Abstract

Most of the theoretical work on decline curve analysis with non-laminar flow in the reservoir consider either a dry gas or liquid flow in an homogeneous system. The purpose of this work is to analyze decline curves considering non-Darcy flow effect in the reservoir, for a slightly compressible liquid flow in dual-porosity systems at constant wellbore pressure.

The transient and boundary-dominated flow periods are examined by means of computer results generated with a finite differences simulator. Analytical expressions of velocity and wellbore rate are presented for the first time in this paper. These equations contain the laminar flow solution as a particular case. A method is proposed to identify the presence of inertial effects by plotting d(log(q))/d(log(t)) against log (t).

The method for area calculation under laminar conditions produces a good approximation for a reservoir under non- laminar flow. However, the presence of inertial effects distort the shape of decline curves resulting in erroneus estimates of wellbore and reservoir parameters by type curve analysis with laminar decline curves.

The utility of the methodology presented in this work is illustrated with synthetic examples.

Introduction

Most of the existing techniques available in the literature for determining the productivities and reservoir parameters, are based on three main assumptions: applicability of Darcy s law and constant inner boundary condition, either constant production rate or constant bottom hole flowing pressure. Neither of these assumptions are frequently fulfilled1.

In a naturally fractured formation we may have wells initially producing at a high rate and in some cases production declines after a few hours2. Analyzing the transient flow-rate behavior will add more information to produce a more complete evaluation. From an engineering viewpoint, the initial decline could be a key factor in deciding whether to complete or abandon a well. In homogeneus systems, this decline is the only one observed, but for fractured reservoirs the initial decline does not allways represent the final state of depletion.

At present, most of the reports on constant bottom-hole pressure tests found in literature, assume that only one phase flows in porous media and that Darcy's law is applicable to both homogeneus as well as fractured reservoirs3–7.

In cases where the Darcy s law is not valid there are some works which consider different kind of tests as well as different reservoirs types8–13. Nevertheless, there are no analytical expressions to analyze flow rate responses for constant bottom-hole pressure tests in naturally fractured reservoirs with non-Darcy flow. The objective of this paper is to present new analytical expressions for non-Darcy liquid flow in dual porosity systems produced at constant bottom-hole pressure.

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