Step 1: Recall what skin factor represents:
The skin factor s is a dimensionless number introduced by Van Everdingen and Hurst to account for the extra pressure drop that occurs near the wellbore compared to the pressure drop predicted by ideal radial Darcy flow. A positive skin factor means there is extra resistance to flow near the well, and a negative skin factor means the near wellbore flow is easier than the ideal case.
Step 2: Effect of formation damage:
Formation damage happens when drilling fluid, mud solids, scale, or fines invade and reduce the permeability of the rock close to the wellbore. Reduced permeability near the well raises the resistance to flow in that zone, so the extra pressure drop increases. This extra pressure drop is captured as a positive addition to the skin factor. Therefore formation damage near the wellbore increases the skin factor, which makes statement C correct and statement D incorrect.
Step 3: Effect of hydraulic fracturing:
A successful hydraulic fracturing job creates a highly conductive fracture that connects the wellbore to a much larger effective drainage area. This fracture behaves like a large increase in the effective wellbore radius, so the extra resistance to flow near the well is removed and often becomes a bonus rather than a penalty. As a result the skin factor becomes smaller, and for a well stimulated well it becomes negative. Therefore successful hydraulic fracturing decreases the skin factor, which makes statement B correct and statement A incorrect.
Step 4: Combine the correct statements:
From the two effects above, the statements that are correct are B, successful hydraulic fracturing decreases the skin factor, and C, formation damage near the wellbore increases the skin factor.
Final Answer:
\[ \boxed{\text{B and C}} \]