## PRESSURE ANALYSIS OF A WELL WITH AN INCLINED HYDRAULIC FRACTURE IN A NATURALLY FRACTURED RESERVOIR

ABSTRACT

Hydraulic fracturing has been an effective technique to stimulate damaged wells or wells producing from low-permeability formation. It has been established that the orientation of a hydraulic fracture is perpendicular to the direction of the least principal stress in the formation. Thus, most pressure transient analysis techniques are based on the assumption that the fracture is vertical. However, it is now generally agreed that the direction of the least principal stress is not always parallel or perpendicular to the plane of the formation. For this reason it is very likely that some hydraulically fractured wells have inclined fractures.

Objectives of study:

(1)   Provide background to justify the conclusion that the direction of least principal stress might be at an orientation different from parallel or perpendicular to the bedding plane of the formation.

(2)     Develop a technique, based on the pressure derivative concept, for interpreting pressure transient tests in wells with an inclined hydraulic fracture. Three cases are possible:
(a)   the fracture is symmetric in both lateral and horizontal directions,

(b)   the fracture is asymmetric in only one of the directions, and

(c)   The fracture is asymmetric in both directions.

CHAPTER 1

INTRODUCTION

1.1        Introduction

Hydraulic fracturing is an important well stimulation technique that has been widely used in the oil and gas industry. The technique involves creation of fractures or fracture system in porous medium to overcome wellbore damage, to improve oil and gas productivity in low permeability reservoirs or to increase production in secondary recovery operations. Most of the pressure transient analysis techniques used to analyze pressure responses of fractured wells are based on the assumption that the fracture is either vertical or horizontal. However, hydraulic fracture could be inclined with a certain angle with respect to the vertical direction because it is now generally agreed that the direction of the least principal stress is not always parallel or perpendicular to the plane of the formation. For this reason it is very likely that some hydraulically fractured wells have inclined fractures. This has been proved by laboratory experiments as well as data from actual field studies with the aid of modern technology such as surface tilt meters. Thus, for an inclined hydraulic fracture, the vertical orientation assumption may lead to serious errors in well test analysis especially when the inclination angle is high. More so, there are very few studies concerning pressure transient analysis of inclined hydraulic fracture and there is not any applicable well test analysis procedure available for inclined fractures. For this reason, it is important to develop well test analysis procedures for this type of fracture in naturally fractured reservoirs.

A naturally fractured reservoir can be defined as a reservoir that contains fractures (planar discontinuities) created by natural processes like diastrophism and volume shrinkage, distributed as a consistent connected network throughout the reservoir. They present unique challenges that differentiate them from conventional reservoirs. It represents over 20% of the world's oil and gas reserves, but is however among the most complicated class of reservoirs to characterize and produce efficiently.

The purpose of this study is to develop a technique, based on the pressure derivative concept, for interpreting pressure transient tests in wells with an inclined hydraulic fracture in a naturally fractured reservoir. This report will provide some background on inclined hydraulic fracture including in-situ stress state, factors that affect the stress state, occurrences of inclined hydraulic fractures and field studies. Two techniques of transient pressure analysis using pressure derivatives will be developed. They are type curve matching and Tiab’s Direct Synthesis (TDS). Both uniform flux and infinite conductivity models would be considered in the study. Analytical solution for each flow regime will be analysed in details.

1.2 Technical Objectives:

·         To provide background to justify the conclusion that the direction of least principal stress might be at an orientation different from parallel or perpendicular to the bedding plane of the formation.

·         To develop a technique, based on the pressure derivative concept, for interpreting pressure transient tests in wells with an inclined hydraulic fracture in naturally fractured reservoirs.

Three cases are possible:

(a)               The fracture is symmetric in both lateral and horizontal directions,

(b)               The fracture is asymmetric in only one of the directions, and

(c)               The fracture is asymmetric in both directions.

1.3  Hydraulically fractured wells

Naturally fractured reservoirs are different from conventional (unfractured) reservoirs. They are heterogeneous in type and consist of matrix blocks separated from one another by the fracture system. The matrix blocks are made of the original rock that was present before fracturing took place. The matrix is characterized by its permeability km and porosity Ï†m . The fracture system is characterized by its permeability kf and porosity Ï† f . It means a naturally fractured reservoir is a double-porosity and double-permeability reservoir.

1.4       Naturally Fractured Reservoirs

Fractures are displacement discontinuities in rocks, which appear as local breaks in the natural sequence of the rock’s properties.It may appear as micro-fissures with an extension of only several micrometers, or as continental fractures with an extension of several thousand kilometres.
In geological terms, a fracture is any planar or curvi-planar discontinuity that has formed as a result of a process of brittle deformation in the earth’s crust.Naturally fractured rocks can be geologically categorized into three main types, based on their porosity systems:
(1)   Intercrystalline-intergranular;

(2)   Fracture-matrix ; and

(3)   Vugular-solution

There are four types of naturally fractured reservoirs, based on the extent to which fractures have altered the porosity and permeability of the reservoir.....

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