An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: II. Finite Difference Treatment

Abstract

An investigation of the effect of well bore storage and skin effect on transient flow was conducted using a finite-difference so lution to the basic partial differential equation. The concept of skin effect was· generalized to include a damaged annular region adjacent to the wellbore (a composite reservoir). The numerical solutions were compared with analytical solutions for cases with the usual steady-state skin effect. It was found that the solutions for a finite-capacity skin effect compared clos~ly with analytical solutions at short times (wellbore storage controlled) and at long times after the usual straight line was reached. For intermediate times, presence of a finite-cap acity skin effect caused· significant departures from the infinitesimal skin solutions. Two straight lines occurred on the drawdown plot for cases of large radius of damage. The first had a slope characteristic of the flow capacity of the damaged region; the second straight line had a slop e characteristic of the flow capacity of the undamaged region. Results are presented both in tabular form and as log-log plots of dimensionless pressures vs dimensionless times. The log-log plot may be used in a type-curve matching pro cedure to analyze short-time (before normal straight line) well-test data.