Abstract: The maximum effective hole-diameter mathematical model describing the flow of slightly
compressible fluid through a commingled reservoir was solved rigorously with consideration
of wellbore storage and different skin factors. The exact solutions for wellbore pressure
and the production rate obtained from layer j for a well production at a constant rate from
a radial drainage area with infinite and constant pressure and no flow outer boundary
condition were expressed in terms of ordinary Bessel functions. These solutions were
computed numerically by the Crump’s numerical inversion method and the behavior of systems
was studied as a function of various reservoir parameters. The model was compared with the
real wellbore radii model. The new model is numerically stable when the skin factor is
positive and negative, but the real wellbore radii model is numerically stable only when
the skin factor is positive.

Key words: well-testing, mathematical model, effective hole diameter, layered reservoir

摘要： The maximum effective hole-diameter mathematical model describing the flow of slightly
compressible fluid through a commingled reservoir was solved rigorously with consideration
of wellbore storage and different skin factors. The exact solutions for wellbore pressure
and the production rate obtained from layer j for a well production at a constant rate from
a radial drainage area with infinite and constant pressure and no flow outer boundary
condition were expressed in terms of ordinary Bessel functions. These solutions were
computed numerically by the Crump’s numerical inversion method and the behavior of systems
was studied as a function of various reservoir parameters. The model was compared with the
real wellbore radii model. The new model is numerically stable when the skin factor is
positive and negative, but the real wellbore radii model is numerically stable only when
the skin factor is positive.

关键词: well-testing;mathematical model;effective hole diameter;layered reservoir