Short-Term Well Testing to Determine Well bore Damage
Authors: Raymond L.R. , Hudson J.L. 
Published: December 2007

Abstract
This paper proposes a comparatively short-term (8 to 10 hours) well test for detecting and characterizing well. bore damage and for measuring mean formation permeability. The proposed test is made by injecting fluid at constant pressure, recording injection rate as a function of injection time. After one to four hours of injection, the well is shut in and fall-off of bottom-hole pressure is obtained as a function of shut-in time.
Formation permeability is estimated by an iterative technique. First, a value of formation permeability is assumed. Then, a plot of the recorded injection rate as a function of dimensionless time is made, using the assumed permeability value. From the slope of the injection-rate curve, a new value of formation permeability is calculated. If the new value agrees with the original assumed value, the assumption was the correct formation permeability. If the values do not agree, the process is repeated using the new permeability value in the calculation. Convergence is rapid, and a reliable permeability value results. Pressure fall-off data are used to check the result.
Graphs of pressure and injection rate as functions of time given in the paper show that changes in permeability of the formation in the neighborhood of the wellbore are disclosed by this technique. Thus, the short-term test can be used to detect formation damage. Also, a rough measure of the radial extent of damage can be inferred, which is helpful in designing stimulation treatments. The mathematical model used for this work was a single-zone, horizontal reservoir with a damaged zone in which permeability decreased continuously as radial distance to the wellbore decreased. This model is more realistic than the usual two-zone, discontinuous permeability model used in published works; calculations indicate the realistic model is valid. Vertical variations in horizontal permeability were studied with this model, and results indicate that the permeability measured by the short-term test is the mean horizontal permeability for the vertical interval tested.
The proposed short-term test thus should be useful in detecting and characterizing formation damage and in measuring formation permeability needed in calculating reservoir transmissibility.

INTRODUCTION
To plan the most efficient production or injection schedule for a well and to design or evaluate the optimal stimulation treatment, it is necessary to know the properties of the reservoir adjacent to the well, particularly the reservoir transmissibility and characteristics of a damaged zone, if one exists.
Several techniques for determining reservoir transmissibility from well tests have been presented in the literature.1,2,5,6 All these techniques rely on conducting constant-rate well tests that often are difficult to execute. A constant-pressure well test is generally easier to carry out, and this paper contains the first available method for the analysis of constant-pressure well tests.
Determination of wellbore damage from transient well tests has been the subject of several papers.3,4,5 From these studies it is apparent that information necessary for determination of the characteristics of a damaged zone is available shortly after the transient well test is initiated. Consequently, it may not be necessary to carry out an extensive well test (for example, a pressure build-up test) if the primary purpose of the test is to detect the existence of wellbore damage.
All previous studies of well testing to determine wellbore damage have been based on the two-zone permeability model.3 In this model the damaged zone has a permeability kd extending to a radius rd, and the formation permeability k obtains from rd to the drainage radius re. Consequently, there is a discontinuity in permeability at r=rd. This discontinuity can be eliminated by assuming a continuous variation in permeability through the damaged zone. The effect of this assumption on transient well tests is discussed in following sections of this paper. In addition, all formations have within them vertical permeability variations associated with lithology changes throughout the zone of interest. This paper also considers the effect of these variations on transient well tests.