Interpretation Of The Pressure Response Of The Repeat Formation Tester
Authors: Stewart George , Wittmann Manfred 
Published: December 2007

Abstract
The analytical theory of the buildup pressure response associated with the pretest stage of the repeat formation tester operation is given. Both an infinite system and the case of a reservoir layer hounded above and below by impermeable barriers are considered. The spherical flow analysis method for the infinite acting case yields the equivalent spherical permeability which is influenced by formation permeability which is influenced by formation anisotropy. For the bounded case two different types of spherical buildup are shown to occur and an analysis technique for each one is presented which yields the spherical permeability and an estimate of the layer thickness. In circumstances where radial cylindrical buildup is observable, in principle, the anisotropy may also be determined. A quantitative result relating the depth of investigation of the permeability measurement to the pressure gauge resolution is given. Computer simulations of composite systems involving a filtrate invaded zone around the well and an outer oil zone have shown how these affect the shape of buildup plots. Recommendations regarding the choice of water plots. Recommendations regarding the choice of water or oil physical properties in data analysis are made.

Introduction
The Repeat Formation Tester (RFT*) is primarily a device for measuring the vertical pressure distribution in a reservoir in open-hole wells. Point measurements are made by inserting a probe into the formation through the mud-cake and extracting a fixed volume of fluid while measuring the associated pressure drawdown and ensuing buildup to local reservoir pressure with a surface-recording gauge; this is known pressure with a surface-recording gauge; this is known as pretest. The success of the operation depends on obtaining a good seal around the probe in order to detect reservoir pressure rather than mud hydrostatic pressure. In low permeability formations the buildup pressure. In low permeability formations the buildup following pretest sampling may be of long duration and an extrapolation of the initial buildup response to reservoir pressure becomes necessary. This extrapolation must be carried out correctly if the true reservoir pressure is to be obtained.
However the dynamics of the drawdown and particularly the buildup pressure responses reflect the formation permeability in the vicinity of the probe. Since permeability is a very important formation parameter and the design of oil recovery processes parameter and the design of oil recovery processes by fluid injection requires a knowledge of its vertical distribution in the reservoir, the possibility of the in-situ measurement of permeability is possibility of the in-situ measurement of permeability is attractive, especially where the coring of many wells is either technically or economically impractical. The scale of permeability measurement using the RFT pretest is intermediate between that of core analysis and pretest is intermediate between that of core analysis and that of conventional well testing. Recent improvements in the accuracy and particularly the resolution of downhole pressure recording instruments, eg quartz crystal gauge, have greatly extended the range of permeabilities which can be measured. The object of permeabilities which can be measured. The object of this paper, which is an extension of previous work by Moran and Finklea on the Formation Interval Tester (FIT*), is to examine how permeability can be estimated from the RFT pretest pressure response.

ANALYTICAL SOLUTIONS FOR SPHERICAL FLOW IN AN INFINITE MEDIUM
When fluid is withdrawn into the probe during pretest this generates a localized flow in the pretest this generates a localized flow in the formation which is essentially spherical in character and directed into a sink of very small dimension. Hence the analysis of the dynamic pressure response of the RFT pretest is based on the theory of spherical flow of a slightly compressible fluid in a homogeneous medium. Two constant-rate solutions to the diffusivity equation in an infinite, isotropic system at uniform initial pressure are available. The spherical sink solution, first proposed in this context by Moran and Finklea, corresponds to a finite, spherically shaped sink of radius rp and, in terms of dimensionless variables, the pressure distribution in the formation as a function of time and position is given by: