This paper presents the results of an investigation of the design and analysis of the boundary-dominated flow production performance of a vertically fractured well located in a closed rectangularly bounded reservoir. The solution for dimensionless productivity index of a finite-conductivity vertically fractured well in a closed rectangularly bounded reservoir and the corresponding pseudosteady state shape factor of this type of well and reservoir completion under boundary-dominated flow conditions has been developed and utilized in this study.
The mathematical model described in this paper has been used to develop predictive and analysis graphical design charts of the dimensionless productivity index and pseudosteady state shape factors for use in improved hydraulic fracture stimulation design and evaluation. Example applications of the dimensionless productivity index and pseudosteady state shape factor solutions developed in this work are provided for fracture stimulation design. A production optimization strategy is presented in this paper based on the dimensionless productivity index solution for a vertically fractured well under pseudosteady state flow conditions.
A number of technical articles have appeared in the literature concerning the use of the dimensionless productivity index as a measure for improved fracture stimulation design under boundary-dominated flow conditions. One of the first investigations that specifically pertained to this subject was reported by Valko and Economides1. Subsequently, a number of other investigators2–5 have developed interpretation models and analyses that employ the dimensionless productivity index as the basis for improved fracture stimulation design.