During drilling, a well is damaged out to a radial distance of 5 ft from the periphery of the wellbore so that the permeability within the damaged zone is reduced to \( \frac{1}{50} \) of the undamaged effective permeability. After completion, the well is stimulated so that the permeability out to a radial distance of 15 ft from the periphery of the wellbore is increased to twenty times the permeability of the undamaged zone.
The radial inflow equation for stabilized flow conditions under semi-steady state conditions is given by:
\[
p_e - p_{wf} = \frac{q \mu}{2 \pi k_e h} \left[ \ln \left( \frac{r_e}{r_w} \right) - \frac{1}{2} + S \right]
\]
Where \( p_e \) is effective pressure, \( p_{wf} \) is flowing bottom-hole pressure, \( q \) is flow rate, \( \mu \) is viscosity, \( k_e \) is average effective permeability, \( h \) is reservoir thickness, \( r_e \) is drainage radius, \( r_w \) is wellbore radius, and \( S \) is skin factor.
If \( r_w = 0.5 \, \text{ft} \) and \( r_e = 500 \, \text{ft} \), then the increase in Productivity Index ratio \( \left( \frac{P_{\text{stimulated}} - P_{\text{well}}}{P_{\text{unstimulated}} - P_{\text{well}}} \right) \) is \(\underline{\hspace{2cm}}\) (round off to one decimal place).