Examples of Pitfalls in Well Test Analysis
Authors: Iraj Ershaghi , Woodbury J.J. 
Published: December 2007

Recent developments in the modeling and prediction of pressure transient tests for various reservoir and flow conditions have indicated the similarities in response that may exist among totally different cases. Several case studies are used to point out pitfalls associated with force-fitting a particular flow regime or reservoir condition on a set of pressure vs. time data.

Introduction

Current diagnostic procedures used to select a reservoir flow model to interpret well tests include various plots of pressure drop or pressure recovery vs. some function of time. These plots include log ?p vs. log ?t, log-log plot; p vs. log ?t, semilog plot; p vs. ?t, linear flow plot; p vs. 4?t, bilinear flow plot; and p vs. (1/?t), spherical flow plot.

The utility of these plots has been shown in a series of published papers during the past decades. A review of these was made recently by Ramey.1

With the advances in analytical and numerical modeling of flow problems in reservoirs, many papers have discussed modeling the response of an idealized reservoir geometry or flow regime under the conditions of a given wellbore flow. Because of many possibilities that may exist in real situations, many investigators are working to formulate and to obtain the pressure response in reservoirs of increasing complexity.

Real-life examples of pressure data to fit a given idealized model are often nonexistent. Consequently, many authors use synthetic data to point out the use of their proposed technique or model. In fact, practicing engineers now are reading about many techniques and models for which there may never be examples of actual data to fit. Some people may even criticize the enormous effort toward prediction of pressure response in certain idealized models.

One must note, however, that all the idealized cases published to data and yet to be published are opening our eyes to response similarities that may exist among the performance of completely different systems.

The purpose of this paper is to present a few examples, make a comparison between the responses of various reservoir models, and point out the errors in interpretation if the radial flow model is forced on the data in all cases.

Reservoir Flow Models

Reservoir geometry and kz/kr are the two major factors controlling the nature of flow between the high-pressure portion of the field and the wellbore. Fig. 1 shows examples where cases of radial, linear, and spherical flow may develop. The bulk of the well testing literature is based on the assumption of a radial flow regime. Studies conducted on complex geometries, such as multilayered with or without crossflow and various wellbore and boundary conditions, have focused primarily on the main frame of a radial flow system.

The case of linear flow has been emphasized mainly for fracture-controlled flow regime. Recently, the pressure behavior in a long and narrow reservoir was reviewed.2 Spherical flow has received very sporadic attention in the literature.3–5

Each of these flow regimes has its own distinct flow equation. The solution to the flow equation in the absence of wellbore effects results in a straight line on a plot of pressure vs. some function of time. The straight line is obtained for radial flow on a p vs. log ?t, for linear flow on p vs. ?t, and for spherical case on p vs. 1/?t.

Selection of the proper flow system depends on what is known about the particular reservoir. For tests conducted during the development stages of a field, such a selection may be possible. The real difficulty is during the exploratory phase, when field data are too few to support a given model strongly.

The question addressed here is whether the formation of a straight line on a given pressure vs. time plot is indicative of the corresponding flow regime. The answer would have been easy if the straight line plots were unique. Evidence shows that pressure vs. time data for a given system may result in pseudostraight lines on two or more characteristic plots. A pseudostraight line is defined here as a trend of data points resembling a straight line on a pressure vs. time plot with no physical condition justifying such a case.

Experimentation With Theoretical Plots

Consider a set of pressure vs. time data where p=f(t) results in a straight line on given plot. The entire set or a portion of the same set may result in a pseudostraight line on other plots.

Figs. 2 through 7 show the results of experimentation with these plots. Each case starts with an assumed condition, and the graphical representation on other scales are presented.