Abstract

Interpretation of pressure transient tests conducted in a dynamic environment, like drilling, is challenging. One of the difficulties arises due to phenomenon known as supercharging which is caused by mud filtrate invasion. The supercharging results in an increase in sandface pressure which is above the reservoir pressure. Therefore, any calculation of initial pressure and permeability must take into account the supercharging effect.

We present an algorithm that takes into account the supercharging effect in analysis of pressure transient tests acquired with a single or multiple probe formation tester. The solution is obtained by successive integral transforms to the governing equations and to the associated initial and boundary conditions. Thus a complex phenomenon can be modeled, using some valid simplifying assumptions, with sufficient accuracy for the purpose of test design or interpretation. The rationale for the initial and boundary conditions deployed here, which are unique to a supercharged system, is explained in detail.

Introduction

Pressure measurement plays an important role in reservoir management. Because of its dynamic nature, pressure measurement provides essential information on well productivity and dynamic reservoir description both in exploration and exploitation scenarios. Static pressure data can be used to compute formation fluid density and contacts. Pressure transient data, on the other hand, is crucial for estimating permeability, heterogeneities and average reservoir pressure.

Traditionally, pressure transient testing took the form of Drill Stem Testing (DST) or conventional well testing where the well is put under test for a relatively long duration. While this is an excellent way to meet test objectives, environmental and cost consideration does not allow us to use these techniques as often as necessary.

Wireline formation testers remove many of the restrictions imposed upon by conventional well tests and require special models. While the theory of pressure transient analysis is applicable to data obtained by formation tests, they require careful formulation to account for additional effects.

Specifically, formation testers can be used during measurement while drilling. However, interpretation of the pressure data acquired in this dynamic environment is challenging. Direct pressure measurement obtained from a formation tester is that of the supercharged zone. Therefore, any interpretation of the data must take this effect into account.

It is possible to account for supercharging effect through numerical simulation. Such models would need a complex initialization process and would require data that is not readily available. The ensuing interpretation would be overtly complex.

We have developed a software tool, which presents a workflow to analyze data acquired with single or multiprobe formation testers. The software consists of a new mathematical model coupled with non-linear regression methods for solving the inverse problem. It is possible to match the pressure transient data acquired in supercharged environment to deduce values of permeabilities, initial pressure and productivity index. The model is generalized and is equally valid where supercharging effect is not profound.

Background

During or immediately after drilling, pressure near the wellbore is influenced by mud filtrate invasion and mud cake formation. Considerable studies have been made in this area. A good summary of the literature on the dynamics of invasion and mud cake formation is presented by Hammond1. In the early nineties Goode and Thambynayagam2 developed a model that exploits the pressure transients to determine reservoir parameters. This model, though widely used in the industry, does not consider phenomenon of supercharging. Since then considerable work has also been done to model the pressure response of a formation tester3,4,5,6. Later Goode and Thambynayagam7 extended their previous work to account for the effect of mud filtrate invasion.

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