Pressure Transient Analysis of a Vertically Fractured Well Produced by Solution Gas Drive
Authors: Raghavan R. 
Published: December 2007

Abstract
Pressure transient data were investigated in a homogeneous and uniform reservoir containing oil and gas and producing at a constant surface oil rate by solution gas drive by means of a vertically fractured well. The well is assumed to be located at the center of a closed-square drainage area. Gravity effects were not included. To my best knowledge, this is the first study ort the pressure transient behavior of a vertically fractured well producing by solution gas drive. producing by solution gas drive. A recent paper presented a new method for analyzing pressure data in wells producing by solution gas drive. The method incorporates changes in effective permeability and fluid properties (formation volume factor, viscosity, and gas solubility) with pressure by means of a pseudo-pressure function however, it dealt exclusively pseudo-pressure function however, it dealt exclusively with plane radial flow. This paper presents the application of that new technique to vertically fractured wells.
Dimensionless groups are used throughout to extend the results to other situations having different permeabilities, spacing, reservoir thickness, porosity, etc, provided the PVT relations and relative-permeability characteristics are identical to those used in this study. The pseudo-pressure function concept used to analyze pseudo-pressure function concept used to analyze drawdown and buildup behavior extends the applicability of the results to a wide range of PVT relations and relative-permeability characteristics.

Introduction
In recent years, the analysis of pressure data of fractured wells has received considerable attention. However, most of this work is related to single-phase flow. An examination of the literature indicated that no rigorous study has been made regarding the pressure behavior of a vertically fractured well producing by solution gas drive.
The first objective of this paper is to discuss the transient floe, behavior of the system described above. The second objective is to demonstrate the applicability of a recent technique for determining absolute formation permeability when two phases (oil and gas) are flowing simultaneously. This technique is based on using a pseudo-pressure function that rigorously incorporates changes in permeability with saturation and fluid properties permeability with saturation and fluid properties with pressure. It will be shown that, by using the procedure suggested here, better estimates of procedure suggested here, better estimates of fracture length also can be obtained.

LITERATURE REVIEW
General equations of motion describing multiphase flow in porous media are well known and will not be discussed here. A summary of the work in this area as if pertains to well test analysis is presented in Ref. 5. This section briefly reviews only the computation of an integral (henceforth called the pseudo-pressure function), which was used in Ref. pseudo-pressure function), which was used in Ref. 5 to analyze drawdown and buildup.
In a recent paper, Fetkovich suggested that if the pseudo-pressure function, m (p), given by:
(1)
is used, then transient, pseudo-steady-state and steady-state multiphase flow through porous media may be described by simple expressions similar to that for the flow of a slightly compressible fluid. For example, Fetkovich suggested that for transient radial flow one can express the flow rate as
(2)
where to is the dimensionless time given by
(3)
In Eq. 2, s' represents the skin effect that, in general, includes the effects of damage in the vicinity of the wellbore, as well as a skin effect caused by the development of a gas saturation.
SPEJ
P. 369