Strength of Water Drive or Fluid Injection From Transient Well Test Data
Authors: Kumar Anil 
Published: December 2007

This paper presents a method for determining the strength of water drive or fluid injection from transient well test data. Graphs are presented for interpreting drawdown and buildup data and for determining drainage-area mean pressure and drainage boundary pressures.

Introduction
Three possibilities exist for time variation of pressure at the drainage boundary of a well or reservoir:pressure decreases with time,pressure increases with time, andpressure remains constant with time. In closed or depletion reservoirs and reservoirs with water drive and partial fluid injection, the pressure at the drainage boundary declines with producing time. Partial fluid injection occurs when fluid volume introduced into a reservoir system from outside, such as in aquifer injection, is less than the volume of fluids withdrawn from a system. In contrast, the reservoir boundary pressure increases with time in reservoirs with excess fluid injection.
The boundary pressure remains constant with time under full injection, which requires that the fluid volumes entering a system be equal to fluid volumes withdrawn, such as occurs in a balanced five-spot fluid injection system. Strictly speaking, a mass balance is required instead of a volume balance as proposed above. However, this approximation is used commonly when using reservoir material-balance equations.
It has been demonstrated recently that well test behavior under a constant pressure condition at the reservoir boundary is quite distinct from that under usual depletion or closed reservoir boundary systems. In practice, one seldom encounters either a truly closed or a truly constant pressure boundary condition, but finds that most reservoirs fall somewhere between these two conditions; that is, pressure and fluid influx is changing with time at the reservoir or well drainage boundaries.
Several important questions are of concern to a practicing reservoir engineer: Is there a way to estimate the strength of water drive early in the life of a reservoir? How effective is a given fluid injection program for pressure maintenance? What kind of well drawdown and buildup pressure behavior would be obtained under these conditions? This paper aims to answer these questions for wells under water drive and under partial, full, or excess fluid injection programs.
To characterize the well pressure behavior in water drive reservoirs Miller et al. (MDH) considered the idealized case of a well in the center of a finite circular reservoir with constant pressure at the drainage boundary. Perrine reviewed the work of MDH and presented a curve to estimate the mean pressure that, in fact, yields the initial pressure in such systems. Hazebroek et al. studied pressure falloff in water injection wells located in isolated five-spot patterns. Dietz proposed a method to incorporate the strength of water drive in mean pressure determination by changing shape-factor values. Earlougher et al. used an infinite-array superposition scheme to show the influence of the constant pressure condition on the MDH-type buildup graph. Ramey et al. and Kumar and Ramey used this superposition scheme to determine the drawdown and buildup behavior for a well in a constant-pressure square.
Well test behavior for wells in closed reservoirs of almost any geometrical shape has been studied in detail and is summarized by Matthews and Russell.
JPT
P. 1497^