Abstract

This work explores the application of automated pressure transient test analysis and deconvolution technique in laboratory scale. To achieve this, a linear core which provides a pressure response corresponding to predetermined mathematical models, has been constructed. The pressure response to applied boundary conditions has been monitored in real-time by means of an A/D converter installed in a microcomputer. Applying specific analysis techniques, permeability (k) and compressibility-porosity product (ct) can be obtained from experimental data. Data analysis includes:

* deconvolution of accumulated production and pressure responses, i.e. the desuperposition of a variable boundary condition;

* least squares nonlinear estimation of system parameters. Greenstadt's modification of classical Newton's method has been selected to perform parameters optimization.

In order to be a reference to related future experiments, practical aspects and problems associated with the materialization practical aspects and problems associated with the materialization of this experiment, specially those related with the interface between physical experiment and computer techniques, are extensively detailed in this work.

Introduction

Well and reservoir parameters, such as permeability, productivity and initial pressure, can be obtained through the analysis of pressure transient tests. Sometimes it is possible to detect pressure transient tests. Sometimes it is possible to detect reservoir heterogeneities such as permeability barriers, reservoir boundaries and natural fractures. Methods commonly used for interpretation of pressure data obtained in well tests consider analytic solutions of the diffusivity equation:

(1)

in which a constant sandface-rate is assumed as internal boundary condition. These methods, although very simple to apply, depend mainly on the ability to maintain a constant sandface rate during the test. And this is often almost impossible, due to the presence of wellbore storage effects. Using Duhamel's superposition theorem, it is possible to obtain the pressure response to a variable sandface-rate test. According to this theorem, the variable rate response is given by the convolution of the constant rate solution and the variable internal boundary condition (i.e. the variable sandface-rate). The inverse problem is known as deconvolution and can be defined as the desuperposition of the variable internal-boundary-condition. Applying deconvolution techniques and with the appropriate tools to measure simultaneously pressure and flow rate, corresponding constant-rate pressure response can be computed. Once collected data are available, pressure response analysis is performed in order to obtain the desired parameters of the well/reservoir system. This analysis is generally performed on a linear-regression-basis, using scales such as log-log, semi-log, Cartesian. System parameters or part of them can be calculated using the straight-line slope and its y-axis intercept. Depending on the selected mathematical model, type curve fitting may be required. As this task is generally performed manually, a high degree of subjectivity is inherent to this type of interpretation.

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