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Abstract

Parameter estimation is one of the two principal functions of well test interpretation. Accurate parameter estimation depends on several factors, including correct reservoir model selection, sufficient test data within the flow regime(s) of interest, and accurate input data. The focus of this paper is the effects of errors in input data such as net pay, porosity, viscosity, formation volume factor, flow rate, and compressibility on the results of well test interpretation.

We consider two of the most commonly used reservoir models - a vertical well with wellbore storage and skin, and a finite-conductivity hydraulically fractured well. For the vertical well case, we allow for the presence of one or more boundaries, and for homogeneous or dual porosity behavior.

Many, if not all, of the observations offered in this paper are part of the working knowledge of the full-time well test analyst. However, these observations have not been systematically catalogued and discussed in the literature. The purpose of this paper is to provide just such a systematic catalog and discussion.

Introduction

The two major functions of pressure transient interpretation are reservoir model identification and parameter estimation. Reservoir model identification depends on an interpretation of the shapes of the pressure and pressure derivative curves, integrated with other geological, geophysical, and petrophysical information. Parameter estimation provides calculated values of the unknown parameters for a particular reservoir model, using as input data petrophysical data, fluid property data, and other data. These input data are inevitably subject to uncertainty. Thus, the resulting parameter estimates are also subject to uncertainty. This paper catalogs the effects of errors in the input data on the calculated results for each of several common reservoir models.

The results of this paper may be used in several different ways. First, the input data having the most effect on the desired parameter estimate may be easily identified. With this knowledge, the engineer may focus his data gathering to obtain better estimates of the critical input data and to avoid spending money and time refining estimates of unimportant input data. Second, by understanding the magnitude and the direction of the effects of errors in the input data on the calculation results, the engineer can quickly estimate the effects of revisions in the input data without having to repeat the entire analysis. Finally, the uncertainty of the calculated results may be estimated from the uncertainty in the input data.

The next section discusses the common sources of errors in the data used in well test interpretation and the expected magnitude of those errors. The following section then discusses how errors in input data affect the results of well test interpretation for several different reservoir models.

Sources of Error

Open Hole Log Analysis

Pressure transient interpretation requires net pay thickness, porosity, and water saturation, which are determined from log analyses. Net pay thickness directly affects the permeability calculated from a pressure transient test. Porosity and fluid saturations both affect the total compressibility. Total compressibility, in turn, affects estimates of skin factor, fracture half length, and distances to boundaries from pressure transient tests.