A Practical Procedure to Predict Cresting Behavior in Horizontal Wells
Authors: Souza A.L.S. , Arbabi S. , Aziz K. 
Published: December 2007

Abstract
Water and gas cresting in horizontal wells are important phenomena in reservoirs that have an aquifer and/or a gas-cap. In practical situations, many reservoirs are produced under supercritical rates and a breakthrough of the displacing phase becomes inevitable. At the beginning of a reservoir simulation study, it is desirable to make an estimate of the breakthrough time and the post-breakthrough behavior. Grid sensitivity runs are also required to obtain the appropriate grid block sizes. An accurate representation of cresting behavior requires a very fine grid, which is not always practical. In this work a procedure was developed to obtain accurate breakthrough times using just coarse grid simulations. The flow equations were written in dimensionless form and important parameters affecting multiphase flow were identified. Simple correlations for a quick estimate of breakthrough time, maximum oil rate and post-breakthrough behavior were derived based on an appropriate set of dimensionless variables and an extensive number of simulation runs. The effects of gridblock size and grid pattern were investigated in detail. Effects of rate, mobility ratio, well drainage area, well height, and end-points and shapes of relative permeability curves were also included. A procedure to derive pseudofunctions either using numerical correlations or coarse grid simulations is also presented. These pseudofunctions can be used to improve the performance of coarse grid simulations. An optimum grid pattern to start a reservoir simulation study is proposed. Application to a real field example shows that the correlations and procedures derived are reliable and accurate, and can be used for quick estimates before starting a reservoir simulation study.

Introduction
Petroleum reservoirs often have a gas cap and/or an aquifer. In these situations they are subjected to rapid gas and/or water movement towards the well, created by a sharp pressure gradient in the well direction. As the production begins, the interface between the fluids, that is, gas-oil contact or water-oil contact, deforms from its initial plane shape to a cone or a crest. When a field is developed by vertical wells, the shape of the deformation is called a cone, but when it is developed by horizontal wells, this deformation is better described as a crest.
The literature reports analytical and semi-analytical solutions for vertical and horizontal wells for critical rate under the steady-state condition reached by the cone or crest with a constant potential on the lateral boundary. There are also analytical and semi-analytical solutions available for infinite acting and closed-boundary reservoirs. Some numerical correlations are also available for predicting breakthrough time and post-breakthrough behavior for supercritical rates.

Dimensionless Equations
Correlations are more general and reliable when based on the fundamental flow equations, so that the important physical mechanisms are automatically incorporated in the correlations. Here, we consider the case of water cresting. The gas cresting case is treated similarly and is discussed in a later Section. Assuming a homogeneous reservoir with constant viscosity, and neglecting capillary effects, equations for two component, twophase flow, under constant total production rate constraint, can be written as:
Oil:
(1)