Abstract

The performance of a horizontal well in the presence of a growing cone before breakthrough is studied. Examining the flow mechanism in rese11loirs with bottom water or gas cap, we consider the interface as a no-flow moving boundary before breakthrough. The paper presents a dimensionless variable, Dimensionless Density, as a function of reservoir thickness, anisotropy coefficient, difference of the fluid densities, production rate and viscosity. This study indicates the existence of a Critical Dimensionless Density (CDD), above which water or gas cone is stable. The results of this study show that the higher the viscosity, the higher is the con~ height and consequently the smaller is the breakthrough time. Thus processes such as steam stimulation can postpone the breakthrough time. The results show that, before breakthrough, a potential solution of a no-flow boundary at the initial interface is a better approximation with respect to those with a constant potential boundary conditions. The shape of the interface during production is developed.

INTRODUCTION

The performance of a horizontal well in reservoirs with bottom water or gas cap has been studied through the assumption of constant potential (pressure) at the initial interface, (Refs. 1 and 2). However, before breakthrough, there is another no-flow boundary between the two fluids which can move toward the wellbore or be stationary (at steady state). To the best of the authors knowledge, this intermediate no-flow boundary has not been considered in the horizontal well performance elsewhere in the literature. However. Ref. 3 considering the interface as a no-flow moving boundary, presented the performance of a vertical well in the presence of a growing cone. To calculate the interface advance based on the equations derived in this paper. One has to have the potential values on the interface and outer boundaries. On the other hand the potential distribution inside the reservoir depends on wellbore configuration. Therefore to calculate the potential distribution inside the reservoir due to a horizontal well with arbitrary geometry, Discrete Flux Element Method (DFE), presented by Azar-Nejad, Tortike and Farouq Ali4–6 has been used. Applying a transformation rule presented in Refs. 3 and 7. The deformed interface is shifted to its initial position.

In a reservoir with a horizontal well this implies that the wellbore geometry be transformed accordingly. The resulting wellbore with irregular geometry, in the transformed space, can only be modeled by DFE Method.

PREVIOUS STUDIES

Coning is a term where has been used to describe the WOC deformation. Numerous papers have been published with the purpose of calculating the critical production rate (Refs. 7 through 16) and the time of the water breakthrough (Refs. 17 through 19). Muskat and Wykoff8 presenting the static equilibrium, developed a solution for the critical production rate for a vertical well under steady state conditions. As the WOC was a no-flow boundary with unknown and irregular configuration and location, Muskat et al8, assumed the original WOC to be a no-flow boundary. However they postulated that if one could consider the real WOC as a no flow boundary, the critical production rate would have been lower. Therefore, the solution for critical production rate given by Muskat et al8 is an approximation and an upper limit on the exact solutions.

This content is only available via PDF.
You can access this article if you purchase or spend a download.