Unsteady Flow to a Well Producing at a Constant Pressure
Authors: Uraiet A.A. , Raghavan Rajagopal 
Published: December 2007

Transient pressure behavior in the drainage area of a well producing at constant wellbore pressure is discussed. Methods used to analyze flow rate behavior to determine formation flow capacity, porosity-compressibility product, skin factor, and drainage volume are discussed. A new type curve is given for analyzing interference test data obtained by producing (or injecting into) a well at constant pressure.

Introduction
In a recent study, the analysis of pressure buildup data subsequent to production at a constant wellbore pressure was discussed. It was found that even though the flow period during constant pressure production is discussed in great detail in the literature, some important aspects of well test analysis were never considered. For example, no study examined the transient pressure behavior when the wellbore pressure is constant. The purpose of this paper is to present a comprehensive study of the transient pressure behavior of a reservoir for the constant-wellbore-pressure boundary condition. Specifically, we will document the average reservoir pressure as a function of flow time. This information will be useful in material balance computations. Second, we intend to establish the validity of the effective wellbore radius and the "infinitesimally thin" skin concepts for a well that flows at a constant pressure. Both of these concepts assume that steady-state conditions prevail in the skin region. All studies in the literature implicitly assumed that the "infinitesimally thin" skin concept is applicable when a well produces at a constant pressure. However, it is not readily evident whether this concept can be used when the sandface flow rate is a continuous function of time. Third, the analysis of interference test data when the wellbore pressure is constant will be discussed. This procedure will prove superior to constant-rate testing whenever wellbore storage effects at the active well influence the observation pressure response. If the wellbore pressure is constant, only the reservoir properties affect the pressure response since wellbore storage effects at the flowing well are nonexistent. Consequently, the possibility of conducting an interference test in this manner should be the first consideration whenever the interwell distance is small.

Mathematical Model and Assumptions
Consider the classic problem of the flow of a slightly compressible fluid in a cylindrical, homogeneous, isotropic reservoir of constant thickness. The outer boundary of the reservoir is either closed or at a constant pressure equal to the initial pressure. The well is located at the center of the cylinder, and fluid is produced at a constant pressure. Initially, the pressure is uniform throughout the reservoir.
The skin region in this model is assumed to be an annular region concentric with the wellbore and with a permeability different from the formation permeability. Wellbore storage effects are not considered since the well flows at a constant pressure. (During the buildup period, however, wellbore storage effects can be important.
JPT
P. 1803＾