Abstract

Most of theoretical work on decline curves considering non-laminar flow is related with dry gas systems. The purpose of this study is to analyze decline curves considering non-Darcy flow effects in the reservoir for both slightly compressible liquid flow and solution gas-drive systems keeping the wellbore pressure constant. The transient and boundary-dominated flow periods are examined by means of computer results generated with a finite difference black-oil reservoir simulator with a variable bubblepoint formulation. The consequences of this formulation under non-Darcy flow are studied. The influence of the mechanical skin factor on the rate response is documented. For the case of liquid flow, it is presented for the first time an expression to evaluate the total skin factor which is a function of the mechanical skin and the skin due to inertial forces. This expression is given in terms of physical properties of the system, it is proportional to the square root of the pressure drop, and it is also equal to the square root of the Reynolds number. This is one of the main findings of this work. It is investigated the possible presence of a semilogarithmic straight line of reciprocal rate for both liquid and solution gas-drive systems, and new insights are provided. In general, when the inertial effects are important and the bottomhole wellbore pressure is kept constant, a true semilogarithmic straight line of the inverse of oil rate does not develop. This result is valid for both liquid and solution gas-drive systems, and it is an important difference with the case of liquid flow under constant oil rate production mode, where a semilog straight line of the pressure drop is evident during the transient period for a big enough drainage area. For liquid flow an apparent straight line may be fitted and its ordinate to the origin is approximately equal to the value of total skin computed with the expression mentioned above. The presence of inertial effects distort the shape of the laminar decline curves for both multiphase and slightly compressible liquid flow, causing that type curve analysis yield wrong estimates of the wellbore and reservoir parameters. Also, if someone attempts to do a history match with data affected by non-Darcy flow using a conventional simulator, that uses Darcy's law in its formulation, an alteration of the reservoir properties will be necessary.

Introduction

In several activities of reservoir engineering the employment of a graph of production versus time is been used routinely to forecast production decline. This technique is also used as a type curve analysis procedure. The decline curves can be grouped into two sets, empirical and analytical. The empirical curves presented by Arps are applicable during the boundary-dominated flow period for saturated reservoirs under different driving mechanisms. The analytical curves, designed for undersaturated reservoirs, are applicable for both transient and boundary-dominated flow periods considering laminar flow. M. Fetkovich has proposed to combine these two sets of curves, yielding in this way a single set of type curves to predict production decline.

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