ABSTRACT
Let us assume that a well is producing at a constant fl ow rate from an infi niteacting reservoir and: reservoir is a homogeneous and isotropic porous medium of uniform thickness, porosity and permeability are constant, fl uid of small and 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 it is necessary to obtain the solution of the diffusivity equation under following boundary and initial conditions:
2 >=⎟⎠
⎞⎜⎝ ⎛
∂ ∂
= t,
πkh qμ
r pr
where h is the reservoir thickness, rw is the well radius, pi is the initial reservoir pressure, q is the fl ow rate, k is the permeability, and μ is the fl uid viscosity . It is well known, that in this case, the diffusivity equation has a solution in complex integral form (Van Everdingen and Hurst 1949; Carslaw and Jaeger 1959).
