Development of Generalized Well Semi- Analytical Coning Models : Current School News

# Development of Generalized Well Semi- Analytical Coning Models

on August 3, 2022

– 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.

Front Page           i

Approval Page          ii

Title Page      iii

Abstract         iv

Dedication       v

Acknowledgement          vi

List of figures             x

List of tables               xii

Chapter One Introduction and Problem Definition

• Introduction 1
• Statement of Problem 2

Chapter TwoBasic Concepts and Literature Review

• The Coning Mechanism 5
• Reservoir and Engineering Factors in Coning 6
• Typical Coning Solution Procedures 9

Chapter Three

Methodology                                                                                                                                                                19

• Preamble 19
• Mathematical Formulation of Horizontal and Vertical Well Coning Model 20

After Ozkan and Raghavan

• Slanted Well Formulation 24
• Post Breakthrough Behaviour 26
• Fundamental Concept 26
• Vertical Well Post-Breakthrough Formulation 27
• Horizontal Well Post-Breakthrough Formulation 28
• Slanted Well Post-Breakthrough Formulation 32

Chapter Four Result and Analysis

• Breakthrough Time 37
• Vertical Well 37
• Horizontal Well 39
• Inclined Well 41
• Critical Rate of Oil Production 42
• After Breakthrough Behaviour 43
• Model Result Comparison 45
• Literature Model 45
• Numerical Simulation 45
• Results and Discussions 46
• Example Calculations Using Correlations 55

Chapter Five Summary, Conclusions and Future Direction

• Summary 63
• Conclusions 63
• Further Studies 64

References    66

### 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.

### REFERENCES

Chaperon I.: “Theoretical Study of Coning Toward Horizontal and Vertical Wells in Anisotropic Formations: Subcritical and Critical Rates”, paper SPE 15377 prepared for presentation at the 1986 SPE Annual Technical Conference and Exhibition, New Orleans, Oct. 5-8
Hoyland, Lelf A. et al.: “Critical Rate for Water Coning: Correlation and Analytical Solution”, SPE Reservoir Engineering (November 1989) pp 495-502
Ozkan E. and Raghavan R.: “A Breakthrough Time Correlation for Coning Toward Horizontal Wells”, paper SPE 20964 prepared for presentation at Europec 90, the Hague, Netherlands, October 22-24.
Papatzacos P. et al.: “Cone Breakthrough Time for Horizontal Wells”, SPE Reservoir Engineering(August 1991) 311-318
Joshi S. D.: “Water and Gas Coning in Vertical and Horizontal Wells”, Horizontal Well Technology, Pennwell Books of Tulsa (1991) 252-325
Ahmed Tarek: Reservoir Engineering Handbook, Gulf Publishing Company, Houston (2000) 569- 635.

CSN Team.