produced through 2 7/8 in., 8.6 lbm/ft tubing in a well that is 3 degrees from vertical. If the tubing wall relative roughness is 0.001, assuming no free gas in tubing string, calculate the pressure drop over 1,000 ft of tubing.

5. Suppose 3 MMscf/d of 0.75 specific gravity gas is produced through a 3 1⁄2 in. tubing string set to the top of a gas reservoir at a depth of 8,000 ft. At the tubing head, the pressure is 1,000 psia and the temperature is 120 °F; the bottom-hole temperature is 180 °F. The relative roughness of tubing is about 0.0006. Calculate the pressure profile and plot the results.

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