Theoritical underpinning for horizontal drillling, and multistage fracking:  Horizontal drilling and fracking increase effective area to flow (represented in the Darcy flow equation as rw), to counteract decreasing reservoir quality (represented by kg).

 

 

Where: qg=gas production

  kg=gas relative permeability

   h=height of productive interval

   pe=reservoir pressur

   pw=pressure at the wellbore/wellhea

   ug=gas viscosity

    zavg=gas compressibility facto

    Tr=formation temperature

     re=drainage radiu

     rw=effective wellbore radius

     S=formation damage factors