ABSTRACT
For stimulated wells the value of dimensionless time based on the apparent radius (Eq. (6-2)) can be large and the wellbore should be considered to be a cylindrical source.
Let’s assume that a well is producing at a constant fl ow rate from an infi niteacting reservoir with the following characteristics: the reservoir is a homogeneous and isotropic porous medium of uniform thickness, the porosity and permeability are constant, the fl uid is small and has constant compressibility, constant fl uid viscosity , small pressure gradient s, negligible gravity forces and laminar fl ow in the reservoir and the Darcy law can be applied. For a well as a cylindrical source we need to obtain the solution to the diffusivity equation under the following boundary and initial conditions:
00 >∞<≤== trrp,r)p(t wi : .0,2 >=⎟⎠ ⎞⎜⎝
⎛ ∂ ∂ t
πkh qμ
r pr
( ) 0ip t,r p t→∞ → > . (6-4) where h is the reservoir thickness, q is the fl uid fl ow rate, pi is the initial reservoir pressure, μ is the viscosity and t is the production/test time.
