## DEVELOPMENT OF GENERALIZED WELL SEMI-ANALYTICAL CONING MODELS

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ABSTRACT

Oil deposits are often found in association with a communicating gas or water zone. The production of the oil often leads to the coning of water or gas. This dynamic interaction can be captured by a properly detailed reservoir simulation, which unfortunately may not always be practical. To brigde the gap, researchers over the years have developed both analytical and empirical methods of modelling gas and water coning in oil reservoir. The fundamental questions have always been: what is the critical rate of oil production; what is the breakthrough time if the critical rate is exceeded; and what is the post-breakthrough behaviour?

Using analytically derived line source vertical and horizontal well breakthrough time expressions, a method has been developed to estimate oil critical rate, breakthrough time and post-breakthrough trend for inclined wells. The Post-breakthrough prediction scheme was extended to vertical and horizontal wells. Simplified correlations have also been generated for the easy application of the method without the need of analyzing complex mathematical functions. Within the accuracy of the numerical simulation results, the breakthrough times for the inclined well were consistently and correctly predicted. Literature correlations and numerical simulation comparisons showed that the post-breakthrough production predictions tended to underpredict oil production, but the trends were much more consistent with simulation results than other correlations studied. To the best of the knowledge of the author, this is the first semi-analytical coning model of an inclined well, as well as, the first semi-analytical post-breakthrough trend prediction for vertical and horizontal wells.

Chapter One

INTRODUCTION AND PROBLEM DEFINITION

1.1 INTRODUCTION

Quite often, oil deposits are associated with an underlying water aquifer and an overriding gas cap. In many situations, the oil reserve is desired at the surface while the associated fluid is preferred within the reservoir either because they are not valuable at the surface as in the case of produced water or the resources to harness the gas if produced to the surface are not readily available. The reservoir water or gas may also be required for pressure maintenance in production optimization within the reservoir. Whatever may be the intention of prefering to keep the water and/or gas within the reservoir, it is found in practice a difficult goal to achieve due to coning of the unwanted fluid(s). Coning is the tendency of the underlying water in contact with the oil to rise locally towards the producing well due to the greater pressure depletion near the producing well and the viscous drag the production of oil is having on the water-oil interface. The same holds for the gas oil interface in which case the gas projects downwards towards the producing well’s perforation against gravitational force arising from gas-oil density difference. The projection is a result of viscous drag on the fluid interface and the local pressure depletion around the well due to oil production.

The production of either water or free gas with the oil will result in the reduction of the rate of oil production and the ultimate recovery of the oil. The reduction of oil production arises from the simple fact that some portion of the well bore that would be transporting oil will have to transport the unwanted fluid. Reduction in recovery arises from pressure depletion and trapping of oil behind the advancing unwanted fluid front. Ordinarily without coning, the unwanted fluid pushes the oil to the well as production progresses but with coning, the unwanted fluid leaves the oil behind, enters the well and may lead to early abandonment of the well.

The production of water has other damaging effect on hydrocarbon production profitability as it increases the spate and damage of corrosion. Corrosive agents like acid anhydride require the presence of water for ionization and chemical activity on metallic materials used in making the production string and other facilities. Obviously, the handling and disposal cost of produced water increases with the rate of coning. Depending on the prevailing environmental policy and the contaminant present in the produced water, this may constitute a huge cost burden. Gas handling, especially in areas with little market for gas, can become very demanding with gas coning. Treatment, pressurization and storage or re-injection may have dear financial implications. The environmentally-damaging alternative to the gas handling problem common in some countries is gas flaring. The latter constitutes enormous economic and environmental hazard.

As can be appreciated, for technical and economic reasons, it is crucial that coning be minimized or delayed. Thus coning minimization or delay is an important aspect of reservoir and production

management. Numerous studies1,2,3,4 have been conducted to understand the initiation and evolution of coning in order to control or minimize the stated negative consequences.

1.2 STATEMENT OF PROBLEM

Work on coning had generally been pursued along the path of preventing or delaying cone generation and evolution, the time to breakthrough if advancement is not checked and the performance of the well after cone breakthrough. A number of empirical and analytical studies

have been conducted to model and determine these properties5. As will be discussed in detail, in the section on literature review, correlations and models for the determination of critical rate of oil production, time to breakthrough when producing at super-critical rate and the performance of the well after breakthrough have been developed for vertical and horizontal wells. These models...

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